Essays in corporate finance

PDF

Download

Open document

Flip pages

Summarize

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content Essays in Corporate Finance by Chong Shu A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Business Administration) August 2021 Copyright 2021 Chong Shu Dedication To My Parents. ii Acknowledgements I am grateful to my advisor John Matsusaka and committe memerbers Kenneth Ahern, Kevin Murphy, João Ramos, and T.J Wong for guidance. I would also like to thank Raphael Boleslavsky, Philip Bond, Odilon C^ amara, Itay Goldstein, Matthew Gentzkow, Michael Magill, Oguzhan Ozbas, Rodney Ramcharan, Alireza Tahbaz-Salehi, Tao Li (Discussant), Carlos Ramirez (Discussant), Hong Ru (Discussant), Christoph Schiller (Discussant), Fabrice Tourre (Discussant), Lucy White (Discussant), Michael Gofman (Discussant), and conference/seminar participants at 2020 CIRF, 2020 FOM conference, University of Utah (Eccles), Uni- versity of Iowa (Tippie), Texas A&M University (Mays), University of Georgia (Terry), Vanderbilt Uni- versity (Owen), University of Kansas, CUHK Business School, CUHK (Shenzhen), City University of Hong Kong, Tsinghua University (PBCSF), Peking University (Guanghua), Peking University (HSBC), Stockholm School of Economics, Western University (Ivey), USC nance Brownbag, 18th Transatlantic Doctoral Con- ference, 2018 Summer Meeting of the Econometric Society, 2018 China International Risk Forum, 19th FDIC/JFSR Annual Bank Research Conference, 8th CIRANO-Sam M. Walton College of Business Work- shop on Networks, the 2nd OFR PhD Symposium on Financial Stability, 2020 EFA Doctoral Tutorial, 2020 Young Economist Symposium, 2020 NFA, and 2020 OFR/Cleveland Fed Financial Stability Conference for helpful comments. iii TableofContents Dedication ii Acknowledgements iii ListofTables vi ListofFigures viii Abstract ix Chapter1: TheProxyAdvisoryIndustry: InuencingandBeingInuenced 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Data and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Data Sources and Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Voting Platforms and Identication of Proxy Advisors . . . . . . . . . . . . . . . . 9 1.2.3 Aggregating to the Fund-Family Level . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Descriptive Statistics for the Proxy Advisory Industry . . . . . . . . . . . . . . . . . . . . . 12 1.3.1 Concentration and Trends in the Proxy Advisory Industry . . . . . . . . . . . . . . 12 1.3.2 Characteristics of ISS and Glass Lewis’s Customers . . . . . . . . . . . . . . . . . . 14 1.4 Robo-Voting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Proxy Advisors’ Inuence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5.1 ISS and Glass Lewis’s Inuence on Their Customers . . . . . . . . . . . . . . . . . 18 1.5.2 Investors that Change Proxy Advisors . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5.3 Mitigating Self-Selection Concerns . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.5.4 The Inuence of Proxy Advice over Time . . . . . . . . . . . . . . . . . . . . . . . 25 1.6 How Can Proxy Advice Be Inuenced? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.6.1 Proxy Advisors Cater to Investors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6.2 Why Do Proxy Advisors Cater? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.6.3 Eects of Proxy Advisors’ Catering on Underlying Firms . . . . . . . . . . . . . . . 29 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Chapter2: EndogenousRisk-ExposureandSystemicInstability 67 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.3 Risk-Taking Equilibrium and Network Distortion . . . . . . . . . . . . . . . . . . . . . . . 77 2.4 Network Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.4.1 Size of interbank liabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 iv 2.4.2 Complete and Ring Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.4.3 Other Regular Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2.4.4 Non-regular Network: European Debt Cross-Holding Example . . . . . . . . . . . 91 2.5 Extension and Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.5.1 Banks’ Incentives to Form Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.5.2 Capital Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.5.3 Government Bailout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.6 Correlated Risk Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 2.7 Discussion and Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Bibliography 133 v ListofTables 1.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.1 Summary Statistics (Continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.1 Summary Statistics (Continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.2 Descriptive Statistics – Snapshot 2008, 2012, and 2017 . . . . . . . . . . . . . . . . . . . . . 35 1.3 Descriptive Statistics - Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.4 Robo Voters and Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.5 Eects of Recommendations on Funds’ Votes . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.6 Proxy Advisors’ Inuences on Informed & Uninformed Funds . . . . . . . . . . . . . . . . 39 1.7 Certication and Sway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1.8 Proxy Advisors’ Sway Eects By Proposal Types . . . . . . . . . . . . . . . . . . . . . . . . 41 1.9 Proxy Advisors’ Inuences On Dierent Funds . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.10 Subsequent Voting For Funds that Switch Proxy Advisors . . . . . . . . . . . . . . . . . . . 43 1.11 Proxy Advisors’ Inuences (Propensity Score Matching) . . . . . . . . . . . . . . . . . . . . 44 1.12 Change of Recommendations By Proxy Advisors . . . . . . . . . . . . . . . . . . . . . . . . 45 1.13 Change of Recommendation – Types of Funds . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.14 Why Do Proxy Advisors Cater? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 1.15 Change of Recommendation and Cumulative Abnormal Return . . . . . . . . . . . . . . . 48 1.16 Change of Recommendation and CAR (Proposal Types and Past Disagreement) . . . . . . 49 vi 1.17 Results of Table 1.10 After Excluding Funds that Changed Proxy Voting Guidelines . . . . 65 vii ListofFigures 1.1 N-PX Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 1.2 Competitive Landscape of the Proxy Advisory Industry . . . . . . . . . . . . . . . . . . . . 51 1.3 Descriptive Statistics on Voting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 1.4 Investor Ideologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 1.5 The Trend Towards Robo-Voting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 1.6 Robo-voting: Size and Indexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 1.7 Voting Patterns For Funds that Switch Proxy Advisors . . . . . . . . . . . . . . . . . . . . . 56 1.8 Proxy Advisors’ Sway Eects By Years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 1.9 Cumulative Abnormal Return Around Annual Meetings . . . . . . . . . . . . . . . . . . . . 58 1.10 Robustness: Dierent Margins for Close-Call Proposals . . . . . . . . . . . . . . . . . . . . 58 1.11 Propensity Score Matching: Before and After . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.1 Timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.2 a complete and a ring network with 5 banks . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.3 Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.4 Other Regular Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2.5 Intermediately Connected Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2.6 Equity Buer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 viii Abstract Chapter 1 – Mutual funds rely on recommendations from proxy advisors when voting in corporate elec- tions. Proxy advisors’ inuence has been a source of controversy, but it is dicult to study because infor- mation linking funds to their advisors is not publicly available. A key innovation of this paper is to show how fund-advisor links can be inferred from previously unnoticed features of a fund’s SEC lings. Using this method to infer links, I establish several novel facts about the proxy advisory industry. During 2007- 2017, the market share of the two largest proxy advisory rms has declined slightly from 96.5 percent to 91 percent, with Institutional Shareholder Services (ISS) controlling 63 percent of the market and Glass Lewis 28 percent in the most recent year. A large fraction of ISS customers appear to have robo-voted – followed ISS’s recommendations in over 99.9 percent of contentious proposals – rising from 5 percent in 2007 to 23 percent in 2017, while almost none of Glass Lewis’ customers have robo-voted. Negative recommendations from ISS or Glass Lewis reduce their customers’ votes by over 20 percent in director elections and say-on- pay proposals. Finally, proxy advisors cater to investors’ preferences, adjusting their recommendations to align with fund preferences independent of whether those adjustments lead to recommendations that maximize rm value. Chapter 2 – Most research on nancial systemic stability assumes an economy in which banks are subject to exogenous shocks, but in practice, banks choose their exposure to risk. This paper studies the determinants of this endogenous risk exposure when banks are connected in a nancial network. I show ix that there exists a network risk-taking externality: connected banks’ choices of risk exposure are strate- gically complementary. Banks in nancial networks, particularly densely connected ones, endogenously expose to greater risks. Furthermore, they choose correlated risks, aggravating the systemic fragility. Banks, however, do have incentives to form networks to protect their charter values. The theory yields several novel perspectives on policy debates. x Chapter1 TheProxyAdvisoryIndustry: InuencingandBeingInuenced 1.1 Introduction The problem with corporate governance is that most shareholders are rationally apathetic, unwilling to invest in information that allows them to eectively monitor and vote [8]. Proxy advisory rms hold the promise of solving this issue by exploiting economies of scale in information collection, allowing investors to vote their interests at low cost. These economies of scale, however, have led the industry to consolidate into eectively two rms – Institutional Shareholder Services (ISS) and Glass Lewis – resulting in little diversity of advice, and the recommendations of proxy advisors are often criticized for containing factual errors and imposing one-size-ts-all governance structures. Given their growing importance for corporate governance, proxy advisors have attracted considerable research attention recently. Much of this research, however, has been hindered by a basic data limitation: the lack of information that links investors to their proxy advisors. Without knowing which investors receive which recommendations, our picture of the impact of advice is necessarily incomplete. For ex- ample, previous papers estimate the inuence of proxy advisors by comparing recommendations with votes that are pooled across all investors [17, 33, 54]. The typical nding in vote-advice regressions of larger coecients for ISS than Glass Lewis could be attributed to Glass Lewis having fewer customers or not inuencing its customers’ votes. Without information that links advisors to voters, it is dicult to 1 reach denitive conclusions on many questions about the industry, ranging from basic issues such as the industry’s concentration to more textured inquiries that relate to the determinants of impact. A key innovation of this paper is to use a previously unnoticed feature of regulatory lings to identify each mutual fund’s subscription to proxy advice, thereby providing a concrete link between fund votes and proxy advice. Since 2003, mutual funds have been required to report their votes to the SEC by ling Form N-PX. Filers have discretion in how they format the form and describe their votes. Mutual funds rarely perform this potentially time-consuming task themselves, which may involve reporting on tens of thousands of votes each year. Instead, they outsource it to their proxy advisors. I show that one can determine the proxy advisor that les the form, based on the way the form is formatted and how issues are described. With the information on proxy advisors’ customer bases, I am able to provide a sharper characteri- zation of the proxy advice market than previously possible and conduct new tests that speak to several controversies in the literature. Critics of the proxy advisory industry claim that the industry’s concen- tration empowers ISS and Glass Lewis to signicantly sway corporate elections. Yet, there is currently no rigorous evidence on the proxy advisory industry’s concentration, although a widely circulated conjecture claims that ISS and Glass Lewis “control” 97 percent of the entire proxy advice market. With the informa- tion on mutual funds’ subscriptions to proxy advice, I nd that, as of 2017, ISS controls 63 percent of the proxy market for mutual funds in the U.S. ($13.4 trillion in assets from 135 fund families), and Glass Lewis controls 28 percent ($6.0 trillion in assets from 27 fund families). Contrary to popular belief, I nd that the proxy advisory industry, although still a duopoly, has become less concentrated over the last decade. Dur- ing 2007-2017, the joint market share of ISS and Glass Lewis has declined from 96.5 percent to 91 percent, with ISS gradually losing its dominance in the industry. Some observers have raised concern about investors blindly following proxy advisors’ recommenda- tions, the so-called practice of robo-voting [46, 26, 69]. Without identifying proxy advisors’ customer bases, 2 researchers tend to underestimate the severity of robo-voting by inating the denominators – comparing the number of ISS customers that robo-vote with the total number of investors rather than with just the number of ISS customers. Accurately measuring the extent to which investors blindly follow their proxy advisors is particularly crucial in light of the SEC’s 2019 proposed rule that gives companies a chance to respond to proxy advisors’ analysis before recommendations are sent to investors. This rule is designed to reduce proxy advisors’ factual or methodological errors, but it becomes eective only if investors review companies’ responses rather than robo-vote with their proxy advisors. 1 I nd that the fraction of ISS cus- tomers who almost entirely follow its recommendations grew from 5 percent in 2007 to 23 percent in 2017, at which time over 40 percent of small funds (and over 50 percent of small index funds) robo-voted. The result implies that without disabling the automatic voting mechanism, the rule will be much less eective in xing factual errors: 23 percent of ISS customers (and over 50 percent small index funds) will not review the company’s response, even if they are given a chance to do so. To estimate proxy advisors’ inuence on their customers’ votes, most previous studies, although nd- ing a meaningful correlation between proxy advisors’ recommendations and vote outcomes, cannot tease out the possibility that investors vote in the same direction as proxy advisors because they both agree on the proposal’s fundamental merits, hence overestimating proxy advisors’ inuence [17]. 2 This fact is espe- cially argued for by ISS to avoid any new regulation: “media reports substantially overstate the extent of ISS’ inuence by failing to control for the underlying company-specic factors that inuence voting out- comes.” On the other hand, previous papers may underestimate proxy advisors’ inuence because votes are pooled across all investors rather than a particular proxy advisor’s customers. With the information that links investors to proxy advisors, I examine the votes from a particular proxy advisor’s customers, and implicitly control for any company-specic factors by comparing those votes with other investors’ 1 As the SEC asked, “In instances where proxy voting advice businesses provide voting execution services (pre-population and automatic submission) to clients, are clients likely to review a registrant’s response to voting advice?” 2 The literature has produced inconclusive evidence of ISS’s inuence, ranging from 6% to 25% [15, 17, 54, 62]. There are few academic studies on Glass Lewis’s inuence. 3 votes on the same proposals. I nd that both ISS and Glass Lewis have signicant inuence over their cus- tomers’ votes. For example, when ISS recommends against a particular director’s election, its customers are 21 percent more likely than other investors to vote against this director. Similarly, when Glass Lewis recommends voting against a director, its customers are 29 percent more likely to vote against the director. The same pattern also applies for non-binding advisory votes on executive compensation (“Say on Pay”), wherein ISS and Glass Lewis can sway 20 percent and 26 percent of their customers’ votes, respectively. One might be concerned that an investor will vote similarly to its proxy advisor because they have similar voting preferences, and the fact that it agrees more with its advisor than other non-subscribers simply reects self-selection. To alleviate this concern, I examine the same fund’s voting pattern after it changes proxy advisors. I nd that after a fund switches its proxy advisor from Glass Lewis to ISS, its vote agreement with ISS increases immediately by 24 percent, and vote agreement with Glass Lewis declines immediately by 21 percent. Similarly, after a fund switches from ISS to Glass Lewis, its vote agreement with Glass Lewis rises immediately by 38 percent, and vote agreement with ISS decreases immediately by 23 percent. Furthermore, this pattern continues to hold after I restrict the sample of switching funds to those that do not change their proxy voting guidelines to further control for funds’ voting preferences. If the result were due solely to self-selection, we would expect investors who are self-informed to vote more similarly to their advisors’ recommendations because votes of informed investors are more likely to represent their preferences. However, this is not consistent with what I nd; instead, I show that an investor is less aected by its advisor’s recommendations if it has viewed the proposal’s proxy statement on the EDGAR website. The result is consistent with the hypothesis that ISS and Glass Lewis inuence votes, especially when their customers perform less due diligence. These results, along with an additional propensity-score matching approach, suggest that the estimation is unlikely due to self-selection. 4 Using a one-time change in ISS’s voting guideline, [62] causally estimate ISS’s inuence on the out- comes of say-on-pay proposals during 2010-2011, and they also nd a strong inuence of ISS’s recommen- dations. A limitation of their approach is that it only reveals the inuence of ISS in a particular year on a particular issue. In contrast, my approach assesses both ISS’s and Glass Lewis’s inuence on all propos- als and over all years in my sample. Estimating eects across multiple years, I nd that after 2011, there was an upward trend in ISS’s inuence on almost every type of proposal: director elections, say-on-pay proposals, and other shareholder-sponsored proposals. I also nd that ISS’s inuence spiked during the 2008-2009 nancial crisis. This result is reconciled with the nding that investors rationally allocate their attention during times of stress [51, 53]. Knowing that proxy advisors’ recommendations inuence votes, an important question is how much their advice aligns with value maximization and whether it is free from conicts of interest. [58] shows that ISS’s advice favors the management with which it has a consulting relationship. [63] argue that there is another potential conict of interest resulting from the fact that proxy advisors compete for customers, es- pecially non-value-maximizing funds. In this paper, I show that both ISS and Glass Lewis cater to investors’ preferences, adjusting their recommendations to align with fund preferences regardless of whether those adjustments lead to recommendations that maximize rm value. Specically, a 10 percent disagreement between investors’ votes and ISS’s recommendation is associated with up to a 5 percent chance that ISS subsequently changes its recommendation when the proposal re-appears on the rm’s ballot. Similarly, for Glass Lewis, a 10 percent vote disagreement can result in a 3 percent chance that it changes the recom- mendation. In addition, I nd that ISS caters more to its existing customers, but Glass Lewis caters more to funds that are not yet its customers. A priori, it is unclear whether catering to investors by proxy advisors creates or destroys value because there are two explanations for proxy advisors’ change of recommendations resulting from investors’ dis- agreement. Investors might possess better information, and proxy advisors learn from their disagreement, 5 in which case the change of the recommendation enhances value-maximization. Alternatively, proxy ad- visors may cater to investors because doing so retains and attracts customers, thus increasing their own prots. In this case, the change of recommendation does not align with value-maximization. To distinguish the two channels, I examine the cumulative abnormal returns (CARs) for annual meetings in which there is at least one close-call proposal on which ISS or Glass Lewis changes recommendations [20]. I nd there is a2 percent abnormal return if the proposal’s vote outcome adopts ISS’s changed recommendation. This nding suggests that ISS’s change of recommendations is not aligned with value-maximization and is consistent with the hypothesis that such catering is for ISS’s own benet. There are three main contributions of this paper. To the best of my knowledge, it is the rst paper to introduce a method to identify which funds are customers of which proxy advisors. With this information, I provide the rst rigorous representation of the leading proxy advisory rms’ market shares. Furthermore, by comparing the votes of a proxy advisor’s customers with those of other investors, I provide plausibly causal estimates of proxy advisors’ inuence by implicitly controlling for any proposal-specic factors. Finally, this paper provides the rst empirical exploration of the feedback loop from investors to proxy advisor recommendations, showing that proxy advisors appear to cater to investors’ preferences, and such catering is not consistent with value-maximization. This paper is related to the growing literature on proxy advisors and corporate governance eorts of institutional investors. [21] provide a survey of this literature, and here, I will summarize several papers that are related to the present paper. The research on the inuence of proxy advisors’ recommendations has produced inconclusive results. [15], [46], [54], and [62] show that ISS has signicant inuence over investors’ votes, ranging from 19% to 25% of votes. In contrast, [17] show a much-dampened eect, 6%–10%. Among these papers, [62] provide causal interpretations for ISS’s inuence on a particular year’s say-on- pay proposals by using a cuto in ISS’s voting guideline. Theoretical works on proxy advisors are sparse 6 but growing. [61] develop a model to study the provision of information by proxy advisors. Recent works, such as [57], [60], and [63], study proxy advisors’ distorted incentives for providing accurate advice. 1.2 DataandMethodology 1.2.1 DataSourcesandSampleSelection Data are compiled across several sources. The initial sample contains the entire mutual fund voting records between 2006 and 2017. Since 2003, mutual funds are required to report their entire voting record on Form N-PX to the SEC each August. I collect those forms directly from the SEC’s EDGAR website. I then link each N-PX form to the ISS Voting Analytics database using the form’s accession number, a unique identier to EDGAR submissions. The ISS Voting Analytics dataset tabulates mutual funds’ votes on those N-PX forms. It also provides each proposal’s nal vote outcome and ISS’s recommendation. Because accession numbers only appear in the Voting Analytics dataset after 2006, I restrict the sample of votes to 2006-2017. The nal sample contains 82 million votes (fund-proposal level) from 15,886 N-PX forms and covers 20,654 mutual funds’ voting records on 438,793 proposals. Glass Lewis’s recommendations are not publicly available [54]. Some papers, such as [54] and [14], in- fer Glass Lewis’s recommendations through a few of its known customers’ voting records. 3 Other papers, such as [17], [33], and [58], obtained Glass Lewis’s recommendations through proprietary methods for certain years. 4 In this paper, I obtained Glass Lewis’s recommendations for the period 2008-2017, through a Freedom of Information Act (FOIA) request to a large public pension. I asked for the name of the pension 3 Specically, they use voting records from Charles Schwab, Neuberger Berman, Loomis Sayles, and Invesco to infer Glass Lewis’s recommendations. My paper calls for caution in this method because the N-PX inference shows that Charles Schwab changed its proxy advisor from ISS to Glass Lewis during 2009. This fact can be additionally veried from Charles Schwab’s 2009/2010 prospectus, available at https://www.sec.gov/cgi-bin/browse-edgar?action=getcompany&CIK= 0000904333&type=485. 4 [58] obtained Glass Lewis’s voting recommendations for the period 2004-2011. [33] obtained for 2011. [17] obtained for 2005-2006. 7 fund’s proxy advisor and recommendations it received for its advisor. I then matched those recommenda- tions with the main dataset (ISS Voting Analytics) using company names, meeting dates, and item numbers. I can nd Glass Lewis’s recommendations for 2590 companies, covering over 80% of the total assets for companies in my main dataset. The online Appendix provides a screenshot for the FOIA response and a detailed description of the matching process. I obtain mutual funds’ characteristics from the CRSP Mutual Fund Database, which provides infor- mation on each fund’s name, total net assets, fund-family name, and ag for an index fund, etc. I then merge funds’ characteristics with my main voting dataset using CIK numbers, which are unique ten-digit numbers that SEC assigns to EDGAR lers. 5 The ISS Voting Analytics does not provide mutual funds’ CIK numbers. I collect CIK numbers from N-PX forms’ header les. Information on mutual funds’ ideology preferences is provided by [11]. I merge the ideology data with my main dataset using “institutionid”, the Voting Analytics’ fund-family identier. I obtain mutual funds’ views of proxy statements through the EDGAR server log le. The log le includes each viewer’s partially anonymized IP address, the time of the view, the accession number of the viewed le. To map partially anonymized IP addresses to fund families, I rst deanonymize IP addresses using the cipher provided by [16] and then map the full IP addresses to organization names using linking datasets provided by MaxMind and American Registry of Internet Numbers (ARIN). 6 Then, I hand match organizations with fund-families in the voting dataset using their names. I can match 282 out of 501 fund families that appear in the voting dataset. 7 To match a proxy statement’s accession number to an annual 5 As noted by [64] and [46], there is no unique fund identier common to both ISS Voting Analytics and CRSP. They proceed by matching the two datasets using fund names. Unlike their methods, I match the two datasets using CIK numbers. My method generates more precision in matching except that dierent mutual funds within the same fund family sometimes have an identical CIK. This is not a concern for my analysis because I aggregate votes to the fund-family level, following [11] and [45]. Section 1.2.3 provides more details about the aggregation. 6 MaxMind is a for-prot intelligence company that provides location/ISP data for IP addresses. This dataset has been used for linking IP addresses to organization names by [16] and [19]. ARIN is a nonprot company that primarily oers IP registration services. This dataset has been used by [9] and [19]. I choose to use both datasets for better results. See [19] for a discussion of the two datasets. 7 There are three reasons why a fund family cannot be matched with any record in the SEC log le. First, it is possible that this family has never visited any SEC ling. Second, it is possible that this family does not use its own name for the internet (e.g., 8 meeting in the voting dataset, I rst scraped the proxy statement’s header le to get its CIK number and “Period of Report”. Then, I match the CIK number and the “Period of Report” with an annual meeting’s CUSIP and meeting date. 8 1.2.2 VotingPlatformsandIdenticationofProxyAdvisors For N-PX lings, a mutual fund must disclose (a) information on issuers (CUSIP, ticker, meeting date, etc.), (b) brief descriptions of proposals, and (c) how it voted. In contrast to requirements for Form 13-F, the SEC does not require a uniform N-PX “information table” for mutual funds to complete. 9 Thus, mutual funds or their proxy service providers have discretion on how to tabulate, format, and characterize their votes and the issues on which they vote. 10 On the other hand, mutual funds rarely prepare or le N-PX forms themselves. This fact is also observed in my data that will be explained shortly. Instead, mutual funds outsource those tasks to their voting platform providers. The reason is obvious: most mutual funds have to cast, manage, or report thousands of votes each year, a complicated and time-consuming process that, for some, is just a distraction from their core business strategies. In the online appendix, I show that the price of voting platform services is as much as twice the price of the proxy advice itself. 11 There are three dominant voting platforms currently on the market: ProxyExchange, Viewpoint, and ProxyEdge. All three platforms provide vote reporting services that tabulate their customers’ votes and prepare the required N-PX forms. They also oer add-on Vote Disclosure Services (VDS) that interactively it can be recorded as AT&T Business). Third, it is possible that neither MaxMind nor ARIN is comprehensive. As a comparison, [45] can match 87 fund families using the linking table from another vendor Digital Elements. 8 To match CIK with CUSIP, I use the linking table provided by WRDS SEC Analytics. The “Period of Report” in a proxy statement denotes its meeting date. Seehttps://www.sec.gov/info/edgar/edgarfm-vol2-v5.pdf (page 6-31). 9 For Form 13-F, the SEC provides a prescribed 8-column table that mutual funds must use. However, the SEC does not provide a similar “information table” for N-PX forms. Instead, it only provides “a guide in preparing the report.” See https: //www.sec.gov/about/forms/formn-px.pdf. Over the years, petitions have been made to standardize N-PX forms. See https://www.sec.gov/comments/265-28/26528-36.pdf. 10 For example, for Proposal 5 in Apple Inc’ 2019 annual meeting, BlackRock’s N-PX form described the proposal as “Disclose Board Diversity and Qualication,” JP Morgan Funds’ N-PX form described it as “A shareholder proposal entitled True Diversity Board Policy,” and TIAA funds’ N-PX form described it as “Shareholder Proposal regarding Disclosure and Board Qualications.” The three funds’ N-PX forms also exhibit dierent formats. 11 Specically, I show that the average payment for proxy advice is $69,080, and a fund needs to pay an additional $161,290 to use its advisor’s proxy voting system. 9 display their customers’ votes on their websites. Owners of two voting platforms are proxy advisors – ISS owns ProxyExchange, and Glass Lewis owns Viewpoint. The third platform, ProxyEdge, is owned by Broadridge, a ntech rm. With the fact that users of a proxy advisor’s voting platform have access to its proxy advice, I can infer an investor’s subscription to proxy advice if I know it uses ISS or Glass Lewis’s voting platform. 12;13 Inferring mutual funds’ uses of voting platforms from their N-PX lings consists of three steps. In the rst step, I look for format commonality among all N-PX lings. I nd that there are four most common N-PX formats. Figure 1.1 provides an example for each of the four formats, denoted A.1, A.2, B, and C. In the second step, I compare proposal descriptions on those four N-PX forms with those of the three voting platforms’ VDS websites to establish the link. I nd that types A.1 and A.2 correspond to ISS VDS, type B corresponds to Glass Lewis VDS, and type C corresponds to Broadridge VDS. 14 In the Online Appendix, I describe in detail how I link the four N-PX tables to their respective voting platforms. In the nal step, I identify each fund’s type from its N-PX’s format and use the type to infer the fund’s use of a voting platform. The inference from voting platforms to proxy advisors may come with Type I and Type II errors. For Type I error, a fund may subscribe to both ISS’s and Glass Lewis’s proxy advice but only use one platform for voting. It is also possible that a fund uses neither ISS’s nor Glass Lewis’s voting platform but instead subscribes to their proxy advice. For Type II error, a fund that does not subscribe to ISS’s or Glass Lewis’s proxy advice may use their voting systems or simply imitate their N-PX formats. I will discuss the eects of those errors when presenting the main results. 12 ProxyExchange’s marketing document states that “[it is] one integrated platform for proxy research, voting, and reporting.” Viewpoint’s marketing document states that “in-depth Proxy Paper reports are accessible for every meeting you vote.” 13 For the funds that use Broadridge’s ProxyEdge, I cannot identify their proxy advisor. As of 2017, they constitute of 5% of the mutual fund market. 14 Due to historical reasons, ISS has two voting systems and two dierent N-PX formats. The two platforms also have dierent VDS websites. Seehttps://www.sec.gov/litigation/admin/2013/ia-3611.pdf. 10 1.2.3 AggregatingtotheFund-FamilyLevel The subscription to proxy advice and the subsequent voting is generally decided at the fund-family level [68, 11]. 15 I hence aggregate fund-level observations to the fund-family level using CRSP’s denition of fund families. The aggregation involves a two-step process. In the rst step, I aggregate fund-level observations (82 million votes from 20,654 funds) to the CIK level (39 million votes from 2,250 CIKs). Using CIKyear as the identier, I then merge the CIK-level voting data with the CRSP Mutual Fund dataset to get information on each CIK’s fund family and characteristics. As a result, I can match 84% of CIK-level observations (33 million votes) with the CRSP dataset. The remaining unmatched votes come from the mutual funds that are not covered by the CRSP dataset. In the second step, I aggregate CIK- level observations to the fund-family level using “mgmt_cd”, the CRSP’s identier for fund families. After this process, the aggregated dataset contains 15 million votes from 501 fund families. It covers 420,391 proposals from 7,897 companies during 2006-2017. To avoid verbosity, I occasionally refer a fund family as a fund throughout the rest of the paper. Table 1.1.A displays the number of fund votes and the number of proposals during my sample years. They are separated by dierent proposal types. 16 Table 1.1.B and 1.1.C report summary statistics at the proposal and the fund-family level. 15 For example, in BlackRock’s prospectus, we know that BlackRock (rather than iShares S&P 500 Index Fund) retained ISS to provide proxy advice, vote execution, and recordkeeping. See https://www.sec.gov/Archives/edgar/data/844779/ 000119312506201228/d497.htm. Another way to conrm this is to look at proxy advisors’ VDS websites. For example, Glass Lewis’s VDS website groups all TIAA funds together. This suggests that the decision to use Glass Lewis’s service is most likely aggregated at the TIAA family level. Seehttps://viewpoint.glasslewis.net/webdisclosure/search.aspx? glpcustuserid=TIA129. In my data, I nd that only 0.3% of fund-years use both ISS’s and Glass Lewis’s voting platforms. They tend to be in the transition year when the fund switches its voting platform. 16 Beginning with the rst annual shareholders’ meeting taking place on or after 2011/1/21, say-on-pay proposals become mandatory as part of the Dodd-Frank Act. They have to be brought up by the management every one to three years. Before that, shareholders can sponsor them as governance measures. Because they are dierent in nature, I treat them as dierent proposal types before and after 2011. 11 1.3 DescriptiveStatisticsfortheProxyAdvisoryIndustry 1.3.1 ConcentrationandTrendsintheProxyAdvisoryIndustry The proxy advisory industry in the U.S. has consolidated into eectively two rms – ISS and Glass Lewis. Critics are concerned that the concentration of the industry empowers the two rms with signicant inuence in corporate elections. Most observers believe that ISS and Glass Lewis jointly control 97 percent of the entire proxy advice market. News articles, such as the Wall Street Journal, Economist, Forbes, and Reuters, have all cited this number. 17 Academic papers, such as [18], [54], and [41], rely on this number as the premise of their analysis. Rule-making, such as the one proposed by the SEC in 2019, hinges on this number’s accuracy. It is hence imperative that we have an accurate and current picture of the proxy advisory industry’s competitive landscape. The widely cited 97% market share that ISS and Glass Lewis jointly control was inferred from a decade- old Government Accountability Oce survey, which unfortunately cannot inform us about the industry’s current and evolving competitive landscape. Perhaps more concerning is that the estimation relied on proxy advisors’ self-reporting and assumed that Egan-Jones, the third-largest proxy advisor, controlled 0% of the market because the rm did not respond to the survey. The challenge to grasp a clear picture for the proxy advisory industry’s concentration is that proxy advisors are precluded from revealing their customer bases due to condentiality agreements. This fact is clearly stipulated in contracts between ISS and its customers: “[ISS should] not disclose the Fund In- formation to any person or business entity other than a limited number of employees or ocers of the Supplier on a need-to-know basis.” 18 As a result, there is currently no way for scholars to identify each proxy advisor’s market share based on publicly available information. Fortunately, with information on 17 WSJ: “SEC Takes Action Aimed at Proxy Advisers for Shareholders;” Economist: “Proxy advisers come under re;” Forbes: “The Law of Unintended Consequences: The Case of Proxy Advisory Firms;” and Reuters: “Proxy adviser ISS sues U.S. markets regulator over guidance aimed at curbing advice.” 18 The agreement was disclosed to the public via an SEC cease-and-desist order against ISS. See note 14. 12 mutual funds’ voting platforms, I can infer their subscriptions to proxy advice and hence calculate proxy advisors’ market shares. Figure 1.2 displays the evolution of the industry from 2007-2017. Panel A shows the number of funds that use each of the three voting platforms, and Panel B shows the number of funds that switch voting platforms each year. Panel C displays the total mutual fund assets that ISS and Glass Lewis advise and the two rms’ market shares. To calculate ISS and Glass Lewis’s total market size in each year, I use the summation of their customers’ total net assets (TNA). 19 The green area represents mutual funds that use Broadridge or other voting systems, e.g., Egan-Jones. We rst notice that there is enormous growth for the size of the proxy advisory industry from 2007-2017. This growth is because the mutual fund industry is growing – both for the number of funds and each fund’s average size. The combined mutual fund assets that ISS and Glass Lewis advise grow from $8.7 trillion to $19.4 trillion, an 123% increase. During the same period, the Russell 3000 index grows by 62%. The result suggests that as the mutual fund industry accumulates more voting powers, it becomes increasingly important that they cast votes informatively, and their proxy advisors provide accurate information. In contrast to popular belief, I nd that the proxy advisory industry has become less concentrated. As of 2017, ISS and Glass Lewis jointly controls 91 percent of the market (dened by total assets), compared with 96.5 percent in 2007. Although there is enormous growth for both ISS and Glass Lewis’s total market size, ISS is gradually losing its relative market share (from 74 percent in 2007 to 63 percent in 2017) to Glass Lewis and other boutique proxy advisors. Nevertheless, this result does not imply that ISS’s inuence is damping. As we well see later in section 1.5, ISS has a strong and growing inuence on its customers’ votes. It is worth noting that the above estimation is a slightly conservative estimation for ISS’s and Glass Lewis’s market size in proxy advice business to mutual funds. This is because even though I can precisely 19 Vanguard has its distinctive N-PX style. According to its prospectus, it subscribes to proxy advice from both ISS and Glass Lewis. I hence split the total assets of Vanguard equally to ISS and Glass Lewis’s market size. 13 identify each fund’s proxy voting system, in some cases, a mega-fund may use one voting system but subscribe to proxy advice from multiple proxy advisors. In addition, the calculation only focuses on the mutual fund industry. Notwithstanding the caveats, the results provide a useful picture for understanding the proxy advisory industry’s evolving competitive landscape. 1.3.2 CharacteristicsofISSandGlassLewis’sCustomers Funds that use dierent voting systems exhibit dierent characteristics. Table 1.2 provides three snapshots (2008, 2012, and 2017) for funds that use the voting systems of ISS, Glass Lewis, or Broadridge. Table 1.3 displays the OLS regressions of funds’ characteristics as a function of their uses of dierent voting systems. From table 1.3’s panel A, we notice that fund families that use neither ISS nor Glass Lewis are much smaller (around 200 percent), have much fewer ballots to vote (around 200 percent), younger (over ten years), and are less likely to provide an index or institutional fund (20 to 30 percent) than fund families that use ISS or Glass Lewis. Many of them are boutique funds with only a few companies in their portfolios (or hundreds of proposals to vote). It is hence unsurprising that they subscribe to proxy boutique advisors if at all. The panel B shows that funds that subscribe to ISS or Glass Lewis are relatively similar except that ISS’s customers are 35 percent smaller in terms of total net assets and 10 percent less likely to provide institutional funds. Table 1.2 also shows that mutual funds vote similarly with their proxy advisors. For example, in 2017, when ISS opposes management, its customers agree with ISS’s recommendations 71 percent of the time while Glass Lewis’s customers agree with ISS’s recommendations only 33 percent of the time. Similarly, when Glass Lewis opposes management, Glass Lewis’s customers agree with Glass Lewis’s recommenda- tions 60 percent of the time while ISS’s customers agree with Glass Lewis only 39 percent of the time. To see the pattern more concretely, gure 1.3 displays the percentage of investors’ votes that support man- agement conditioning on proxy advisors’ recommendations. In Panel A, we see that if either ISS or Glass 14 Lewis opposes management, investors become more likely to disagree with management. Panel B shows that ISS’s and Glass Lewis’s recommendations have greater eects on their own customers’ votes than other investors’ votes. Those observations suggest that proxy advisors inuence their customers’ votes. Section 1.5 discusses the identication in further detail. [11] show that investors’ votes exhibit heterogeneous preferences. They map each investor’s votes into a two-dimensional score using a popular political-science approach. The two scores, both in the range of [1; +1], are interpreted as being socially responsible and being tough-on-governance. Figure 1.4.A plots fund votes’ ideology scores, grouped by the use of dierent voting systems. We immediately notice that ISS and Glass Lewis customers are clustered together – ISS’s customers appear on the lower left, and Glass Lewis’s customers appear on the upper right. Figure 1.4.B plots the distribution of the social and governance score for funds that subscribe to ISS and Glass Lewis. The result suggests that ISS customers’ votes emphasize more on social issues (have a lower score in the rst dimension) but less about governance issues (have a lower score in the second dimension). The opposite is true for Glass Lewis’s customers – their votes emphasize less on social issues but more on governance issues. 1.4 Robo-Voting The problem with investors blindly following proxy advisors, a so-called practice of robo-voting, is always a great concern for industry participants and regulators. A 2020 survey shows that 90 percent of retail investors support disabling robo-voting when proxy advisors’ reports provide additional analysis. 20 While there is no uniform denition for robo-voting, it generally denotes the practice of investors automatically relying on proxy advisors’ recommendations without evaluating the analysis underpinning them. 20 “Spectrem Group Study Reveals Wide Retail Investor Support for Proposed SEC Amendments”, https://www. prnewswire.com/news-releases/spectrem-group-study-reveals-wide-retail-investor-support-for-proposed-sec-amendments--january-10-2020-300984956. html. Another survey done by four major U.S. law rms shows that around 20 percent of votes are executed within three business days after ISS issues its recommendations [69]. 15 Accurately measuring the extent to which investors automatically execute votes is particularly crucial in light of the SEC’s proposed rule in 2019 giving companies a chance to respond to a proxy advisor’s analysis before recommendations are sent to investors. The rule is intended to reduce proxy advisors’ fac- tual errors or methodological weaknesses, but it will become eective only if investors review companies’ responses rather than robo-vote with their proxy advisors. 21 Researchers have attempted to measure the extent to which investors blindly follow the proxy advice [46, 26, 69, 12]. However, without being able to identify proxy advisors’ customers, they tend to underestimate the severity of the problem by inating the denominator – they compare the number of ISS customers that robo-vote with the total number of investors rather than with just the number of ISS customers. For example, [46] mention that "to the extent that some funds rely on a proxy advisory service other than ISS, we actually underestimate the frequency of passive voting." With the help of my dataset, I can provide a more accurate estimate of the practice of robo-voting. I dene an investor as an ISS robo-voter in a particular year if its votes agree with ISS on more than 99.9 percent of proposals where ISS disagrees with management. This is a restrictive denition because it implies that robo-voters side with management fewer than 0.1 percent of the time. 22 It is hence unlikely that the ag of robo-voting is due to the coincidental agreement between the investors and ISS. Similarly, I ag an investor as a Glass Lewis robo-voter in a particular year if its votes agree with Glass Lewis on more than 99.9 percent of proposals where Glass Lewis disagrees with management. Figure 1.5.A displays the total number of ISS robo voters and their relative fractions among funds that subscribe to ISS, Glass Lewis, or neither. The result shows that the practice of robo-voting among ISS 21 As the SEC itself asked, “In instances where proxy voting advice businesses provide voting execution services (pre- population and automatic submission) to clients, are clients likely to review a registrant’s response to voting advice?”. See https://www.sec.gov/rules/proposed/2019/34-87457.pdf at 9. 22 My denition is more restrictive than those of [46], [26], and [12], who dene an investor as a robo-voter if the investor’s votes agree with ISS on more than 99 percent of all proposals. Given that most proposals are not contentious, using the 99 percent threshold on all proposals will unlikely to be an accurate indicator for robo-voting. For example, [26] ags the mutual fund family AQR as a robo-voter because the fund family follows ISS’s recommendations on more than 99.9% of all proposals. However, if we restrict the sample to contentious proposals, AQR agrees with ISS only 97.5% of the time. This is not within my denition of robo-voting. In fact, there are 36 contentious proposals that AQR’s votes deviate from ISS’s recommendations. 16 customers is prevalent and has been rising in popularity. In 2017, 29 fund families combined managing over $200 billion of assets almost entirely followed ISS recommendations. From 2007 to 2017, the fraction of robo-voting ISS customers grew from 5 percent to 23 percent. The results provide a direct answer to the SEC’s solicited comment: 23 percent of ISS’s customers will not review companies’ responses even if they are given a chance to do so. On the other hand, Figure 1.5.B suggests that the practice of robo-voting among Glass Lewis’s customers appears to be less prevalent. So far, we have focused on one form of robo-voting – blindly following proxy advisors’ recommen- dations. When making voting decisions, investors face another source of information: managements’ recommendations. There is an often-ignored risk that investors may blindly follow management’s recom- mendations, especially investors who do not subscribe to any proxy advice. Indeed, Figure 1.5.C shows that robo-voting with management is also widespread and growing among those investors. In 2017, 15 investors, combined with over $10 billion, blindly follow management’s recommendations. One immediate question is who those robo-voters are? Are they indexers who arguably perform less due diligence of reviewing proxy advisors’ recommendations, as suggested by [59] and [45]? Alternatively, are index funds active participants in voting due to their large voting blocs, as suggested by [6]? Table 1.4 reports the results of OLS regressions on whether a fund is a robo-voter as a function of its characteristics. The result shows that ISS customers that provide any index product are 8 percent more likely to blindly follow ISS’s advice. This nding is consistent with [59], who argue that index funds lack incentives to ensure well-run companies as they do not seek to outperform the index. Nevertheless, the result is not inconsistent with [6], who argue that passive investors exert inuence on corporate governance through their large voting blocs. In fact, table 1.4 shows that doubling a fund family’s total assets decreases the probability of it being an ISS robo-voter by 5 percent and being a management robo-voter by 2 percent. Figure 1.6.A illustrates the prevalence of robo-voting among investors in dierent quantiles of total net assets. The gure shows that in 2017 more than half of the small indexers that subscribe to ISS robo-vote. 17 It also shows that larger investors and non-indexer investors are less likely to robo-vote, as in table 1.4. Figure 1.6.B illustrates the trend of robo-voting among small, middle, and large ISS customers. We can see that the rise of popularity in robo-voting is particularly salient among smaller investors, rising from less than 5 percent to more than 45 percent. 1.5 ProxyAdvisors’Inuence 1.5.1 ISSandGlassLewis’sInuenceonTheirCustomers Proxy advisors advise on a large number of elections while maintaining a tiny workforce. 23 Their advice has been criticized for exerting undue inuence on the governance of corporations, without explaining why it hinges on conclusions that academics are unable to reach. Research on the role of proxy advice on investors’ votes has produced inconclusive results. 24 The diculty of estimating proxy advisors’ inuence arises from the unobserved rm and proposal characteristics, and using correlations between investors’ votes and proxy advisors’ recommendations can upward bias the interpretation of proxy advisors’ inuence. This is because two reasons can explain shareholders’ vote agreement with proxy advisors’ recommendations. First, investors and proxy advisors observe the same set of information so that they can agree on a proposal’s fundamental merits independent of proxy advisors’ inuence. For example, in 2017, ISS supported the compensation package of Berkshire Hathaway’s Warren Buet, who earned an annual salary of $100,000. Most of Berkshire Hathaway’s share- holders also voted to support this compensation package, which received 99.7 percent of the total votes. In this example, the shareholders’ vote agreement with ISS would probably not be a good measure of ISS’s inuence. Alternatively, investors can vote with proxy advisors’ recommendations because they follow the recommendations regardless of the proposal’s fundamentals. The diculty in disentangling these two 23 For example, [71] notes that in 2017 ISS produced recommendations for 250,000 elections across 40,000 shareholder meetings with a research and data sta of 460 persons. 24 For example, [15], [46], [54], and [62] show that ISS can inuence a large amount of votes, ranging from 19% to 25% of votes. On the contrary, [17] show a much-dampened eect, 6%–10%. 18 possibilities is that we can not observe all proposal-specic fundamentals. Hence, most eorts to estimate proxy advisors’ inuence are upward biased due to the omitted variable problem [17]. On the other hand, the literature also under-estimates proxy advisors’ inuence because votes are pooled across all investors rather than a particular proxy advisor’s customers. Fortunately, with the information on proxy advisors’ customer bases, I can compare a proxy advisor customers’ votes with other investors’ votes on the same proposals. This method implicitly controls for any proposal-specic factors because both groups face the same proposals’ fundamentals. The only dierence is that one has access to the proxy advisor’s recommendations, and the other most likely does not. 25 Using the previous example to illustrate, if both 99.7 percent of votes from ISS’s customers and 99.7 percent of votes from non-customers supported the proposal, then ISS has little inuence on its customers’ votes for this particular proposal. On the other hand, if 99.7 percent of the votes from ISS’s customers supported it, but only 97.7 percent of the votes from other investors supported it, we can infer that ISS’s recommendation aects 2 percent of its customers’ votes on this proposal. I use the following OLS regression to estimate the eect of a proxy advisor’s recommendations on its customers’ votes. One observation is a fund’s vote in a proposal: i denotes the fund, p denotes the proposal, andt denotes the year. The dependent variable “Vote For ip ” equals one if the fund voted “for” the proposal. 26 The regression includes fund characteristics as controls, and more importantly, it includes 25 To the extent that some investors subscribe to both ISS and Glass Lewis’s proxy advice, those estimations are actually conservative measures for proxy advisors’ inuence. 26 Similar to [46], I group “Against” and “Withhold” together as negative votes. 19 the proposal xed eect. As argued earlier, the proposal xed eect controls for any unobserved proposal- specic factors. Vote For ip = ISS For p 1 + 2 ISS Customer it + 3 GL Customer it + GL For p 4 + 5 ISS Customer it + 6 GL Customer it (1.1) + Mgmt For p 7 + 8 ISS Customer it + 9 GL Customer it +a p +" ip Table 1.5 reports the result. Column 1 establishes the benchmark, showing the correlation between funds’ votes and each proxy advisor’s recommendations. Other columns include interaction terms be- tween proxy advisors’ recommendations and investors’ proxy advisors. Columns 2 and 3 include the companyyear or the proposal-type xed eects, and column 4 includes the proposal xed eect to con- trol any proposal-specic fundamentals. The results show that ISS customers are 27 percent more likely than other investors (that subscribe to neither ISS nor Glass Lewis) to vote “for” a proposal when ISS rec- ommends doing so. Similarly, Glass Lewis’s customers are 31 percent more likely than other investors to vote “for” a proposal when Glass Lewis recommends doing so. The results remain qualitatively unchanged after including the fundyear xed eect to control for unobserved fund-family characteristics. Those results suggest that both ISS and Glass Lewis have signicant inuence on their respective customers’ votes. In an ideal experiment, we want to estimate equation 2.1 after randomly assigning investors to dier- ent proxy advisors. Without a random assignment, one may be concerned that investors vote similarly with their proxy advisors’ recommendations because they have similar ideologies. Or in other words, the fact that investors agree with their proxy advisors more than other investors may simply reect the self-selection. To test whether table 1.5’s results are due to proxy advisors’ inuence or investors’ self- selection, I interact the variables of interest (“ISS For ISS Customer” and “GL For GL Customer”) with 20 fund families’ own information set. If table 1.5’s results were purely due to the self-selection, we would expect investors who are better informed to vote more similarly with their proxy advisors’ recommenda- tions because votes of informed investors are more likely to represent their preferences. In other words, the degree of self-selection will be greater for investors who are better self-informed. To measure whether an investor is self-informed, I use its internet visit to a proposal’s proxy statement on the EDGAR website. Table 1.6 shows that informed investors’ votes are actually less similar to their advisors’ recommendations. The results reject the self-selection hypothesis; instead, they are consistent with the hypothesis that ISS and Glass Lewis inuence votes, especially when their customers perform less due diligence. Equation 2.1’s estimation does not separately study a proxy advisor’s inuence when it supports or opposes the management. I dene a proxy advisor’scerticationeect as its inuence on proposals where it supports the management (uncontentious proposals) andswayeect as its inuence on proposals where it opposes the management (contentious proposals). Most of the existing literature focuses on proxy advi- sors’ sway eect. 27 However, knowing a proxy advisor’s certication eect is also important because many investors do not dig into a proposal’s detail when their proxy advisor supports the management. Instead, they only pay attention to proposals where the proxy advisor alerts an issue. 28 To separately study proxy advisors’ certication and sway eects, I use the following OLS regressions, separately done for proposals where the proxy advisor supports or opposes the management. The dependent variable “Agree with ISS ip ” (“Agree with GL ip ”) is a dummy that equals one if the vote is in the same direction as ISS’s (Glass Lewis’s) recommendation. The regressions again include the proposal xed eect. Agree with ISS ip = 1 ISS Customer it + 0 Z +a p +" ipt Agree with GL ip = 1 GL Customer it + 0 Z +a p +" ipt (1.2) 27 For example, both [54] and [62] use some variations of equation 2.1 as their regressions. 28 The head of BlackRock’s corporate governance once said, the rm does not comb through every shareholder pro- posal but only the ones that proxy advisors have identied an issue. (https://www.nytimes.com/2013/05/19/business/ blackrock-a-shareholding-giant-is-quietly-stirring.html) In my sample, ISS agrees with the management on 89 percent of director elections and 87 percent of say-on-pay proposals (Table 1.1.B) 21 Table 1.7 reports the results. We see that when ISS (or Glass Lewis) supports the management, its customers are two percent more likely than other non-customers to support the management. Because most uncontentious proposals are for routine matters, the baseline agreement between investors’ votes with proxy advisors’ recommendations is already high (over 90 percent). A two percent additional support appears to be a meaningful inuence from ISS or Glass Lewis’s certication. Also from Table 1.7, we nd that ISS can sway 21 percent of its customers’ votes when it opposes the management, and Glass Lewis can sway 22 percent of its customers’ votes. The above estimation for ISS’s sway eect (21 percent) is consistent with that of [62], who show that a negative ISS recommendation on say-on-pay proposals can sway 25 percent of investors’ votes. As argued earlier, my approach also enables me to study proxy advisors’ inuence on other types of proposals. One obviously important type is the director election, which [15] and [36] show has far-reaching implications for corporate governance. Table 1.8 repeats the analysis separately for each proposal type. It shows that both ISS and Glass Lewis can sway over 20 percent of their customers’ votes for director elections, com- parable to their inuence on say-on-pay proposals. Another interesting nding is that Glass Lewis has greater inuence than ISS on director elections and say-on-pay proposals, but ISS has greater inuence on social-related proposals. Proxy advisors’ inuence can vary for dierent funds. For example, investors with large ballots may not comb through every proposal, especially when their proxy advisors and management agree. To test the hypothesis, Table 1.9 studies the relationship between a fund’s vote agreement with its proxy advisor and its characteristics. The nding is consistent with the conjecture – proxy advisors have greater certication eects on funds with more ballots to vote. The result also shows that, once an issue is alerted by the proxy advisor, they start their due diligence. Moreover, the larger the fund’s size, the more it performs its due diligence and hence becomes less swayed by its advisors. We also notice that Glass Lewis’s customers that 22 provide an index fund are more likely to be swayed by the advisor. This result is consistent with [59], [45], and [43], who show that indexers do signicantly less governance research. 1.5.2 InvestorsthatChangeProxyAdvisors Another way to gauge proxy advisors’ inuence is to examine an investor’s voting pattern if it switches proxy advisors. Throughout my sample, 22 fund families have switched from using ISS’s voting platform to using Glass Lewis’s platform, which I interpret as switching voting advice from ISS to Glass Lewis, and 10 fund families have switched from Glass Lewis to ISS. If a proxy advisor’s recommendations inuence its customers’ votes, we expect that the voting patterns for funds that switch proxy advisors will change after the switch. To test this hypothesis, consider the following di-in-di regression estimating the eect of switching advisors on the fund’s vote patterns. Agree i;t+1 Agree i;t = 0 + 1 Switch it + 0 Z +" it (1.3) where Agree i;t is the fraction of fundi’s votes that agree with ISS (or Glass Lewis) in yeart. As in equation 1.2, this fraction can be calculated for proposals where the proxy advisor supports or opposes the manage- ment. The independent variable Switch it denotes whether the fund switches from being an ISS customer to a Glass Lewis customer or vice versa from the yeart tot + 1. Table 1.10 reports the results of estimating equation 1.3. In Panel A, we see that after a fund switches its advisor from Glass Lewis to ISS, its votes become 3 percent less likely to agree with Glass Lewis on proposals where Glass Lewis supports the management (GL’s certication eect). Similarly, after a fund switches from ISS to Glass Lewis, its votes become 4 percent less likely to agree with ISS but 4 percent more likely to agree with Glass Lewis on uncontentious proposals. The results are consistent with Table 1.7, which uses cross-sectional variations to estimate the proxy advisors’ certication eect. Similar results can be obtained for ISS and Glass Lewis’s sways eect in Panel B. 23 To see the eect visually, gure 1.7 displays the evolution of a fund’s vote pattern if it switches proxy advisors. Panel A includes funds that have switched from being an ISS customer to being a Glass Lewis customer, and Panel B includes the funds that have switched from Glass Lewis to ISS. All gures’ x-axes denote the relative year to the year of the switch. Each Panel’s rst two gures plot the switching funds’ "relative agreement" with ISS, which is the percentage of a fund’s votes on contentious proposals that agree with ISS minus that of the benchmark. For the benchmark, the rst gure uses the same fund’ vote agreement with ISS in the switching year (for time-series comparison). The second gure uses the average vote agreement with ISS among all ISS’s customers (for cross-sectional comparison). The third and fourth gures are constructed analogously for funds’ "relative agreement" with Glass Lewis. 1.5.3 MitigatingSelf-SelectionConcerns One diculty in estimating proxy advisors’ inuence is the endogeneity problem arriving from the unob- servable rm and proposal characteristics [17]. Thus far, I have addressed this issue by comparing a proxy advisor customers’ votes with those of other investors on the same proposal. In an ideal experiment, we want to do so after randomly assigning investors to dierent advisors to tease out investors’ self-selection. To distinguish proxy advisors’ inuence from investors’ self-selection, table 1.6 shows that informed investors’ votes are less similar to their advisors’ recommendations, in contrast to what the self-selection hypothesis would predict. The result is consistent with the hypothesis that ISS and Glass Lewis inuence votes, especially when their customers perform less due diligence. In addition, section 1.5.2 examines a fund’s voting pattern after it switches proxy advisors. This ap- proach is similar to including a fund xed eect to equation 1.2, and hence controls for the time-invariant fund characteristics. One may still be concerned that a fund’s intrinsic propensity to agree with a proxy advisor may be time-variant, and both the decision to switch advisors and the subsequent votes can result from the changing fund characteristics. To further alleviate the endogeneity concern, I restrict the sample 24 of switching funds to those who do not change their proxy voting guidelines to further control for funds’ voting preferences. 29 The results continue to hold and are provided in the Online Appendix. Furthermore, I use the propensity score matching method (PSM) to match the characteristics of a proxy advisor’s customers with those of other investors within the same year when estimating equations 2.1 and 1.2. The PSM method used is a one-to-one matching without replacement and with a tolerance of 0.001 for the score on characteristics in Table 1.1.C. Table 1.11 reports the result of OLS regressions for equations 2.1 and 1.2 after the matching. The result shows that ISS and Glass Lewis’s inuence estimated after the PSM are qualitatively similar to the estimation before the PSM (Table 1.7). The online appendix shows the distribution of funds’ characteristics before and after the matching and validates the common support assumption. 1.5.4 TheInuenceofProxyAdviceoverTime As mentioned earlier, in contrast to [62], my method can identify both ISS and Glass Lewis’s inuence on every proposal type every year. This enables me to answer many other important questions, such as whether ISS’s inuence is ever-growing. A priori, the answer is not obvious. On the one hand, the mu- tual fund industry has become growingly more passive. Some research shows that passive funds conduct signicantly less research on corporate governance [45]. If that is the case, we expect that proxy advisors have growing inuence on their customers’ votes. On the other hand, investors over the years developed stronger standpoints on social and governance issues. For example, BlackRock CEO Larry Fink sent a letter in 2019 to corporate executives, demanding them to be aware of ESG risk. If this is the case, we expect that investors rely less on proxy advisors. The debate is manifested in a Bloomberg’s survey – “practitioners disagreed on whether the proxy advisory rms’ inuence has grown, decreased, or stayed about the same.” 29 Mutual funds generally disclose their proxy voting guidelines in the SAI section of their prospectus, which may explain how they would vote on dierent issues (e.g., board composition, executive compensation, or ESG matters, etc.). For example, see Thrivent Funds’ prospectus: https://www.sec.gov/cgi-bin/browse-edgar?action=getcompany&CIK=0000811869& type=485. The fund changed its proxy advisor from Glass Lewis to ISS between 2011 and 2012 but didn’t change any word of its 3-page proxy voting guidelines (except “Glass Lewis” was changed to “ISS”) on its 2011/2012 prospectus. 25 To investigate whether proxy advisors’ inuence has been changing over time, I repeat the estimation of proxy advisors’ sway eects (equation 1.2) for each year. Figure 1.8 illustrates the result. It shows that after 2011, ISS’s inuence is growing for proposals of almost any type. For director elections, it could sway 15 percent of its customers’ votes in 2011, but the inuence grows to 21 percent in 2017. ISS’s sway inuence on say-on-pay proposals grows from 12 percent to 22 percent, and its sway inuence on shareholder-sponsored proposals grows from 13 percent to 25 percent. Another interesting nding is that there is a spike in ISS’s inuence during the 2008-2009 nancial crisis. This result can be reconciled with the nding that investors rationally allocate their attention during times of stress [51, 53]. The trend for Glass Lewis’s inuence is more volatile during my sample period. There is a slight decrease in Glass Lewis’s sway eects in the last decade. This is particularly salient for its inuence on say-on-pay proposals – when Glass Lewis opposed a compensation package, it could sway 32 percent of its customers’ votes in 2011, but only 17 percent in 2017. 1.6 HowCanProxyAdviceBeInuenced? So far, we have seen that proxy advisors signicantly inuence their customers’ votes for both director elections and say-on-pay proposals. Specically, over 20 percent of ISS customers almost entirely follow ISS’s recommendations. Nevertheless, it is not clear whether proxy advisors’ inuence creates or destroys value from a normative perspective. On the one hand, proxy advisors provide an additional independent source of information [61]. On the other hand, they are for-prot companies, and their advice suers from conicts of interest. For example, [58] shows that ISS’s recommendations favor the management with which it has a consulting business. [63] show theoretically that proxy advisors cater to investors, especially non-value-maximizing ones. In this section, I rst establish that both ISS and Glass Lewis cater to investors’ preferences to attract and retain business. Then I show that such catering departs from value- maximization. 26 1.6.1 ProxyAdvisorsCatertoInvestors Table 1.12’s Panel A shows the percentage of proposals that ISS or Glass Lewis changes its recommenda- tions. I dene a proposal on which ISS or Glass Lewis changes its recommendations if it supports/opposes the proposal in yeart but opposed/supported the same company’s same proposal in yeart 1. For direc- tor elections, I use the director’s name to link elections across dierent years within a company, and for proposals of other types, I use their general descriptions to link them. 30 We see that both ISS and Glass Lewis have changed their recommendations for every proposal type, except for the proposals on board declassication, which both proxy advisors always support (Table 1.1.B). To test the hypothesis of whether proxy advisors cater to investors. I estimate an OLS regression of whether ISS or Glass Lewis changes its recommendation as a function of investors’ past disagreement with the advisor. Table 1.12 Panel B shows the result. Columns 3 and 6 include the FirmProposal eect to control for the rm and proposal-specic fundamentals. The result shows that a 10 percent additional disagreement between ISS’s customers and its recommendation will result in a 5 percent additional chance that it changes the recommendation when the same proposal reappears in the same company. Glass Lewis also caters to investors, but to a much less extent – a 10 percent additional disagreement between Glass Lewis and its customers will result in a 0.5 percent additional chance that it changes its recommendation. Those results conrm the hypothesis that proxy advisors cater to investors. Another interesting nding is that ISS caters more to its existing customers while Glass Lewis caters more to funds that are not yet its customers. This suggests that ISS’s main objective is to maintain its dominance, while Glass Lewis’s objective is to expand its business. There are two potential explanations for the observation that proxy advisors’ change of recommen- dations comes after investors’ disagreement. On the one hand, investors may possess better information, 30 The ISS Voting Analytics dataset does not provide identiers for director names. I extract director names from proposal descriptions – for example, I extract “Steven P. Jobs” from the description “Elect Director Steven P. Jobs.” On occasions, the same director can appear with dierent variations of their names (e.g., Bill Gates and William Gates). The Online Appendix provides additional details on attracting director names. 27 and proxy advisors learn from their disagreement. For example, [4] show that proxy advisors’ recommen- dations are associated with changing public opinions. Denote this explanation as the information channel. On the other hand, proxy advisors cater to investors because doing so can retain and attract customers, hence increasing their prots. Denote this explanation as the catering channel. To disentangle the two channels, I examine what types of investors that proxy advisors listen to the most. If the information chan- nel is the case, we expect proxy advisors to listen relatively more to active investors because they are more likely to possess better information. If the catering channel is the case, we expect proxy advisors to listen relatively more to passive investors because passive funds conduct signicantly less research on corporate governance and hence are more likely to seek proxy advice [45]. Regardless of the two channels, we expect proxy advisors to listen more to larger investors because they have more resources to be informed while also mean greater revenues for proxy advisors. Table 1.13 shows the OLS regression results of whether a proxy advisor changes its recommendation as a function of the past disagreement between its advice and votes of investors with dierent characteristics. In Panel A, I denote an investor a large fund if its total net asset is above the median among all fund families in the same year, and I denote an investor an active fund if the percentage of its votes disagrees with managements is above the median. In Panel B, I double sort according to the above two metrics (size and activism) to alleviate the concern that they are correlated – a large fund is also more active. Both Panels show that ISS and Glass Lewis listen more to large and non-active funds. This is consistent with the catering channel: non-active funds perform less governance research by themselves and hence are more likely to be potential proxy advisor customers. 1.6.2 WhyDoProxyAdvisorsCater? Proxy advisors cater to investors because doing so can attract and retain customers. To see this, Table 1.14.A examines the relationship between an investor’s past one-year or past three-year agreement with 28 the two proxy advisors and its subsequent choice of its advisor. It shows that a 10 percent additional agreement with ISS results in an 8.5 to 11 percent more chance for Glass Lewis’s customers to switch to ISS, and 2.1 to 2.7 more chance for other investors to switch to ISS. Similarly, a 10 percent additional agreement with Glass Lewis results in an 11 to 12 percent more chance for other investors to switch to Glass Lewis. Furthermore, column 2 also shows that a 10 percent additional agreement with Glass Lewis can result in a 7.4 percent reduction in the chance for Glass Lewis’s existing customers to leave the rm. Those results suggest that having the same stance with investors helps proxy advisors attract potential customers and retain existing ones. Table 1.14.B repeats the analysis by separately studying the eect of investors’ past agreement with the two proxy advisors on dierent proposals. It shows that investors pay more attention to the alignment of preference on director elections than on say-on-pay proposals or shareholder-sponsored proposals. This suggests that ISS and Glass Lewis have particular interests in listening to investors’ disagreement on di- rector elections. Section 1.6.3, however, will show that it is such catering that particularly destroys value. 1.6.3 EectsofProxyAdvisors’CateringonUnderlyingFirms Thus far, we have established the fact that proxy advisors listen to investors. In particular, they listen more to non-active investors. This result provides suggestive evidence that proxy advisors cater to investors for their own prots. To further disentangle the information channel and the catering channel, I examine the eect of proxy advisors’ changes of recommendations on the underlying rm values. If it is the case that investors possess better information and proxy advisors learn from their disagreement, then the change of recommendation is consistent with value-maximization and should increase rm value. If it is the case that proxy advisors cater to investors because doing so increases their own prots, then the change of recommendation is not aligned with value-maximization and should decrease rm value. 29 Table 1.15 shows the eect of whether the vote outcome eventually adopts the proxy advisor’s recom- mendations on the rm’s cumulative abnormal return (CAR). To exclude proposals with widely anticipated outcomes (e.g., ratication of auditors or other routine proposals), I only focus on close-call proposals within 20% of the passing requirement. Figure 1.10 shows the robustness for dierent choices of close-call margins. 31 Most importantly, I separately examine the eect of proxy advisor’s recommendations on rms’ CAR for proposals where they do or do not change recommendations. The result shows that there is a negative two percent abnormal return if the vote outcome adopts ISS’s changed recommendations. This suggests that most shareholders do not appreciate ISS’s changed recommendations, or in other words, ISS’s catering is not aligned with value-maximization. 32 The result is consistent with the hypothesis that the catering is for ISS’s own benet rather than with the information hypothesis. This result is in line with [54] who show that rms’ compensation changes desired by proxy advisors produce a net cost (0.44 percent) to shareholders. The result also shows that when ISS does not change its recommendation, whether or not the vote outcome adopts the recommendation does not aect the underlying rm value. This replicates the re- sults of [46], and casts double on the value of ISS’s recommendation by and large. For Glass Lewis, its recommendations, changed or not, do not seem to matter to the underlying rm value. Table 1.16.A repeats the analysis for each proposal type. The result shows that it is particularly value- decreasing when ISS changes recommendations for director elections. This is reconciled with the results of Section 1.6.2 – ISS has more incentives to cater to investors on director elections because they matter the most to investors when choosing proxy advisors. Table 1.16.B examines the eects of ISS’s changed recommendations when it listens to dierent investors. The result shows that it is when ISS listens to 31 I choose a larger margin than [20]’ 5% for my main analysis because I specically focus on proposals where ISS or Glass Lewis changed their recommendations. They are contentious in nature, and using a too narrow margin may pose issues because they are more likely to be manipulated by management [7]. This is particularly true for my analysis – unlike [20] who only study governance proposals, my sample includes director elections, which managements have more incentives to manipulate. 32 A 2016 GAO report and [55] show that only a relatively small number of institutional investors drive ISS’s policy formation process. In addition, [65] show that as many as 40 percent of institutional investors do not use proxy advisors. 30 non-active investors that its changed recommendations destroy value the most. This again conrms the hypothesis that catering, particularly when it’s for ISS’s own prot, destroys value. 1.7 Conclusion The value of the proxy advisory industry is a matter of continual debate. Many questions – even the most basic ones such as each proxy advisory rm’s market share – remain unanswered due to the lack of information that links investors to their proxy advisors. A key innovation of this paper is that I use a previously unnoticed feature of regulatory lings to identify each mutual fund’s subscription to proxy advice. With this information in hand, I provide what appears to be the rst accurate representation of the proxy advisory industry’s competitive landscape. During 2007-2017, the market share of the two largest proxy advisory rms has declined slightly from 96.5 percent to 91 percent, with ISS controlling 63 percent of the market and Glass Lewis 28 percent in the most recent year. Both ISS and Glass Lewis have strong inuence: negative recommendations from ISS or Glass Lewis reduce their customers’ votes by over 20 percent in both director elections and say-on-pay proposals. The inuence is stronger on funds with smaller assets and on fund families that provide an index product. Fur- thermore, the practice of robo-voting is increasing in prevalence, especially among ISS customers. In 2017, 23 percent of ISS customers, managing over $200 billion of assets combined, follow ISS recommendations almost entirely, rising from only 5 percent of ISS customers in 2007. Proxy advisors cater to investors’ preferences – adjust their recommendations to align with fund pref- erences – because doing so can attract and retain customers. They particularly cater to large and non- active investors. Examining the underlying rm value shows that such catering is not aligned with value- maximization: the stock price responds negatively when the vote outcome adopts ISS’s altered recommen- dation. 31 Table 1.1: Summary Statistics (A)NumberofVotes(Proposals)byYear This table reports the number of votes and the number of proposals from 2006-2017. For each year and each proposal type, the number of votes is displayed at the top, and the number of proposals is displayed at the bottom in parentheses. Votes are aggregated at the fund-family level. After 2011, say-on-pay proposals become mandatory as part of the Dodd-Frank Act, and they have to be brought up by the management every one to three years. Before that, shareholders can sponsor them as governance measures. Because they are dierent in nature, I treat say-on-pay proposals as dierent proposal types if happened before and after 2011. Director Elections Say-on-Pay (before 2011) Say-on-Pay (after 2011) Compensation: Other Financial Policy Golden Parachutes Adopt Poison Pill Board Declass. Proxy Access Independent Chairman Political Contributions Animal Rights Environ- mental Social Proposal 2006 398,944 (15,682) 151 (4) 0 (0) 25,490 (1,009) 9,996 (408) 0 (0) 95 (4) 3,786 (107) 0 (0) 2,044 (49) 1,917 (35) 0 (0) 684 (14) 2,549 (44) 2007 457,725 (15,733) 2,791 (48) 0 (0) 27,553 (949) 11,833 (473) 0 (0) 106 (4) 3,483 (87) 0 (0) 2,205 (39) 1,862 (33) 0 (0) 1,591 (27) 3,576 (55) 2008 520,593 (16,399) 4,738 (82) 0 (0) 32,282 (1,031) 10,916 (353) 0 (0) 185 (8) 4,896 (145) 0 (0) 1,659 (28) 1,784 (31) 514 (10) 1,537 (25) 74 (1) 2009 642,132 (17,877) 10,699 (307) 0 (0) 41,754 (1,132) 11,809 (381) 0 (0) 615 (19) 4,638 (115) 0 (0) 2,173 (37) 2,168 (32) 858 (14) 1,309 (23) 0 (0) 2010 700,604 (17,696) 10,276 (213) 0 (0) 41,726 (1,057) 10,864 (347) 0 (0) 485 (16) 4,774 (110) 0 (0) 2,831 (42) 2,590 (36) 946 (15) 2,585 (39) 0 (0) 2011 731,016 (20,328) 0 (0) 109,840 (3,137) 41,207 (1,152) 12,060 (392) 1,241 (39) 237 (9) 4,926 (97) 0 (0) 1,966 (29) 4,101 (53) 718 (9) 2,021 (30) 0 (0) 2012 796,741 (21,865) 0 (0) 104,227 (2,569) 40,176 (1,130) 11,609 (419) 2,450 (98) 338 (14) 7,542 (130) 672 (12) 3,963 (56) 6,063 (72) 923 (13) 1,199 (16) 0 (0) 2013 780,276 (23,971) 0 (0) 99,851 (3,026) 44,046 (1,252) 11,726 (481) 3,679 (147) 323 (16) 6,825 (133) 1,091 (17) 4,137 (63) 5,438 (76) 288 (6) 1,795 (23) 33 (1) 2014 933,399 (25,341) 0 (0) 126,707 (3,219) 44,801 (1,230) 13,265 (456) 3,666 (122) 174 (6) 4,854 (102) 2,024 (23) 4,599 (64) 6,798 (84) 424 (6) 3,163 (41) 87 (1) 2015 1,204,561 (25,717) 0 (0) 142,254 (2,755) 58,370 (1,258) 17,398 (499) 6,413 (153) 236 (11) 3,302 (70) 9,224 (105) 6,650 (65) 6,967 (65) 696 (10) 5,038 (50) 144 (1) 2016 1,159,292 (25,126) 0 (0) 134,638 (2,788) 56,627 (1,270) 18,587 (571) 7,428 (174) 159 (5) 3,107 (63) 8,577 (112) 4,605 (49) 7,081 (67) 119 (2) 4,766 (50) 538 (5) 2017 1,052,208 (20,487) 0 (0) 132,384 (2,547) 50,348 (1,065) 11,205 (333) 3,095 (77) 0 (0) 2,580 (51) 3,770 (44) 3,984 (43) 5,792 (58) 184 (3) 4,876 (51) 563 (4) 32 Table 1.1: Summary Statistics (Continued) (B)ProposalCharacteristics This table reports summary statistics for dierent proposal types. It covers 7489 rms across 2006-2017. Except for “# of items”, all numbers shown in the table represent the mean. “# of items” denotes the number of occurrences. “Mgmt Sponsor” is a dummy that equals one if the management sponsors the proposal. “Mgmt For”/“ISS For”/“GL For” equals 1 if management/ISS/GL recommends for the proposal. “% For (ISS)”/“% For (GL)” denotes the fraction of ISS/GL’s customers that vote “For” the proposal. “Prop Passed” is a dummy that equals one if the proposal is passed. # of Items Mgmt Sponsor Mgmt For ISS For GL For % For (ISS) % For (GL) % For (others) Prop Passed RoutineProposals Director Elections 247,528 100% 100% 89% 90% 90% 91% 91% 100% Say-on-Pay (before 2011) 637 59% 59% 87% 90% 76% 52% 71% 65% Say-on-Pay (after 2011) 19,893 100% 100% 88% 83% 89% 87% 88% 98% Compensation: Other 14,380 100% 100% 78% 84% 77% 78% 79% 99% Financial Policy 5,029 100% 100% 92% 85% 92% 91% 87% 98% GovernanceProposals Golden Parachutes 777 100% 100% 74% 83% 78% 80% 69% 93% Adopt Poison Pill 111 100% 97% 67% 8% 60% 40% 56% 81% Board Declassication 1,281 62% 62% 100% 100% 96% 97% 91% 83% Proxy Access 305 17% 19% 90% 79% 77% 64% 63% 54% Independent Chairman 595 0% 0% 65% 93% 43% 45% 42% 5% SocialProposals Political Contributions 688 0% 0% 73% 49% 40% 28% 28% 1% Animal Rights 85 0% 0% 7% 4% 8% 6% 4% 1% Environmental 398 0% 0% 64% 22% 36% 20% 20% 1% Other Social Proposal 172 0% 3% 15% 10% 10% 7% 7% 3% 33 Table 1.1: Summary Statistics (Continued) (C)MutualFunds This table displays the summary statistics at the fund-family level. A fund family is dened as a unique fund management in the CRSP Mutual Fund Dataset (variable mgmt_cd). One observation is a family-year. A fund is an “ESG” fund if its name contains any of the following words: esg, social, climate, environment, impact, responsible, carbon, and fossil. A fund is an “institutional” fund if it’s agged by CRSP as an institutional fund. A fund is an “index” fund if either it’s agged by CRSP as an index fund or its name contains any of the following words: index, idx, indx, inds, russell, s & p, s and p, s&p, sandp, sp, dow, dj, msci, bloomberg, kbw, nasdaq, nyse, stoxx, ftse, wilshire, morningstar, 100, 400, 500, 600, 900, 1000, 1500, 2000, 5000 [46]. Management fee and expense ratio for the family are the TNA-weighted averages among all funds in the family. Fund families’ uses of voting platforms are inferred from their N-PX lings. “% agree with ISS/GL/Mgmt” denotes the fraction of proposals that the fund votes in the same direction ISS/GL/Mgmt’s recommendations. I dene a fund-family as an ISS (GL) robo-voter if it agrees in a year with ISS (GL) on more than 99.9 percent of proposals where ISS (GL) disagrees with management. I dene a fund-family as a management robo-voter if it agrees in a year with Mgmt on more than 99.9 percent of proposals when either ISS or GL disagrees with the Mgmt. Obs Mean Std 5% 25% Median 75% 95% Characteristics Age of the Mgmt 2,491 29.20 22.76 3.00 14.00 23.00 35.00 80.00 Total Net Asset (in $10^6) 2,491 60.41 243.81 0.03 0.56 4.42 26.83 236.43 Number of Votes (in 1000) 2,491 5.40 6.85 0.06 0.69 2.37 7.43 22.22 Provide ESG Fund 2,491 0.07 0.26 0.00 0.00 0.00 0.00 1.00 Provide Institutional Fund 2,491 0.76 0.43 0.00 1.00 1.00 1.00 1.00 Provide Index Fund 2,491 0.31 0.46 0.00 0.00 0.00 1.00 1.00 Management Fee 2,474 0.64 0.43 0.13 0.44 0.63 0.86 1.16 Expense Ratio 2,474 0.01 0.00 0.00 0.01 0.01 0.01 0.02 VotingPlatform Use ISS ProxyExchange 2,491 0.51 0.50 0.00 0.00 1.00 1.00 1.00 Use GL Viewpoint 2,491 0.07 0.26 0.00 0.00 0.00 0.00 1.00 Use Broadridge ProxyEdge 2,491 0.24 0.43 0.00 0.00 0.00 0.00 1.00 Use Others 2,491 0.18 0.39 0.00 0.00 0.00 0.00 1.00 Votes % agree with ISS 2,491 0.91 0.12 0.72 0.89 0.93 0.97 1.00 % agree with GL 2,156 0.87 0.10 0.71 0.85 0.89 0.92 0.98 % agree with Mgmt 2,491 0.90 0.12 0.72 0.89 0.92 0.96 1.00 Robo - Vote with ISS 2,491 0.10 0.30 0.00 0.00 0.00 0.00 1.00 Robo - Vote with GL 2,491 0.01 0.09 0.00 0.00 0.00 0.00 0.00 Robo - Vote with Mgmt 2,491 0.06 0.24 0.00 0.00 0.00 0.00 1.00 34 Table 1.2: Descriptive Statistics – Snapshot 2008, 2012, and 2017 This table provides the descriptive statistics for fund-families that use ISS ProxyExchange, Glass Lewis Viewpoint, and Broadridge ProxyEdge as their proxy voting systems for the years 2008, 2012, and 2017. The denitions for characteristics variables and voting variables are the same as those of table 1.1.C. The two-dimensional ideology scores in 2012 are provided by [11]. Both in the range of (-1,1), the two scores are interpreted as investors’ toughness on social issues and toughness on governance issues. The scores’ polarity is arbitrary, and I keep the original authors’ convention: socially oriented investors have a lower score in the rst dimension, and tough-on-governance investors have a larger score in the second dimension. 2008 2012 2017 ISS GL BR ISS GL BR ISS GL BR Characteristics Family Age 32.2 (2.4) 72.3 (7.4) 25.9 (3.3) 33.6 (2.4) 30.9 (5.6) 23.9 (2.5) 33.8 (2.1) 35.8 (4.9) 23.9 (2.3) Asset ($10^6) 47.4 (12.8) 279 (245) 8.3 (2.2) 75.2 (19.7) 86.2 (52.4) 10.7 (3.1) 82.6 (21.7) 134.1 (69) 17.5 (8.7) # votes (1000) 5.68 (0.6) 6.18 (1.9) 2.11 (0.4) 7.42 (0.8) 9.45 (1.8) 3.44 (0.7) 8.34 (0.7) 8.18 (1.6) 3.39 (0.6) Index Fund 0.40 (0.0) 0.00 (0.0) 0.18 (0.1) 0.41 (0.1) 0.50 (0.1) 0.21 (0.1) 0.42 (0.0) 0.35 (0.1) 0.25 (0.1) Institutional 0.79 (0.0) 1.00 (0.0) 0.59 (0.1) 0.82 (0.0) 1.00 (0.0) 0.68 (0.1) 0.87 (0.0) 0.96 (0.0) 0.72 (0.1) ESG Fund 0.07 (0.0) 0.33 (0.3) 0.00 (0.0) 0.06 (0.0) 0.17 (0.1) 0.00 (0.0) 0.17 (0.0) 0.27 (0.1) 0.07 (0.0) Expense Ratio 0.01 (0.0) 0.01 (0.0) 0.01 (0.0) 0.01 (0.0) 0.01 (0.0) 0.01 (0.0) 0.01 (0.0) 0.01 (0.0) 0.01 (0.0) Mgmt Fee 0.54 (0.0) 0.46 (0.1) 0.77 (0.1) 0.59 (0.0) 0.52 (0.1) 0.75 (0.0) 0.56 (0.0) 0.59 (0.0) 0.73 (0.0) Voting Agree with ISS 0.93 (0.0) 0.87 (0.0) 0.85 (0.0) 0.94 (0.0) 0.87 (0.0) 0.87 (0.0) 0.95 (0.0) 0.90 (0.0) 0.82 (0.0) (contentious) 0.66 (0.0) 0.37 (0.1) 0.36 (0.1) 0.70 (0.0) 0.45 (0.0) 0.40 (0.0) 0.71 (0.0) 0.33 (0.0) 0.34 (0.0) Agree with GL 0.84 (0.0) 0.88 (0.1) 0.79 (0.0) 0.86 (0.0) 0.91 (0.0) 0.85 (0.0) 0.90 (0.0) 0.95 (0.0) 0.85 (0.0) (contentious) 0.29 (0.0) 0.44 (0.2) 0.26 (0.0) 0.29 (0.0) 0.60 (0.1) 0.29 (0.0) 0.39 (0.0) 0.60 (0.1) 0.32 (0.0) Agree with Mgmt 0.90 (0.0) 0.90 (0.0) 0.87 (0.0) 0.91 (0.0) 0.88 (0.0) 0.88 (0.0) 0.91 (0.0) 0.93 (0.0) 0.86 (0.0) (contentious) 0.55 (0.0) 0.63 (0.2) 0.71 (0.0) 0.57 (0.0) 0.51 (0.1) 0.69 (0.0) 0.44 (0.0) 0.63 (0.0) 0.69 (0.0) Robo - Vote with ISS 0.05 (0.0) 0.00 (0.0) 0.00 (0.0) 0.12 (0.0) 0.00 (0.0) 0.04 (0.0) 0.24 (0.0) 0.00 (0.0) 0.04 (0.0) Robo - Vote with GL 0.00 (0.0) 0.00 (0.0) 0.03 (0.0) 0.01 (0.0) 0.00 (0.0) 0.00 (0.0) 0.00 (0.0) 0.04 (0.0) 0.01 (0.0) Robo - Vote with Mgmt 0.00 (0.0) 0.00 (0.0) 0.06 (0.0) 0.01 (0.0) 0.00 (0.0) 0.06 (0.0) 0.00 (0.0) 0.00 (0.0) 0.09 (0.0) Ideology (1st) Social . . . -0.11 (0.0) 0.01 (0.1) 0.12 (0.1) . . . (2nd) Governance . . . -0.40 (0.0) 0.57 (0.1) 0.01 (0.1) . . . N 98 3 34 96 18 53 132 26 75 35 Table 1.3: Descriptive Statistics - Regression This table displays OLS regressions of fund-families’ characteristics as functions of their uses of dierent proxy voting systems. Panel A’s regressions include all mutual fund families. Independent variables are dummies that denote whether the fund is an ISS/GL/Broadridge customer. Dependent variables are fund families’ characteristics, which are dened in the table 1.1.C. The baseline group is fund families that use none of ISS/GL/Broadridge’s voting system. Panel B’s regressions include fund families that use either ISS or Glass Lewis’s voting system only. The baseline group is fund families that use GL’s voting system. Standard errors in both tables are clustered at the fund-family level. *,**, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. (A)Baseline: FundfamiliesthatuseneitherISS/GL/Broadridge log asset log votes Age Provide Index Provide Inst. Provide ESG Expense Ratio Mgmt. Fee (1) (2) (3) (4) (5) (6) (7) (8) ISS Customer 2.69 1.86 11.47 0.20 0.19 0.05 -0.00 -0.10 (0.39) (0.24) (3.29) (0.06) (0.05) (0.04) (0.00) (0.05) Glass Lewis Customer 2.95 2.26 13.89 0.16 0.29 0.13 -0.00 -0.13 (0.58) (0.27) (5.76) (0.09) (0.05) (0.08) (0.00) (0.07) Broadridge Customer 0.89 0.81 2.80 -0.00 0.03 -0.02 -0.00 0.07 (0.42) (0.26) (3.46) (0.05) (0.06) (0.03) (0.00) (0.07) Year Eect Yes Yes Yes Yes Yes Yes Yes Yes AdjustedR 2 0.18 0.19 0.05 0.05 0.05 0.02 0.05 0.02 Observations 2,482 2,482 2,482 2,482 2,482 2,482 2,465 2,465 # of cluster 476 476 476 476 476 476 474 474 (B)Baseline: FundfamiliesthatuseGlassLewis log asset log votes Age Provide Index Provide Inst. Provide ESG Expense Ratio Mgmt. Fee (1) (2) (3) (4) (5) (6) (7) (8) ISS Customer -0.19 -0.35 -2.01 0.04 -0.10 -0.07 0.00 0.04 (0.53) (0.21) (5.65) (0.09) (0.04) (0.07) (0.00) (0.05) Year Eect Yes Yes Yes Yes Yes Yes Yes Yes AdjustedR 2 -0.00 0.01 -0.01 -0.01 0.02 0.01 -0.00 -0.00 Observations 1,437 1,437 1,437 1,437 1,437 1,437 1,429 1,429 # of cluster 235 235 235 235 235 235 234 234 36 Table 1.4: Robo Voters and Characteristics Panel A provides examples of robo-voters. I dene a fund-family as an ISS (GL) robo-voter if it agrees in a year with ISS (GL) on more than 99.9 percent of proposals where ISS (GL) disagrees with management. I dene a fund-family as a management robo-voter if it agrees in a year with Mgmt on more than 99.9 percent of proposals when either ISS or GL disagrees with the Mgmt. Panel B illustrates the characteristics of robo-voters. It shows the OLS regression of being a robo-voter as a function of the fund family’s characteristics. Each observation represents a fund-year. Column 1 includes only ISS customers. Column 2 includes only GL customers. Column 3 includes fund families that use neither ISS nor GL. All regressions include the year xed eect. Standard errors are clustered at the fund-family level. *,**, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. (A)ExamplesofRoboVoters(in2017) Fund-Family Name Robo-vote with Total # of votes Total # of votes when PA & Mgmt do not agree % of votes sided with ISS/GL/Mgmt Guggenheim Investments ISS 30,230 3,579 100% ProFunds Group ISS 26,446 2,853 100% Rydex Investments ISS 21,661 2,402 100% Forward Management GL 1,016 42 100% Miller/Howard Investments GL 864 56 100% Nashville Capital Mgmt 2,548 255 100% Leuthold Weeden Capital Mgmt 1,992 152 100% (B)DeterminantsofRobo-Voting (1) (2) (3) Robo Voting with ISS Robo Voting with GL Robo Voting with Mgmt. log(# votes) -0.02 -0.05 -0.01 (0.01) (0.04) (0.01) log(asset) -0.05 -0.00 -0.02 (0.01) (0.01) (0.01) Provide Index Fund 0.08 -0.01 0.01 (0.04) (0.03) (0.03) Provide Inst. Fund 0.02 -0.00 -0.03 (0.06) (0.13) (0.04) Provide ESG Fund 0.02 -0.01 -0.01 (0.05) (0.02) (0.04) Age -0.00 -0.00 0.00 (0.00) (0.00) (0.00) Mgmt. Fee 0.12 -0.03 0.03 (0.08) (0.08) (0.04) AdjustedR 2 0.17 0.10 0.04 Observations 1,243 168 959 # of cluster 219 42 274 37 Table 1.5: Eects of Recommendations on Funds’ Votes This table displays the eects of proxy advisors’ recommendations and the management’s recommendations on votes of mutual funds that subscribe to dierent proxy advisors. Each observation is a fund-vote. For all columns, dependent variables are dummy variables that equal one if the fund voted “For” the proposal.“ISS For”/“GL For”/“Mgmt For” are dummy variables that equal 1 if ISS/GL/management recommends voting “For” the proposal. Standard errors are clustered at the fund-family level. *, **, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. Regressions are of the form Vote Forip = ISS Forp 1 +2 ISS Customerit +3 GL Customerit + GL Forp 4 +5 ISS Customerit +6 GL Customerit + Mgmt For p 7 +8 ISS Customerit +9 GL Customerit +"ip Dependent variable: Vote For (1) (2) (3) (4) (5) ISS For 0.47 0.32 0.31 (0.03) (0.04) (0.04) ISS For ISS Customer 0.27 0.27 0.27 0.27 (0.05) (0.05) (0.05) (0.05) ISS_for GL Customer -0.21 -0.21 -0.21 -0.21 (0.05) (0.05) (0.05) (0.05) GL For 0.14 0.17 0.15 (0.02) (0.03) (0.03) GL For ISS Customer -0.10 -0.10 -0.10 -0.10 (0.03) (0.03) (0.03) (0.03) GL For GL Customer 0.31 0.32 0.31 0.31 (0.08) (0.08) (0.08) (0.08) Mgmt For 0.33 0.43 0.29 (0.02) (0.04) (0.04) Mgmt For ISS Customer -0.15 -0.15 -0.15 -0.15 (0.05) (0.05) (0.05) (0.05) Mgmt For GL Customer -0.08 -0.09 -0.08 -0.07 (0.07) (0.07) (0.07) (0.07) Company Year Eect Yes Yes Proposal Type Eect Yes Proposal Eect Yes Yes Fund Year Eect Yes AdjustedR 2 0.38 0.42 0.35 0.43 0.49 Observations 8,035,567 8,035,566 6,826,083 8,035,460 8,035,459 # of cluster 463 463 463 463 463 38 Table 1.6: Proxy Advisors’ Inuences on Informed & Uninformed Funds This table displays proxy advisor recommendations’ dierential eects for proposals on which fund families are informed and uninformed. Each observation is a fund-vote. For all columns, dependent variables are dummy variables that equal one if the fund voted “For” the proposal.“ISS For”/“GL For”/“Mgmt For” are dummy variables that equal 1 if ISS/GL/management recommends voting “For” the proposal. “Visited EDGAR” equals 1 if the fund has visited the proposal’s proxy statement before its annual meeting. Column 1 and 2 separates the sample by whether “Visited EDGAR” equals 1. Columns 3 and 4 include the full sample. Standard errors are clustered at the fund-family level. *, **, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. Dependent variable: Vote For Visited EDGAR = 0 Visited EDGAR = 1 Full Sample (1) (2) (3) (4) ISS For ISS Customer 0.27 0.22 0.19 0.19 (0.05) (0.06) (0.07) (0.08) ISS_for GL Customer -0.21 -0.13 -0.22 -0.22 (0.05) (0.06) (0.07) (0.07) GL For ISS Customer -0.11 0.01 -0.08 -0.08 (0.03) (0.02) (0.04) (0.04) GL For GL Customer 0.32 0.09 0.21 0.21 (0.08) (0.05) (0.10) (0.11) Mgmt For ISS Customer -0.14 -0.29 -0.11 -0.10 (0.05) (0.09) (0.07) (0.07) Mgmt For GL Customer -0.06 -0.12 0.00 -0.01 (0.07) (0.12) (0.10) (0.10) ISS For ISS Customer Visited EDGAR -0.02 -0.02 (0.01) (0.01) GL For GL Customer Visited EDGAR -0.03 -0.05 (0.01) (0.02) Visited EDGAR 0.01 0.01 (0.01) (0.01) Proposal Eect Yes Yes Yes Yes Fund Year Eect Yes Yes Yes AdjustedR 2 0.49 0.56 0.46 0.49 Observations 7,734,768 283,627 3,940,294 3,940,294 # of cluster 463 144 151 151 39 Table 1.7: Certication and Sway This table reports OLS regressions for whether a fund votes in the same direction as a proxy advisor’s recommendation as a function of whether the fund is a customer of this proxy advisor. Columns 1-4 estimate the eect of being an ISS customer on a fund’s votes, and columns 5-9 estimate the eect of being a GL customer on a fund’s votes: Agree with ISS ip =0 +1 ISS Customerit + 0 Z +"p +"ipt Agree with GL ip =0 +1 GL Customerit + 0 Z +"p +"ipt Columns 1-2 (5-6) include all proposals on which ISS (GL) supports the management’s recommendation, and columns 3-4 (7-8) include all proposals on which ISS (GL) opposes the management’s recommendation. Each observation is a fund-vote. The independent variable of interest is ISS Customer (GL Customer), which is a dummy that equals one if the fund family is an ISS customer (GL customer) in the current year. All columns include proposal xed eect and controls for fund-family characteristics as in Table 1.1.(C). Standard errors are clustered at the fund-family level. *, **, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. Dependent Variable: “Agree with ISS” Dependent Variable: “Agree with GL” ISS with mgmt (certication eect) ISS against mgmt (sway eect) GL with mgmt (certication eect) GL against mgmt sway eect (1) (2) (3) (4) (5) (6) (7) (8) ISS Customer 0.02 0.01 0.21 0.18 -0.00 0.00 (0.01) (0.01) (0.04) (0.05) (0.01) (0.03) GL Customer -0.01 -0.10 0.02 0.02 0.22 0.22 (0.01) (0.05) (0.01) (0.01) (0.07) (0.07) Controls Yes Yes Yes Yes Yes Yes Yes Yes Proposal Eect Yes Yes Yes Yes Yes Yes Yes Yes Observations 13,539,188 13,539,188 1,408,934 1,408,934 7,209,993 7,209,993 808,038 808,038 AdjustedR 2 0.07 0.07 0.13 0.13 0.23 0.23 0.35 0.35 # of cluster 498 498 488 488 459 459 455 455 40 Table 1.8: Proxy Advisors’ Sway Eects By Proposal Types This table shows ISS’s (Panel A) and Glass Lewis’s (Panel B) sway eects on their respective customers for proposals of dierent types. Each column includes funds’ votes on proposals of only a particular type. The regressions for Panel A are of the form Agree with ISS ip =0 +1 ISS Customerit + 0 Z +"p +"ipt on proposals where ISS and management disagree. Panel B is constructed analogously for Glass Lewis. Each observation is one fund-vote. All columns include proposal xed eect and controls for fund-family characteristics as in Table 1.1.(C). Standard Errors are clustered at the fund-family level. *, **, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. (A)ISS’sSwayEect Dependent Variable: “Agree with ISS” Routine Proposals Governance Proposals Social Proposals board election say on pay nancial policy golden parachute poison pill board declass. ind. chair proxy access political disclos. environ- mental animal rights (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) ISS Customer 0.21 0.20 0.16 0.21 0.03 0.08 0.15 0.22 0.26 0.27 0.24 (0.05) (0.05) (0.05) (0.07) (0.06) (0.03) (0.05) (0.04) (0.05) (0.05) (0.07) Proposal Eect Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes AdjustedR 2 0.09 0.13 0.13 0.12 0.13 0.08 0.07 0.19 0.12 0.15 0.12 Observations 749,135 108,804 8,056 10,602 1,061 20,368 28,605 20,626 46,491 19,957 483 # of cluster 472 442 345 351 157 362 435 403 436 426 164 (B)GlassLewis’sSwayEect Dependent Variable: “Agree with GL” Routine Proposals Governance Proposals Social Proposals board election say on pay nancial policy golden parachute poison pill board declass. ind. chair proxy access political disclos. environ- mental animal rights (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) GL Customer 0.29 0.26 0.33 -0.01 0.24 0.00 0.11 -0.11 0.01 0.09 0.20 (0.08) (0.07) (0.09) (0.15) (0.06) (0.04) (0.07) (0.07) (0.08) (0.05) (0.13) Proposal Eect Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes AdjustedR 2 0.30 0.29 0.26 0.02 0.30 0.06 0.18 0.09 0.07 0.33 0.07 Observations 451,694 81,190 5,210 84 968 11,932 33,831 14,338 22,879 6,697 124 # of cluster 450 425 291 84 172 321 419 395 416 387 94 41 Table 1.9: Proxy Advisors’ Inuences On Dierent Funds This table reports OLS regressions for whether a fund votes in the same direction as its proxy advisor’s recommendation as a function of the fund’s characteristics. Regressions in columns 1-4 contain uncontentious proposals, and regressions in columns 5-8 contain contentious proposals. Each observation is one fund-vote. The dependent variable of columns 1, 3, 5, and 7 is a dummy that denotes whether the vote is in the same direction as ISS’s recommendation. Those columns include only the votes from ISS’s customers. Columns 2, 4, 6, and 8 are constructed analogously for Glass Lewis’s customers. All regressions include the proposal xed eect. Standard errors are clustered at the fund-family level. *,**, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. Certication Eect Sway Eect Director Elections Other Proposals Director Elections Other Proposals (1) (2) (3) (4) (5) (6) (7) (8) Agree ISS Agree GL Agree ISS Agree GL Agree ISS Agree GL Agree ISS Agree GL log(asset) 0.01 -0.00 0.00 -0.00 -0.01 -0.05 -0.02 -0.04 (0.00) (0.00) (0.00) (0.00) (0.01) (0.02) (0.01) (0.01) log(# votes) 0.02 0.03 0.01 0.04 -0.02 -0.06 -0.03 -0.07 (0.01) (0.02) (0.00) (0.02) (0.04) (0.07) (0.03) (0.06) Provide Index Fund -0.03 -0.03 -0.01 -0.03 -0.02 0.37 0.03 0.21 (0.02) (0.03) (0.01) (0.02) (0.07) (0.12) (0.05) (0.10) Provide ESG Fund -0.04 -0.03 -0.02 -0.03 -0.04 -0.30 -0.00 -0.14 (0.02) (0.03) (0.01) (0.02) (0.10) (0.18) (0.06) (0.13) AdjustedR 2 0.05 0.08 0.08 0.10 0.03 0.20 0.10 0.18 Observations 6,443,333 638,489 2,473,812 234,178 506,114 48,326 431,722 41,581 # of cluster 231 48 231 48 230 48 231 48 42 Table 1.10: Subsequent Voting For Funds that Switch Proxy Advisors This table reports OLS regressions for the change in a fund’s vote agreement with ISS’s recommendations and vote agreement with Glass Lewis’s recommendations as a function of whether it switches from being an ISS customer to being a GL customer (or vice versa). Each observation is one fund-year. The dependent variable agreeISSt+1 equals agreeISSt+1 - agreeISSt, where agreeISSt is the percentage of the fund’s votes in yeart that agree with ISS’s recommendation for uncontentious proposals (Panel A) or contentious proposals (Panel B). The independent variable “GL! ISS” is a dummy variable that equals one if the fund is a GL customer in yeart and becomes an ISS customer in yeart + 1. Columns 1 and 2’s samples include only the funds that are Glass Lewis’s customers in yeart. “ISS! GL” is dened analogously. Columns 3 and 4’s samples include only the funds that are ISS’s customers in yeart. Standard errors are clustered at the fund-family level. *,**, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. (A)CerticationEect(UncontentiousProposals) All GL Customers All ISS Customers (1) (2) (3) (4) agreeISSt+1 agreeGLt+1 agreeISSt+1 agreeGLt+1 GL! ISS 0.01 -0.03 (0.01) (0.01) ISS! GL -0.04 0.04 (0.01) (0.01) AdjustedR 2 0.01 0.03 0.01 0.08 Observations 131 128 993 827 # of cluster 35 35 177 162 (B)SwayEect(ContentiousProposals) All GL Customers All ISS Customers (1) (2) (3) (4) agreeISSt+1 agreeGLt+1 agreeISSt+1 agreeGLt+1 GL! ISS 0.24 -0.21 (0.09) (0.09) ISS! GL -0.23 0.38 (0.07) (0.09) AdjustedR 2 0.14 0.07 0.03 0.23 Observations 131 128 980 820 # of cluster 35 35 177 162 43 Table 1.11: Proxy Advisors’ Inuences (Propensity Score Matching) This table repeats the results in table 1.5 and table 1.7 after the propensity score matching (PSM) method. The PSM method used is a one-to-one match without replacement and with a tolerance of 0.001 for the score. I match an ISS’s customer (or GL’s customer) with a non-ISS-customer (or non-GL-customer) within the same year. The propensity score is estimated by the logit regression on funds’ characteristics that appear in table 1.1.C. Both panel’s standard errors are clustered at the fund-family level. *,**, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. (A)EectsofPA’sRecommendationsonFunds’Votes PSM for ISS Customer PSM for GL Customer (1) (2) (3) (4) Vote For Vote For Vote For Vote For ISS For ISS Customer 0.38 0.38 (0.06) (0.05) GL For ISS Customer -0.22 -0.23 (0.05) (0.05) Mgmt For ISS Customer -0.14 -0.14 (0.05) (0.05) ISS For GL Customer -0.38 -0.39 (0.04) (0.05) GL For GL Customer 0.41 0.40 (0.08) (0.08) Mgmt For GL Customer -0.02 -0.02 (0.07) (0.07) Proposal Eect Yes Yes Yes Yes Fund Family Eect Yes Yes AdjustedR 2 0.42 0.48 0.46 0.49 Observations 1,657,423 1,657,423 1,017,935 1,017,935 # of cluster 250 250 122 122 (B)FundVotes’AgreementwithProxyAdvisors’Recommendations PSM for ISS Customer PSM for GL Customer ISS with mgmt (certication eect) ISS against mgmt (sway eect) GL with mgmt (certication eect) GL against mgmt sway eect (1) (2) (3) (4) Agree with ISS Agree with ISS Agree with GL Agree with GL ISS Customer 0.03 0.25 (0.01) (0.04) GL Customer 0.03 0.24 (0.01) (0.06) Controls Yes Yes Yes Yes Proposal Eect Yes Yes Yes Yes AdjustedR 2 0.10 0.16 0.16 0.27 Observations 2,655,654 261,649 920,888 97,047 # of cluster 257 256 122 122 44 Table 1.12: Change of Recommendations By Proxy Advisors Panel A shows the total number of proposals, the number of proposals that reappear in the same rm, and the fraction of the reappeared proposals that ISS or Glass Lewis changes its recommendations. I dene a proposal on which ISS (or GL) changes its recommendations if ISS (or GL) supports/opposes the proposal in yeart and opposes/supports the same company’s same proposal (using director name for elections and using agenda general description for non-election proposals) in yeart 1. Panel B displays OLS regressions of whether ISS (or GL) changes its recommendation as a function of investors’ past disagreement with ISS (or GL). For investors’ past disagreement with ISS or Glass Lewis, I group investors by ISS customers, GL customers, and others. Each observation represents a proposal. Standard errors are clustered at the company level. *,**, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. (A)TypesofProposalsthatISSorGLChangesRecommendations Total Number of Proposals # that Re-appear % that ISS Changes Rec. % that GL Changes Rec. Director Elections 263,591 183,391 9% 9% Say-on-Pay (before 2011) 630 270 14% 13% Say-on-Pay (after 2011) 22,550 18,218 15% 15% Compensation: Other 14,777 6,568 17% 21% Financial Policy 5,931 1,450 9% 11% Golden Parachutes 945 20 40% 0% Adopt Poison Pill 122 29 14% 20% Board Declassication 1,366 458 0% 0% Proxy Access 337 56 23% 12% Independent Chairman 657 387 27% 8% Political Contributions 725 437 12% 15% Animal Rights 91 29 14% 6% Environmental 399 158 13% 13% Social Proposal 122 36 14% 50% Others 64,242 42,359 2% 3% (B)ChangeofRecommendationsandInvestors’PastDisagreement Dependent Variable: ISS Changes Rec. Dependent Variable: GL Changes Rec. (1) (2) (3) (4) (5) (6) Past Disagreement with 0.45 0.44 0.53 ISS by ISS customers (0.02) (0.02) (0.03) Past Disagreement with 0.08 0.08 0.07 ISS by GL customers (0.01) (0.01) (0.01) Past Disagreement with 0.26 0.26 0.23 ISS by other investors (0.01) (0.01) (0.01) Past Disagreement with 0.12 0.14 0.10 GL by ISS customers (0.02) (0.02) (0.03) Past Disagreement with 0.07 0.07 0.05 GL by GL customers (0.02) (0.02) (0.02) Past Disagreement with 0.31 0.28 0.31 GL by Other Investors (0.03) (0.03) (0.03) Year Eect Yes Yes Yes Yes Yes Yes Firm Eect Yes Yes FirmProposal Eect Yes Yes AdjustedR 2 0.17 0.24 0.34 0.17 0.21 0.30 Observations 180,367 180,116 163,337 64,971 64,824 57,166 # of cluster 4936 4685 4236 1992 1845 1477 45 Table 1.13: Change of Recommendation – Types of Funds This table reports OLS regressions of whether ISS (or GL) changes its recommendation as a function of the past disagreement with ISS (or GL) from investors with dierent characteristics. Panel A separates investors according to the size of their total net assets (TNA) or their activism score. The activism score is dened as the percentage of votes that the fund disagrees with managements’ recommendations. I denote a fund family as a large (small) fund family if its TNA is above (below) the median among all fund families in the same year, and I denote a fund family as an active (non-active) fund family if its activism score is above (below) the median. The dependent variable for columns 1-2 (3-4) is a dummy that equals one if ISS (or GL) supports/opposes the current proposal (or director) but opposed/supported the same proposal (or director) of the same rm when it appeared last time. Each observation represents a proposal. Panel B separates investors by double sorting their TNA and activism score. Standard errors are clustered at the company level. *,**, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. (A)SortbySizeorActivism Dependent Variable: ISS Changes Rec. Dependent Variable: GL Changes Rec. (1) (2) (3) (4) Past Disagreement 0.73 0.33 by Large Funds (0.02) (0.03) Past Disagreement 0.05 0.11 by Small Funds (0.01) (0.03) Past Disagreement 0.11 -0.03 by Active Funds (0.01) (0.03) Past Disagreement 0.51 0.47 by Non-Active Funds (0.01) (0.03) Year Eect Yes Yes Yes Yes FirmProposal Eect Yes Yes Yes Yes AdjustedR 2 0.33 0.33 0.30 0.31 Observations 198,820 211,353 60,123 60,155 # of cluster 4,583 4,928 1,588 1,590 (B)DoubleSortbySizeandActivism Dependent Variable: ISS Changes Rec. Dependent Variable: GL Changes Rec. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Past Disagreement 0.50 0.14 0.35 -0.04 by Large Active (0.02) (0.02) (0.01) (0.03) Past Disagreement 0.53 0.52 0.44 0.36 by Large Non-Active (0.01) (0.02) (0.02) (0.03) Past Disagreement 0.11 -0.01 0.34 0.02 by Small Active (0.01) (0.01) (0.01) (0.02) Past Disagreement 0.35 0.09 0.38 0.12 by Small Non-Active (0.01) (0.01) (0.01) (0.02) Year Eect Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes FirmProposal Eect Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes AdjustedR 2 0.28 0.32 0.25 0.29 0.35 0.28 0.31 0.27 0.29 0.31 Observations 210,999 213,776 185,191 193,114 164,417 60,208 60,179 59,487 59,535 58,904 # of cluster 4,983 5,094 4,270 4,357 3,737 1,591 1,590 1,547 1,573 1,528 46 Table 1.14: Why Do Proxy Advisors Cater? Panel A reports OLS regressions of whether a fund switches its proxy advisor as a function of its past agreement with ISS and Glass Lewis. Each observation represents a fund-year. The dependent variable “GL! ISS” is a dummy that equals one if the fund subscribes to Glass Lewis in yeart but changes to ISS in yeart + 1. “Other! ISS”, “Other! GL”, and “ISS! GL” are dened analogously. The independent variable agreeISSi;t (agreeGLi;t) is the percentage of the fund’s votes in yeart that agree with ISS’s (Glass Lewis’s) recommendations. Panel B denes agreeISSi;t (agreeGLi;t) separately for dierent proposal types. Standard errors are clustered at the fund-family level. *,**, and *** denote statistical signicance at the 10%, 5%, and 1% levels, respectively. (A)AgreementonAllProposals One-year Agreement Three-year Agreement (1) (2) (3) (4) (5) (6) (7) (8) Other # ISS GL # ISS Other # GL ISS # GL Other # ISS GL # ISS Other # GL ISS # GL agreeISSi;t 0.21 1.10 -0.10 -0.06 (0.09) (0.51) (0.05) (0.10) agreeGLi;t -0.16 -0.74 0.11 0.07 (0.09) (0.38) (0.06) (0.12) 1 3 2 P s=0 agreeISSi;ts 0.27 0.85 -0.11 -0.01 (0.09) (0.43) (0.06) (0.08) 1 3 2 P s=0 agreeGLi;ts -0.23 -0.50 0.12 0.02 (0.10) (0.30) (0.06) (0.11) Controls Yes Yes Yes Yes Yes Yes Yes Yes Year Eect Yes Yes Yes Yes Yes Yes Yes Yes Observations 907 166 907 1,059 917 166 917 1,063 # of cluster 257 42 257 200 257 42 257 200 (B)DirectorElections,Say-on-Pay,andShareholder-SponsoredProposals Director Elections Say on Pay Shareholder Proposals (1) (2) (3) (4) (5) (6) Other! ISS Other! GL Other! ISS Other! GL Other! ISS Other! GL 1 3 2 P s=0 agreeISSi;ts 0.20 -0.09 0.12 -0.02 0.09 -0.02 (0.08) (0.05) (0.05) (0.02) (0.03) (0.01) 1 3 2 P s=0 agreeGLi;ts -0.17 0.10 -0.09 0.03 -0.02 0.02 (0.09) (0.05) (0.05) (0.02) (0.05) (0.03) Controls Yes Yes Yes Yes Yes Yes Year Eect Yes Yes Yes Yes Yes Yes Observations 917 917 765 765 885 885 # of cluster 257 257 243 243 249 249 47 Table 1.15: Change of Recommendation and Cumulative Abnormal Return This table illustrates the eect of proxy advisors’ recommendations on rms’ cumulative abnormal returns separately done for whether the advisor changes its recommendation on the same rm’s same proposal across two adjacent occurrences. The sample includes all proposals (including director elections) that receive close votes, dened as within 20% of passing requirement. Each observation represents a close-call proposal. Panel A’s columns 1-4 and 5-8 separate the sample by whether or not ISS changes its recommendation. I dene ISS’s change of recommendation as ISS supports/opposes the current proposal (or director) but opposed/supported the same proposal (or director) of the same rm when it appeared last time. The dependent variable is the rm’s cumulative abnormal return by dierent Fama-French factors and dierent event windows. The independent variable “ISS Wins” is a dummy variable that denotes whether the voting outcome is in the same direction as ISS’s recommendation. Panel B for Glass Lewis is constructed in the same fashion. All columns include the proposal-type eect and the year xed eect. (A)EectofISS’sChangedRecommendationsonFirms’Return ISS Changes the Recommendation ISS Does Not Change the Recommendation (1) (2) (3) (4) (5) (6) (7) (8) 1 factor [5; 5] 1 factor [10; 10] 3 factors [5; 5] 3 factors [10; 10] 1 factor [5; 5] 1 factor [10; 10] 3 factors [5; 5] 3 factors [10; 10] ISS Wins -0.02 -0.03 -0.02 -0.03 0.00 0.00 0.00 0.01 (0.01) (0.01) (0.01) (0.01) (0.00) (0.01) (0.00) (0.01) Constant 0.14 0.11 0.11 0.13 -0.03 0.01 -0.03 -0.04 (0.09) (0.12) (0.09) (0.14) (0.04) (0.05) (0.04) (0.06) AdjustedR 2 0.02 0.03 0.02 0.01 0.01 0.01 0.01 0.01 Observations 1,399 1,399 1,399 1,399 2,201 2,201 2,201 2,201 (B)EectofGlassLewis’sChangedRecommendationsonFirms’Return GL Changes the Recommendation GL Does Not Change the Recommendation (1) (2) (3) (4) (5) (6) (7) (8) 1 factor [5; 5] 1 factor [10; 10] 3 factors [5; 5] 3 factors [10; 10] 1 factor [5; 5] 1 factor [10; 10] 3 factors [5; 5] 3 factors [10; 10] GL Wins -0.00 -0.00 -0.00 0.01 -0.00 -0.01 0.00 -0.00 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) Constant 0.06 0.10 0.05 -0.02 0.05 0.06 0.04 -0.01 (0.07) (0.10) (0.07) (0.11) (0.04) (0.06) (0.04) (0.06) AdjustedR 2 0.00 0.05 -0.01 -0.03 0.02 0.02 0.01 -0.00 Observations 318 318 318 318 890 890 890 890 48 Table 1.16: Change of Recommendation and CAR (Proposal Types and Past Disagreement) Panel A repeats the regression of Table 1.15 columns 3 for each proposal type. It shows the eect of proxy advisors’ recommendations on rms’ cumulative abnormal returns if the recommendation is changed across the same rm’s two adjacent occurrences. Each observation represents a close-call proposal, dened as within 20% of passing requirement. The dependent variable is the Fama-French three-factor cumulative abnormal return with the event window [-5, 5]. The independent variable “ISS Wins” (“GL Wins”) is a dummy variable that denotes whether the voting outcome is in the same direction as ISS’s (GL’s) recommendation. Panel B repeats table 1.15 columns 3’ regression after interacting “ISS Wins” or “GL Wins” with dierent investors’ past disagreement. I dene a fund family as a large (small) fund family if its TNA is above (below) the median among all fund families in the same year, and I dene a fund family as an active (non-active) fund family if its activism score is above (below) the median. The activism score is dened as the percentage of votes that the fund disagrees with management’s recommendations. (A)ProposalTypes Dependent Variable: CAR (FF3 with [5; 5] window) Sample: ISS Changes Recommendations Sample: GL Changes Recommendations Any Proposal Director Elections Say on Pay All Others Any Proposal Director Elections Say on Pay All Others (1) (2) (3) (4) (5) (6) (7) (8) ISS Wins -0.02 -0.04 -0.01 -0.02 (0.01) (0.02) (0.01) (0.01) GL Wins -0.00 -0.02 0.01 0.01 (0.01) (0.01) (0.01) (0.01) ProposalType Eect Yes Yes Year Eect Yes Yes Yes Yes Yes Yes Yes Yes AdjustedR 2 0.02 0.06 0.00 -0.01 -0.01 0.13 0.01 0.01 Observations 1,399 370 718 404 318 109 136 134 (B)InteractionwithInvestors’PastDisagreement Dependent Variable: CAR (FF3 with [5; 5] window) Sample: ISS Changes Recommendations Sample: GL Changes Recommendations (1) (2) (3) (4) (5) (6) (7) (8) Active Non-active Large Small Active Non-active Large Small ISS Wins -0.02 -0.01 -0.01 -0.01 (0.01) (0.01) (0.01) (0.01) GL Wins -0.00 -0.01 -0.00 -0.01 (0.01) (0.01) (0.01) (0.01) Past Disagreement -0.03 0.02 -0.01 0.01 0.01 -0.02 -0.00 -0.01 (0.02) (0.02) (0.03) (0.02) (0.02) (0.03) (0.02) (0.02) PA Wins Past Pisagreement 0.02 -0.06 -0.02 -0.03 -0.00 0.03 0.01 0.02 (0.04) (0.03) (0.04) (0.02) (0.03) (0.03) (0.03) (0.03) ProposalType Eect Yes Yes Yes Yes Yes Yes Yes Yes Year Eect Yes Yes Yes Yes Yes Yes Yes Yes AdjustedR 2 0.03 0.03 0.02 0.01 -0.02 -0.02 -0.02 -0.02 Observations 1,349 1,392 1,353 1,331 317 318 318 317 49 Figure 1.1: N-PX Types This gure shows one example for each of the four most-used N-PX table formats (denoted A.1, A.2, B, C). All tables display Apple Inc’s Annual meeting in 2019. They are led by BlackRock, Fidelity, Putnam Investments, and John Hancock Financial, respectively. Types A.1 and A.2 correspond to the reporting style of ISS’s ProxyExchange, type B corresponds to Glass Lewis’s Viewpoint, and type C corresponds to Broadridge’s ProxyEdge. The online Appendix explains the link between the four N-PX styles to their respective voting platforms through the comparison between the four N-PXs’ proposal descriptions with those of platforms’ vote disclosure service (VDS) websites. TypeA.1: ISSProxyExchange ® TypeA.2: ISSProxyExchange ® TypeB:GlassLewisViewpoint ® TypeC:BroadridgeProxyEdge ® 50 Figure 1.2: Competitive Landscape of the Proxy Advisory Industry Panel A shows the number of fund families that use each of the following three voting systems: ISS ProxyExchange, Glass Lewis Viewpoint, and Broadridge ProxyEdge. Funds’ uses of voting systems are inferred from their N-PX lings. Panel B displays the number of fund families that change their voting systems. Panel C displays proxy advisor ISS and Glass Lewis’s customers’ total net assets (TNA) and the inferred market shares of the proxy advisory industry. Vanguard has its distinctive N-PX style and subscribes to both ISS and Glass Lewis’s proxy advice. I split its TNA equally to ISS and Glass Lewis. (A)NumberofFundsthatUseISS/GL/Broadridge 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 ISS 94 98 109 103 97 96 89 109 124 124 134 Glass Lewis 3 3 4 15 18 18 20 20 28 26 26 Broadridge 32 34 34 36 50 53 56 63 73 75 75 (B)NumberofFundsthatSwitchVotingSystems 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 ISS! GL 0 1 2 4 1 1 1 1 0 1 - ISS! BR 2 1 0 1 0 3 1 3 1 0 - GL! ISS 0 0 0 1 1 1 0 1 2 2 - GL! BR 0 0 0 0 0 0 0 0 0 1 - BR! ISS 1 0 0 0 1 0 1 2 0 2 - BR! GL 0 0 1 0 0 0 1 1 1 0 - (C)TotalNetAssetsandMarketShares TotalNetAssets ProxyAdvisors’MarketShares 51 Figure 1.3: Descriptive Statistics on Voting This gure shows the percentage of investors’ votes that support management for proposals with dierent proxy advisors’ recommendations. Panel A’s sample includes all mutual funds, and Panel B separates the sample by funds’ proxy voting platforms. In both panels, the x-axis denotes the identity of the proxy advisor(s) that recommend against the management, and the y-axis denotes the average of investors’ votes (=1 if support the management and =0 if oppose the management). The vertical bar denotes the 95% condence interval with standard errors clustered at the fund-family level. (A)AllMutualFunds (B)SeparatebyProxyVotingPlatforms 52 Figure 1.4: Investor Ideologies Panel A scatter plots the ideology of every mutual fund family in 2012. The left gure’s sample includes fund families that use ISS or Glass Lewis as their voting platforms. The right gure’s sample includes all other fund families. Each dot presents a fund family, and its location represents its ideology, which is the two-dimensional W-NOMINATE scores provided by [11]. Socially oriented investors have a lower score in the rst dimension (i.e., appear to the left). Tough-on-governance investors have a larger score in the second dimension (i.e., appear to the top). The ideologies of ISS and Glass Lewis themselves are also pointed. Panel B displays the distribution of ideologies for ISS and GL’s customers. The left gure plots the distribution of the rst dimension (social orientation), and the right gure plots the distribution of the second dimension (tough-on-governance). (A)TwoDimensionalIdeologies ISSandGlassLewisCustomers FundFamiliesthatuseneitherISSorGL (B)DistributionofSocialandGovernanceScores Tough-on-Social Tough-on-Governance 53 Figure 1.5: The Trend Towards Robo-Voting This gure displays the number (left gures) and the fraction (right gures) of ISS’s customers, Glass Lewis’s customers, and other mutual funds that robo-vote with ISS’s recommendations (Panel A), Glass Lewis’s recommendations (Panel B), or managements’ recommendations (Panel C). I dene a fund-family as an ISS (GL) robo-voter if it agrees in a year with ISS (GL) on more than 99.9 percent of proposals where ISS (GL) disagrees with management. I dene a fund-family as a management robo-voter if it agrees in a year with Mgmt on more than 99.9 percent of proposals when either ISS or GL disagrees with the Mgmt. Each panel’s left gure displays the number of funds that robo-vote and each panel’s right gure displays the fraction of funds that robo-vote out of the group’s total number of funds. I exclude fund-years that have less than 100 votes. (A)Robo-VotingwithISS # of Fund Families Fraction (B)Robo-VotingwithGlassLewis # of Fund Families Fraction (C)Robo-VotingwithManagement # of Fund Families Fraction 54 Figure 1.6: Robo-voting: Size and Indexer Figure 1.6.A shows the percentage of ISS customers that robo-vote with ISS, separately for dierent quantiles of total net assets and for whether the fund family is an indexer. I dene a fund family as an indexer if it provides any index funds. Figure 1.6.B displays the trend of robo-voting popularity among ISS customers with small (rst 1=3 quantile), middle (second 1=3 quantile), and large (third 1=3 quantile) total net assets. (A)Robo-votingPopularitybyQuantilesinTotalNetAssets %Robo-votewithISS (B)TrendofRobo-votingPopularitybySmall,Middle,andLargeFundFamilies %Robo-votewithISS 55 Figure 1.7: Voting Patterns For Funds that Switch Proxy Advisors This gure shows the evolution of fund families’ vote agreement with ISS’s (and GL’s) recommendations if they have changed their voting platforms from ISS to Glass Lewis (or vice versa). Panel A’s sample includes fund families that have switched their voting platforms from ISS to GL. In both panels’ all gures, the x-axis denotes the relative year to the year of the switch. In both panels, the rst two gures plot the average “excess agreement with ISS”, and the last two gures plot the average “excess agreement with GL”. The “excess agreement with ISS (GL)” is the percentage of the fund’s votes on contentious proposals that agree with ISS’s (GL’s) recommendation, minus that of the benchmark. For the benchmark, the rst (third) gure uses the same fund’s “agreement with ISS” (“agreement with GL”) of the switching year. The benchmark of the second (fourth) gure is the average “agreement with ISS” (“agreement with GL”) among all ISS’s (GL’s) customers. Panel (B) is constructed analogously and includes fund families that have switched from being a GL customer to being an ISS customer. (A)ISS!GL AgreewithISS (time-series comparison) AgreewithISS (cross-sectional comparison) AgreewithGL (time-series comparison) AgreewithGL (cross-sectional comparison) (B)GL!ISS AgreewithISS (time-series comparison) AgreewithISS (cross-sectional comparison) AgreewithGL (time-series comparison) AgreewithGL (cross-sectional comparison) 56 Figure 1.8: Proxy Advisors’ Sway Eects By Years This gure displays ISS’s (Panel A) and Glass Lewis’s (Panel B) sway eects on their respective customers for years 2006-2017. Each gure in Panel A plots the ^ 1 coecient of the OLS regression, Agree with ISS ip =0 +1 ISS Customerit +"p +"ipt, where the sample includes funds’ votes on contentious proposals. The grey displays the 95% condence intervals with standard errors clustered at the fund-family level. The rst gure’s sample contains all contentious proposals, and the second to fourth gure’s samples contain contentious proposals of dierent types (director elections, say on pay proposals, and shareholder-sponsored proposals). Panel B is constructed analogously for Glass Lewis’s sway eect. (A)ISS’sSwayEect Any DirectorElections SayonPay ShareholderProposals (B)GlassLewis’sSwayEect Any DirectorElections SayonPay ShareholderProposals 57 Figure 1.9: Cumulative Abnormal Return Around Annual Meetings This gure displays companies’ cumulative abnormal returns (Fama-French 3 factors) around annual meetings where there is at least one proposal that receives close votes, dened as within 20% of the passing requirement. The left gure’s sample includes meetings with at least one close-call proposal that ISS changes its recommendation. The right gure includes meetings with close-call proposals, but ISS does not change its recommendations on any of them. Each gure’s blue (orange) line plots the average cumulative abnormal returns if ISS wins (loses). The grey area represents the 5% condence interval. ISSChangesRec. ISSDoesNotChangeRec. Figure 1.10: Robustness: Dierent Margins for Close-Call Proposals This gure replicates the results of table 1.15.A for dierent denitions of close-call margins. It plots the coecient ^ 1 of the OLS regression CARp =0 +1ISS Winsp +"p, where CARp is the three-factor cumulative abnormal return with [5; 5] window. The regression includes proposal-type eect and year xed eect. The left gure’s sample includes close-call proposals that ISS changes its recommendations, and the right gure’s sample includes close-call proposals that ISS does not change its recommendations. ISSchangesitsrecommendation ISSdoesnotitsrecommendation 58 OnlineAppendix–A PublicRequestonGlassLewis’sRecommendations I obtained Glass Lewis (GL)’s recommendations to a large public pension fund for 2008-2017 through a Freedom of Information Act (FOIA) request. Part (A) provides a screenshot of the response, which contains the name of issuers, meeting dates, item numbers, proposal descriptions, GL’s general recommendations, GL’s customized recommendations to this particular investor, and the vote cast. Part (B) shows the details of the matching process between this data and ISS Voting Analytics. Part (C) shows the coverage of companies (measured by total assets) in the main sample (i.e., ISS Voting Analytics) that can be found with Glass Lewis’s recommendations from the FOIA sample. (A)SampleoftheFOIAResponse (B)MatchingSteps Stepone: matchcompanies The GL recommendations provided by the FOIA request do not contain company identiers but only company names. ISS and GL may use dierent company names for the same company. For example, the ISS Voting Analytics dataset uses “Apple Inc.” throughout sample years, but GL uses “Apple Computer Inc.” in the early years. To match companies between GL’s recommendations and ISS Voting Analytics, I rst match each company name in GL’s rec- ommendations exactly with names that appeared in Type B N-PX forms to get the company’s ticker. The assumption of this step is that company names in Glass Lewis’s voting system do not dier for dierent customers. I then use tickers to match companies between the FOIA data and ISS Voting Analytics. Steptwo: matchannualmeetings Matching annual meetings between GL’s recommendations and ISS Voting Analytics is a straightforward one-to-one match of (ticker, meeting date) between the two datasets. 59 Stepthree: matchproposals One diculty comes from the fact that ISS and Glass Lewis sometimes use dierent styles of sub-item numbers for director elections. For example, Glass Lewis uses item number “1” to denote the election of Howard Schultz in Starbucks’s 2013 annual meeting, but ISS uses item number “1a” for the same election. As a result, using item number alone will result in a large number of missing matches. To ensure better matches, I perform the following steps. • When both ISS and Glass Lewis use the same style (either digit or letter) for annual meetings, I use the item number to match. • When ISS and Glass use dierent styles, I use the sequence number to match each proposal if the annual meeting’s total number of proposals is the same between the two datasets. • When ISS and Glass use dierent styles and if the annual meeting’s total number of proposals is not the same between the two datasets, I treat those cases as errors and drop them. 33 (C)CoverageofGlassLewisRecommendations 33 There are 89 (out of 13,246) annual meetings where the total number of proposals is dierent between the two datasets. It mainly arises from the fact that the FOIA response is in the pdf format and non-English characters cannot be converted and hence become lost (e.g., Elect Øivind Lorentzen). 60 OnlineAppendix–B LinkN-PXStylestoVotingPlatforms: There are four most common N-PX styles. N-PX styles are linked with their respective voting platforms by comparing their proposal descriptions and item-number styles with ISS/GL/Broadridge’s vote disclosure websites (VDS). To ensure comparison, all N-PX forms and VDS interfaces display Apple Inc’s 2019 annual meeting. The proposal descriptions and the item-number styles (of the last proposal in particular) establish the link. The N-PX forms are displayed to the left, and the VDS websites are displayed to the right. N-PXTypeA.1ÖISSVDSVersion1 (Source: http://vds.issproxy.com/SearchPage.php?CustomerID=1615) N-PXTypeA.2ÖISSVDSVersion2 (Source: https://vds.issgovernance.com/vds/#/NDM3Mg==) 61 N-PXTypeBÖGlassLewisVDS (Source: https://viewpoint.glasslewis.net/webdisclosure/search.aspx? glpcustuserid=TIA129) N-PXTypeCÖBroadrigeVDS (Source: https://central-webd.proxydisclosure.com/WebDisclosure/ wdFundSelection?token=JPMFunds) 62 OnlineAppendix–C ProcessingDirectorNamesfromISSVotingAnalytics 1. Extract name-like sub-strings from proposal descriptions by striping o phrases “Elect Director”, “Re-elect”, “Management Nominee”, “Elect Trustee”, “as class x Director”, etc . For example, • “Elect Director Arthur D. Levinson, Ph.D.”! Arthur D. Levinson, Ph.D. • “Elect Director Robert C. Nolan as Class I Director”! Robert C. Nolan • “Management Nominee Teresa Beck”! Teresa Beck (This step requires hand correction for typos in ISS Analytics: Direcctor, Eect, DElect, etc) 2. Strip o prex and sux (e.g., numerous versions of Ph.D., Jr., M.D., etc). For example, • “Helen R. Bosley, CFA ”! “Helen R. Bosley” • “John Michael Palms Ph.D., D. Sc.”! “John Michael Palms” • “Hal V. Barron, M.D., FACC”! “Hal V. Barron” (Certain sux needs to be carefully hand matched. For example, MA can be both a last name and a sux.) 3. Unify rst name variations, nicknames, and royal titles. For example, • “Bill Gates”! “William Gates” • “Triple H Levesque”! “Paul Levesque” • “Lord Stevenson of Coddenham”! “Dennis Stevenson” 4. Generate a processed name from each of the full names as the rst letter of the rst name and the entire last name. For example, • “William Gates”! “W Gates” • “Paul Levesque”! “P Levesque” • “Dennis Stevenson”! “D Stevenson” 63 OnlineAppendix–D CostofProxyAdviceandVotingPlatforms The prices that proxy advisors charge their customers are generally condential. To shed some light on the cost of proxy advice, I sent Freedom of Information Act (FOIA) requests to the 30 largest public pension funds. I asked about their subscription to proxy advice, the voting platform they use, and the price they pay. Eleven of them responded and provided me with the information. The rest either declined my request or did not subscribe to any proxy advice. The rst gure below plots the total price each pension pays and its total assets (as of 2017). Among the eleven pension funds, seven of them subscribe to only one rm between ISS and Glass Lewis. Four of them subscribe to both ISS and Glass Lewis for proxy advice but use only one platform for vote execution. This fact enables me to estimate the dierence between the cost of proxy advice and the cost of the bundled package of proxy advice and vote execution. The right gure plots the prices separately for proxy advice and bundled packages. The following table displays the OLS regression of payment as a function of vendor identity, whether the pay- ment is for the proxy advice only or vote execution service bundle, and the total asset assets. It shows that if a fund also uses the proxy advisor’s voting platform, the fund has to pay $161,290 more than if it only subscribes to its advice (the unconditional mean for advice is $69,080). Payment (in $1000) Recipient = ISS -45.61 (42.37) Bundled with platform 106.55 161.29 (43.69) (45.11) Total Asset (in $ billion) 0.82 (0.23) Fund Eect Yes AdjustedR 2 0.53 0.65 Observations 16 16 64 Omitted Table 1.17: Results of Table 1.10 After Excluding Funds that Changed Proxy Voting Guidelines This table repeats the results of table 1.10 after excluding the switching funds that also changed their “proxy voting guidelines” during the switching year. The “proxy voting guidelines” are manually collected from each fund’s Prospectus (section of Statement of Additional Information). After the exclusion, there are 8 funds that have switched from Glass Lewis to ISS, and there are 13 funds that have switched from ISS to Glass Lewis. (A)CerticationEect(UncontentiousProposals) All GL Customers All ISS Customers (1) (2) (3) (4) agreeISSt+1 agreeGLt+1 agreeISSt+1 agreeGLt+1 GL! ISS 0.01 -0.03 (0.01) (0.02) ISS! GL -0.04 0.03 (0.02) (0.01) AdjustedR 2 0.00 0.02 0.01 0.07 Observations 126 123 969 813 # of cluster 33 33 168 155 (B)SwayEect(ContentiousProposals) All GL Customers All ISS Customers (1) (2) (3) (4) agreeISSt+1 agreeGLt+1 agreeISSt+1 agreeGLt+1 GL! ISS 0.17 -0.14 (0.08) (0.10) ISS! GL -0.19 0.35 (0.07) (0.12) AdjustedR 2 0.10 0.01 0.02 0.19 Observations 128 125 958 808 # of cluster 35 35 168 155 65 Omitted Figure 1.11: Propensity Score Matching: Before and After This gure shows the distribution of fund characteristics before (left gure) and after (right gure) the propensity score matching. The propensity score is estimated using a logit regression of funds’ characteristics that appear in table 1.1.C as a function of whether the fund is an ISS customer. The propensity score matching method used is a one-to-one match without replacement and with a tolerance of 0.001 for the score. log(Asset) log(#ofVotes) FamilyAge 66 Chapter2 EndogenousRisk-ExposureandSystemicInstability 2.1 Introduction Since the 2008 nancial crisis, the relationship between nancial networks and systemic stability has been an important subject of research [40]. Most of the existing literature assumes exogenous shocks and stud- ies how these idiosyncratic shocks are propagated across a nancial network. 1 However, banks’ exposure to which particular shock is an endogenous choice variable. For example, a bank chooses between safe borrowers and subprime borrowers, or chooses its exposure on asset-backed securities. 2 This paper ex- tends the theory of interbank networks and systemic stability by incorporating endogenous risk exposure. The introduction of a risk exposure choice changes the received intuition about nancial stability in an important way and yields novel policy implications. Pioneering works by [5] and [37] show that connected networks are more resilient to the contagion of exogenous shocks than unconnected ones due to a co-insurance mechanism. They conclude that a highly connected banking sector promotes nancial stability. In contrast to the conclusions of the above papers, I show that although shocks are better co-insured in densely connected networks, banks in those networks initially choose greater risk exposure. Furthermore, they choose correlated risks. In other words, 1 For example, [5], [37] and [38] consider exogenous liquidity shocks. [73], [29] and [2] considers exogenous economic shocks. 2 [66] empirically documented an unprecedented growth of subprime credit right before the 2008 nancial crisis. They also found a concurrent rapid increase in the securitization of subprime mortgages. 67 in densely connected networks, bank-specic endogenous losses are more likely, and they tend to happen simultaneously. As a result, the banking sector as a whole becomes more fragile. The basic intuition for this result relies on a network risk-taking externality. Banks in networks, if solvent, partially reimburse failed banks through interbank payments, which I dub as cross-subsidy. The cross-subsidy reduces banks’ upside payos (the payos when their own assets succeed). On the other hand, banks’ downside payos are always zero due to limited liability. The asymmetric distortion disin- centivizes banks from being prudent because they become less interested in increasing the probability of success when trading o risk and return. This risk-taking distortion is higher when each bank anticipates a higher likelihood of having to cross-subsidize other banks, that is when its counterparties take greater risks. As a result, banks’ choices of risk exposure are strategically complementary. Moreover, banks in greater connected networks will be more aected by such risk-taking externality. In particular, I show that banks in networks with a greater level of connections, in a maximum connected complete structure, or in networks with more counterparties will choose greater risk exposure. The model contributes to the debates on the relationship between a nancial network’s connectedness and systemic stability. 3 My result stands in contrast to the “connected-stability” view that argues for nancial networks’ co-insurance benets. I show that the losses that are better co-insured, as in [5]’s complete network, will be more likely to endogenously evolve in the rst place. Nevertheless, I also show that banks’ choices of risk exposure are not monotonically increasing in the network’s degree of connectedness. On the one hand, greater connectedness increases a bank’s exposure to more counterparties’ risk-taking externalities. On the other hand, the bank becomes less sensitive to particular other banks’ failure. This nonmonotonicity result is similar to the observation of [29], who use random networks to show that the ex-post contagion is not monotonic to a nancial system’s connectedness. 3 For “connected-stability” view, [5] show that a complete network is more robust to the loss contagion due to a co-insurance mechanism. For “connected-fragility” view, [2] argue that the “complete-stability” relationship does not apply to larger shocks due to a propagation mechanism. [29] nd similar non-monotonic relationships for equity networks. 68 Notwithstanding the network distortion, banks do have incentives to form a nancial network. With valuable expected present value of their future prots (charter values), banks do not want to risk defaulting on their deposits [52, 44]. This implies that even though the interbank connection hurts banks’ upside payos, being in a network can protect them from losing their valuable charter values as it provides co- insurance to their depositors. It is also worth noting that this paper’s network risk-taking externality is distinct from the asset substitution problem as in [50]. A conventional asset substitution model shows that the level of debt can encourage banks’ risk-taking. Using the machinery of networks, my model shows that thetopology of the nancial system also matters for the risk-taking conditioning on the same level of debt. This paper’s model builds on a payment equilibrium model by [28], which has later been utilized by [72, 73] and [2]. My innovation is to allow banks to choose their risk exposure endogenously after anticipating the payment equilibrium and their counterparties’ risk exposure. One important contribution of this model is to show that the standard intuition about the stabilizing eect of nancial networks reverses with endogenous risk-taking. The theory also yields several novel perspectives on policy debates: • CentralClearingCounterparty(CCP). According to LCH-Clearnet, the second-largest clearing- house in the world, a CCP reduces risks by insuring members against counterparty losses. 4 In this paper, instead, I show that the risk-taking equilibrium with a CCP is equivalent to the outcome of a maximum connected complete network. This is because the CCP “forces” each member bank to be exposed to the risk-taking externalities of other banks. That implies, contrary to popular belief, a CCP may instead increase risk-taking incentives for banks in originally loosely connected networks. This result is echoed by the concern of a former SEC Chief Economist, stating “the clearinghouse is subject to considerable moral hazard and systemic risk”. 5 4 See LCH-Clearnet’s presentation to the New York Fed, https://www.newyorkfed.org/medialibrary/media/ banking/international/11-LCH-Credit-Risk-2015-Lee.pdf 5 See Chester Spatt’s statement to the Senate Banking Committee, https://www.govinfo.gov/content/pkg/ CHRG-112shrg71411/pdf/CHRG-112shrg71411.pdf 69 • Network-adjustedCapitalRegulation: I show that each bank’s equity buer has a network eect on systemic stability. It not only reduces a bank’s risk-taking [50] but also reduces the risk-taking of other connected banks. A failed bank’s equity rst absorbs part of the loss, which may be otherwise propagated to other banks. That implies every bank in the nancial network anticipates a smaller cross-subsidy to failed banks, and will ex-ante choose to expose to fewer risks. The result suggests that policymakers should consider banks’ systemic footprint when deciding their regulatory capital. It provides a rationale for a recently proposed rule by FRB and OCC. 6 • GovernmentBailouts. Conventional wisdom states that a government bailout, or simply anticipa- tion of it, is harmful to the systemic stability since it encourages excessive risk-taking by reducing banks’ “skin in the game”. I show that a government bailout may instead reduce connected banks’ risk-taking distortion. In presence of the possibility of a government bailout, every bank will antic- ipate a smaller cross-subsidy to its failed counterparties. Hence the network risk-taking distortion is reduced and so does every bank’s choices of risk exposure. In the nal part of the paper, I endogenize banks’ decisions to correlate their risk exposure. I show that in a nancial network, banks will choose to expose to a single systemic risk. In anticipation of counterpart risks, a correlated portfolio reduces the possibility of a bank having to cross-subsidize others. Hence the correlated portfolios will increase each bank’s expected prot. As a result of the correlation, a nancial crisis (or simultaneous failure of several banks) will be more likely to evolve in a connected banking system endogenously. This observation explains the empirical ndings of the [35] on the 2008 nancial crisis, stating “some nancial institutions failed because of a common shock: they made similar failed bets on housing.” 6 The proposed rule calibrates a bank’s enhanced supplementary leverage ratio (eSLR) to its systemic importance rather than a xed leverage standard. Seehttps://www.federalreserve.gov/newsevents/pressreleases/bcreg20180411a.htm 70 The paper makes several contributions to the topic of systemic stability. In contrast to previous papers that study the ex-post contagion, this paper provides a tractable model to study banks’ choices of risk exposure in nancial networks. It reverses the previous intuition about the stabilizing eect of a highly connected nancial system. The paper also explains the observation that connected banks tend to make similar bets, especially in the 2008 global nancial crisis. Finally, the theory yields several novel perspec- tives on policy debates. It appeals to regulators to consider the nancial system’s topology when designing prudential policies. RelatedLiterature This paper is related to a recent and growing literature on the relationship between the interconnectedness of modern nancial institutions and systemic stability. Most research focuses on the question do more connections tend to amplify or dampen systemic shocks. [40] provide a survey of this literature, and here I will summarize a few related to the present paper. One branch of literature conforms to a “connected-stability” view: a connected network provides better liquidity insurance against some exogenous shocks to one individual bank. The view is supported by [5], [37], [56]. [5] argues that the initial loss will be widely divided in a complete network. Therefore banks will be less likely to default in such a network. In [37], depositors face uncertainties about where they will consume. They also show that the interbank connections enhance the resiliency. [56] argues that the interbank connection is optimal ex-ante due to the probability of private-sector bailouts. On the other hand, the “connected-fragility" view is supported by [38], [2], and [25]. Using numerical simulations, [38] demonstrate that a more complex and concentrated nancial network may amplify the fragility. [2] use [28]’s model to study the shock propagation. They conclude that a highly connected com- plete network becomes least stable under a large exogenous shock. [25] study the liquidity co-insurance benets of long-term interbank debts. None of the above papers, nevertheless, studies how those initial shocks evolved in the rst place. 71 Some recent papers study endogenous network formations and interbank liquidity. [1] study the net- work externalities of bilateral lending on other third parties in the same nancial system. They show that although banks internalize the bilateral counterparty risks through the interest rate, they fail to in- ternalize the externalities on the rest of the network. In this case, banks may “overlend” in equilibrium. The present paper utilizes the same framework to illustrate another nancial network externalities: risk- taking externalities. [23] study the interbank intermediation capacity with moral hazard. They show that the collateral’s liquidity may have a huge eect on haircuts and intermediation capacity due to the moral hazard’s cumulative nature. There is sparse research on banks’ portfolio choices when they are connected in nancial networks. [13] study banks’ contracting behaviors in nancial networks. They utilize the models of [24] to study bankers’ private benet from gambling and their contracting behaviors with depositors. Contemporaneous papers such as [30] and [49] also study banks’ choices of correlation with each other in nancial systems. [30] use German banks to show that banks are more likely to form connections with the ones with similar exposure to the real economy. [49] argue that banks do not internalize the ineciency resulting from their counterparties’ bankruptcy cost. While the conclusions of their papers are complementary to mine, the structure of the underlying models is very dierent. The key innovation of this paper is that it provides the rst micro-foundation showing how the nancial system’s risk-taking externality is the equilibrium outcome of the network structure of the banking system. 2.2 Model The economy consists ofN2N + risk-neutral banks that are interconnected through the cross-holdings of unsecured debt contracts d ij > 0, where d ij is the face value of the interbank debt that bankj owes to banki. Assume that all interbank liabilities have equal seniority. Denote d j P i d ij as bankj’s total interbank liabilities. Following [2], I restrict most of the analysis to regular network structures in which 72 the total interbank liabilities and claims are equal for all banks (i.e., P j d ij = P j d ji = d for alli). In this way, we abstract away the eect of network asymmetry (e.g. the existence of a dominant player). Dene ij d ij = d j as banki’s share inj’s total interbank liabilities. By the regularity assumption, we have P j ij = P i ij = 1. Denote [ ij ] as an NN matrix, which determines the network connectedness and will be further discussed in section 2.4. A topology is path-connected if every two nodes in the network can be connected by some path [48]. It is symmetric if each row of has the same set of elements. Besides the interbank liabilities, each bank also owes a more senior outside debtv i =v> 0 that needs to be paid in full before the interbank debt. One example of such outside debt is banks’ retail deposits. In summary, an economy is characterized by ( d; ;N;v), which is publicly observable. In the initial date, each banki simultaneously chooses one projectZ i among a set of available projects [Z;Z]. This project Z i will produce a random return of ~ e i (Z i ) with the following payo distribution. 7 ~ e i = 8 > > < > > : Z i w.p P (Z i ) 0 w.p 1P (Z i ) (2.1) P (Z)2 (0; 1) is some deterministic function that denotes the probability of projectZ’s success. In the benchmark model, I assume each bank’s project is independent. This assumption is later relaxed in Section 2.6. It’s worth noting thatP (Z i ) denotes the success probability of banki’s primitive asset rather than the probability of it being solvent (i.e., able to fully pay back its deposits). As we will see in section 2.5.1, the probability that a bank is solvent also depends on the primitive assets of other banks in the network. To avoid confusion, throughout the rest of the paper, I use the word “successful” to denote that the primitive asset pays o (i.e. ~ e i =Z i ) and the word “solvent” to denote that the bank can fully pay back its deposits. To guarantee a non-trivial banking sector, a bank will be able to pay o its total liabilities whenever its 7 The payo function assumes that a failed project generates a 0 return. In the online Appendix, I show that the main results of the paper still hold if the downside payo is positive. 73 project succeeds. That impliesZ v + d, and suppose this condition holds throughout the rest of the paper. 8 Let’s further impose the following assumption. ASSUMPTION1. P (Z) is decreasing inZ, andP (Z)Z is concave inZ. The rst part captures the fact that high-return projects come with high risks. Each bank faces a trade- o between project payo and project safety. A largeZ denotes a project with a large return along with high risks. Therefore, we can interpretZ i as banki’s choice of its risk exposure. The Pareto optimal risk exposure for each individual bank is whenE[~ e] is maximized: Z = argmax Z P (Z)Z. An economy’s total surplus will be later formalized in denition 3. The second part of the assumption is to ensure a unique interior risk exposure. A sucient condition is to letP () be concave: the project risk increases at a growing rate in the project return. After all banks choose their risk exposureZ = (Z 1 ;:::;Z N ), the state of nature! = (! 1 ;:::;! N ) will be independently drawn from the distribution according to equation (??). 9 For each bank,! i can take one of the two values: success (! i =s) or fail (! i =f). As a result,!2 = 2 N . After realization of the state of nature, interbank debts’ reimbursement will be determined from a payment equilibrium. A bank’s total payments depend on what it possesses, which depends on the interbank payments from other banks. As a result, the payment equilibrium is solved by a xed point system. This notion of the payment equilibrium is introduced by [28] and then utilized by [72, 73] and [2]. The current paper diers from theirs in that the payment vector of my model is now parametrized by a vector of risk exposureZ and a vector of states!. Denition 1 formally denes the payment equilibrium. 8 This condition describes reality well. For example, in Morgan Stanley’s 2020 Q1 call report, the bank has an interest income of 966 million dollars, of which 51 million dollars is interbank interest revenue. The bank needs to pay 303 million dollars as its total interest expense. This implies that even if Morgan Stanley receives nothing from its counterparties, it can fulll its total liabilities, conrming the assumptionZ v + d. The same observation applies to all current major banks and even Lehman Brothers before its 2008 crash. 9 For the remaining text, I refer a vector as in bold letters. For example,x = (x1;:::xN ) andx i = (x1;::;xi1;xi+1;::xN ) 74 DEFINITION1. For a network structure ( d; ;N) and given a risk vectorZ, the payment equilibrium is a vector of functionsd (!;Z) = [d 1 (!;Z);:::;d N (!;Z)] that solves d i (!;Z) = ( min h X j ij d j (!;Z) +e i (! i ;Z i )v; d i ) + 8i2N 8!2 (2.2) d i (!;Z) denotes banki’s total payments of its interbank liabilities in state! after banks choosing risk exposureZ. On the right hand side, P j ij d j (!;Z) +e i (Z;!) is banki’s available resources for pay- ments to its total liabilities (deposits and interbank debts). The function min[:; d] captures banks’ limited liabilities, so they pay either what they owe or what they have, whichever is smaller.f:g + maxf:; 0g denotes the fact that banks’ interbank payments are non-negative. It binds when the bank is not solvent (i.e., cannot fulll its deposits). A bank starts to pay its interbank liabilities only after it fully fullls its deposits. We observe that the paymentd i (!;Z) is a function of!. For each state of nature!, we will have a separate xed-point system. Therefore, given a risk vectorZ, we need to solve 2 N xed-point systems, one for each state of nature. Before we proceed, one immediate task is to show that the above payment equilibrium exists and is unique. LEMMA1. [Eisenberg-Noe] For any risk vectorZ, the payment equilibrium exists and is generic unique. The proof is a simple utilization of the Brouwer xed point theorem and is identical to Eisenberg and Noe (2000) and Acemoglu et al. (2015). Part of the proof is subsumed in the proof of proposition 2. Hence, it is omitted here to conserve space. Acemoglu et al. (2015) show that for each ~ e, the xed point exists and is generic unique. It is identical to say that for every combination of (!;Z), the xed point exists and is generic unique. Hence lemma 1 naturally follows. 75 After the realization of! and the interbank paymentsd (!;Z), each bank’s prot at the nal date becomes i (!;Z) = X j ij d j (!) +e i (Z;!)v i d i (!;Z) + (2.3) The prot i (!;Z) depends on the risk exposure of all other banks. In Equilibrium, each bank choose its own risk exposureZ i to maximize the expected payoE ! [ i (!;Z)]. The following gure summarizes the timeline. Figure 2.1: Timeline date 1 choose risk exposureZ i date 2 state!2 realized date 3(a) paymentd (!;Z) date 3(b) (!;Z) realized From equation 2.3, we can derive each bank’s expected prot as E h i (!;Z) i = X !2 i (!;Z) Pr(!) = X !2 h i (!;Z) Y j Pr(! j ) i The last equality is due to the assumption that each bank’s project outcome is independent. Each bank chooses its risk exposure to maximize the expected prot. Therefore, the Nash Equilibrium for banks’ risk exposure can be expressed as the solution of the following xed-point system: Z i = argmax Z i X !2 h i (!;Z i ;Z i ) Y j Pr(! j ) i 8i2N (2.4) We observe thatZ i enters banki’s expected prot in two ways: rst through the distribution of the state of nature,Pr(! j =s) =P (Z j ), and second through the payment equilibriumd (!;Z). In the next 76 section, I will show that the second channel has no eect and bankj’s risk choice aects banki’s expected prot only through the distribution of!. 2.3 Risk-TakingEquilibriumandNetworkDistortion It’s immediate that we can dene a risk-taking equilibrium as every bank chooses its risk exposure simul- taneously, anticipating other banks’ optimal risk exposure and the resulting payment equilibrium. DEFINITION 2. The risk-taking equilibrium in a nancial network ( d; ;N) is a pair (d (!;Z);Z ) consisting of a vector of payment functionsd (!;Z) and a vector of risk exposureZ such that: 1. The vector of functionsd (!;Z) is a payment equilibrium for anyZ. 2. For eachi2N,Z i is optimal and solves equation 2.4, givend (!;Z) andZ i . We rst observe that the above risk-taking equilibrium is the solution of two intertwined systems of equations (equation 2.2 and 2.4): when choosing the risk vectorZ i , each bank anticipates the payment equilibrium. When determining the interbank debt paymentd (!;Z), banks’ chosen risk vector is a parameter. At rst glance, the xed point solutions to the two intertwined systems look complicated to derive. Thanks to the following lemma 2 and proposition 1, the existence and analytical solutions for the risk- taking equilibrium can be obtained. LEMMA2. The payment equilibriumd (!;Z) is constant in the risk exposure vectorZ. Proof. In the Appendix As a result, we can rewrited (!) = d (!;Z). The idea is that when a bank’s project succeeds, its total interbank payment is the face value d, independent of any bank’s chosen risk exposure. On the other 77 hand, when a bank’s project fails, its contribution to the payment system is 0, also independent of any bank’s chosen risk exposure. 10 Therefore, the payment equilibrium is independent of the risk exposure vectorZ. As a result of lemma 2, we can disentangle the two intertwined xed-point systems. We rst solve the xed-point vectors for the payment equilibrium (equation 2.2), and then use them to derive the xed-point solution for the risk-taking Nash Equilibrium (equation 2.4). We also observe that a bank will earn a positive prot only if its project succeeds. Suppose a bank’s project fails, at most its available resource will be max ! P j ij d j (!) = d, that is when its interbank claims get paid in full. That implies this bank will default on its interbank debts (i.e. P j ij d j (!)v< d). Therefore the bank with a failed project will earn a zero prot at the nal date. Hence, we can rewrite banki’s expected prot as: E h i (!;Z) i =P (Z i ) X ! i h Z i v d X j ij d j (! i=s ) i Pr(! i ) where! i 2 2 N1 denotes the vector of states for all banks except banki. With a slight abuse of notation, I denote! i=s (! 1 :::;! i1 ;s;! i+1 ;:::! N ) as the vector that appends banki’s success to other banks’ states of nature! i . Dene the functionD(Z i ) as D(Z i ) X ! i d X j ij d j (! i=s ) Pr(! i ) (2.5) Note thatD(Z i ) is non-negative and is parameterized by the network structure ( d; ;N). Plugging D(Z i ) into the bank’s expected prot, we have E h i (!;Z) i =P (Z i )(Z i v)P (Z i )D(Z i ) (2.6) 10 Although a failed bank’s contribution to the payment system is zero, its interbank payments may be positive. 78 Equation 2.6 consists of two parts. The rst termP (Z i )(Z i v) is the expected payo of a stand-alone bank. The second termD(Z i ) is banki’s expected net interbank payment (or “cross-subsidy”) to other banks when its project succeeds. This cross-subsidyD(Z i ) can be interpreted as a risk-taking distortion as it will become clear in the next proposition. SinceZ i enters banki’s expected payo through this distortion, we will be interested to know how it aects bank i’s choice of risk exposure. Proposition 1 provides the answer. PROPOSITION 1. The choice of risk exposureZ is strategically complementary among all banks in the same nancial network. Proof. In the Appendix The proposition states that a bank’s optimal risk exposure is increasing in the risk exposure of any other banks in the network. To see the intuition, suppose a counterparty bank, say bank m, increases its risk exposure. As a result, bankm’s project becomes more likely to fail. When it does fail, banki’s cross-subsidies to other banks will increase. This will decrease banki’s upside payo (the payo when its project succeeds). As a result of this distortion, banki will be less interested in increasing the probability of success when trading o risk and return. In other words, banki will optimally choose a greater risk exposure in response to bankm’s increased risk exposure. As a result, banks’ choices of risk exposure are strategically complementary. Proposition 1 conveys the rst important message of this paper. It assigns a new meaning to the view of the “too connected to fail” in the sense that a bank not only aects other connected banks through an ex-post loss contagion, as in [5], [29], or [2]. It also creates an ex-ante moral hazard problem due to a risk-taking externality. With the supermodular property for banks’ choices of risk exposure at hand, we are now able to es- tablish the existence of the risk-taking equilibrium. 79 PROPOSITION2. In any network structure ( d; ;N), the risk-taking equilibrium exists. Proof. In the Appendix The proof is a simple application of the Tarski (1955) xed point theorem to a supermodular game. In general, the equilibrium is not unique. For the remaining text, let’s focus on the Pareto-dominant equilibrium whenZ is the smallest among the set of xed points. 11 . After establishing the existence of the risk-taking equilibrium, we can now compare connected banks’ choices of risk exposure with that of a stand-alone bank. The following proposition shows that the inter- connectedness indeed encourages banks to expose to more risks. COROLLARY 1. A bank in any network structure ( d; ;N) will choose a greater exposure to risks than a stand-alone bank. Proof. In the Appendix. In nancial networks, a bank with a successful project pays a net positive amount of cross-subsidy to failed banks’ depositors. This cross-subsidy is reected in the network distortionD(Z i ) of a bank’s upside payo. As argued by proposition 1, every bank in the nancial network, anticipating this distortion, will increase its exposure to risks. This leads to an amplication mechanism for banks’ risk exposure as the increased risk, in turn, increases the distortion. In equilibrium, no bank will internalize the eect of its risk exposure on other banks’ payos. There exists a risk-taking externality, and connected banks will endogenously expose to greater risks than stand-alone banks. 11 Focusing on the least exposure equilibrium is to abstract away a self-fullling failure. See [29] for more details. They also consider the “best-case” equilibrium, in which as few organizations as possible fail. Furthermore, all of the following results are robust to any stable equilibria. 80 It’s worth noting that a bank’s risk-shifting incentive in a nancial network is distinct from the asset substitution problem as in [50], who argue that the level of debt can encourage risk-taking. To see this, let’s rst dene the total social welfare. DEFINITION3. The social welfare is the sum of the expected returns to all agents in the economy, namely banks and retail depositors. Formally, u =E ( X i X j ij d j (!) +e i (Z;!)v i d i (!;Z) + | {z } expected return to banks + X i min h v i ; X j ij d j (!) +e i (Z;!)d i (!) i | {z } expected return to depositors ) The rst part is the expected return to banks’ shareholders, and the second part is the expected return to their depositors. We can rewriteu as u =E ( X i e i (Z;!) + X j ij d j (!)d i (!;Z) ) =E ( X i e i (Z;!) ) = X i P (Z i )Z i Comparing the social welfareu with each individual bank’s objective function (equation 2.6), we notice that there exist two risk-taking distortions in a nancial network: (i) friction between banks and depositors, and (ii) a risk-taking externality among connected banks, which is the main focus of this paper. The rst distortion is known as the asset substitution problem of [50], who show that the level of debt nancing can encourage risk-taking. In the next section, I will show that the topology of the debt also matters for banks’ risk-taking even with the same level of total debt. 2.4 NetworkStructures 2.4.1 Sizeofinterbankliabilities So far, we have seen that a connected bank will endogenously expose to greater risks due to a network risk- taking distortion. Let’s now examine the extent of this network distortion for dierent network structures. 81 To begin with, I study in this section the eect of the interbank liabilities’ size d on the network risk- taking distortionD(Z i ) and the subsequent equilibrium risk exposureZ . I do so by xing the network topology . Lemma 3 shows the result. LEMMA 3. In any network structure ( d; ;N), the network risk-taking distortionD(Z i ; d) is increasing and concave in the size of interbank liabilities d. Proof. In the Appendix. To understand the intuition behind lemma 3, it is helpful to rst notice that there are three types of bank outcomes at the nal date. The rst type contains banks with successful projects. Denote themS ! fi :! i =sg. The second type contains banks that failed its project but are still “solvent” (can fully fulll their deposits). Denote themF + ! fi : ! i = f; P j ij d j (!) vg. Since those banks can fulll their deposits, they will contribute back to the interbank payment system. The third type contains banks that failed its project and cannot fully fulll their deposits. Denote themF ! fi :! i =f; P j ij d j (!)<vg and call them “insolvent” failed banks. The depositors of those banks will incur losses. In a network with larger interbank liabilities, successful banksS will expect larger net interbank pay- ments (cross-subsidies) to failed banks (F [F + ). Those cross-subsidies are due to the dierence between what a successful bank pays, d, and what it receives, P j ij d j (!). They are naturally increasing in the size of the interbank liabilities. As argued earlier, those cross-subsidies are the causes of the network risk-taking distortion. Therefore, the network risk-taking distortion is increasing in the size of interbank liabilities. On the other hand, the larger cross-subsidies also increase the likelihood for a failed bank to be solvent (F !F + ). A solvent failed bank will contribute back to the payment system, which in turn partially lowers the cross-subsidies that a successful bank needs to pay. As a result of the above two countervailing eects, the network risk-taking distortion is increasing (due to larger interbank payment) and concave 82 (due to more solvent failed banks) in the size of interbank liabilities. We can then apply lemma 3 to obtain the following equilibrium result on banks’ choices of risk exposure. PROPOSITION3. In any network structure ( d; ;N), each bank’s choice of risk exposureZ i is increasing in the size of interbank liabilities d. Proof. In the Appendix. Proposition 3 is an equilibrium result stating that banks will choose greater risk exposure if the net- work has larger interbank liabilities. The proof is a simple application of the monotone selection theorem. Lemma 3 shows that each bank will experience a larger risk-taking distortion resulting from a larger d. This will directly increase each bank’s choice of risk exposure. From the strategic complementarity result, every bank’s counterparties will also take greater risks, which in turn feedback to its risk-taking incen- tives. In equilibrium, a larger size of interbank liabilities will induce every bank in the network to expose to greater risks. From the concavity result of lemma 3, we know that the size of interbank liabilities has a diminishing marginal eect on connected banks’ risk-taking distortion. This implies that d will eventually cease to have an additional eect onD(Z i ; d) after a certain threshold. The following corollary formalizes this fact. COROLLARY2. In a network withN banks, (a) For any network topology , the network distortionD(Z i ) is bounded from above. (b) If the network is path-connected and symmetric, the upper bound is D max (Z i ) = N1 X f=1 f Nf v N 1 f h P (Z i ) i N1f h 1P (Z i ) i f (2.7) 83 Proof. In the Appendix. Part (a) states that there exists an upper bound for the network risk-taking distortion. We have shown that the network risk-taking distortion is the result of a bank’s expected “cross-subsidy” to failed banks’ depositors. That implies the distortion will stop increasing when the “cross-subsidy” can cover every connected bank’s deposits in every state of nature. Part (b) gives the analytical solution for this upper bound when the network is path-connected and symmetric. The maximum distortion in equation 2.7 has a clean interpretation. Suppose in some state of nature!, there aref number(s) of banks with failed projects and (Nf) number(s) of banks with successful projects. The maximum amount of money that needs to be bailed out isfv, the total amount of deposits from failed banks. Because of the symmetry, a successful bank is expected to cross-subsidize an amount offv=(Nf). The probability with whichf banks fail is N1 f [P (Z i )] N1f [1P (Z i )] f . Taking the expectation, we will have equation 2.7. It’s worth mentioning thatD max (Z i ) is independent of the network topology if the network is symmetric (e.g. ring or complete networks). 2.4.2 CompleteandRingNetworks Let’s now turn our attention to two particular network structures: the complete network and the ring network. The ex-post contagion of those two networks has been studied by [5] and [2] among others. Here we will study their eects on banks’ ex-ante risk-taking incentives. In a ring network, every bank is connected only to its direct neighbors. In a complete network, every bank is connected to every other bank. Denition 4 formalizes the above description. 84 DEFINITION 4. In a nancial network withN banks, a ring network and a complete network are dened as R = 2 6 6 4 0 0 N1 1 I N1 0 N1 3 7 7 5 and C = 1 N 1 (1 N;N I N ) where 0 N1 is a vector ofN 1 zeros,1 N;N is a matrix of ones with a dimension (N;N), andI is an identity matrix. Figure 2.2 illustrates a complete and a ring network with 5 banks. Figure 2.2: a complete and a ring network with 5 banks 1 2 3 4 5 d 21 = 0:25 d d 12 = 0:25 d (a) complete network 1 2 3 4 5 d 21 = d (b) ring network We observe that the total debt levels of banks in a complete and a ring network are identical: d+v. This implies that the conventional asset substitution model, as in [50], is not suited to study connected banks’ risk-taking incentives. With the help of my model, the following proposition compares banks’ equilibrium risk exposure in a complete and a ring network. PROPOSITION 4. In any network structure ( d;N), each bank’s choice of risk exposureZ i is larger in a complete network than in a ring network. Proof. In the Appendix. 85 The above proposition states that banks in a complete network choose greater risk exposure than banks in a ring network. The result stands in sharp contrast to the view of [5]. They argue that a complete network is better at co-insurance and hence more resilient. Instead, I show that such co-insurance also creates an ex-ante risk-taking distortion. Banks with successful projects will anticipate a greater amount of “cross-subsidy” to failed banks’ depositors. As argued earlier, due to such distortion, every bank will have an ex-ante incentive to expose to greater risks. As a result, in equilibrium, every bank in a complete network chooses a greater risk exposure. The same intuition can also be applied to networks with greater numbers of banks. Because the di- mension of N varies with N, the topology N+1 may not be well dened from an arbitrary N . I hence focus on the maximum risk-exposure of symmetric networks, which, according to corollary 2.(b), is independent of the network topology. PROPOSITION5. In any symmetric nancial networks, the upper bound for each bank’s risk exposureZ i is increasing in the number of banks,N, in the network. Proof. In the Appendix. Figure 2.3: Numerical Analysis (a) Benchmark 1 2 3 4 5 6 7 8 9 10 11 1 1.5 2 2.5 3 3.5 (b) DecreaseN 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 1 1.5 2 2.5 3 3.5 (c) With a CCP 1 2 3 4 5 6 7 8 9 10 11 12 1 1.5 2 2.5 3 3.5 Proposition 5 conrms our conjecture. Figure 2.3 illustrates the numerical analysis summarizing the eects of network topologies we have studied so far. Figure 2.3.(a) displays the benchmark case where 86 N = 10,v = 1, andP (Z i ) = 0:3. It plots the network risk-taking distortion against the size of interbank liabilities for a complete and a ring network. We observe that the network distortion is increasing and concave in the size of interbank liabilities, conrming proposition 3. We also see that the distortion is larger in a complete network (red) than a ring network (blue), conrming proposition 4. In gure 2.3.(b), I decrease the number of banks from 10 to 5, and we see that the maximum risk-taking distortion decreases for both the ring and the complete network, conrming proposition 5. 2.4.3 OtherRegularNetworks The machinery of networks also allows us to study the nancial structures that are widely observed in the current nancial systems, for example, central clearing counterparties (CCP). According to LCH-Clearnet, the world’s leading multinational clearinghouse, a CCP nets down payment obligations across all the cleared contracts to one payment obligation to the CCP per member. In other words, it acts as inter- bank debts’ buyer to all sellers and seller to all buyers. 12 This is equivalent to a core-periphery structure where the core acts as the clearing party with no asset and no outside liability. In this network, every bank has interbank claims and liabilities of size d to the core. Figure 2.4.(a) illustrates such a structure. The next proposition studies the risk-taking incentives for banks in networks with a CCP. 12 See LCH-Clearnet’s presentation to the Federal Reserve Bank of New York, https://www.newyorkfed.org/ medialibrary/media/banking/international/11-LCH-Credit-Risk-2015-Lee.pdf 87 Figure 2.4: Other Regular Networks 1 2 3 4 5 (a) central-clearing 1 2 3 4 5 d 21 = 0:85 d d 12 = 0:05 d (b) = 0:2 network 1 2 3 4 5 d31 = 0:5 d d21 = 0:5 d (c)r = 2 generalized ring network PROPOSITION6. In any network structure ( d; ;N) with a central clearing counterparty, the risk-taking equilibrium is equivalent to that of a complete network with ( N1 N d; C ;N). Proof. In the Appendix. From proposition 6, we observe that a CCP has two opposite eects on member banks’ risk-taking incentives. First, a CCP increases banks’ risk-taking incentives by increasing the network’s completeness. Through central clearing, each bank is “forced” to connect to every other bank and become exposed to their risk-taking externalities. This “CCP-riskier” eect is greater for a loosely connected ring network than a complete network, on which a CCP has no eect. Second, a CCP reduces banks’ risk-taking incentives by netting out some ex-post payment of interbank debts; it reduces the size of the connection from d to N1 N d. 13 . This eect is equivalent the netting eciency considered by [27]. 14 Summing up the two forces, the eect of a CCP on banks’ risk exposure depends on the banking system’s original network topology. 13 To illustrate this point, suppose there are four banks. In one state of nature, three succeed, and one fails. Suppose the failed bank is “insolvent”. In this case, the distortion for a successful bank in a complete network is d 2 1 3 d = 1 3 d. However, the distortion for a successful bank in a network with a CCP is d 3 1 4 d = 1 4 d 14 [27] study the CCP’s ex-post netting eciency by treating banks’ defaults as unrelated events. The netting eciency in my model is a (generalized) version of theirs after considering the joint determination of defaults using the technique of [28]. 88 Figure 2.3.c illustrates the eects of a CCP on a complete and a ring network. We obverse that the eect depends on the original network’s topology. For a complete network, a CCP can decrease the network risk- taking distortion. This is because banks in a complete network enjoy more of CCP’s netting eciency. However, for a ring network with a modest d, a CCP increases the network risk-taking distortion. This is because the CCP “forces” each member bank to be exposed to every other bank’s risk-taking externalities. This implies, for loosely connected networks, the “CCP-riskier” dominates. In those cases, a CCP can create systemic instability, in contrast to conventional wisdom. Notwithstanding greater risk exposure, banks still have incentives to join a CCP if they care suciently about their charter values. That is because a CCP can increase the likelihood of their depositors being paid in full. Section 2.5.1 will discuss this point in greater detail. Figure 2.5: Intermediately Connected Networks (a) networks (b) generalized ring networks We have studied the risk-taking externalities for banks in two extreme networks: a fully-connected complete network and a loosely-connected ring network. Proposition 4 shows that banks in a com- plete network will choose greater risks than banks in a ring network. One may think that banks in an intermediately-connected network will choose a risk-exposure somewhere between the risk exposure of a complete and a ring network. The basis for this conjecture relies on the fact that the payment equilibrium 89 of an intermediately-connected network is between that of a complete and a ring network, as shown by [28] and [2]. 15 However, this is not true for the network risk-taking externalities. There are two ways to dene an intermediately-connected network. A network is the convex com- bination of a ring and a complete network: = (1) R + C . According to [29], can be interpreted as a nancial network’s degree of diversication. From this deniteness, = 0 is a ring net- work and = 1 is a complete network. Another way to dene an intermediately-connected structure is from the generalized ring network: each bank connects tor number of adjacent neighbors. From this deniteness,r = 1 is a ring network andr =N1 is a complete network. Figure 2.4.(b) and (c) displays a = 0:2 network and ar = 2 generalized ring network. To illustrate the relationship between a network’s degree of connectedness and the risk-taking distortion it induces, Figure 2.5 displays the distortion for dierent parameter values of,r, and d for an 8-bank network. Online Appendix provides a numerical example. We notice that when d is low, the network distortion is increasing in both andr. This is because a higher degree of connectedness increases a bank’s exposure to more counterparties’ risk-taking exter- nalities. This is consistent with the ndings of [28] and [2], who show that the payment equilibrium is increasing in. However, when d is large, the network distortion is not monotone in either orr. In this case, a network or ar generalized ring network may have a lower network distortion than a ring network. This is because as orr increases, banks become less sensitive to particular other banks’ risk- taking externalities. This non-monotonicity result is consistent with the observation of [29], who show that contagion is most likely to occur when integration (similar to d) and diversication (similar to) are in the middle range. Finally, if d is large enough such that all failed banks’ depositors can be repaid, the degree of connectedness orr is irrelevant (corollary 2.b). 15 See [28] lemma 6 and [2] proposition 4. To see why, suppose an intermediately-connected network has a that is the- convex combination of a ring and complete network. Because the RHS of equation 2.2 is monotone in, the xed point solution is monotone in. 90 2.4.4 Non-regularNetwork: EuropeanDebtCross-HoldingExample So far, the analysis has focused on regular networks where all banks’ total interbank liabilities and claims are equal. Nevertheless, the model’s tractability allows us in addition to study other types of networks, including those observed in the real world. In this section, I use the European debt cross-holding of [29] as an example to illustrate the risk-taking equilibrium when countries are interconnected. The example serves to give conceptual insight and is based on simplied estimates. The objective of this section is to show how systemic risks can endogenously evolve in a nancial network. The nancial network consists of six European countries’ banking systems: France, Germany, Greece, Italy, Portugal, and Spain. The data on the countries’ cross-holdings of debt is directly taken from [29], who collected the information from the BIS Quarterly Review. I also use their estimate that a country’s debt held internally is two-thirds of its total debt. To normalize the scale of the economy, I use 20 years of each country’s GDP as the denominator. 16 The idea is to let each country choose a safe or risky economy with a 0.95 discount factor. The resulting network structure is given by = 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 0 0:41 0:47 0:66 0:16 0:37 0:70 0 0:39 0:27 0:23 0:47 0:01 0:01 0 0:00 0:00 0:00 0:16 0:47 0:03 0 0:02 0:09 0:03 0:00 0:10 0:00 0 0:07 0:11 0:11 0:01 0:06 0:59 0 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 d = 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 0:004 0:007 0:015 0:011 0:027 0:011 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 v = 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 0:009 0:013 0:029 0:022 0:054 0:021 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 To interpret the above matrices, 21 = 0:70 means that France owes Germany 70% of France’s total interbank debt, which is d 1 = 0:438% of France’s 20-year GDP. This means that France owes Germany $175 trillion ($2.861 trillion200:438%70%). It’s worth noting that the network is non-regular in that 16 The GDP is measured in 2011, to be consistent with the cross-holding data. They are $2.861 trillion, $3.744 trillion, $287.8 billion, $2.292 trillion, $244.8 billion, and $1.479 trillion, respectively. 91 a country’s total inter-country debt does not equal to its inter-country liability. To study the risk-taking incentives of each banking system, let each country choose a risk structure consisting of one of the two following choices. safe economy = 8 > > < > > : 1 w.p 1 0 w.p 0 risky economy = 8 > > < > > : 1:1 w.p P risky 0 w.p 1P risky There are two choices for each country’s banking system. Choosing a safe economy guarantees the country no economic shock. Choosing a risky economy will increase the country’s output by 10% but reduces the certainty toP risky . By construction, if a country is debt-free, it will choose a safe economy ifP risky < 1=1:1. For dierent values ofP risky , I will explore each country’s choice of the economy on scenarios when they are (i) interconnected; (ii) stand-alone, or (iii) debt-free. To construct the counterfac- tual scenario where each country is stand-alone, I net-out each country’s inter-country debt and add this to its internal debtv. The following table displays the identity of countries that choose the safe economy for dierent values ofP risky , ranging from 90.2% to 91%. Countries that Choose Safe Economies P risky 90.20% 90.60% 90.90% 91.00% (i) interconnected All All except Greece and Portugal None None (ii) stand-alone All All except Greece and Portugal France None (iii) debt-free All All All None We rst observe that, asP risky grows, it becomes less attractive for countries to choose safe economies for every scenario. This is because the risky choice’s fundamental becomes better. We also see that coun- tries choose safer economies when they are debt-free. This reects the canonical asset substitution problem that arises from debt nancing [50]. Greece and Portugal are more subject to this risk-shifting due to their 92 large amount of debt. More interestingly, countries choose riskier economies if they are connected com- pared with if stand-alone, conrming corollary 1. IfP risky = 90:90%, France chooses a safe economy when it is stand-alone, but a risky economy when it is connected. Intuitively, France anticipates its cross- subsidies to Greece and Portugal and optimally increases its own risk exposure. This illustrates the concept of endogenous systemic instability resulting from the network risk-taking distortion. 2.5 ExtensionandPolicyImplications In this section, I will rst illustrate why banks have incentives to form a network in the rst place. In other words, I will show why banks do not want to net out of their interbank claims and liabilities. 17 Then I will extend the benchmark model to study several widely adopted prudential policies that aim at stabilizing the nancial system. Understanding the network eects of those government policies is particularly important in the current growingly connected nancial systems. 2.5.1 Banks’IncentivestoFormNetworks A natural question is why banks have incentives to form a network in the rst place. In fact, in the bench- mark model, a successful bank paysD(Z i ) as cross-subsidies to its counterparties. It does not benet from those cross-subsidies when it fails. In this section, I will illustrate that banks, possessing valuable expected present value of their future prots (charter values), do have incentives to form interbank con- nections, notwithstanding the risk-taking distortion. The introduction of banks’ charter values is relevant to their risk-taking incentives. 18 It also describes reality well: in nancial systems with deposit insurance, 17 The literature has proposed several reasons. [1] argue that banks may form interbank claims and liabilities because they have heterogeneous investment opportunities. [25] argues that the interbank debts embed the option to dilute with new debt to a third party. In this section, I will show that banks have incentives to form networks for co-insurance purposes. 18 For example, [44] show that reducing banks’ charter values can create instability. 93 regulators (e.g., the FDIC in the U.S.) seize insolvent banks and put them into receivership. 19 As a result, banks do not want to risk defaulting on their deposits to protect their continuation values. To model this, letc i 2R + denote banki’s charter value. 20 The bank can preserve this charter value if and only if its depositors get paid in full, either through its own project or other banks’ cross-subsidies. From here, we can rewrite banki’s expected payo as E h i (!;Z) i =P (Z i ) h Z i vD(Z i ) i +c i h 1P (Z i ) i Pr i2F ! j! i =f c i | {z } expected charter value (2.8) =P (Z i ) h Z i vD(Z i ) + Pr i2F ! j! i =f c i i +c i Pr i2F ! j! i =f c i whereF ! fi : ! i = f; P j ij d j (!) < vg denotes the set of insolvent banks – the ones that cannot adequately reimburse their depositors. Thus Pr(i2F ! j! i =f) is the probability that banki is insolvent given that its project fails. For example, if it is in a “fully” connected nancial network as in corollary 2.(b), Pr(i2F ! j! i = f) = Q j6=i 1P (Z j ). It means that banki will become insolvent and lose its charter value only when all of its counterparties fail in addition to its own failure. In contrast, if banki is stand- alone, it will lose its charter value simply when its own project fails. This implies that a stand-alone bank has an expected payo ofE h SL i (!;Z) i =P (Z i )(Z i v)+P (Z i )c i . Comparing this with equation 2.8, we observe that being in a nancial network can increase the probability of a bank being solvent, hence protecting its charter value. BecauseD(Z i ) + Pr(i2F ! j! i =f)c i <c i , we can verify that corollary 1 still holds: connected banks choose greater risk exposure than stand-alone banks. Intuitively, there are two forces that make a connected bank choose greater risks: (i) a network risk-taking distortion as in the benchmark model, and (ii) a downside protection from the nancial network’s co-insurance. The second force is new here due to 19 During the global nancial crisis of 2008, FDIC seized over 500 banks. For example, Washington Mutual, the sixth-largest bank in the United States at the time, ceased to exist after FDIC placed it into receivership. 20 For expository purpose,ci is assumed to be exogenous. One can micro-foundci as banki’s discounted future payo streams: ci ==(1)E[i]. The result is not driven by this abstraction. 94 the introduction of banks’ charter values. Both forces induce banks to become less interested in increasing the probability of success, hence creating systemic instability. Let’s now examine whether banks have incentives to form interbank connections in the face of the network risk-taking distortion. From banki’s expected payo, it will prefer to form the connection (over stand-alone) if P (Z i ) h Z i vD(Z i ) i +c i h 1P (Z i ) i Pr i2F ! j! i =f c i >P (Z i ) h Z i v +c i i (2.9) whereZ i is equilibrium risk-taking of a bank in the network: Z i = argmaxE h i (!;Z ) i , andZ i is the optimal risk-taking of a stand-alone bank: Z i = argmaxP (Z i )(Z i v +c i ). The next proposition shows that condition 2.9 is possible if banks care suciently about their charter values. PROPOSITION7. Thereexists c2R + ,suchthatif minfc i g> c,bankshaveincentivestoformanetwork. Proof. In the Appendix. To decide whether to form a network, banks face three considerations : (i) protection of their charter values, (ii) cross-subsidyD(Z i ), and (iii) distorted investmentZ . On the one hand, being in a network can protect banks from losing their valuable charter values, as it provides co-insurance to their depositors. On the other hand, due to this co-insurance, banks expect to cross-subsidize other banks, decreasing their upside payos. This also distorts investment and results in systemic instability. Proposition 7 states that banks will form an interbank network if they care suciently about their charter values. The proposition is silent on the optimal topology that banks want to connect. A natural direction for further research is to fully endogenize the network formation while taking into account the risk-taking externalities. 95 2.5.2 CapitalRequirement So far, we have been studying banks’ risk-taking equilibrium in nancial networks where banks do not hold any equity. Since the 1980s, regulators began using capital adequacy requirements to ensure that banks do not take excessive risks [42]. With more “skin in the game”, banks are less willing to gamble with their equity [50]. In this section, I will extend the benchmark model to study the network eects of banks’ capital when connected in nancial networks. Now suppose each bank is required to hold equity of sizer i =r. The amount of deposits that a bank needs to borrow decreases tovr. Let’s assume equity is junior to both deposits and interbank liabilities. That implies when a bank’s total cash ow is smaller than its total liabilities, equity holders will be the rst to incur a loss. As a result, the payment equilibrium becomes d i (!;r) = ( min h X j ij d j (!;r) +e i (Z;!)v +r; d i ) + 8i (2.10) The expected prot becomes E h i (!;Z) i =P (Z i )(Z i v +r)P (Z i )D(Z i ;r) (2.11) where D(Z i ;r) X ! i d X j ij d j (!;r) Pr(! i ) We notice that equity enters a bank’s expected payo in two ways: the upside payo (Z i v +r) and the network risk-taking distortionD(Z i ;r). The next proposition studies how an equity buer will aect the network risk-taking distortion. 96 LEMMA4. Inanynetworkstructure( d; ;N;r),thenetworkrisk-takingdistortionD(Z i ;r)isdecreasing and concave in the size of equity buersr. Proof. In the Appendix. If a bank fails, its equity holders will rst incur the loss before its depositors or interbank counter- parties. The loss that may be otherwise propagated to other banks will now be absorbed by this equity buer. In other words, the equity buer decreases the cross-subsidy that successful banks pay to failed counterparties. The network risk-taking distortion is hence reduced. Moreover, with greater equity, failed banks are more likely to become solvent, hence contributing back to the payment system. This further reduces successful banks’ cross-subsidy to other failed banks. As a result, the network risk-taking distor- tion is decreasing at a growing rate in the size of an equity buer. Figure 2.6 plots the network risk-taking distortion against the size of the equity buer. Lemma 4 immediately implies that banks’ equilibrium risk exposure will be reduced by an equity buer. Figure 2.6: Equity Buer 0 0.2 0.4 0.6 0.8 1 1.2 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 PROPOSITION8. Inanynetworkstructure( d; ;N;r),eachbank’schoiceofriskexposureZ i isdecreasing in the size of equityr. 97 Proof. In the Appendix. There are two eects of an equity buer on banks’ choices of risk exposure. First, an equity buer has a direct impact on a bank’s risk-taking. A bank will choose to expose to fewer risks if it has a higher equity ratio: it is unwilling to gamble if there is more “skin in the game” [50]. More interestingly, lemma 4 shows that equity buers have a network eect on reducing systemic risks. An equity buer curbs failed banks’ loss at the origin, hence mitigating the network risk-taking distortion. This implies that one bank’s equity can reduce the risk-taking incentives of its counterparties. Moreover, the strategic complementarity implies that reducing a bank’s risk-taking will, in return, reduce other banks’ risk-taking. The nding suggests that when deciding banks’ capital requirement, policymakers should consider not only its eect on a bank’s own “skin in the game” but also the network eect on the bank’s counterparties. A recently proposed rule by FRB and OCC steps in this direction by tailoring leverage ratio requirements to banks’ systemic footprint. The result is also related to [32], who also study the network response of capital regulation. They show that a capital requirement can discontinuously discourage interbank connections, hence reducing the ex-post co-insurance benets. Combining our results, a tighter regulation can, on the one hand, decreases the interbank network’s risk-taking externalities. On the other hand, it can also break the interbank connections if beyond a tipping point. This implies that the eect of capital requirement on systemic stability may exhibit a phase transition. 2.5.3 GovernmentBailout The 2008 bailout of Bear Stearns and the subsequent Troubled Asset Relief Program (TARP) have sparked continuing debates among both policy-makers and academics. Government bailouts have been widely argued to incentivizes harmful ex-ante behaviors [39, 34, 31]. In this section, I will study the eect of a government bailout on banks’ ex-ante risk-taking incentives when connected in nancial networks. 98 Similar to [31], I assume government bailouts only occur in crisis when a large number of banks have failed. 21 I dene a government bailout (n;t) as a transfert from the government to each failed bank if the number of failed banks exceedsn. With the government bailout in place, the payment equilibrium becomes d i (!;Z) = ( min h X j ij d j (!;Z) +e i (! i ;Z i ) +t i (!)v; d; i ) + 8i2N 8!2 (2.12) where the transfer is state-contingent and is dened as t i (!)t1(! i =f)1(# failed banksn) The rest of the denition for the network risk-taking equilibrium remains unchanged from equation 2.4. The following proposition shows that a government bailout can contribute to systemic stability by reducing the network risk-taking distortion. PROPOSITION9. Inanynancialnetwork( d; ;N),eachbank’snetworkrisk-takingdistortionandequi- librium risk exposure is reduced if there exists a government bailout. Proof. In the Appendix. In contrast to the conventional wisdom, proposition 9 states that a credible government bailout can in- stead discourage ex-ante risk-taking. During Crises, a government bailout can curb the loss before spread- ing to successful banks. The network risk-taking distortion resulting from cross-subsidy is hence reduced. This will encourage connected banks to reduce their choices of risk exposure. 21 This denition is consistent with section 101 of the 2008 Emergency Economic Stabilization Act (EESA). It states “TARP was only part of the government’s response to the crisis” and is “to restore liquidity and stability to the nancial system”. See https://www.treasury.gov/initiatives/nancial-stability/about-tarp. 99 Proposition 9 stands in contrast to [31], who show that a government bailout can create systemic in- stability by encouraging excessive network formation. In his model, banks will not worry about contagion during network formation if there exists a government bailout. In contrast, this paper shows that because banks do not worry about the cross-subsidy, they will be subject to less network risk-taking externalities. While both eects (excessive network formation and less risk-taking externalities) are reasonable, the net eect of a government bailout is an empirical question. 2.6 CorrelatedRiskExposure In previous sections, we assumed that banks’ project outcomes are independent. While this is a reasonable assumption for local banks serving mortgages in dierent regions, large national banks’ portfolios may be well correlated. In this section, I model each bank’s decision whether to expose to correlated risks and explain why a systemic crisis can endogenously evolve due to interbank connectedness. Suppose each bank, besides choosing its project outcome’s marginal distributionP (Z i ), also chooses its conditional distribution i = [ 1 ;::::; N ] on the project outcomes of other connected banks in the network. Dene the matrix [ ij ] as ij Pr(! i =sj! j =s) where 0 i 1. We can interpret ij as bank i’s choices of correlation with bank j. This notion of pairwise conditional probabilities matrix was proposed in the IMF’s Global Financial Stability Review (2009) and later utilized by [10]. From the above denition, the pairwise correlation between banki andj’s projects is ij ij P (Z j )P (Z i )P (Z j ) P (Z i ) 1=2 P (Z j ) 1=2 [1P (Z i )] 1=2 [1P (Z j )] 1=2 100 In contrast to the benchmark model, each banks’ project outcomes are no longer independent. Bank i’s expected prot becomes E h i (!;Z i ; i ) i =P (Z i )(Z i v) X ! i d X j ij d j (! i=s ) Pr(! i ) Pr(! i =sj! i ) The above equation uses the property Pr(! i=s ) = Pr(! i ) Pr(! i =sj! i ). The dependence vector i enters the last term. DEFINITION5. Thecorrelatedrisk-takingequilibriuminanancialnetwork( d; ;N)isatriplet (d (!;Z);Z ; ) consistingofavectorofpaymentfunctionsd (!;Z),avectorofriskexposureZ ,andamatrixofconditional distribution [ ij ] such that: 1. The vector of functionsd (!;Z) is a payment equilibrium for anyZ. d i (!;Z) = ( min h X j ij d j (!;Z) +e i (! i ;Z i )v; d; i ) + 8i2N 8!2 2. For each banki2N, (Z i ; i ) is optimal and solves the following equation, givend (!;Z),Z i and i (Z i ; i ) = argmax ZZ i Z 0 i 1 E h i (!;Z i ; i ) i 8i2N 3. The pairwise correlations are compatible among all banks. i.e. = [ ij ] is symmetric and positive semi-denite. Part 2 of the above denition implies that banks are unrestricted in choosing their conditional depen- dence with their counterparties. Any bank can choose a project that is arbitrarily correlated with any other bank: a notion similar to [22]. However, part 3 of the above denition states that the conditional 101 dependence has to be mutually and jointly compatible in equilibrium. 22 Part 3 also implies ij = ji = P (Z i )=P (Z j ) for alli;j. This shows a dependence between andZ. In equilibrium, the marginal and conditional distribution should also be compatible. PROPOSITION 10. In any network structure ( d; ;N), the correlated risk-taking equilibrium exists and every bank’s risk exposure is perfectly correlated: ij = 1 for alli;j2N. Proof. In the Appendix. Proposition 10 states that connected banks will coordinate to expose to one single systemic risk. In anticipation of the interbank transfers (cross-subsidy) to failed banks, each bank will optimally align their project outcomes with other connected banks, for any chosen risk exposure. By doing so, there will be no downward distortion when the bank’s project succeeds, and hence each bank will enjoy a higher expected prot. The perfect correlation, however, will be harmful to the economy as a whole. Since every bank chooses to exposure to one single systemic risk, there is no co-insurance among economic agents. Proposition 10 predicts that a nancial crisis will be more likely to endogenously evolve in a highly connected banking system. It conrms the empirical ndings of [47] and [10] that there existed a large distress dependence among major banks before the 2008 nancial crisis when the banking system became unprecedentedly connected. The result is also consistent with the observation of [3], who argues that banks choose correlated investments due to a pecuniary externality: a failed bank reduces counterparties’ protability through an increase in the market-clearing rate for deposits. The result is also related to recent papers such as [30] and [49]. Using data on German banks, [30] illustrate banks’ incentive to form partners with similar portfolios. [49] show that banks have incentives to minimize the set of states where they pay debts and have have their values diluted. 22 For example,ij = 1 andji = 0 is not compatible because ( 1 1 0 1 ) is not symmetric. For another example,ij = 1, jk = 1, ik = 0 is not compatible because 1 1 1 1 1 0 1 0 1 is not positive semi-denite. 102 2.7 DiscussionandConcludingRemarks This paper studies banks’ incentives to choose their risk exposure in nancial networks, where banks are connected through cross-holdings of unsecured debts. In contrast to previous literature that focuses on the co-insurance mechanism for exogenous shocks, I show that connected banks ex-ante choose to expose to greater risks. In addition, they choose to expose to correlated risks, aggravating the systemic fragility. Nevertheless, banks do have incentives to form a network as it provides co-insurance to their charter values. This paper brings about several testable empirical predictions. For example, the strategic complemen- tarity result suggests that an individual bank’s risk-taking is positively related to the risks of the entire nancial system. This is exactly what [67] have found. Using granular bond portfolio of EU banks, they nd that regulatory solvency shocks (proxied by the banking system’s tier 1 capital ratio) can induce banks to shift into riskier assets (higher-yielding sovereign debt) and correlated assets (domestic bonds). Another interesting real-world example of nancial networks is the credit union industry. Individual natural person credit unions (NPCU), like community banks, make loans to and take deposits from local consumers. Geographically proximate NPCUs often form interbank networks through a corporate credit union (CCU), commonly referred to as “the credit union’s credit union”. 23 One empirical prediction of this paper is that the NPCUs in highly connected CCUs choose riskier loan portfolios. By studying banking networks, this paper sheds new insights on several government policies. For example, the paper formalizes the conjecture that a CCP, although providing co-insurance to its member banks, can create moral hazard and systemic instability. The model also suggests that capital regulation should consider banks’ systemic footprint. However, the paper does not aim to design actual government 23 In 2005, there were around 7500 NPCUs and 26 CCUs. For more details about NPCUs and CCUs, see [70]. They also document that geography proximity is an important factor in explaining the topology of CCUs, lending variations for empirical identication. 103 policies or provide a holistic study of each particular policy. A natural step for further research is to examine how interbank connectedness can aect dierent aspects of government policies. 104 PROOFS PROOF OF LEMMA 2: From the assumptionZ v + d, a successful bank’s interbank payment isd i = d, inde- pendent of its choice of risk exposureZ i . A failed bank’s cash ow that will contribute to the interbank payment system ise i = 0, also independent of its choice of risk exposure. Reordering equation 2.2 gives us, d i (!;Z) = d 8! i =s d i (!;Z) = ( X j ij d j (!;Z)v ) + 8! i =f (2.13) We can see that the vector of risk exposureZ does not enter the system of equations. As a result, the xed point (d 1 (!);:::d N (!)) is constant inZ. Before proving proposition 1, it is useful to have the following auxiliary lemma. AUXILIARY LEMMA: the payment vectord is weakly increasing in any bank’s cash ow ~ e j . In particular,d (!) is higher when any bank’s project succeeds (! j =s) compared with when it fails (! j =f). 24 Proof. The above lemma is identical to Eisenberg and Noe (2000) Lemma 5. The payment equilibrium (equation 2.2) is a xed point solution of a functiond = (d ; ~ e j ). Since both min and max operator preserve monotonicity, is increasing in ~ e j . By monotone selection theorem (Milgrom and Roberts, 1990 Theorem 1), the xed pointd is increasing in ~ e j . PROOFOFPROPOSITION1: Taking the rst- and second-order conditions of the equation 2.6, we have F (Z i ;Z i ) =P 0 (Z i )(Z i v) +P (Z i )P (Z i ) 0 D(Z i ) = 0 S(Z i ;Z i ) =P 00 (Z i )(Z i v) + 2P 0 (Z i )P (Z i ) 00 D(Z i )< 0 24 Throughout this paper, whenever the ordering of a vector is mentioned, it refers to a pointwise ordering. i.exy,xi yi for alli. For the following text, all orderings are weakly. 105 From assumption 1, we obtainS(Z i ;Z i )< 0. From the total derivative of the FOC, we have d b Z i dD(Z i ) = @F ( b Z i ;Z i )=@D(Z i ) @F ( b Z i ;Z i )=@Z i = P 0 ( b Z i ) S( b Z i ;Z i ) > 0 (2.14) The above inequality implies that whatever increasesD(Z i ) will increase bank i’s optimal b Z i . Intuitively, the distortionD(Z i ) decreases banki’s upside payo (the payo when its project succeeds). As a result, it will make banki care less about the probability of success when trading o risk and return. To see the eect from bankm’s risk exposureZ m on banki’s risk-taking distortionD(Z i ), let’s vary it from Z m toZ 0 m withZ 0 m > Z m . LetZ 0 i denote the new risk-exposure vector that diers fromZ i only inZ m . We have D(Z 0 i )D(Z i ) = X ! im Pr(! im ) h P (Z 0 m ) d X j ij d j (! m=s ) + 1P (Z 0 m ) d X j ij d j (! m=f ) i X ! im Pr(! im ) h P (Z m ) d X j ij d j (! m=s ) + 1P (Z m ) d X j ij d j (! m=f ) i = X ! im Pr(! im ) h P (Z 0 m )P (Z m ) X j ij d j (! m=f ) X j ij d j (! m=s ) i 0 (2.15) With slight abuse of notation,! im denotes a vector of! without the elementi andm,! m=s denotes a vector that appends! im with! m = s and! i = s, and! m=f denotes a vector that appends! im with! m = f and! i =s. The last inequality is from the auxiliary lemma. The inequality states that banki’s risk-taking distortion is increasing in bankm’s risk-exposure. To see the intuition, suppose bankm has a greater risk exposureZ m , its project becomes more likely to fail. When bankm’s project fails, banki’s net interbank payments to other banks will increase due to a greater amount of cross-subsidy. Finally, joining equation 2.14 and 2.15, we have d b Z i dZ i = d b Z i dD(Z i ) dD(Z i ) dZ i > 0 8i and i 106 PROOF OF PROPOSITION 2: The payment equilibrium in any state of nature is the xed-point solution to a system of equations (equation 2.13). Denote the xed point asd = (d ), where a continuous mapping with a convex and compact domain [0; d] N . By the Brouwer xed point theorem, the payment equilibriumd (!;Z) exists for all! andZ (Eisenberg and Noe, 2001). This establishes the existence of the payment equilibrium for all! and Z. From proposition 1, d b Z i =Z i 0 for alli andi. It implies the Nash equilibrium is a supermodular game. The domain for the risk-exposure vector [Z; Z] N is a complete lattice. By Tarski’s theorem, the xed-point solution to the rst order conditionsF (Z i ;Z i ) = 0 exists. The equilibrium risk exposureZ = (Z 1 ;:::;Z N ) is this xed point. PROOFOFCORROLARY1: DenoteZ N andZ S as the equilibrium risk exposure of a bank in a nancial network and a stand-alone bank respectively. Formally, they are the solutions to their respective rst order conditions, i.e. P 0 (Z N )(Z N v) +P (Z N )P (Z N ) 0 D(Z N ) = 0 P 0 (Z S )(Z S v) +P (Z S ) = 0 By equation 2.14, dZ N =dD(Z N )> 0. We also know that the distortionD(Z N ) is positive becauseP (Z j )< 1 for allZ j . Therefore,Z N >Z S . PROOF OF LEMMA 3: For any state of nature!, conjecture that there exists two vectors,a(!) andb(!), such thatd i (!) =fa i (!) db i (!)vg + . By denition, they should satisfy equation 2.13. After plugginga(!) andb(!) into equation 2.13, we have (a i ;b i ) = (1; 0)8! i =s, and d i (!) = ( X !j=s ij d + X j2F + ! ij a j (!) db j (!)v v ) + = ( X j2F + ! ij a j (!) + X !j=s ij d X j2F + ! ij b j (!) + 1 v ) + 8! i =f 107 whereF + ! fi : ! i = f;a i db i v 0g. We call it “solvent” failed banks. Similarly, deneF ! fi : ! i = f;a i db i v< 0g as the “insolvent” failed banks, andS ! fi :! i =s) as successful banks. Per the conjecture, we need8! i 2f, a i (!) = X j2F + ! ij a j (!) + X !j=s ij (2.16) b i (!) = X j2F + ! ij b j (!) + 1 (2.17) Since the RHS of above equations are increasing ina(!) andb(!) respectively, the xed points exist by the Tarski’s theorem. The conjecture is hence veried. Let’s rewrite the above equations in a matrix form for banks in F + ! . a + (!) = ++ a + (!) + +s 1 s (2.18) b + (!) = ++ b + (!) +1 + (2.19) wherea + (!) andb + (!) are truncated vectors ofa(!) andb(!) with rows that belong toF + ! . Similarly, ++ is a truncated matrix of with rows and columns that belong toF + ! , and +s is the truncated matrix of where each row belongs toF + ! and each column belongs toS . 1 + and1 s are column vectors of ones with appropriate dimension. Note that ++ , +s ,1 + , and1 s are all state-contingent. To conserve space, I suppress their underscript !. By the Markovian property of (row-sum equals to one), we have ++ 1 + + + 1 + +s 1 s = 1 + . By equation 2.18 a + (!) = (I + ++ ) 1 +s 1 s <1 + (2.20) 108 After plugging (a + ;b + ) into the network risk-taking distortion, We can rewriteD(Z i ) in a matrix form as D(Z i ) = X ! i Pr(! i ) h d is 1 s d + i+ (a + db + v) + i 0 i = X ! i Pr(! i ) h i+ (1 + a + ) d +b + v + i 1 d + is 1 s 0 i (2.21) Each part of the above denition has a clean interpretation: i+ [(1 + a + ) d +b + v] is banki’s subsidy to “solvent" failed banks , i 1 d is banki’s subsidy to “insolvent" failed banks, and is 1 s 0 is banki’s subsidy to successful banks. To prove lemma 3, compare three nancial networks with same andN but dierent interbank liabilities d 1 , d 2 , and d 3 , with d 3 d 2 = d 2 d 1 =". To prove the monotonicity and concavity, it suces to proveD 3 (Z i ) D 2 (Z i )D 1 (Z i ) andD 2 (Z i )D 1 (Z i )D 3 (Z i )D 2 (Z i ) with inequality happens somewhere. Observe thatF + ! fi : ! i = f;a i db i v 0g is a function of d. We hence denoteF + 1 (!),F + 2 (!), and F + 3 (!) the set of “solvent” failed bank in state! for network ( d 1 ; ;N), ( d 2 ; ;N), and ( d 3 ; ;N) respectively. By monotone selection theorem (see auxiliary lemma), d 3 i (!) d 2 i (!) d 1 i (!);8i2N and!2 . That impliesF + 1 (!)F + 2 (!)F + 3 (!) for all!2 . It means that increasing d can make more failed banks “solvent”. Let’s consider the following four cases: (1)F + 1 (!) =F + 2 (!) =F + 3 (!) for all!. (2)F + 1 (!)F + 2 (!) = F + 3 (!) for some!. (3)F + 1 (!) =F + 2 (!)F + 3 (!) for some!. (4)F + 1 (!)F + 2 (!)F + 3 (!) for some!. Case I:F + 1 (!) =F + 2 (!) =F + 3 (!) for all! From equation 2.18 and 2.19, it’s easy to see thata 1 + =a 2 + =a 3 + andb 1 + =b 2 + =b 3 + . We also have i+ ,1 + , i , and1 unchanged for the three networks. Therefore, D 3 (Z i )D 2 (Z i ) = X ! i Pr(! i ) h i+ (1 + a + )( d 3 d 2 ) + i 1 ( d 3 d 2 ) i > 0 D 2 (Z i )D 1 (Z i ) = X ! i Pr(! i ) h i+ (1 + a + )( d 2 d 1 ) + i 1 ( d 2 d 1 ) i > 0 109 The last inequality is due to equation 2.20. With d 3 d 2 = d 2 d 1 = ", we haveD 3 (Z i )D 2 (Z i ) = D 2 (Z i )D 1 (Z i )> 0. Intuitively, this case means that the network risk-taking is linearly increasing in d, if the change of d does not make additional “insolvent” banks “solvenet”. Case II:F + 1 (!)F + 2 (!) =F + 3 (!) for some!. We rst compare the interbank liabilities d 2 with d 1 . In some state of nature!, some otherwise “insolvent” failed banks for ( d 1 ; ;N) become “solvent” for ( d 2 ; ;N). Denote those banks t 1 ;t 2 ;:::;t T , where T 1. Due to continuity of the payment equilibrium in terms of d (equation 2.2). There exists d 1 < ~ d 1 < ~ d 2 ::: < ::: < ~ d S < d 2 (where 1 S T ), such that when the interbank liabilities d = ~ d s , some bank t t is exactly “solvent", or ~ a t (!) ~ d s ~ b t (!)v = 0. In other words, this margin bankt is “solvent” when d2 [ ~ d s ; ~ d s+1 ) and “insolvent” when d2 ( ~ d s1 ; ~ d s ] respectively. Denote e D s (Z i ) the network risk-taking distortion at those cut-os ~ d s . We have D 2 (Z i ) e D S (Z i ) = X ! i Pr(! i ) h 2 i+ (1 + a 2 + )( d 2 ~ d S ) + 2 i 1 ( d 2 ~ d S ) i > 0 e D s+1 (Z i ) e D s (Z i ) = X ! i Pr(! i ) h e s i+ (1 + ~ a s + )( ~ d s+1 ~ d s ) + e s i 1 ( ~ d s+1 ~ d s ) i > 0 e D 1 (Z i )D 1 (Z i ) = X ! i Pr(! i ) h 1 i+ (1 + a 1 + )( ~ d 1 d 1 ) + 1 i 1 ( ~ d 1 d 1 ) i > 0 (2.22) where each column of 1 i+ corresponds to an “solvent” failed bank at the state! in a network with d2 [ d 1 ; ~ d 1 ]. Each column of e s i+ corresponds to an “solvent” failed bank at the state! in a network with d2 [ ~ d s ; ~ d s+1 ]. Each column of 2 i+ corresponds to an “solvent” failed bank at the state! in a network with d2 [ ~ d S ; d 2 ]. The same notation applies toa + and e i as well. They are state-contingent, and to conserve space we suppress the underscript. 110 The above inequalities show thatD 2 (Z i ) e D S (Z i )::: e D 2 (Z i ) e D 1 (Z i )D 1 (Z i ) and hence the monotonicity result follows. To prove the concavity, we observe that e s i+ 1 + + e s i 1 = if 1 f for alls and !. By denition, e s i+ and ~ a s + are sub-matrix of e s+1 i+ and ~ a s+1 + respectively. Hence we have e s i+ (1 + ~ a s + ) + e s i 1 > e s+1 i+ (1 + ~ a s+1 + ) + e s+1 i 1 8s = 1;:::;S 1 After summing every dierence in equation 2.22 and replacing all of RHS with the rst line, i.e. the smallest, we have D 2 (Z i )D 1 (Z i )> X ! i Pr(! i ) h 2 i+ (1 + a 2 + )( d 2 d 1 ) + 2 i 1 ( d 2 d 1 ) i SinceF + 2 (!) =F + 3 (!), we have the following identity as in case I, D 3 (Z i )D 2 (Z i ) = X ! i Pr(! i ) h 2 i+ (1 + a 2 + )( d 3 d 2 ) + 2 i 1 ( d 3 d 2 ) i HenceD 3 (Z i )D 2 (Z i )<D 2 (Z i )D 1 (Z i ) and the concavity follows. Intuitively, this case means that the network risk-taking distortion is increasing in d, but at a slower rate. This is because the change of d (from d 1 to d 2 ) makes some “insolvent” banks “solvenet” in some state of nature. Case III:F + 1 (!) =F + 2 (!)F + 3 (!) for some!. The proof is identical to case II with a slight twist. Instead of replacing all RHS of equation 2.22 with the rst line, we replace it with the last line. Hence, we obtain, D 3 (Z i )D 2 (Z i )< X ! i Pr(! i ) h 2 i+ (1 + a 2 + )( d 3 d 2 ) + 2 i 1 ( d 3 d 2 ) i D 2 (Z i )D 1 (Z i ) = X ! i Pr(! i ) h 2 i+ (1 + a 2 + )( d 2 d 1 ) + 2 i 1 ( d 2 d 1 ) i The monotonicity and concavity result follows. 111 Case IV:F + 1 (!)F + 2 (!)F + 3 (!) for some!. The proof is a combination of case 2 and case 3: D 3 (Z i )D 2 (Z i )< X ! i Pr(! i ) h 2 i+ (1 + a 2 + )( d 3 d 2 ) + 2 i 1 ( d 3 d 2 ) i D 2 (Z i )D 1 (Z i )> X ! i Pr(! i ) h 2 i+ (1 + a 2 + )( d 2 d 1 ) + 2 i 1 ( d 2 d 1 ) i The monotonicity and concavity result follows. BecauseF + 1 (!)F + 2 (!)F + 3 (!) for all!2 , Case I-IV (or some combination of them) exhaust all the possibilities. Intuitively, the proof shows that the network risk-taking distortion is increasing in d, but at a slower rate. This is because the change of d makes some “insolvent” banks “solvenet” and this decreases the marginal eect of d. PROOFOFPROPOSITION3: By lemma 1, the Nash Equilibrium for risk exposureZ is a supermodular game. By lemma 3, bank’s expected prot exhibits an increasing dierence inZ i and d. Then the Pareto-dominant equilibrium risk exposure is increasing in d (Milgrom and Roberts 1990, theorem 6). PROOFOFCOROLLARY2: Part(a): Let e denote the largest path-connected sub-network of where banki belongs to. Suppose when d = d 1 , all failed banks in this sub-network are “solvent” in any state of nature. This means e ++ 1 + + e +s 1 s = 1 + . As a result, equation 2.20 becomesa + (!) = (I + e ++ ) 1 e +s 1 s = 1 + for all!. If this is the case, equation 2.21 impliesD(Z i ; d 2 )D(Z i ; d 1 ) = 0 for all d 2 > d 1 . To show the upper bound exists, it remains to prove that d 1 exits: i.e. there exists a d 1 such that all failed banks in e are “solvent” in any state of nature. Because e is path-connected by construction, there is a chainfj;a;b;c;:::;ig from any failed bankj to the successful banki. Then consider 112 d max j = 1 e bc ( 1 e ab ( 1 e ja v j +v a ) +v b ) +v c +::: Clearly, d max j is nite because the network is path-connected ( e ja , e ab , e bc .. are all strictly positive). Suppose d = d max j , then even when any bank outside this chain failed and “insolvent” (i.e. unable to contribute to the chain), bankj can fulll its deposits and become “solvent”. Intuitively, that means d is so large that banki can itself bail out bankj even though they may not be directly connected. Then let’s dene d max = max j d max j When d 1 = d max , then in any state of nature, all failed bank are “solvent”. This completes the proof. Part(b): From path-connectedness, e = . From part (a),D(Z i ) reaches the maximum when every failed banks are ‘solvent” in all possible states of nature. In this case, we can rewrite failed banks’ equilibrium payment (equation 2.13) as d f (!) = ff d f (!) + fs 1 s d1 f v 8! It implies d f (!) = (I f ff ) 1 ( fs 1 s d1 f v) =1 f d (I f ff ) 1 1 f v 8! The interbank payments received by the successful banks are sf d f (!) + ss 1 s d =1 s d sf (I f ff ) 1 1 f v 8! 113 That means successful banks’ network distortion vector in state! is ~ D(!) = sf (I f ff ) 1 1 f v. By the network symmetry, the expected distortion conditional on the setf fails will be the ratio of column sum of ~ D(!) and the number of columns. That is E[D max jsetf fails] = 1 0 s sf (I f ff ) 1 1 f v 1 0 s 1 s = 1 0 f 1 f 1 0 s 1 s v Then a bank’s unconditional expected network distortion is P f 1 0 f 1 f 1 0 s 1s v Pr(F =f). Again due to the symmetry, the permutation among the failed banks is irrelevant. Therefore, the maximum network risk-taking distortion is D max (Z i ) = N1 X f=1 f Nf v N 1 f h P (Z i ) i N1f h 1P (Z i ) i f It’s worth mentioning thatD max (Z i ) is independent of the network topology when it’s symmetric (e.g. ring or complete networks). PROOFOFPROPOSITION4: Let’s separately analyze the two types of networks. CompleteNetwork In A complete network, failed banks are either altogether “solvent" or “insolvent". That means we have either F + (!) =F(!) orF + (!) =;. Let’s solve the payment equilibrium (equation 2.16 and 2.17) in those two types of states of nature. 1. For! whereF + (!) =F(!) (i.e. failed banks are “solvent”), If! i =f, thena i (!) = 1 andb i (!) = 1=(1 P j2F! ij ). 2. For! whereF + (!) =; (i.e. failed banks are “insolvent”), If! i =f, thena i (!) = P !j=s ij andb i (!) = 1. 114 By denition, a bank is “solvent” ifa i db i v 0. Plugging the solution in case 1, we knowF(!) + =F(!) if and only if d 1=(1 P j2F! ij )v. We can hence solve the payment equilibrium as d C i (!) = 8 > > < > > : d 8 ! i =s d 1 P ! j 2s ij v + 8 ! i =f where 1= P !j=s ij = (N 1) / # of successful banks. We observe that conditioning onm numbers of banks fail, d C i (!) is independent of!. We can rewrite the network risk-taking distortion as D C (Z i ) = N1 X m=1 d d N 1 Nm v + m N 1 | {z } payment from failed banks d N 1m N 1 | {z } payment from successful banks Pr(m banks failed) = N1 X m=1 min mv Nm ; m d N 1 Pr(m banks failed) (2.23) where Pr(m banks failed) = N 1 m 1P (Z i ) m P (Z i ) N1m RingNetwork For a failed bank, there are three scenarios: (1) its debtor succeeds, (2) its debtor failed but “solvent”, and (3) its debtor failed and “insolvent”. Let’s solve the payment equilibrium (equation 2.16 and 2.17) in those three types of states of nature. 1. Fori2F with! i1 2S(!), a i (!) = 1 andb i (!) = 1. 2. Fori2F with! i1 2F + (!), a i (!) =a i1 (!) andb i (!) =b i1 (!) + 1. 3. Fori2F with! i1 2F (!), a i (!) = 0 andb i (!) = 1. 115 By induction, we have d R i (!) = 8 > > < > > : d 8 ! i =s dK i (!)v + 8 ! i =f whereK i (!) minfo :! io =sg is the number of failed debtors in the chain before reaching the rst successful bank. Conditioning onm number(s) of banks failed, the total interbank payments received by banki is X j 0 ij d R j (!) = 8 > > > > > > > > > > < > > > > > > > > > > : d w.p. N2 N2m . N1 m dv + w.p. N3 N2m . N1 m :::::: dmv) + w.p. N2m N2m . N1 m (2.24) Equation 2.24 has a clean interpretation. The rst line corresponds to the scenario wherei’s direct debtor suc- ceeded. In this case, bank i will receive an interbank payment of d. Conditioning on m number of bank failed, the probability of this scenario is N2 N2m . N1 m . Similarly, the second line corresponds to the scenario where i’s direct debtor failed but its debtor’s debtor succeeded. In this case, banki will receive an interbank payment of ( dv) + . The probability of this scenario is N3 N2m . N1 m . The same logic applies till allm banks failed. It is easy to conrm by Hockey-stick identity (emma I.A) that the total probability in equation 2.24 is one. Taking the expectation, the network risk-taking distortion of a ring network is D R (Z i ) = N1 X m=1 " d m X l=0 dlv + N 2l N 2m . N 1 m # Pr(m banks failed) To compare it with the network distortion of a complete network, D R (Z i ) N1 X m=1 " d m X l=0 dlv N 2l N 2m . N 1 m d N 1m N 1 ! + d N 1m N 1 # Pr(m banks failed) (BylemmaI.B) = N1 X m=1 d d N 1 Nm v + m N 1 d N 1m N 1 Pr(m banks failed) (BylemmaI.A) =D C (Z i ) 116 It’s worth noting thatD R (Z i ) =D C (Z i ) =D max (Z i ) if dmv 0 for allm. A necessary and sucient condition is d (N 1)v. It conrms Corollary 2. Finally, by monotone selection theorem, the equilibrium risk exposure of banks in a complete network is larger than that of banks in a ring network. PROOFOFPROPOSITION5: By binomial theorem, we can rewrite equation 2.7 as D max (Z i ) = 1P (Z i ) [1P (Z i )] N P (Z i ) v It is immediate that dD max (Z i )= dN > 0. By monotone selection theorem, each bank’s maximum risk expo- sureZ i is increasing in the number of banksN in the network. PROOFOFPROPOSITION6: Denote the central clearing counterparty (CCP) as bank 0. Because the CCP has no outside liability, it’s always “solvent”. Hence, the payment equilibrium whenm banks fail can be solved by d s = d d f = (d 0 =Nv) + d 0 = (Nm)d s +md f The above xed point system is solved as d CCP i (!) = 8 > > < > > : d 8 ! i =s d N Nm v + 8 ! i =f As a result, the risk-taking distortion of a successful bank is D CCP (Z i ) = N1 X m=1 d d N Nm v + m N | {z } payment from failed banks d Nm N | {z } payment from successful banks Pr(m banks failed) = N1 X m=1 min mv Nm ; m d N Pr(m banks failed) (2.25) 117 Compare equation 2.25 with 2.23, it’s easy to see thatD CCP (Z i ; d) =D C (Z i ; N1 N d). PROOF OF PROPOSITION 7: Consider a network ( d; ;N) where d > v. From denition of the Nash equilib- rium, the LHS of equation 2.9 is greater than AP (Z i ) h Z i vD(Z i ) i +c i h 1P (Z i ) i Pr i2F ! j! i =f c i Dene the RHS of equation 2.9 asBP (Z i ) h Z i v +c i i AB = h 1P (Z i ) ih 1 Pr i2F ! j! i =f i c i P (Z i )D(Z i ) The condition d>v implies Pr(i2F ! j! i =f)< 1. This means that it is possible that banki’s deposits get fully fullled from counterparties’ cross subsidies. SinceZ andZ are bounded, there exists c2 R + such that if all c i > c,AB > 0. PROOF OF LEMMA 4 The proof is similar to that of lemma 3. In any state of nature!, the payment vector for “solvent” failed banks isd + = ++ d + + +s 1 s d +1 + (rv), or d + = (I + ++ ) 1 ( +s 1 s d +1 + (rv)) To conserve space, I suppress the state! ind + (!), ++ (!), +s (!),1 s (!) and1 f (!). We can again write the risk-taking distortion in a matrix form as D(Z i ) = X ! i Pr(! i ) h i+ (1 + dd + ) + i 1 d i (2.26) To prove the lemma 4, compare three nancial systems with dierent sizes of equity buersr 1 , r 2 , r 3 , with r 3 r 2 = r 2 r 1 =". Similar to the proof of lemma 3, we need to consider the following four cases. 118 Case I:F + 1 (!) =F + 2 (!) =F + 3 (!) for all! For all!,d + is linearly increasing inr:d 3 + d 2 + =d 2 + d 1 + = (I + ++ ) 1 1 + "> 0. Then it is easy to see that the network risk-taking distortion is linearly decreasing inr. D 3 (Z i )D 2 (Z i ) =D 2 (Z i )D 1 (Z i ) = X ! i Pr(! i ) h i+ (d 1 + d 2 + ) i < 0 Case II:F + 1 (!)F + 2 (!) =F + 3 (!) for some!. We rst compare the equity r 2 with r 1 . In some state of nature!, some otherwise “insolvent” failed banks for ( d; ;N;r 1 ) become “solvent” for ( d 2 ; ;N;r 2 ). Denote those banks t 1 ;t 2 ;:::;t T , where T 1. Due to the continuity of the payment equilibrium in terms ofr (equation 2.10), there existsr 1 < ~ r 1 < ~ r 2 ::: < ::: < ~ r S < r 2 (where 1 S T ), such that when the equity buerr = ~ r s , some bankst t are exactly “solvent”. As a result, those margin bankst t are “solvent” whenr2 (~ r s ; ~ r s+1 ) and “insolvent” whenr2 (~ r s1 ; ~ r s ) respectively. Denote e D s (Z i ) the network risk-taking distortion whenr = ~ r s . We have D 2 (Z i ) e D S (Z i ) = X ! i Pr(! i ) h 2 i+ ( ~ d S + d 2 + ) i 0 e D s+1 (Z i ) e D s (Z i ) = X ! i Pr(! i ) h e s i+ ( ~ d s + ~ d s+1 + ) i 0 8s = 1;:::;S 1 (2.27) e D 1 (Z i )D 1 (Z i ) = X ! i Pr(! i ) h 1 i+ (d 1 + ~ d 1 + ) i 0 Summing above equations, it is easy to see thatD 2 (Z i ) e D 1 (Z i ) 0. It then remains to prove the concavity. By construction, e s i+ is a submatrix of e s+1 i+ . We also know ~ b s + = (I s + s ++ ) 1 1 s + is a submatrix of ~ b s+1 + . This is due to the construction that at the cutor = ~ r s , bankt can be treated either as solvent or insolvent. With those two facts, we have ~ s i+ (I s + ~ s ++ ) 1 1 s + < ~ s+1 i+ (I s+1 + s+1 ++ ) 1 1 s+1 + 119 After summing every dierence in equation 2.27 and replacing all of RHS with the 2 i+ (I 2 + 2 ++ ) 1 1 2 + (the largest), we have D 2 (Z i )D 1 (Z i )> X ! i Pr(! i ) h 2 i+ (I 2 + 2 ++ ) 1 1 2 + (") i SinceF + 2 (!) =F + 3 (!), we have the following identity as in case I, D 3 (Z i )D 2 (Z i ) = X ! i Pr(! i ) h 2 i+ (I 2 + 2 ++ ) 1 1 2 + (") i HenceD 3 (Z i )D 2 (Z i )<D 2 (Z i )D 1 (Z i ) and the concavity follows. Case III:F + 1 (!) =F + 2 (!)F + 3 (!) for some!. The proof is identical to case II with a slight twist. When comparingr 3 withr 2 . Again replacing all RHS of equation 2.27 with 2 i+ (I 2 + 2 ++ ) 1 1 2 + , the smallest, we obtain D 3 (Z i )D 2 (Z i )< X ! i Pr(! i ) h 2 i+ (I 2 + 2 ++ ) 1 1 2 + (") i =D 2 (Z i )D 1 (Z i ) Case IV:F + 1 (!)F + 2 (!)F + 3 (!) for some!. The proof is a combination of case 2 and case 3: D 2 (Z i )D 1 (Z i )> X ! i Pr(! i ) h 2 i+ (I 2 + 2 ++ ) 1 1 2 + (") i D 3 (Z i )D 2 (Z i )< X ! i Pr(! i ) h 2 i+ (I 2 + 2 ++ ) 1 1 2 + (") i The monotonicity and concavity result follows. 120 BecauseF + 1 (!)F + 2 (!)F + 3 (!) for all!2 , Case I-IV (or some combination of them) exhaust all the possibilities. PROOFOFPROPOSITION8: The rst and second order conditions of maximizing bank’s expected prot (equa- tion 2.11) over its choice of risk exposureZ i : F (Z i ;Z i ;r) =P 0 (Z i )(Z i +rv) +P (Z i )P (Z i ) 0 D(Z i ;r) S(Z i ;Z i ;r) =P 00 (Z i )(Z i +rv) + 2P 0 (Z i )P (Z i ) 00 D(Z i ;r) Taking the total derivative of FOC, we have dZ i dr = @F @D dD dr + @F @r S(Z i ;Z i ;r) = 1 S h P 0 (Z i ) dD dr +P 0 (Z i ) i < 0 8Z i whereP 0 (Z i )< 0 is the direct eect of an equity buer and dD= dr< 0 is the network eect. PROPOSITION9: The proof is similar to the proof of lemma 4. The payment vector for “solvent” failed banks is d + (!) = 8 > > < > > : (I + ++ ) 1 ( +s 1 s d +1 + (tv)) if #flj! l =fgn (I + ++ ) 1 ( +s 1 s d +1 + (0v)) if #flj! l =fg<n The rst line corresponds to the state of nature where a bailout occurs. The second line corresponds to the other cases. Compare two bailout amountt 1 andt 2 witht 2 t 1 ="> 0. We again have two cases: (1)F + 2 (!) =F + 1 (!) for all!. (2)F + 1 (!)F + 2 (!) for some!. Denote the bailout event indicator1[#flj! l =fg>n] asB(!). Sincen<N,B(!) = 1 for some!. For case 1, d 2 + (!)d 1 + (!) =B(!)(I + ++ ) 1 1 + " 8!2 121 From equation 2.26, D 2 (Z i )D 1 (Z i ) = X ! i Pr(! i ) h i+ (d 1 + d 2 + ) i = X ! i B(! i=s )Pr(! i ) h i+ (I + ++ ) 1 1 + " i < 0 The proof of case 2 is identical to case 2 of lemma 3 and 4. I omit here to avoid repetition. From monotone selection theorem, banks’ equilibrium risk exposure is lower ift =t 2 compared witht 1 . Intuitively, the proof shows that a government bailout decreases the cross-subsidy a successful bank pays during crises. PROOFOFPROPOSITION10: From equation 2.13, the payment vectord is still independent of the risk vector Z or the correlation matrix. Let’s compare banki’s expected prot when it chooses between ij and e ij with e ij > ij E h i (!;Z i ; e ij ) i E h i (!;Z i ; ij ) i = X ! ij d X l il d l (! i=s;j=s ) Pr(! ij j! i =s;! j =s)P (Z j ) ( e ij ij ) + X ! ij d X l il d l (! i=s;j=f ) Pr(! ij j! i =s;! j =f)P (Z j ) ( e ij ij ) Suppose j;k = 1 for allk6= i. That implies Pr(! ij j! i = s;! j = s) = 1 if and only if every element of ! ij iss. Similarly, Pr(! ij j! i =s;! j =f) = 1 if and only if every element of! ij isf. By Auxiliary Lemma in the appendix above, P l il d l (! i=s;i=s ) P l il d l (! i=s;i=f ). This implies bank i’s expected prot is increasing in its project’s dependence ij with other banks. Therefore, for allZ, bank i’s choices of conditional dependence with bankj won’t deviate from i;j = 1. With perfect correlation, the network risk-taking distortion disappears:D(Z i ;1) = 0 for allZ i . Hence, the equilibrium is characterized by ij = 1 8i;j2N P 0 (Z i )(Z i v) +P (Z i ) = 0 8i2N 122 And ij = 1 for alli;j. 123 OnlineAppendix A.OmittedProofs LEMMAI.A [Hockey-stick Identity] For alln>r, we have (i) n X l=r l r ! = n + 1 r + 1 ! and (ii) n X l=r l r ! (nl) = n + 1 r + 1 ! nr r + 2 PROOF We proceed by induction. For an initialn =r + 1 (i) r r ! + r + 1 r ! = r + 2 r + 1 ! (ii) r r ! 1 + r + 1 r ! 0 = r + 2 r + 1 ! 1 r + 2 = 1 The above equations are to conrm the initial conditions hold. Now suppose that forn =k, the two equality holds. Forn =k+1, we have (i) k+1 X l=r l r ! = k X l=r l r ! + k + 1 r ! = k + 1 r + 1 ! + k + 1 r ! = k + 2 r + 1 ! (ii) k+1 X l=r l r ! (k + 1l) = k X l=r l r ! (k + 1l) = k + 1 r + 1 ! kr r + 2 + k + 1 r + 1 ! = k + 2 r + 1 ! k + 1r r + 2 Q.E.D by induction. LEMMAI.B [Triangle Inequality] For any sequencefAig andB2R withB< maxi(Ai), we have X i Ai + X i AiB + +B 124 PROOF Without loss of generality, letA0 = maxi(Ai) X i Ai + B = X i6=0 Ai + + (A0B) + X i AiB + 125 B.NumericalExample: intermediately-connectednetworks 1 1.5 2 2.5 3 3.5 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ‘ We consider a ring, a = 0:5, and a complete network with four banks. Let the bank of interest be banki = 4. The purpose of this section is to numerically solve the network risk-taking distortion for the three kinds of net- works. LetP (Zj ) = 0:5 8j6=i. R = 2 6 6 6 6 6 6 6 6 6 6 4 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 3 7 7 7 7 7 7 7 7 7 7 5 = 2 6 6 6 6 6 6 6 6 6 6 4 0 1=6 1=6 2=3 2=3 0 1=6 1=6 1=6 2=3 0 1=6 1=6 1=6 2=3 0 3 7 7 7 7 7 7 7 7 7 7 5 C = 2 6 6 6 6 6 6 6 6 6 6 4 0 1=3 1=3 1=3 1=3 0 1=3 1=3 1=3 1=3 0 1=3 1=3 1=3 1=3 0 3 7 7 7 7 7 7 7 7 7 7 5 dene R 4 , 4 , and C 4 as vectors that represent the last row of each. (i)Small d( d = 1:5) ! = (s;s;s;s): D R (!) = 1:5 1:5 1:5 1:5 R 4 + 1:5 = 0 D (!) = 1:5 1:5 1:5 1:5 4 + 1:5 = 0 D C (!) = 1:5 1:5 1:5 1:5 C 4 + 1:5 = 0 ! = (s;s;f;s): D R (!) = 1:5 1:5 0:5 1:5 R 4 + 1:5 = 1 D (!) = 1:5 1:5 0:5 1:5 4 + 1:5 = 2=3 D C (!) = 1:5 1:5 0:5 1:5 C 4 + 1:5 = 1=3 ! = (s;f;s;s): D R (!) = 1:5 0:5 1:5 1:5 R 4 + 1:5 = 0 D (!) = 1:5 0:5 1:5 1:5 4 + 1:5 = 1=6 D C (!) = 1:5 0:5 1:5 1:5 C 4 + 1:5 = 1=3 ! = (f;s;s;s): D R (!) = 0:5 1:5 1:5 1:5 R 4 + 1:5 = 0 D (!) = 0:5 1:5 1:5 1:5 4 + 1:5 = 1=6 D C (!) = 0:5 1:5 1:5 1:5 C 4 + 1:5 = 1=3 126 ! = (s;f;f;s): D R (!) = 1:5 0:5 0 1:5 R 4 + 1:5 = 1:5 D (!) = 1:5 0:25 0 1:5 4 + 1:5 = 29=24 D C (!) = 1:5 0 0 1:5 C 4 + 1:5 = 1 ! = (f;s;f;s): D R (!) = 0:5 1:5 0:5 1:5 R 4 + 1:5 = 1 D (!) = 0:3 1:5 0:3 1:5 4 + 1:5 = 1 D C (!) = 0 1:5 0 1:5 C 4 + 1:5 = 1 ! = (f;f;s;s): D R (!) = 0:5 0 1:5 1:5 R 4 + 1:5 = 0 D (!) = 0:25 0 1:5 1:5 4 + 1:5 = 11=24 D C (!) = 0 0 1:5 1:5 C 4 + 1:5 = 1 ! = (f;f;f;s): D R (!) = 0:5 0 0 1:5 R 4 + 1:5 = 1:5 D (!) = 0 0 0 1:5 4 + 1:5 = 1:5 D C (!) = 0 0 0 1:5 C 4 + 1:5 = 1:5 Letm denotes the number failed banks. Conditioning on banki succeeds, Pr(m = 0) = 1 8 , Pr(m = 1) = 3 8 , Pr(m = 2) = 3 8 , and Pr(m = 3) = 1 8 . From here we can calculate the network risk-taking distortion as D R = Pr(m = 0) 0 + Pr(m = 1) 1 3 + Pr(m = 2) 5 6 + Pr(m = 3) 3 2 = 5 8 D = Pr(m = 0) 0 + Pr(m = 1) 1 3 + Pr(m = 2) 8 9 + Pr(m = 3) 3 2 = 31 48 D C = Pr(m = 0) 0 + Pr(m = 1) 1 3 + Pr(m = 2) 1 + Pr(m = 3) 3 2 = 11 16 (ii)Large d( d = 2:5) ! = (s;s;s;s): D R (!) = 1:5 1:5 1:5 1:5 R 4 + 2:5 = 0 D (!) = 1:5 1:5 1:5 1:5 4 + 2:5 = 0 D C (!) = 1:5 1:5 1:5 1:5 C 4 + 2:5 = 0 ! = (s;s;f;s): D R (!) = 2:5 2:5 1:5 2:5 R 4 + 2:5 = 1 D (!) = 2:5 2:5 1:5 2:5 4 + 2:5 = 2=3 D C (!) = 2:5 2:5 1:5 2:5 C 4 + 2:5 = 1=3 ! = (s;f;s;s): D R (!) = 2:5 1:5 2:5 2:5 R 4 + 2:5 = 0 D (!) = 2:5 1:5 2:5 2:5 4 + 2:5 = 1=6 D C (!) = 2:5 1:5 2:5 2:5 C 4 + 2:5 = 1=3 ! = (f;s;s;s): D R (!) = 1:5 2:5 2:5 2:5 R 4 + 2:5 = 0 D (!) = 1:5 2:5 2:5 2:5 4 + 2:5 = 1=6 D C (!) = 1:5 2:5 2:5 2:5 C 4 + 2:5 = 1=3 ! = (s;f;f;s): D R (!) = 2:5 1:5 0:5 2:5 R 4 + 2:5 = 2 D (!) = 2:5 19=16 5=8 2:5 4 + 2:5 = 47=32 D C (!) = 2:5 1 1 2:5 C 4 + 2:5 = 1 ! = (f;s;f;s): D R (!) = 1:5 2:5 1:5 2:5 R 4 + 2:5 = 1 D (!) = 1:3 2:5 1:3 2:5 4 + 2:5 = 1 D C (!) = 1:5 2:5 1 2:5 C 4 + 2:5 = 1 127 ! = (f;f;s;s): D R (!) = 1:5 0:5 2:5 2:5 R 4 + 2:5 = 0 D (!) = 19=16 5=8 2:5 2:5 4 + 2:5 = 17=32 D C (!) = 1 1 2:5 2:5 C 4 + 2:5 = 1 ! = (f;f;f;s): D R (!) = 1:5 0:5 0 2:5 R 4 + 2:5 = 2:5 D (!) = 2=3 0 0 2:5 4 + 2:5 = 43=18 D C (!) = 0 0 0 2:5 C 4 + 2:5 = 2:5 D R = Pr(m = 0) 0 + Pr(m = 1) 1 3 + Pr(m = 2) 1 + Pr(m = 3) 2:5 = 13 16 D = Pr(m = 0) 0 + Pr(m = 1) 1 3 + Pr(m = 2) 1 + Pr(m = 3) 43 18 = 115 144 D C = Pr(m = 0) 0 + Pr(m = 1) 1 3 + Pr(m = 2) 1 + Pr(m = 3) 2:5 = 13 16 As we see from this example, if d = 2:5, bank 4’s risk-taking distortion is not monotonic to the degree of connectedness: the distortion of a = 0:5 network is lower than that of a complete and a ring network. 128 C:Robustness RelaxtheAssumptionofzerodownsidepayo In this section, I will show that the network risk-taking externality is not dependent on the assumption that a failed project generates 0 gross return. To do so, let’s assume a projectZi will produce a random return of ~ ei(Zi) with the following payo distribution. ~ ei = 8 > > < > > : Zi w.p P (Zi) " w.p 1P (Zi) where"<Zi is a constant. Consider the following two parameter specications. (a)Suppose"<v The payment equilibrium (equation 2.13) becomes d i (!;Z) = d 8!i =s d i (!;Z) = ( X j ijd j (!;Z) +"v ) + 8!i =f This implies Lemma 2 still holds: the payment equilibriumd (!;Z) is constant in the risk exposure vectorZ. Equation 2.6 is the same as before because any failed bank will default on its interbank debts (i.e. P j ijd j (!) +"v< d). As a result, the proof of corollary 1 will be the same as before. (b)Suppose"v From equation 2.2, we know that the payment equilibrium will be d i (!;Z) = d 8i2N 8!2 All banks are solvent in all states of nature. Then there is no risk-taking externality resulting from banks’ cross-subsidy. However, this also implies that nancial networks will not exist in the rst place. To see why, consider the setup in Section 4.1. The following equation displays each bank’s payo regardless of whether it is connected. max Z P (Z)(Zv) + 1P (Z) ("v) +c As a result, this is no incentives for banks to form networks. 129 EndogenizingDepositRate In the main text, the deposit ratev is assumed to be constant. In this section, I model depositors’ rational decisions to lend to a bank while being aware of the interbank connections. In other words, I endogenize the deposit rates. To be more specic, each bank in the network ( d;;N) needs to borrowMi = 1 (normalized to 1) from atomistic depositors to nance a productive projectZi. The borrowing takes the form of a standard debt contract with a face valuevi, which will be determined in equilibrium.vi can be interpreted as the gross interest rate. For expository purposes, I assume depositors are risk neutral and have time discount rate. After each bank receives the deposits, they simultaneously choose their project choices. The subsequent timeline follows gure 2.1. A competitive market results in a zero prot for atomistic depositors. The equilibrium (d i (!);v ;Z ) is hence characterized by d i (!) = ( min h X j ijd j (!;Z) +ei(!i;Zi)v i ; d; i ) + 8i2N; 8!2 Z i = argmax Z i E h B i (!;Z;v i ) i 8i2N 0 =Mi +E h D i (!;v i ;Z ) i 8i2N where B i (!) is banki’s payo in state!, which is the same as equation 2.3, and D i (!) is banki’s depositors’ payo in state!. With deposit insurance, D i (!) =v i for all!. In this case, the return to depositors are guaranteed by the government. Without deposit insurance, D i (!) = min[v ; P j ijd j (!) +ei(Z ;!)d i (!)] as a debt contract. It’s worth noting that, in this case, D i (!) is a function of andZ : depositors perfectly observe the network structure and perfectly anticipate banks’ optimal risk exposure. The following results show the equilibrium for the two cases. (a) Without deposit insurance, (i) banks’ equilibrium risk exposure is identical in any network structure:Z C =Z R =Z S (ii) banks’ equilibrium deposit rates are higher in a ring network than in a complete network:v S >v R v C . (b) With deposit insurance, (i) banks’ equilibrium risk exposure is higher in a complete network than in a ring network: Z C Z R >Z S . (ii) banks’ equilibrium deposit rates are identical in any network structure:v C =v R =v S . (where the superscriptC denotes complete network,R denotes ring network, andS denotes stand-alone) Part (a) states that without deposit insurance, banks’ choices of risk exposure are identical in any network structure, in contrast to proposition 3 of the benchmark model. The benchmark model assumes xed deposit rates and shows that banks in highly connected networks expose to greater risks due to a network risk-taking distortion. To understand the dierence, let’s rst recall that this network risk-taking distortion is the result of “cross-subsidy” from successful banks to failed banks’ depositors. Without deposit insurance, depositors in highly connected networks will feel more co-insured from the interbank connections 130 and will demand lower interest rates. Both the lowered deposit rates and the “cross-subsidy” aect connected banks’ upside payos. Their countervailing eects will equalize banks’ choices of risk exposure in any network structure. Part (b) considers nancial systems where depositors are fully insured by the government. The result is identical to the benchmark model with a xed deposit rate. With a government’s guarantee, depositors are “informative insensitive” to banks’ nancial structures. As a result, the deposit rates are constant across all network structures and equal to depositors’ time cost (1=). Without deposit rates’pricedisciplining, banks in highly connected networks will face greater network risk-taking distor- tion and choose greater exposure to risks (proposition 3 to 5). Proof Suppose there is no deposit insurance. Banki’s depositors’ the expected return is E h D i (!;v ;Z ) i =E ( min h v ; X j ijd j (!) +ei(Z ;!)d i (!) i ) =E ( ei(Z ;!) ) | {z } =P(Z )Z +E ( X j ijd j (!)d i (!) ) | {z } =0 E ( X j ijd j (!) +ei(Z ;!)d i (!)v + ) | {z } =P(Z )(Z v )P(Z )D (Z ) =P (Z ) v +D(Z ) With a slight abuse of notation, the subscript represents the full network structure ( d;;N). The second line follows the rst line because for allx;y2R, min(x;y) =y (yx) + . From the symmetry assumption,E[d j (!)] =E[d i (!)],8i6=j. Hence E[ P j ijd j (!)d i (!)] = 0. PluggingE[ D i (!;v ;Z )] to the equilibrium condition P (Z ) v +D(Z ) M = 0 (2.28) where bank’s risk exposureZ is the result of a Nash equilibrium dened by equation 2.4. Explicitly, P 0 (Z ) Z v D(Z ) +P (Z ) = 0 (2.29) Equation 2.28 and 2.29 jointly determine banks’ equilibrium risk exposure as P 0 (Z ) Z M P (Z ) +P (Z ) = 0 (2.30) 131 It is easy to see that the equilibrium risk exposureZ =Z is independent of the network structure ( d;;N). From equation 2.28, the equilibrium deposit rates are determined by v = M P (Z ) D(Z ) From proposition 4,DS <DR(Z)DC (Z) for allZ. Finally, we havev C v R <v S . With deposit insurance, D i (!) =v i for all!. The equilibrium condition becomes: v M = 0 Orv =v =M=, independent of the network structure. Plugging into equation 2.29, we have P 0 (Z ) Z M D(Z ) +P (Z ) = 0 It’s identical to the benchmark case with xed deposit rates. Corollary 1 and proposition 4 impliesZ C Z R >Z S . 132 Bibliography [1] Daron Acemoglu, Asuman E. Ozdaglar, and Alireza Tahbaz-Salehi. “Systemic Risk in Endogenous Financial Networks”. In: Working Paper (2014). [2] Daron Acemoglu, Asuman Ozdaglar, and Alireza Tahbaz-Salehi. “Systemic Risk and Stability in Financial Networks”. In: American Economic Review 105.2 (Feb. 2015), pp. 564–608.doi: 10.1257/aer.20130456. [3] Viral V Acharya. “A theory of systemic risk and design of prudential bank regulation”. In: Journal of nancial stability 5.3 (2009), pp. 224–255. [4] Reena Aggarwal, Isil Erel, and Laura T Starks. “Inuence of public opinion on investor voting and proxy advisors”. In: Fisher College of Business Working Paper No. WP (2014), pp. 03–12. [5] Franklin Allen and Douglas Gale. “Financial Contagion”. In: Journal of Political Economy 108.1 (2000), pp. 1–33. [6] Ian R Appel, Todd A Gormley, and Donald B Keim. “Passive investors, not passive owners”. In: Journal of Financial Economics 121.1 (2016), pp. 111–141. [7] Laurent Bach and Daniel Metzger. “How close are close shareholder votes?” In: The Review of Financial Studies 32.8 (2019), pp. 3183–3214. [8] Adolf Berle and Gardiner Means. The modern corporation and private property. Transaction Publishers, 1932. [9] Darren Bernard, Terrence Blackburne, and Jacob Thornock. “Information ows among rivals and corporate investment”. In: Journal of Financial Economics 136.3 (2020), pp. 760–779. [10] Dimitrios Bisias, Mark Flood, Andrew W Lo, and Stavros Valavanis. “A survey of systemic risk analytics”. In: Annu. Rev. Financ. Econ. 4.1 (2012), pp. 255–296. [11] Patrick Bolton, Tao Li, Enrichetta Ravina, and Howard Rosenthal. “Investor ideology”. In: Journal of Financial Economics 137.2 (2020), pp. 320–352. 133 [12] Audra L Boone, Stuart Gillan, and Mitch Towner. “The Role of Proxy Advisors and Large Passive Funds in Shareholder Voting: Lions or Lambs?” In:Texas Christian University, Universityof Georgia, and University of Arizona Working Paper (2020). [13] Sandro Brusco and Fabio Castiglionesi. “Liquidity Coinsurance, Moral Hazard, and Financial Contagion”. In: Journal of Finance 62.5 (2007), pp. 2275–2302. [14] Ryan Bubb and Emiliano Catan. “The party structure of mutual funds”. In: New York University School of Law Working Paper (2019). [15] Jie Cai, Jacqueline L Garner, and Ralph A Walkling. “Electing directors”. In: The Journal of Finance 64.5 (2009), pp. 2389–2421. [16] Huaizhi Chen, Lauren Cohen, Umit Gurun, Dong Lou, and Christopher Malloy. “IQ from IP: Simplifying search in portfolio choice”. In: Journal of Financial Economics (2020). [17] Stephen Choi, Jill Fisch, and Marcel Kahan. “The power of proxy advisors: Myth or reality”. In: Emory Law Journal 59 (2009), p. 869. [18] James Copland, David F Larcker, and Brian Tayan. “The big thumb on the scale: An overview of the proxy advisory industry”. In: Stanford University Closer Look Series No. CGRP-72 (2018), pp. 18–27. [19] Alan D Crane, Kevin Crotty, and Tarik Umar. “Hedge funds and public information acquisition”. In: Rice University Working Paper (2020). [20] Vicente Cuñat, Mireia Gine, and Maria Guadalupe. “The vote is cast: The eect of corporate governance on shareholder value”. In: The journal of nance 67.5 (2012), pp. 1943–1977. [21] Amil Dasgupta, Vyacheslav Fos, and Zacharias Sautner. “Institutional Investors and Corporate Governance”. In: London School of Economics, Boston College, and Frankfurt School of Finance Working Paper (2020). [22] Tommaso Denti. “Unrestricted information acquisition”. In: Cornell Working Paper (2018). [23] Marco Di Maggio and Alireza Tahbaz-Salehi. “Financial intermediation networks”. In: Working Paper (2014). [24] Douglas W. Diamond and Philip H. Dybvig. “Bank Runs, Deposit Insurance, and Liquidity”. In: Journal of Political Economy 91.3 (1983), pp. 401–419.doi: 10.1086/261155. eprint: https://doi.org/10.1086/261155. [25] Jason Roderick Donaldson and Giorgia Piacentino. “NETTING”. In: Working Paper (2017). [26] Timothy M. Doyle. The Realities of Robo-Voting. https://accfcorpgov.org/wp-content/uploads/ACCF-RoboVoting-Report_11_8_FINAL.pdf. 2018. [27] Darrell Due and Haoxiang Zhu. “Does a central clearing counterparty reduce counterparty risk?” In: The Review of Asset Pricing Studies 1.1 (2011), pp. 74–95. 134 [28] Larry Eisenberg and Thomas H. Noe. “Systemic Risk in Financial Systems”. In:ManagementScience 47.2 (2001), pp. 236–249.issn: 00251909, 15265501.url: http://www.jstor.org/stable/2661572. [29] Matthew Elliott, Benjamin Golub, and Matthew O. Jackson. “Financial Networks and Contagion”. In: American Economic Review 104.10 (Oct. 2014), pp. 3115–53.doi: 10.1257/aer.104.10.3115. [30] Matthew Elliott, Jonathon Hazell, and Co-Pierre Georg. “Systemic risk-shifting in nancial networks”. In: Cambridge University Working Paper (2018). [31] Selman Erol. “Network hazard and bailouts”. In: Working Paper (2019). [32] Selman Erol and Guillermo Ordoñez. “Network reactions to banking regulations”. In: Journal of Monetary Economics 89 (2017), pp. 51–67. [33] Yonca Ertimur, Fabrizio Ferri, and David Oesch. “Shareholder votes and proxy advisors: Evidence from say on pay”. In: Journal of Accounting Research 51.5 (2013), pp. 951–996. [34] Emmanuel Farhi and Jean Tirole. “Collective moral hazard, maturity mismatch, and systemic bailouts”. In: American Economic Review 102.1 (2012), pp. 60–93. [35] Financial Crisis Inquiry Commission. The Financial Crisis Inquiry Report. U.S. Government Printing Oce, 2011. [36] Vyacheslav Fos, Kai Li, and Margarita Tsoutsoura. “Do director elections matter?” In: The Reviewof Financial Studies 31.4 (2018), pp. 1499–1531. [37] Xavier Freixas, Bruno M. Parigi, and Jean-Charles Rochet. “Systemic Risk, Interbank Relations, and Liquidity Provision by the Central Bank”. In: Journal of Money, Credit and Banking 32.3 (2000), pp. 611–638.issn: 00222879, 15384616.url: http://www.jstor.org/stable/2601198. [38] Prasanna Gai, Andrew Haldane, and Sujit Kapadia. “Complexity, concentration and contagion”. In: Journal of Monetary Economics 58.5 (2011), pp. 453–470. [39] Douglas Gale and Xavier Vives. “Dollarization, bailouts, and the stability of the banking system”. In: The Quarterly Journal of Economics 117.2 (2002), pp. 467–502. [40] Paul Glasserman and H. Peyton Young. “Contagion in Financial Networks”. In: Journal of Economic Literature 54.3 (Sept. 2016), pp. 779–831.doi: 10.1257/jel.20151228. [41] James K. Glassman and Hester Peirce. “How Proxy Advisory Services Became So Powerful”. In: George Manson University Mercatus Center Working Paper (2014). [42] Gary B. Gorton. Misunderstanding Financial Crises: Why We Don’t See Them Coming. Oxford University Press, 2012. [43] Davidson Heath, Daniele Macciocchi, Roni Michaely, Matthew Ringgenberg, et al. “Do index funds monitor?” In: The Review of Financial Studies (2021). 135 [44] Thomas F Hellmann, Kevin C Murdock, and Joseph E Stiglitz. “Liberalization, moral hazard in banking, and prudential regulation: Are capital requirements enough?” In: American economic review 90.1 (2000), pp. 147–165. [45] Peter Iliev, Jonathan Kalodimos, and Michelle Lowry. “Investors’ attention to corporate governance”. In:PennStateUniversity,OregonStateUniversity,andDrexelUniversityWorkingPaper (2020). [46] Peter Iliev and Michelle Lowry. “Are mutual funds active voters?” In: The Review of Financial Studies 28.2 (2015), pp. 446–485. [47] International Monetary Fund. “Assessing the systemic implications of nancial linkages”. In: IMF Global Financial Stability Report, Vol. 2 (2009). [48] Matthew O Jackson. Social and economic networks. Princeton university press, 2010. [49] Matthew O Jackson and Agathe Pernoud. “Distorted Investment Incentives, Regulation, and Equilibrium Multiplicity in a Model of Financial Networks”. In: Stanford University Working Paper (2020). [50] Michael C Jensen and William H Meckling. “Theory of the rm: Managerial behavior, agency costs and ownership structure”. In: Journal of Financial Economics 3.4 (1976), pp. 305–360. [51] Marcin Kacperczyk, Stijn Van Nieuwerburgh, and Laura Veldkamp. “A rational theory of mutual funds’ attention allocation”. In: Econometrica 84.2 (2016), pp. 571–626. [52] Michael C Keeley. “Deposit insurance, risk, and market power in banking”. In: The American economic review (1990), pp. 1183–1200. [53] Elisabeth Kempf, Alberto Manconi, and Oliver Spalt. “Distracted shareholders and corporate actions”. In: The Review of Financial Studies 30.5 (2017), pp. 1660–1695. [54] David F Larcker, Allan L McCall, and Gaizka Ormazabal. “Outsourcing shareholder voting to proxy advisory rms”. In: The Journal of Law and Economics 58.1 (2015), pp. 173–204. [55] David F Larcker, Allan L McCall, and Brian Tayan. “And then a miracle happens!: How do proxy advisory rms develop their voting recommendations?” In: Rock Center for Corporate Governance at Stanford University Closer Look Series: Topics, Issues and Controversies in Corporate Governance and Leadership No. CGRP-31 (2013). [56] Yaron Leitner. “Financial networks: Contagion, commitment, and private sector bailouts”. In: Journal of Finance 60.6 (2005), pp. 2925–2953. [57] Doron Levit and Anton Tsoy. “One-Size-Fits-All: Voting Recommendations by Proxy Advisors”. In: University of Pennsylvania and University of Toronto Working Paper (2019). [58] Tao Li. “Outsourcing corporate governance: Conicts of interest within the proxy advisory industry”. In: Management Science 64.6 (2018), pp. 2951–2971. 136 [59] Dorothy S Lund. “The case against passive shareholder voting”. In: Journal of Corporation Law 43 (2017), p. 493. [60] Shichao Ma and Yan Xiong. “Information bias in the proxy advisory market”. In: Review of Corporate Finance Studies Forthcoming (2020). [61] Andrey Malenko and Nadya Malenko. “Proxy advisory rms: The economics of selling information to voters”. In: The Journal of Finance 74.5 (2019), pp. 2441–2490. [62] Nadya Malenko and Yao Shen. “The role of proxy advisory rms: Evidence from a regression-discontinuity design”. In: The Review of Financial Studies 29.12 (2016), pp. 3394–3427. [63] John Matsusaka and Chong Shu. “A Theory of the Proxy Advice Market when Investors have Social Goals”. In: USC Marshall School of Business Working Paper (2020). [64] Gregor Matvos and Michael Ostrovsky. “Heterogeneity and peer eects in mutual fund proxy voting”. In: Journal of Financial Economics 98.1 (2010), pp. 90–112. [65] Joseph A McCahery, Zacharias Sautner, and Laura T Starks. “Behind the scenes: The corporate governance preferences of institutional investors”. In: The Journal of Finance 71.6 (2016), pp. 2905–2932. [66] Atif Mian and Amir Su. “The consequences of mortgage credit expansion: Evidence from the US mortgage default crisis”. In: The Quarterly Journal of Economics 124.4 (2009), pp. 1449–1496. [67] Mark Mink, Rodney Ramcharan, and Iman van Lelyveld. “How banks respond to distress: Shifting risks in Europe’s banking union”. In: (2020). [68] Morningstar. Passive Fund Providers Take an Active Approach to Investment Stewardship. https://www.morningstar.com/lp/passive-providers-active-approach. 2017. [69] Frank M. Placenti. Are Proxy Advisors Really a Problem? https://accfcorpgov.org/wp-content/uploads/2018/10/ACCF_ProxyProblemReport_FINAL.pdf. 2018. [70] Rodney Ramcharan, Stephane Verani, and Skander J Van den Heuvel. “From Wall Street to main street: the impact of the nancial crisis on consumer credit supply”. In: The Journal of nance 71.3 (2016), pp. 1323–1356. [71] Bernard S Sharfman. “The Risks and Rewards of Shareholder Voting”. In: SMU Law Review Forthcoming (2020). [72] Hyun Song Shin. “Risk and liquidity in a system context”. In: Journal of Financial Intermediation 17.3 (2008), pp. 315–329.issn: 1042-9573.doi: https://doi.org/10.1016/j.jfi.2008.02.003. [73] Hyun Song Shin. “Securitisation and Financial Stability”. In: The Economic Journal 119.536 (2009), pp. 309–332.issn: 00130133, 14680297.url: http://www.jstor.org/stable/20485321. 137

Abstract (if available)

Abstract Chapter 1 ? Mutual funds rely on recommendations from proxy advisors when voting in corporate elections. Proxy advisors' influence has been a source of controversy, but it is difficult to study because information linking funds to their advisors is not publicly available. A key innovation of this paper is to show how fund-advisor links can be inferred from previously unnoticed features of a fund's SEC filings. Using this method to infer links, I establish several novel facts about the proxy advisory industry. During 2007?2017, the market share of the two largest proxy advisory firms has declined slightly from 96.5 percent to 91 percent, with Institutional Shareholder Services (ISS) controlling 63 percent of the market and Glass Lewis 28 percent in the most recent year. A large fraction of ISS customers appear to have robo-voted?followed ISS's recommendations in over 99.9 percent of contentious proposals?rising from 5 percent in 2007 to 23 percent in 2017, while almost none of Glass Lewis' customers have robo-voted. Negative recommendations from ISS or Glass Lewis reduce their customers' votes by over 20 percent in director elections and say-on-pay proposals. Finally, proxy advisors cater to investors' preferences, adjusting their recommendations to align with fund preferences independent of whether those adjustments lead to recommendations that maximize firm value. ? Chapter 2 ? Most research on financial systemic stability assumes an economy in which banks are subject to exogenous shocks, but in practice, banks choose their exposure to risk. This paper studies the determinants of this endogenous risk exposure when banks are connected in a financial network. I show that there exists a network risk-taking externality: connected banks' choices of risk exposure are strategically complementary. Banks in financial networks, particularly densely connected ones, endogenously expose to greater risks. Furthermore, they choose correlated risks, aggravating the systemic fragility. Banks, however, do have incentives to form networks to protect their charter values. The theory yields several novel perspectives on policy debates.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Executive compensation: the trend toward one size fits all

Asset Metadata

Creator Shu, Chong (author)

Core Title Essays in corporate finance

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Degree Conferral Date 2021-08

Publication Date 07/18/2021

Defense Date 07/16/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag asset substitution,corporate voting,financial networks,OAI-PMH Harvest,proxy advisor,robo-voting,shareholder rights,systemic risks

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Matsusaka, John G. (committee chair), Ahern, Kenneth (committee member), Murphy, Kevin (committee member), Ramos, Joao (committee member), Wong, T.J. (committee member)

Creator Email chong.shu@eccles.utah.edu,chongshu@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC15610961

Unique identifier UC15610961

Legacy Identifier etd-ShuChong-9794

Document Type Dissertation

Format application/pdf (imt)

Rights Shu, Chong

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu