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Essays in financial economics

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Essays in financial economics

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Content ESSAYS IN FINANCIAL ECONOMICS by Qi Sun 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 (ECONOMICS) May 2014 Copyright 2014 Qi Sun Acknowledgments I am grateful to my advisor Vincenzo Quadrini for his invaluable guidance, and to members of the committee Harry DeAngelo, Robert Dekle, and Michael Michaux for many insightful comments and suggestions. ii Table of Contents Acknowledgments ii List of Tables vi List of Figures vii Abstract viii 1 Cash Holdings and Risky Access to Future Credit 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Three-Period Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 The Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.1 Equity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.2 Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.3 Long-Term Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.4 Unused Lines of Credit . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.5 Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3.6 The Firm's Optimization Problem . . . . . . . . . . . . . . . . . . . 17 1.4 Model Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4.1 Normalized Optimization Problem . . . . . . . . . . . . . . . . . . . 20 1.4.2 Functional Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5.2 Parameters and Target Moments . . . . . . . . . . . . . . . . . . . . 24 1.5.3 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5.4 Counterfactual Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.5.5 Comparative Statics of Debt Maturity . . . . . . . . . . . . . . . . . 30 1.6 Model Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.6.1 Credit Crisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.6.2 Credit Boom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1.6.3 Credit Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 iii 1.6.4 Negative Productivity/Investment Shock . . . . . . . . . . . . . . . . 40 1.6.5 Productivity/Investment Uncertainty . . . . . . . . . . . . . . . . . . 41 1.6.6 The 2008 Financial Crisis . . . . . . . . . . . . . . . . . . . . . . . . 42 1.7 Model Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.8 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2 Labor Liability Dynamics and Corporate Debt 59 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.2 A Model of Wage Contract with Financial Frictions . . . . . . . . . . . . . 63 2.2.1 The Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.2.2 The Firm's Optimization Problem . . . . . . . . . . . . . . . . . . . 66 2.3 Optimal Wage Contract and Liability Allocation . . . . . . . . . . . . . . . 68 2.3.1 Optimal Wage Contract . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.3.2 Financial Eects of Long-Term Wage Contract . . . . . . . . . . . . 75 2.4 Model Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.4.1 Normalized Wage Contract . . . . . . . . . . . . . . . . . . . . . . . 76 2.4.2 Policy Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.4.3 Impulse Response Functions . . . . . . . . . . . . . . . . . . . . . . . 79 2.5 Structural Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.5.2 Simulated Method of Moments . . . . . . . . . . . . . . . . . . . . . 82 2.5.3 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.5.4 Counterfactual Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.5.5 Volatility Eect vs. Overhang Eect . . . . . . . . . . . . . . . . . . 87 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3 Credit and Hiring 92 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.2 A Firm Dynamics Model with Bargaining . . . . . . . . . . . . . . . . . . . 94 3.2.1 Firm's Policies and Wages . . . . . . . . . . . . . . . . . . . . . . . . 95 3.2.2 First Order Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.2.3 Special Case with q t =. . . . . . . . . . . . . . . . . . . . . . . . . 100 3.3 Financial Distress Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.3.1 First Order Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.3.2 Computation of the Optimal Policies . . . . . . . . . . . . . . . . . . 106 3.4 Structural Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.4.2 Simulated Method of Moments . . . . . . . . . . . . . . . . . . . . . 108 3.4.3 Parameters and Moments . . . . . . . . . . . . . . . . . . . . . . . . 109 3.5 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 iv 3.5.1 The Importance of the Bargaining Channel . . . . . . . . . . . . . . 112 3.5.2 Non-linear Impulse Response Functions . . . . . . . . . . . . . . . . 115 3.6 Reduced-Form Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.6.1 Unionization Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.6.2 Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.6.3 Robust Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Appendix A Appendix to Chapter 1 125 A.1 A Micro-Interpretation of the Enforcement Constraint . . . . . . . . . . . . 125 A.2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 A.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 A.3.1 Main Programming Routine . . . . . . . . . . . . . . . . . . . . . . . 131 A.3.2 Occasionally Binding Constraints . . . . . . . . . . . . . . . . . . . . 132 A.4 Simulated Method of Moments . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.5 Variable Denitions in the Structural Estimation . . . . . . . . . . . . . . . 137 Appendix B Appendix to Chapter 2 138 B.1 Equivalence of the Recursive Problem and the Original Problem . . . . . . 138 B.2 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 B.3 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 B.4 Numerical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 B.5 Sensitivity Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Appendix C Appendix to Chapter 3 144 C.1 Variables Used in the Structural Estimation . . . . . . . . . . . . . . . . . . 144 C.2 Additional Variables Used in the Reduced-Form Estimation . . . . . . . . . 144 v List of Tables 1.1 Moments and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.2 Counterfactual exercises (I): The role of shocks . . . . . . . . . . . . . . . . 28 1.3 Counterfactual exercises (II): The value of liquidity . . . . . . . . . . . . . . 29 1.4 Estimation with stochastic discount factor . . . . . . . . . . . . . . . . . . . 46 1.5 Counterfactual exercises with stochastic discount factor . . . . . . . . . . . 47 1.6 Determinants of cash accumulation (cash it ) . . . . . . . . . . . . . . . . . 49 1.7 Determinants of cash-to-liquidity ratio ( cash it cash it +unusedlines it ) . . . . . . . . . . 50 2.1 Moments and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.2 Counterfactual: Explaining the decline in net leverage . . . . . . . . . . . . 86 2.3 Decompose the impact of labor liability on nancial debt . . . . . . . . . . 88 3.1 Moments and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3.2 The contribution of the three shocks . . . . . . . . . . . . . . . . . . . . . . 113 3.3 The contribution of the three shocks (xed debt) . . . . . . . . . . . . . . . 114 3.4 Employment growth regression. Baseline regression . . . . . . . . . . . . . . 119 3.5 Employment growth regression. Firm-level unionization . . . . . . . . . . . 120 A.1 Comparative statics of estimated parameters . . . . . . . . . . . . . . . . . 136 A.2 Variable denitions in the structural estimation . . . . . . . . . . . . . . . . 137 B.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 vi List of Figures 1.1 Timing of short-term and long-term borrowing . . . . . . . . . . . . . . . . 8 1.2 A sketch of the dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Comparative statics of debt maturity . . . . . . . . . . . . . . . . . . . . . . 31 1.4 Credit crisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.5 Long-term debt (with cash) provides nancial exibility . . . . . . . . . . . 35 1.6 Credit boom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.7 Where does precautionary cash come from . . . . . . . . . . . . . . . . . . . 37 1.8 Where does precautionary cash go . . . . . . . . . . . . . . . . . . . . . . . 37 1.9 Credit uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.10 Negative productivity/investment shock . . . . . . . . . . . . . . . . . . . . 40 1.11 Productivity/investment uncertainty . . . . . . . . . . . . . . . . . . . . . . 42 1.12 Investment, cash, and unused lines during the 2008 nancial crisis . . . . . 43 2.1 Firm-level net debt ratio and organizational capital ratio . . . . . . . . . . . 60 2.2 Policy functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.3 Impulse response functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.4 Stickiness of labor leverage . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.1 Change of employment growth after credit shocks . . . . . . . . . . . . . . . 115 vii Abstract This dissertation studies how rms make investment and employment decisions when they face frictions in capital and labor markets. Specically, I study (i) how rms manage liquidity under uncertain nancing conditions; (ii) how long-term labor contracts change rms' capital structure decisions; and (iii) how labor bargaining aects rms' nancial and employment policies. In rst chapter entitled \Cash holdings and risky access to future credit," I quantify a new motive of holding cash through the channel of nancing risk. I show that if the access to future credit is risky, rms may issue long-term debt now and save funds in cash to secure the current credit capacity for the future. I structurally estimate the model and nd that this motive explains about 30% of cash holdings in the data. Counterfactual experiments indicate that the value of holding cash is around 8% of shareholder value. The second chapter \Labor liability dynamics and corporate debt," co-authored with Xiaolan Zhang, studies the impact of long-term wage contracts on rms' capital structure decisions. We show that rms not only borrow directly from external investors through debt contracts, but also borrow implicitly from workers by paying lower wage today and promising higher compensation in the future. As a result, rms hold two types of liabilities: nancial debt and labor liability. We also demonstrate that given the rm's total liability viii capacity (captured by the distance to default), the motive of employee retention crowds out nancial debt. That is, rms with higher labor liability have lower nancial leverage. The third chapter \Credit and hiring," jointly written with Vincenzo Quadrini, presents a model in which the compensation of workers is determined through bargaining and rms choose the nancial structure and employment jointly. The purpose of our model is to understand the linkage between nancial markets and employment through a bargaining channel. The basic mechanism of the model is a follows: Higher debt allows rms to negotiate lower wages and therefore increases the incentive to hire more workers. At the same time, however, higher debt also increases the nancial fragility of the rm, that is, the probability of nancial distress. The solution to this trade-o determines simultaneously optimal debt and optimal hiring. When the nancial condition of the rm improves, the likelihood of nancial distress declines, making the debt more attractive. This, in turn, improves the rm's bargaining position with workers, increasing the incentive to hire more employees. It is through this mechanism that improved nancial market conditions generate a hiring boom. Overall, my dissertation seeks to understand the interaction eects between rms' nan- cial policies (nancing and liquidity) and real decisions (investment and employment). Essentially, rms make decisions jointly in a dynamic setting. They choose dierent vari- ables to maximize the shareholders' value, subject to various frictions in capital and labor markets. The results of value maximization imply that in equilibrium marginal bene- ts/costs of all possible tradeos are equalized. I consider three tradeos in the those three chapters: (i) the tradeo between cash and unused lines of credit in liquidity man- agement; (ii) the tradeo between borrowing from external investors through debt contracts and borrowing from internal workers through wage contracts; and (iii) the tradeo between increasing debt to negotiate lower wages and decreasing debt to avoid nancial distress. ix Chapter 1 Cash Holdings and Risky Access to Future Credit In this chapter, I quantify a new motive of holding cash through the channel of nancing risk. I show that if the access to future credit is risky, rms may issue long-term debt now and save funds in cash to secure the current credit capacity for the future. I structurally estimate the model and nd that this motive explains about 30% of cash holdings in the data. Counterfactual experiments indicate that the value of holding cash is around 8% of shareholder value. 1.1 Introduction Holding cash is costly. 1 But, in the data, U.S. public rms on average hold as high as 19% cash in their assets, particularly when they also hold 10% unused lines of credit which could be substitutes for cash. Moreover, during the 2008 nancial crisis rms became increasingly cautious about their access to future credit, and they drew down existing credit lines and held the proceeds in cash even if there were no immediate nancing needs (e.g., Ivashina and Scharfstein (2009)). So, why do rms stockpile cash? In this paper, I qualify a new motive of holding cash by developing a dynamic model of long-term debt with nancing risk. I show that if the access to future credit is risky, 1 The direct return on cash is lower than the interest paid on debt. Also, holding cash may create some agency problems that make the overall return on cash even lower. 1 rms may want to issue long-term debt right now and save the funds in cash, and they do so in order to secure the current credit capacity for the future. Further, I structurally estimate the model using a sample of U.S. public rms and nd that this motive explains about 30% of total cash holding in the data, even after controlling for transactional cash and unused lines of credit. In the model, rms face uncertain nancing conditions and they have two choices to preserve future nancial exibility. The rst choice is to reduce debt and stay away from the borrowing limit. This is explained by the typical precautionary motive and it is similar to the nding of DeAngelo, DeAngelo, and Whited (2011) in which rms choose to keep leverage low to maintain the option to issue more debt in the future. The second choice is to increase long-term debt now and keep the raised funds in cash. The direct cost of the rst choice|unused credit|is lower than the cost of borrowing and holding the funds in cash. This is because the rm does not pay interest on unused credit, while the interest paid on debt is higher than the interest earned on cash. On the other hand, however, unused credit does not provide perfect liquidity insurance as cash does. The current unused credit may not continue to be available in the future. The central assumption of the model is that rms have risky access to future credit. Specically, I assume that the rm's borrowing limit is captured by the value of its collateral assets, which depends on stochastic credit market conditions. Since the potential borrowing limit may shrink in the future, the unused credit can disappear also. Thus, to hedge the risk that the option to borrow may go away in the future, the rm may want to execute the borrowing option earlier and save the proceeds in cash. This is the primary motivation in the model that rms want to hold cash. 2 In the paper's quantitative analysis, I interpret the option to borrow, the dierence between the potential borrowing limit and the actual debt, as unused lines of credit. 2 In that sense, the model's assumption that unused credit is contingent receives considerable support in the data. First, credit lines are short-term. The rollover of credit lines is not guaranteed upon expiration. Second, credit lines may come with borrowing base formulas, which impose a mark-to-market borrowing limit in addition to the existing credit limit. As a result, the amount of available credit is directly linked to the market value of the rm's collateral assets. If the value of collateral assets uctuates, so does the availability of credit lines. 3 Third, the access to lines of credit is also contingent on the lender's ability or willingness to supply funds. The model is an extension of the standard framework with investment and nancing frictions (e.g., Cooley and Quadrini (2001), Hennessy and Whited (2005)). I add three new ingredients. The rst is to add a cash-in-advance constraint to capture the liquid- ity mismatch between nancing and investing. I assume that the rm's cash ows are realized at the end of the period, which implies that the rm needs to hold liquidity (cash or unused credit) for inter-period payments associated with capital expenditures, expiring credit market liabilities, and dividend payout. Because of the stochastic nature of payments, the cash-in-advance constraint may be occasionally binding and generate a precautionary motive to hold cash. The second extension is to allow for long-term debt, which is important for distinguish- ing cash from negative debt. With only one-period debt, there is no reason to borrow and 2 The precise dierence between the borrowing limit and the actual debt is unused debt capacity. How- ever, in the data, we only observe the amount of unused lines of credit, but not the total unused debt capacity. Thus, I use unused lines of credit as lower-bound approximations of unused debt capacity. 3 According to the data of a random sample of 600 Compustat rms hand-collected by Berrospide and Meisenzahl (2013), the average ratio of available credit to total credit limit is 89% which declines during the 2008 nancial crisis. 3 hold cash since cash gives a lower direct return than the cost of debt. Firms will simply use all the available cash to reduce the liabilities that are due in the next period. With long-term debt, however, rms may have an incentive to borrow and temporarily hold cash to secure the current availability of credit for the future. This is possible because the long-term debt does not need to be repaid in full in the next period, even if the rm loses access to credit. The third extension is the consideration of shocks that aect the nancial condition of rms, that is, their access to credit. This is in addition to a standard productiv- ity/investment shock. The model is solved numerically by a non-linear approach, the projection method, and most model parameters are estimated by the simulated method of moments. After the estimation, I conduct two counterfactual exercises. First, I examine the impact of each shock on rms' cash holdings. Since my model has two shocks, I can turn o one to study the impact of the other. In this counterfactual experiment, I nd that nancing risk is the key to understand rms' cash behaviors; it explains about 90% of precautionary cash in the benchmark model. The investment risk, however, explains only 10%. The second counterfactual exercise I do is to shut down the channel of precautionary cash, that is, I set the cash-in-advance constraint to be always binding. In that case, I nd that the shareholder value decreases by 8%, and I interpret this 8% as the value of holding precautionary cash. I also use the model to study the impact of shocks that aect the nancing conditions of rms and compare the prediction of the model to the real data. I nd that in response to a credit crisis, rms reduce precautionary cash and unused lines of credit dramatically, while they do not cut investment much. This result is consistent with Duchin, Ozbas, and Sensoy (2010) who show that rms used their cash holdings as buers to smooth investment at the onset of the 2007-2008 credit crisis. In response to a credit boom, instead, rms not only 4 keep most new credit as unused lines, but also save cash out of borrowing. Such behavior demonstrates the precautionary motive of holding liquidity: even if rms are in favorable market conditions, they are still cautious about the possibility of future adverse nancing conditions. Another exercise conducted in the paper is to study the implications of an increase in credit uncertainty, that is, the volatility of the nancial shock. In this way the paper also relates to the literature on time-varying volatility. In response to an increase in credit uncertainty, rms draw down credit lines and keep the proceeds in cash, that is, they shift the composition of liquidity from risky credit lines to safer cash holdings. This prediction is consistent with the nding of Ivashina and Scharfstein (2009) that rms increasingly drew down their credit lines in the second half of 2008, but draw-downs were not driven by rms' investment opportunities since they were held largely in cash. This paper relates to several strands of literature. The rst strand of literature tries to explain why cash could be dierent from negative debt. A feature shared by many dynamic corporate nance models is that holding cash is dominated by the use of cash to repay the outstanding debt. 4 To explain why cash is not negative debt, there are generally two approaches in the literature. The rst is to impose debt issuance costs such as in Gamba and Triantis (2008), Boileau and Moyen (2009). Although those studies provide testable implications on rms' choices between debt and cash holdings, the economic interpretation of the reduced-form debt issuance cost is controversial. The other approach is to allow dierent maturities between cash and debt. Chaderina (2012) develops a model with two- period defaultable debt in which rms hold precautionary cash to hedge shocks that aect their future protability prospects. The main dierence between my paper and Chaderina 4 For example, Cooley and Quadrini (2001), Hennessy and Whited (2005, 2007), Moyen (2004), Riddick and Whited (2009), DeAngelo, DeAngelo, and Whited (2011), Bolton, Chen, and Wang (2011), Hugonnier, Malamud, and Morellec (2012), and Eisfeldt and Muir (2012). 5 (2012) is that I consider multi-period debt with enforcement constraints. Further, instead of studying the role of shocks that aect future prospects, I focus on the nancing risk, i.e., the risk of losing access to future credit. The paper also contributes to the theory of dynamic capital structure. Recent studies show that nancial exibility in the form of unused debt capacity plays an important role in the choice of the capital structure (e.g., DeAngelo, DeAngelo, and Whited (2011), Denis and McKeon (2012)). According to these studies, rms choose to borrow less (low leverage) to maintain the option to borrow in the future. In this paper, I show that under the setting of uncertain nancing conditions, unused debt capacity may disappear before the rm taps it. As a result, the risk of losing unused debt capacity would induce rms to borrow more now (high leverage) and keep the funds in cash. Thus, this paper implies that rms might make capital structure decisions jointly with liquidity policies. Third, the paper also relates to the recent literature studying the impacts of nancial shocks on rms' investment and nancing decisions. Jermann and Quadrini (2012) study the macroeconomic eects of nancial shocks and show that standard productivity shocks can only partially explain the movements in real and nancial variables. The addition of nancial shocks brings the model closer to the data. Instead of focusing on the aggregate economy, my paper focuses on individual rms with special attention paid to publicly listed U.S. corporations. This allows me to show from a micro prospective, as opposed to a macro approach, that nancial shocks do play an important role in explaining rms' nancing and investment decisions, especially for liquidity management policies. This paper is also closely related to Bolton, Chen, and Wang (2011) and Eisfeldt and Muir (2012), who consider stochastic nancing opportunities, and to Hugonnier, Malamud, and Morellec (2012) who adopt a similar interpretation of the credit supply shocks. 6 1.2 Three-Period Model To illustrate the central idea of the paper, I start presenting a simple three-period model. There are three days: day 1, day 2, and day 3. On day 1, a rm makes borrowing and saving decisions and it has access to external nancing up to a xed borrowing limit . On day 2, the rm faces an investment opportunity of sizei and still has access to the external nancing but with a stochastic borrowing limit . The value of is revealed at the beginning of day 2. On day 1, the rm knows only that there are two possible realizations: H and L , with probabilities p H and 1p H , respectively. The expected credit limit is = p H H + (1p H ) L . To create a possible liquidity shortage on day 2, I assume that under adverse nancing conditions the rm cannot borrow enough funds to nance investment, that is, L <i. However, the expected credit limit is greater than the investment, that is, >i. At the beginning of day 2 the rm could face two situations. In the rst situation, the total available funds (cash savings plus new debt issuances minus debt repayment) are larger than the investment. Therefore, the rm is able to make the investment. In the second situation, the available funds are insucient to fund the investment and the rm is unable to make the investment. On day 3, the rm receives the revenue R H if it invested on day 2, or receives R L otherwise. Then, the rm pays o the debt. The remaining funds are paid out as dividends. The timing of decisions and events is summarized in the top panel of Figure 1.1. In this simple model I assume that the discount factor is 1 and the gross interest rate of one-period debt is also 1. The gross interest rate of two-period debt is 1 +r. I also assume that the revenue R H is suciently larger than R L so that if the rm has enough liquid funds on day 2 it would always take the investment project. 7 day 1 day 2 day 3 borrow or save invest i, credit shock liquidity constraint revenue short-term debt b 1 # repay debt on day 2 b1i b1 <i RH RL long-term debt m 1 " repay debt on day 3 maxfb2; 0g+m1i maxfb2; 0g +m1 <i RH (1 +r)b2 RL (1 +r)b2 Figure 1.1: Timing of short-term and long-term borrowing 8 Let's rst consider the scenario that cash and debt have the same maturity. In this case cash is equivalent to negative one-period debt. The middle panel in Figure 1.1 illustrates the timing of short-term borrowing. I use backward induction to study the rm's decisions. Consider the rm's choices on day 2: to take advantage of the investment opportunity, the rm has to satisfy the cash-in-advance constraint (or liquidity constraint) such that: b 1 i. Here, the variable b 1 denotes the rm's net debt on day 1. Given that is the maximum amount the rm can borrow on day 2 and that b 1 is the amount of debt that needs to be repayed, the available funds for investment are b 1 . Thus, the rm makes the investment only if b 1 i. Now, consider the rm's borrowing and saving decisions on day 1. On day 1, the borrowing limit of day 2 is unknown. However, the rm knows there are only two realizations: 2f H ; L g. Thus, given the assumption that the investment project is suciently protable, on day 1 the rm wants to make sure that it will always have enough funds to nance the investment project on day 2, irrespective of the borrowing conditions it will encounter on day 2. As a result, to hedge the worst nancing condition L on day 2, the rm would like to borrow less on day 1 (b 1 < 0) so that the cash-in-advance constraint on day 2 will always be satised ( L b 1 i). In the three-period model considered here, the state variables at the beginning of day 1 are not specied. In the dynamic model I will consider later, the rm holds debt outstanding at the beginning of the period. Thus, in that case the rm would choose to reduce its debt balances on day 1 in order to hedge the adverse nancing conditions on day 2. To sum up, with only one-period debt, although the rm can access amount of external nance on day 1, it chooses not to tap it. Instead, the rm keeps b 1 of unused credit. This is the later-borrowing motive which induces rms to hold unused lines of credit. In other words, the rm does not borrow now in order to be able to borrow later when the investment opportunity becomes available. 9 Consider now the scenario in which the rm can borrow with two-period debt. The bottom panel of Figure 1.1 illustrates the timing. In this scenario, if the rm borrows on day 1, it does not need to pay back the debt on day 2. Instead, it repays the debt on day 3 with interest rate r. Now, to take advantage of the investment opportunity on day 2, the rm would tap the credit market on day 1 and save the proceeds in cash. Denote by b 2 the amount of two-period debt that the rm borrows on day 1 and by m 1 the amount of cash that the rm carries from day 1 to day 2. The cash-in-advance constraint on day 2 becomes: maxfb 2 ; 0g +m 1 i, where the term maxfb 2 ; 0g is unused credit on day 2. To satisfy this cash-in-advance constraint even in the worst nancing condition L , the rm would borrow positively and save cash on day 1: b 2 = m 1 = i. Notice that this is possible because of the assumption that >i. That is, the borrowing limit on day 1 is sucient to nance the investment on day 2. To sum up, when there is access to two-period debt, the rm has the incentive to borrow earlier and save the proceeds in cash to hedge against adverse future credit conditions ( = L ). This is the pre-borrowing motive that induces rms to borrow now and save the cash for the later period when investment opportunities become available. The goal of borrowing now is to secure enough funds in the later period, something that would not be guaranteed if the debt was only for one-period. The full dynamic model I describe in the next section will feature both the later- borrowing motive and the pre-borrowing motive. The presence of these two motives allows the model to generate the coexistence of cash and unused lines of credit in the optimal liquidity policies of rms. 10 1.3 The Dynamic Model Figure 1.2 provides a sketch of the dynamic model. Consider a non-nancial rm's balance sheet: on the assets side, it contains physical capital, cash holdings, and unused lines of credit; 5 on the liabilities side, it has equity and debt. In the model, equity is sticky and debt is subject to an enforcement constraint. The goal of the model is to understand how does a credit shock aect a rm's investment decisions and how does the rm manage its liquidity to hedge against the credit shock. In the following subsections, I discuss the elements of the balance sheet one by one. Assets Liabilities Capital investment Equity sticky enforcement Debt# Cash liquidity management Unused Lines credit shock Figure 1.2: A sketch of the dynamic model 5 In the data, used lines of credit are debt obligations, whereas unused lines of credit remain o the balance sheet. 11 1.3.1 Equity Each rm is run by a manager who behaves in the interests of incumbent shareholders and maximizes the expected discounted present value of dividends. The rm's objective function is V t =Max :d t +E t [ t+1 V t+1 ]: (1.1) The variableV t represents the rm's equity value at the beginning of time t,d t is dividend payout during time t, and t+1 = is the shareholders' discount factor from time t to t + 1. 1.3.2 Capital The rm does not employ labor to produce goods. Capital is the only input. At each period t, the rm can access a production technology F (z t ;k t ), in which k t is capital and z t is a productivity shock. In line with DeAngelo, DeAngelo, and Whited (2011), I refer to z t as investment shock to capture the idea that variations in z t re ect the marginal productivity of capital and therefore the protability of investment opportunities. Capital evolves according to k t+1 (1)k t =( i t k t )k t : (1.2) The variable is capital depreciation rate, and the function ( it kt ) species the capital adjustment costs. 1.3.3 Long-Term Debt The rm borrows in the form of long-term debt. I use a version of the exponential model introduced in Leland and Toft (1996), and recently used by Hackbarth, Miao, and Morellec 12 (2006), Gourio and Michaux (2012), and among others. In each period, the rm rst repays a xed proportion of its existing debt, and then it issues new debt with repayment rate b and price p t ( b ). Specically, with repayment rate b , one unit of debt issued at time t receives a payment b at time t + 1, a payment b (1 b ) at time t + 2, and a payment b (1 b ) 2 at time t + 3, and so on. As in the literature, I assume that the economy only contains a single type of maturity structure b and all debtholders have the same seniority without regard to when the debt was issued. Thus, in each period t, I only need to keep track of the total amount of debt instead of the distribution of debt with dierent maturity dates. Denote b t as the debt balances at the beginning of period t, then the total amount of repayment is b b t . The dynamics of long-term debt are given by b t+1 = (1 b )b t +n t ; (1.3) where, the variableb t represents the debt balances at the beginning of periodt,n t represents the debt issuances during periodt, andb t+1 denotes the debt balances at the end of period t. When n t > 0, the rm issues new debt after repayment; when n t < 0, the rm chooses to repay more than b percent of existing debt. Firms do not default in the model. However, in each period t rms are subject to the following enforcement constraint: p t b t+1 max n t k t+1 ; (1 b )p t b t o : (1.4) The variable t represents the collateral rate of capital and it also re ects the market price of capital (credit market conditions). This enforcement constraint implies that the maximum amount of debt the rm holds at the end of period t should be either less than 13 the value of collateral assets at the end of period t or be less than the value of non-paid debt of period t. In Appendix A.1, I provide a micro-interpretation for this enforcement constraint. If debt is one-period b = 1, the equation (1.4) becomes p t b t+1 t k t+1 , which is the collateral constraint in Kiyotaki and Moore (1997). However, if debt is multiple-period b < 1, the rm may hold debt more than the value of collateral assets, i.e.,p t b t+1 t k t+1 . This happens only when t k t+1 (1 b )p t b t . It is due to the arrangement of long-term debt: in each period t, the rm is only obligated to repay b t amount of debt. After that, the lender cannot force the rm to repay more, even if the credit market condition ( t ) or the rm's credit quality ( t k t+1 ) uctuates. The pricing of long-term debt is straightforward. Dene the debtholders' discount factor as t+1 , the same as the shareholders', then the price of long-term debt before the tax shield is ^ p t =E t [ t+1 b + t+1 (1 b )^ p t+1 ]: (1.5) The current price of long-term debt is the sum of discounted future repayment and dis- counted value of non-paid debt. Denote as the corporate tax rate, then the price of long-term debt after the tax shield is p t = 1 1 + (1)(^ p 1 t 1) : (1.6) Thus, the nal price of long-term debt depends on the debt repayment rate b , the corporate tax rate , and the debtholders' discount factor t+1 . 1.3.4 Unused Lines of Credit The denition of unused lines of credit is based on the following assumption: 14 Assumption 1 The lender honors the rm's outstanding debt, but it cannot fully commit to the unused portion of credit lines. In the model, the enforcement constraint (1.4) is occasionally binding. I dene the rm's unused lines of credit as the dierence between the right side and the left side of the enforcement constraint: the total borrowing capacity minus the actual borrowing. Denote l t as the amount of unused lines of credit during the period t, then l t =! t+1 p t b t+1 ; (1.7) where the variable! t+1 is the rm's total debt capacity dened as! t+1 = max t k t+1 ; (1 b )p t b t . Notice that although the second term (1 b )p t b t in the parentheses is pre- committed, the rst term t k t+1 is contingent on the current credit market condition t and the size of the rm's capital assetsk t+1 . Thus, the amount of unused credit during the period t is not fully committed, and the actual availability of credit depends on the rm's credit quality t k t+1 . This denition of unused lines of credit captures the following lending procedures in practice. First, the rm applies for a loan. Second, the bank evaluates the rm's collateral assets. Then, based on the collateral assets, the bank issues a credit line to the rm. Fourth, given the credit line, the rm decides how much to borrow now and how much to save as unused lines. Finally, on the top of above steps, the bank reevaluates the rm's collateral assets period by period and adjusts the credit limit accordingly. However, the denition of unused lines of credit in this paper is not exactly the same as the one used in the literature (e.g., Holmstrom and Tirole (1998)). First, in the cur- rent setting, for simplicity, rms do not pay a commitment fee to secure a credit line, although introducing a xed fee will not change the results. Second, credit line is not a pre-commitment contract in the sense that the availability of credit line is contingent on 15 the rm's credit quality as well as the lender's nancial health (credit market conditions). Third, to avoid high-dimensional computation problems and to highlight the risk of losing unused credit, I do not model lines of credit as state-contingent claims. Instead, I focus on the timing of credit line usage: given the access to a credit line with its limit depends on the rm's credit quality and the bank's willingness to supply funds, the rm makes choices about how much to draw down right now and how much to save as unused credit for future needs. 1.3.5 Cash The timing of a rm's decision is as follows. In each period t, the rm starts with capital assets k t , debt outstanding b t , and cash holdings m t . Then the rm observes the period t's investment condition z t , and credit condition t . After that, the rm rst repays b percent of its debt outstanding b t , and then decides the amount of new debt issuance n t , investment i t , dividend payout d t , and nally cash savings m t+1 . k t ;b t ;m t z t ; t b b t n t i t d t F t m t+1 Timing However, the rm's revenuesF (z t ;k t ) are realized at the end of periodt, while payments need to be made at the beginning of the period. Thus, at the beginning of period t the rm faces a cash-in-advance constraint (liquidity constraint): the sources of funds must be sucient to support the uses of funds, m t |{z} cash holdings + p t n t |{z} debt issuance b b t |{z} debt repayment + i t |{z} investment + d t |{z} payout : (1.8) The left side of equation (1.8) includes the nancing sources: cash holdings and debt issuance; and the right side of equation represents the nancing needs: debt repayment, 16 investment, and dividend payout. In this section, I assume that the rm cannot issue equity (or pay negative dividend). That is, d t 0. But I will relax this assumption in the quantitative studies. To sum up, given the rigidities of adjusting the nancing needs: mandatory debt repay- ment, non-negative dividend payout, and capital adjustment costs, to satisfy the period t's cash-in-advance constraint, in period t 1 the rm has two choices: either to accumulate cash or to reserve unused credit. All the rm's decisions are subject to the budget constraint: F (z t ;k t ) +m t +p t n t =p m t m t+1 + b b t +i t +d t ; (1.9) where the variablep m t is dened as the price of cash. After combining this budget constraint with the cash-in-advance constraint, the cash-in-advance constraint can be rewritten as p m t m t+1 F (z t ;k t ): (1.10) This cash-in-advance constraint is occasionally binding in the model, and when it does not bind, I dene the precautionary cash as c t =p m t m t+1 F (z t ;k t ): (1.11) When the precautionary cashc t > 0, the cash balances carried into the next period are larger than the cash generated from cash ows in the current period. 1.3.6 The Firm's Optimization Problem To sum up the model, recall a rm's balance sheet. 17 Assets Liabilities Capital k t+1 Equity V t Cash m t+1 Debt b t+1 The rm considers three tradeos. (1) On the assets side of the balance sheet, the rm makes choices between cash and capital. Although cash earns a lower rate of return than capital, cash is more liquid than capital since the rms faces capital adjustment costs. (2) On the liabilities side, the rm prefers debt nance to equity nance because of the tax shield of debt. However, debt nance is limited by the enforcement constraint. (3) Between the assets side and the liabilities side, cash is not negative debt because of the maturity dierences. While cash helps to smooth the funds from long-term borrowing between periods, holding cash incurs an opportunity cost. The above three tradeos imply two motivations of holding liquidity. (a) Later- borrowing motive: given the rigidities of adjusting the nancing needs, the rm chooses to keep distances from the borrowing limit and to save unused credit to hedge future credit contractions. (b) Pre-borrowing motive: given the maturity mismatch between cash and debt, the rm also chooses to borrow more with long-term debt and save funds in cash, and it does so also as insurance against future credit contractions. Let V (k;m;b;s) be the rm's equity value at the beginning of period t, where s rep- resents the exogenous state variables z and . The rm's problemP can be written down recursively: 18 V (k;m;b;s) = max k 0 ;m 0 ;b 0 ;d d +E[ 0 V (k 0 ;m 0 ;b 0 ;s 0 )] subject to: p m m 0 F (z;k) (1.12) F (z;k) +m +pn =p m m 0 + b b +i +d (1.13) d 0 (1.14) k 0 (1)k =( i k )k (1.15) b 0 = (1 b )b +n (1.16) pb 0 max k 0 ; (1 b )pb (1.17) The manager maximizes the equity value of the rm subject to six constraints: the cash-in-advance constraint, the budget constraint, the non-negative dividend constraint, the capital accumulation equation, the dynamics of long-term debt, and the enforcement constraint. I summarize the following two propositions for the rms' problem and their proofs are in Appendix A.2. Proposition 1 If the debt repayment rate b = 1, the cash-in-advance constraint is always binding and precautionary cash c t = 0. Proposition 2 There exists a cuto b < 1 such that: if b < b , the cash-in-advance constraint is occasionally binding and precautionary cash c t > 0. The economic intuition of these two propositions is as follows. When the debt repay- ment rate b = 1, cash is the same as negative debt. As a result, rms do not hold precautionary cash because they can always save interest expenses by using cash to reduce 19 debt. However, when the repayment rate b < b , the benet of holding cash can be larger than the direct costs holding cash. This is because, if the rm borrows with long-term debt today and saves the funds in cash, it can ensure itself from future credit contractions. 1.4 Model Solution The model is solved numerically by the projection method, and the numerical procedures are discussed in Appendix A.3. 1.4.1 Normalized Optimization Problem To keep the model computation tractable, I detrend all rm-level variables by capital k, using the assumption of linear technology F (z;k) = zk. After detrending, the rm's optimization problem becomes: ~ V ( ~ m; ~ b;s) = max g 0 ; ~ m 0 ; ~ b 0 ; ~ d ~ d +g 0 E[ 0 ~ V ( ~ m 0 ; ~ b 0 ;s 0 )] subject to: p m ~ m 0 g 0 z (1.18) z + ~ m +p~ n =p m ~ m 0 g 0 + b ~ b + ~ i +'( ~ d) (1.19) g 0 (1) =( ~ i) (1.20) p ~ b 0 g 0 = (1 b )p ~ b +p~ n (1.21) p ~ b 0 g 0 g 0 + (1)(1 b )p ~ b (1.22) 20 where, g 0 =k 0 =k is the growth rate of capital, ~ m =m=k, ~ b =b=k are detrended state variables, and ~ x = x=k are other derended variables. In this normalized optimization problem, there are only two state variables left, the cash-to-capital ratio ~ m and the debt- to-capital ratio ~ b, and this makes the numerical computation much easier. To make the model closer to explaining the real data, in the following quantitative analysis I will relax the assumption of no negative dividend payout. Instead of imposing the non-negative dividend constraint (1.14), I add a smooth equity adjustment cost func- tion '( ~ d) in the budget constraint (1.19) to capture the frictions in adjusting equity. For numerical purposes, I also replace the debt enforcement constraint (1.17) with its stochastic version, the equation (1.22), in which I take away the term `max' and introduce a renanc- ing probability . In Appendix A.1, I show that these two enforcement constraints (1.17) and (1.22) are equivalent. 1.4.2 Functional Forms In this section, I discuss the functional forms of capital and equity adjustment cost, and also the assumptions on the process of the shocks. The capital adjustment cost function ( it kt ) is given by ( i t k t ) = a 1 (1) ( i t k t ) 1 +a 2 : (1.23) This function is concave in i t and decreasing in k t . The concavity of () captures the idea that it is more costly to change the capital stock quickly. The value 1= is the elasticity of investment-capital ratio with respect to the marginal q. The parameters a 1 = and a 2 = 1 are set so that in the steady state the capital adjustment cost is zero and the marginal q is equal to one. This adjustment cost function has been widely used in 21 the investment and production-based asset pricing literature. See, for example, Jermann (1998). As in Jermann and Quadrini (2012), the equity adjustment cost function '( ~ d) is given by '( ~ d) = ~ d +( ~ d ~ d target ) 2 ; (1.24) where is a parameter measuring the rigidities of adjusting equity, and ~ d target is a long- term targeted dividend payout ratio calibrated to match the average dividend payout ratio in the data. This equity adjustment cost function implies: if the rm pays dividend at its long-term target ratio, it does not occur any cost; however, if the rm deviates from its long-term target ratio, it needs to pay an additional cost; and particularly, if the rm wants to pay negative dividend, that is, to issue equity, it needs to pay a cost that is convex in the amount of issuances. 6 The productivity shock z t follows a rst order autoregressive process log(z t ) = z + z log(z t1 ) 2 z =2 + z u t ; (1.25) where u t is i:i:d innovation with standard normal distribution N(0; 1). The variable z refers to the drift of the process log(z t ), z refers to the persistence, and z refers to the volatility. The model allows large-scale shocks. Thus, given the log-normal specication, the impact of volatility z on the conditional expectation of the productivity shock z t can not be ignored. Following Gilchrist, Sim, and Zakrajsek (2010), I subtract the term 2 z =2 in equation (1.25) to remove this second-order impact. Since u t is distributed normally, 6 To this end, I also provide three interpretations for why there are rigidities through equity adjustment costs. (1) Equity issuance cost. The rm pays an additional cost when it issues equity to shareholders. And the cost is convex in the sense that underwriting fees display increasing marginal cost in the size of the oering, e.g., Altinkilic, and Hansen (2000). (2) Dividend smoothing. The rm has a long-term targeted payout ratio, and it actively adjusts the payout ratio when the ratio was deviated from the target. (3) Dividend tax. Shareholders need to pay income tax on dividends they received. 22 simple algebra showsE(e 2 z =2+zut j z ) = 1. Thus, increases in the volatility z represent a mean-preserving spread to the conditional distribution of productivity z t . For numerical purposes, I approximate the dynamics of AR(1) process in equation (1.25) with a nite- state Markov chain. The renancing probability t in equation (1.22) is stochastic, and I refer to it as nancing shock or credit shock. Similar to the productivity shock, the nancing shock t follows a AR(1) process: t = + ( t1 ) +v t ; (1.26) where the variables and are respectively the mean and the persistence of process t . The variablev t isi:i:d innovation with distributionN(0; 2 ), and refers to the volatility of the nancing shock. Also, I approximate this AR(1) process with a nite-state Markov chain in the quantitative analysis. 1.5 Estimation In this section I conduct a structural estimation of the model. I start by describing the data, and then discuss the estimation procedures and results. 1.5.1 Data I obtain data from the Compustat annual les except for the variable unused lines of credit. Data about unused lines of credit is not available in Compustat, and most existing research manually collects the credit line data from rms' SEC 10-K les (see, for example, Su (2009), Yun (2009)). For this study, I use the data from the Capital IQ database, which contains a large sample of unused lines of credit from 2002 to 2010. In Capital IQ, the variable unused lines of credit refers to total undrawn credit, which includes undrawn revolving credit, undrawn commercial paper, undrawn term loans, and other undrawn 23 credit. (See Filippo and Perez (2012) for a detailed description of total undrawn credit in the Capital IQ database.) Following the literature, I exclude nancial rms and utilities with SIC codes in the intervals 4900-4949 and 6000-6999, and rms with SIC codes greater than 9000. I also exclude rms with a missing value of book value of assets, debt, cash, unused line, invest- ment, payout, and cash ow. I winsorize all variables at the 2:5% and 97:5% percentiles to limit the in uence of outliers. All variables are de ated by the Consumer Price Index. The nal sample for the structural estimation is a balanced panel of 1,999 rms over 9 years from 2002 to 2010. Table A.2 provides the denitions and sources of the variables used in the structural estimation. 1.5.2 Parameters and Target Moments The choice of model parameters is done by the simulated method of moments (SMM). The basic idea of SMM is to choose the model parameters so that moments generated by the model are as close as possible to the corresponding real data moments. The detailed estimation steps and identication strategies are discussed in Appendix A.4. The rst panel in Table 1.1 lists the 14 target moments used in the estimation. The choice of target moments is based on the following principle: First, to estimate most of the parameters in the model, I choose the mean and the standard deviation of all six key variables in the model, except the standard deviation of investment which is replaced by the autocorrelation of investment. Second, to identify the persistence of shocks, I also include the autocorrelation of cash and the autocorrelation of cash ows. The second panel in Table 1.1 lists the 10 parameters estimated by the simulated method of moments. They are the drift, the persistence, and the standard deviation of productivity shock z , z , z ; the persistence and the standard deviation of credit shock 24 Table 1.1: Moments and parameters Data Model Target Moments Mean of Cash/Assets 0.189 0.154 Mean of Unused Line/Assets 0.100 0.047 Mean of Debt/Assets 0.162 0.184 Mean of Investment/Assets 0.050 0.053 Mean of Payout/Assets 0.029 0.041 Mean of Cash Flow/Assets 0.098 0.093 Std of Cash/Assets 0.116 0.046 Std of Unused Line/Assets 0.055 0.074 Std of Debt/Assets 0.082 0.091 Std of Payout/Assets 0.027 0.025 Std of Cash Flow/Assets 0.070 0.033 Auto-Corr of Cash/Assets 0.188 0.191 Auto-Corr of Investment/Assets 0.205 0.220 Auto-Corr of Cash Flow/Assets 0.297 0.315 Estimated Parameters Estimates SE The drift of productivity shock, z 0.041 (0.007) Persistence of productivity shock, z 0.466 (0.086) Volatility of productivity shock, z 0.421 (0.077) Persistence of credit shock, 0.410 (0.063) Volatility of credit shock, 0.457 (0.054) Capital depreciation rate, 0.087 (0.012) Collateral rate, 0.456 (0.041) Equity rigidity parameter, 0.533 (0.118) Capital adjustment cost, 0.779 (0.199) Price of cash, p m 0.975 (0.023) Calibrated Parameters Subjective discount factor, 0.97 Corporate eective tax rate, 0.15 Debt repayment rate, b 0.31 , ; the capital depreciation rate ; the collateral rate ; the equity rigidity parameter ; the capital adjustment parameter ; and the price of cash p m . 25 The third panel in Table 1.1 lists the 3 parameters that are calibrated directly form the data. I set the subjective discount rate = 0:97 such that the implied one-period interest rate is approximately equal to the average of the real interest rate 1:03 over sample period 2002-2010. I use the eective corporate tax rate = 0:15. The debt repayment rate b = 0:31 is set to match the average long-term debt retirement rate in the data. 1.5.3 Estimation Results Table 1.1 reports the estimation results. The model matches the data quite well, except for three moments: the mean of unused lines of credit, the standard deviation of cash, and the standard deviation of cash ows. The model is unable to match those three moments for the following reasons: To generate a higher standard deviation of cash or cash ows, the model requires a lower capital adjustment cost. However, on the other hand, the model needs a higher capital adjustment cost to match the level of unused lines of credit. There is thus a tension between matching the level of the rm's liquidity holdings and matching the standard deviation of the rm's real decisions. The second panel in Table 1.1 shows the estimated value of model parameters. The estimated standard deviation of productivity shock is 0.466, and the persistence is 0.421. Compared to the literature (for example, DeAngelo, DeAngelo, and Whited (2011)), the estimated standard deviation of productivity shock is higher while the persistence is lower. The reason is that the data I considered includes the recent nancial crisis. Thus, it is reasonable to nd that rms' decisions are more volatile in my estimation. The estimated standard deviation of credit shock is 0.457, and the persistence is 0.410. Since these two estimates of credit shocks are new in the literature, it is useful to explain the magnitude of the shocks. Suppose that during normal periods the rm can renance its debt with a probability of 50%, then the estimated magnitude means that: if the rm 26 is hit by the worst credit shock, it cannot renance its debt anymore; if the rm receives the best credit shock, it can renance its debt with probability 100%. The estimated collateral rate is 0.456, which implies that the rm can borrow up to 45:6% of its capital assets. The equity rigidity parameter is 0.533, which means that for a rm with $10 in the book value of assets, if the rm issues $1 in equity, its issuance cost is 5% of the proceeds; if the rm issues $2 in equity, its issuance cost doubles to 10% of the proceeds. That is, the equity issuance cost is convex. The capital adjustment cost is 0.779, which implies that the elasticity of investment-capital ratio with respect to the marginal q is 1.28. The estimated price of cash p m is 0.975, which is higher than the price of one-period debt 0.97. The dierence between the price of cash and the price of one-period debt can be interpreted as the opportunity cost of holding cash, or the liquidity premium. In terms of return, the interest rate earned on cash is 1=0:975 1:026, while the interest rate paid on debt is 1:03. Thus, the estimated liquidity premium is about 40bps. 1.5.4 Counterfactual Exercises Given the estimated model, I conduct a counterfactual exercise to nd out which types of risks are better in explaining the rm's liquidity decisions: nancing risks or investment risks. I rst simulate the model using the estimated parameters to generate benchmark moments, and then I remove the productivity/investment shock from the model and sim- ulate a new set of moments as a comparison. Similarly, I also remove the nancing shock from the model and simulate another set of moments. Table 1.2 shows the results of the experiment. First, compared to the data (column one), the benchmark model (column two) explains 67% precautionary cash and 47% unused 27 Table 1.2: Counterfactual exercises (I): The role of shocks Data Benchmark Financing Productivity Model Shock Shock Moments Mean of PrecautionaryCash/Assets 0.091 0.061 0.057 0.004 Mean of Unused Line/Assets 0.100 0.047 0.033 0.010 Mean of Cash/Assets 0.189 0.154 0.151 0.103 Mean of Debt/Assets 0.162 0.184 0.204 0.258 Mean of Investment/Assets 0.050 0.053 0.056 0.057 Mean of Payout/Assets 0.029 0.041 0.038 0.033 Mean of Cash Flow/Assets 0.098 0.093 0.094 0.098 Std of Cash/Assets 0.116 0.046 0.039 0.031 Std of Unused Line/Assets 0.055 0.074 0.054 0.017 Std of Debt/Assets 0.082 0.091 0.084 0.025 Std of Payout/Assets 0.027 0.025 0.024 0.021 Std of Cash Flow/Assets 0.070 0.033 0.004 0.035 Auto-Corr of Cash/Assets 0.188 0.191 0.115 0.207 Auto-Corr of Investment/Assets 0.205 0.220 -0.053 0.020 Auto-Corr of Cash Flow/Assets 0.297 0.315 0.258 0.256 lines of credit. 7 Second, the model with only nancing shock (column three) generates 63% precautionary cash and 33% unused lines of credit as observed in the data. Third, the model with only productivity shock (column four) generates 4% precautionary cash and 10% unused lines of credit. Thus, this counterfactual exercise implies that nancing risk is the driving force for rms to hold liquidity, particularly for the precautionary cash. Further, the precautionary cash generated by nancing risk accounts for 0:057 0:189 30% of total cash holdings in the data. A second counterfactual exercise I conduct is to examine the value of holding liquidity. I run the following three experiments. In the rst experiment, I shut down both the channel of holding precautionary cash and the channel of holding unused lines of credit. That is, I 7 According to the model, precautionary cash of period t is dened as cash holdings at the beginning of period t + 1 minus cash ows at the end of period t. 28 assume that both the cash-in-advance constraint and the debt enforcement constraint are always binding in the model. In the second experiment I shut down only the channel of holding unused lines of credit, and in the third experiment I shut down only the channel of holding precautionary cash. Finally, I compare the rm's performances under these three experiments. Since in the model the level of nancial risk endogenously depends on the size of collat- eral assets and non-paid debt, when comparing the rm's performances under those three experiments, I set the value of capital and the value of debt in the experimental models to be the same as in the benchmark model. 8 As a result, rms in those experiments are identical expect for having dierent channels of holding liquidity. Table 1.3: Counterfactual exercises (II): The value of liquidity Benchmark Model (1) Model (2) Model (3) Model Neither NoLines NoPcash Normalized Value of Cash Flow 0.110 0.110 0.110 0.110 Normalized Value of Debt 0.245 0.245 0.245 0.245 Normalized Value of Precautionary Cash 0.063 0.000 0.103 0.000 Normalized Value of Unused Credit Line 0.077 0.000 0.000 0.138 Normalized Value of the Firm 1.000 0.798 0.996 0.937 Normalized Value of Equity 0.755 0.553 0.751 0.692 Normalized Costs of Adjusting Capital 0.101 0.322 0.117 0.108 Normalized Costs of Adjusting Equity 0.023 0.219 0.069 0.014 Normalized Value of Equity Payout 0.042 0.044 0.041 0.036 Normalized Volatility of Equity Payout 0.034 0.110 0.061 0.020 8 This can done by re-calibrating the mean of productivity and nancing shock such that the simulated mean of capital and debt are the same as in the benchmark model. However, the volatility of those two shocks remains the same. 29 Table 1.3 shows the results of the above experiments. Compared to the benchmark model, in the model without any liquidity holdings (Model 1), the equity value decreases by (0:755 0:553)=0:755 27%. The economic explanation behind this result is simple: in the case of no liquidity holdings, the rm needs to adjust equity or capital very frequently, which in turn causes large value losses in the presence of adjustment costs. In the second model (Model 2), the channel of holding unused lines of credit is closed, and therefore the rm holds more precautionary cash as substitutes for unused lines. How- ever, the equity value barely changes. This implies that the rm is doing a good job in substituting unused lines of credit by cash holdings. In the third model (Model 3), the rm is not allowed to hold precautionary cash. Intu- itively, in this case the rm increases unused lines of credit as substitutes for cash. Inter- estingly, however, the shareholder value decreases by (0:755 0:692)=0:746 8%, which is smaller than that of Model 1, but larger than that of Model 2. Thus, this experiment suggests that unused lines of credit are not perfect substitutes for cash holdings. 1.5.5 Comparative Statics of Debt Maturity In this section, I study the comparative statics of the rm's cash holdings and nancing dynamics with respect to the exogenous changes of debt maturity. The top panel in Figure 1.3 shows the rm's cash-to-assets ratio as a function of debt maturity. The solid line represents the model, while the dashed line represents the data. As can be seen from the graph, the rm's cash-to-assets ratio decreases with the maturity of debt, both in the data and in the model. This is because long-term debt provides more stable funds than short-term debt, and hence, when the maturity of debt is long, rms need less liquidity to hedge against renancing risks. Thus, this result is consistent with the nding of Harford, Klasa, and Maxwell (2011) that rms had increased their cash holdings 30 1 2 3 4 5 6 7 8 9 10 5% 15% 25% 35% Debt Maturity (Years) cash it /assets it Model Data 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 Debt Maturity (Years) corr(Δcash it ,Δdebt it ) 1 2 3 4 5 6 7 8 9 10 −0.05 0.05 0.15 0.25 0.35 Model Data Figure 1.3: Comparative statics of debt maturity to mitigate the renancing risk caused by shortening debt maturity over the 1980-2008 period. Moreover, the model-predicted cash-to-asset ratio is quite close to the one observed in the data. Notice that in the model there is only a single type of debt maturity, while in the data there are multiple structures of debt maturity; thus, the comparison here between the model and the data can be taken as an out-of-sample test. 31 A key implication of the model is that rms have incentives to issue long-term debt and save funds in cash to hedge against future credit contractions. Further, this motive of holding cash increases with the maturity of debt. Thus, the model predicts that the correlation between cash accumulation and debt issuance is positive, and the strength of the correlation increases with the maturity of debt. The bottom panel in Figure 1.3 depicts the correlation between cash accumulation and debt issuance as a function of debt maturity. The solid line represents the model, while the dashed line represents the data. As shown in the gure, both in the data and in the model, the correlation is positive and increases in the maturity of debt. Thus, the model's key mechanism is supported by the data. However, the model-predicted correlation is much higher than the one observed in the data. The explanation for this discrepancy is as follows: In the model there are no frictions to prevent rms from saving cash out of debt issuance, and therefore the correlation between cash saving and debt issuance is quite strong, while in the data there might be restrictions on the use of the proceeds from debt issuance, which in turn could weaken the correlation between cash accumulation and debt issuance. Another caveat is that, in the data, I use the maturity of outstanding debt to approximate the maturity of new issued debt, but in the model those two are the same given that there is only a single type of debt structure. In Section 1.8, I test this relation between cash accumulation and debt issuance further by running xed eect regressions in which I control for other sources and uses of cash accumulations. 1.6 Model Implications In this section, I simulate the model to investigate the rm's response to dierent types of shocks. I simulate ve types of shocks to mimic ve hypothetical scenarios: credit crisis, 32 credit boom, credit uncertainty, productivity crisis, and productivity uncertainty. Since the model allows for large-scale shocks, the rm's responses to shocks are not linearized around the steady state; instead, they are the actual nonlinear transition paths after the shocks. When calculating the transition paths, I use the previous estimated structural parameters. 1.6.1 Credit Crisis 0 10 20 30 0 0.5 1 A. financing opportunity 0 10 20 30 10% 20% 30% B. debt and cash debt cash 0 10 20 30 0% 5% 10% C. unused lines of credit 0 10 20 30 0% 5% 10% D. precautionary cash 0 10 20 30 0% 5% 10% Year E. investment 0 10 20 30 0% 5% 10% Year F. net payout Figure 1.4: Credit crisis 33 Figure 1.4 shows the rm's transition paths after a negative credit shock/nancing shock. Panel A plots the process of the negative credit shock. During the rst 10 periods, the rm can access a lender with probability 0.5. At the period of 11, there is a negative credit shock, which reduces the probability of nancing to zero. Here, the size of the shock is derived from the previous estimated value of the shock. From period 12 and so on, the nancing opportunity recovers according to the estimated AR(1) process of the credit shock. Panel B depicts the transition paths of debt-to-assets ratio and cash-to-assets ratio, and Panels C to F describe the transition paths of unused line-to-assets ratio, precautionary cash-to-assets ratio, investment-to-assets ratio, and net payout-to-assets ratio, respectively. As can be seen in Panel B, after a negative credit shock, the rm reduces debt as well as cash holdings. This is because a negative credit shock temporally freezes the rm's access to credit markets. The rm needs to reduce external borrowing and to rely on internal nance. At the same time, as shown in Panels C and D, the rm reduces its liquidity holdings dramatically: both unused lines of credit and precautionary cash hit the zero bound when the rm has trouble accessing the credit market. However, as shown in Panel E, the rm does not cut much of its investment because of its sizable liquidity holdings. This is consistent with the nding of Duchin, Ozbas, and Sensoy (2010) that rms used their cash holdings as buers to smooth investment at the onset of the credit crisis of 2007-2008. Finally, the rm also reduces its net payout after the negative credit shock, which is shown in Panel F. Figure 1.5 shows the sensitivity of the rm's transition paths with respect to the debt repayment rate b , after a negative credit shock. I consider three cases of debt repayment rate: b = 0:10, b = 0:20, and b = 0:33, which represent 10-Year, 5-Year, and 3-Year debt maturity. As shown in Figure 1.5, rms with 10-Year debt maturity respond relatively less 34 0 10 20 30 10% 30% 50% A. debt 10−year 5−year 3−year 0 10 20 30 8% 12% 16% B. cash 0 10 20 30 0% 3% 6% C. unused lines of credit 0 10 20 30 0% 3% 6% D. precautionary cash 0 10 20 30 5.4% 5.8% 6.2% Year E. investment 0 10 20 30 0% 3% 6% Year F. net payout Figure 1.5: Long-term debt (with cash) provides nancial exibility to the negative credit shock than rms with 5-Year or 3-Year debt maturity. This implies that long-term debt (with cash) provides insurance against credit shocks. 1.6.2 Credit Boom Figure 1.6 shows the rm's transition paths after a positive credit shock. Panel A plots the process of the positive credit shock. Panel B depicts the transition paths of debt and cash, and Panels C to F depict the transition paths of unused lines of credit, precautionary cash, investment, and net payout, respectively. 35 0 10 20 30 0 0.5 1 A. financing opportunity 0 10 20 30 10% 20% 30% B. debt and cash debt cash 0 10 20 30 0% 5% 10% C. unused lines of credit 0 10 20 30 0% 5% 10% D. precautionary cash precautionary cash new borrowing 0 10 20 30 0% 5% 10% Year E. investment 0 10 20 30 0% 5% 10% Year F. net payout Figure 1.6: Credit boom Two take-away results from Figure 1.6 are (1) although a credit boom provides better nancing opportunities, the rm does not choose to borrow all the available credit. Instead, the rm keeps most new credit as unused lines, which is shown in Panel C; (2) within the amount of debt the rm has borrowed during the credit boom, the rm saves some of the proceeds as precautionary cash. To draw a comparison between the new borrowing and the new cash savings, I also plot the changes in borrowing (solid line) in Panel D. As can be seen from Panel D, some of the new borrowing has been saved as precautionary cash. 36 Those two results demonstrate the precautionary motive of holding liquidity: even if rms are in favorable market conditions, they are still cautious about the possibility of future adverse nancing conditions. To highlight the timing of the rm's borrowing and saving decisions, Figure 1.7 pro- vides an example of how the rm accumulates precautionary cash during a credit boom. Suppose the rm has an initial debt capacity with 30% of assets, which consists of 20% debt outstanding and 10% unused lines of credit. A positive credit shock raises the rm's total debt capacity to 45%. Given the 15% increase in new credit, the rm borrows only 5% as new debt outstanding, while leaving the other 10% as unused credit lines. Further, within the 5% increase in new debt, the rm saves 2:5% as precautionary cash. 0 30% inital debt capacity credit boom 45% 0 30% 20% debt outstanding unused lines 45% 35% new lines new debt cash Figure 1.7: Where does precautionary cash come from 0 30% 15% reduced debt capacity credit crisis 0 30% 15% debt outstanding cut in lines 20% cut in debt cash Figure 1.8: Where does precautionary cash go 37 Figure 1.8 shows how the rm spends its precautionary cash during a credit crisis. Similarly, suppose the rm has an initial debt capacity with 30% of assets, which consists of 20% debt outstanding and 10% unused lines of credit. A negative credit shock reduces the rm's debt capacity to 15%. Given the 15% decrease in total credit, the rm rst uses the 10% unused lines of credit as buers, and then cuts debt by 5%. To ll up the 5% decrease in debt outstanding, the rm spends its 2:5% precautionary cash. 1.6.3 Credit Uncertainty 0 10 20 30 0 0.5 1 A. credit volatility 0 10 20 30 10% 18% 26% B. debt and cash 0 10 20 30 10% 18% 26% debt cash 0 10 20 30 0% 5% 10% C. unused lines of credit 0 10 20 30 0% 5% 10% D. precautionary cash 0 10 20 30 0% 5% 10% Year E. investment 0 10 20 30 0% 5% 10% Year F. net payout Figure 1.9: Credit uncertainty 38 Figure 1.9 depicts the rm's transition path after a credit uncertainty shock, that is, after an increase in credit volatility. In this exercise, I change only the second moment of credit shock, while leaving the expected level of credit shock unchanged. Panel A plots the change of the credit volatility. Panels B to F depict the transition path for each variable. As shown in Panel B, when credit volatility increases, the rm increases cash holdings immediately, but cuts debt one period after the shock. This is because under the setting of long-term debt, reducing the current debt would shrink the next period's borrowing capacity and hence the rm is hesitant to cut debt. Panel C shows that after the credit uncertainty shock, the rm rst reduces unused lines of credit and then rebuilds them. Panel D shows that the rm increases precautionary cash immediately after the shock. The economic interpretation is as follows. When credit uncertainty increases, the rm wants to prepare more liquidity for the future, through either cash or unused lines of credit. However, the increase in credit uncertainty also raises the chance that very bad credit conditions will prevail in the future, which in turn makes reserving unused credit lines less reliable than stockpiling cash since the access to future credit lines depends on future credit conditions. As a result, when credit uncertainty increases, the rm wants to shift the funds under risky credit lines into safer cash holdings. This oers a plausible explanation for why rms wanted to draw down credit lines and stockpile cash during the recent nancial crisis (e.g., Ivashina and Scharfstein (2009)) | because of the increases in credit uncertainty. Panel E shows that the level of investment declines after the credit uncertainty shock, and Panel F shows that the rm temporally cuts dividend payout to help build up cash reserves. 39 0 10 20 30 0 0.1 0.2 A. productivity 0 10 20 30 20% 26% 32% B. debt and cash 0 10 20 30 6% 12% 18% debt cash 0 10 20 30 0% 2% 4% C. unused lines of credit 0 10 20 30 0% 2% 4% D. precautionary cash 0 10 20 30 4% 6% 8% Year E. investment 0 10 20 30 0% 2% 4% Year F. net payout Figure 1.10: Negative productivity/investment shock 1.6.4 Negative Productivity/Investment Shock Figure 1.10 shows the rm's transition paths after a negative productivity shock. Panel A plots the process of the negative productivity shock. Panel B depicts the transition paths of debt and cash, and Panels C to F depict the transition paths of unused lines of credit, precautionary cash, investment, and net payout. The negative productivity shock generates a negative correlation between debt and cash, and also a negative correlation between unused lines of credit and precautionary 40 cash. The reason is as follows. After the negative productivity shock, the rm's cash ows decline and therefore it is optimal for the rm to borrow more (reduce unused lines) to smooth investment and payout. Meanwhile, the rm's total cash holdings decline because of the decrease in cash ows. However, the decline in total cash is less than the decline in cash ows, and therefore the precautionary cash increases. To sum up, after the negative productivity shock, the rm has incentives to save more precautionary cash to hedge the potential increases in future investment opportunities. This scenario illustrates the demand-side eect on rms' cash policies, which complicates the interpretation of the supply-side eect (credit risk) on rms' liquidity decisions. How- ever, as has been shown in the counterfactual exercise, i.e., Table 1.2, this demand-side eect (investment risk) is not the driving force behind rms' precautionary cash savings. 1.6.5 Productivity/Investment Uncertainty Figure 1.11 depicts the rm's transition path after a productivity uncertainty shock. Panel A plots the change of the productivity volatility. Panels B to F depict the transition path for each variable. As shown in Panel E, an increase in productivity/investment uncertainty generates a wait-and-see eect and signicantly reduces the rm's investment. This result is consistent with the growing literature on investment under uncertainty, which shows that when rms face convex costs of capital adjustment, they would wait to invest because of the investment uncertainty. However, as shown in Panels C and D, unlike the credit uncertainty, the investment uncertainty cannot generate a shape switch of the rm's liquidity position from risky unused credit lines to safer cash holdings. 41 0 10 20 30 0 0.5 1 A. productivity volatility 0 10 20 30 20% 26% 32% B. debt and cash 0 10 20 30 6% 12% 18% debt cash 0 10 20 30 0% 2% 4% C. unused lines of credit 0 10 20 30 0% 2% 4% D. precautionary cash 0 10 20 30 4% 6% 8% Year E. investment 0 10 20 30 2% 4% 6% Year F. net payout Figure 1.11: Productivity/investment uncertainty 1.6.6 The 2008 Financial Crisis In this section, I discuss the model implications for the recent nancial crisis. Figure 1.12 plots the average investment-to-assets ratio, cash-to-assets ratio, and unused lines-to-total lines ratio during the period of 2006q1-2010q4, for a random sample of 600 Compustat rms hand-collected by Berrospide and Meisenzahl (2013). As can be seen from the graph, starting from 2007q4, rms' liquidity holdings, both cash and unused lines, decline. However, until 2008q4, investment does not change much. After 42 A. Investment and Cash Holdings 2006q4 2007q4 2008q4 2009q4 2010q4 3.2% 4.0% 4.8% 5.6% 6.4% 2006q4 2007q4 2008q4 2009q4 2010q4 19% 20% 21% 22% 23% invest/assets cash/assets B. Investment and Unused Lines of Credit 2006q4 2007q4 2008q4 2009q4 2010q4 3.2% 4.0% 4.8% 5.6% 6.4% 2006q4 2007q4 2008q4 2009q4 2010q4 52% 54% 56% 58% 60% 62% invest/assets unused lines/total lines Figure 1.12: Investment, cash, and unused lines during the 2008 nancial crisis 2008q4, investment drops signicantly, while liquidity holdings increase. Furthermore, cash holdings increase after 2009q1 and then decrease after 2009q4, while unused lines of credit increase after 2009q2 (one quarter behind cash) and accelerate after 2009q4. An interesting question is: does the model explain rms' investment and liquidity decisions during the 2008 nancial crisis? To address this question, I divide the crisis into two stages. (1) At the onset of the crisis (2007q4), there is a negative credit shock, which forces rms to reduce both cash holdings and unused lines of credit. However, at this stage of the crisis, investment remains relatively stable thanks to the liquidity holdings. (2) At the middle stage of the crisis (2008q4), there are two uncertainty shocks (credit 43 and investment uncertainty), which induce rms to cut investment and build up liquidity holdings. Moreover, rms tend to draw down credit lines and increase cash after the credit uncertainty shock, and then they reduce cash and rell unused lines of credit as the economy stabilizes (2009q4). Of course, my model provides only one perspective of understanding rms' investment and liquidity decisions during the 2008 nancial crisis. There might be other explanations. See for example the discussion in Kahle and Stulz (2012). 1.7 Model Robustness In this section, I check the model robustness by adding the investor's stochastic discount factor. Following the literature, I specify the investors' stochastic discount factor as 9 t+1 =( z at+1 z at ) ; (1.27) where the variable is the subjective discount rate, is the risk aversion coecient, and z at denotes aggregate productivity level at time t. This discount factor implies that the investors have a higher valuation on rms that pay out dividends (repay debt) in an economic downturn. To capture the aggregate business cycle uctuations in the data, as in Warusawitharan and Whited (2013), I specify two aggregate states, an expansionary state z aH = 1:01 and a recessionary state z aL = 0:97, with transition matrix = 2 4 0:71 0:29 0:75 0:25 3 5 . I set the investor's risk aversion coecient 9 See, for example, Zhang (2005). If the consumer side of the economy can be described by one repre- sentative agent with power utility and a risk aversion coecient , then the pricing kernel can be written as t+1 = ( C t+1 C t ) . Moreover, if the aggregate consumption Ct is linear in the aggregate productivity zat, I have the pricing kernel in the Equation (1.27). 44 = 2. I also assume that the aggregate productivity shock z at is independent of the rm- level productivity shock z t specied in Section 1.3.2. Thus, the rm's total productivity can be written as ^ z t =z at z t . Table 1.4 reports the estimation results when the stochastic discount factor is included. Compared to the results in Table 1.1, the model-predicted cash-to-assets ratio in Table 1.4 becomes lower while the unused lines-to-assets ratio is higher. This is because under the setting of stochastic discount factor, rms are more risk averse toward borrowing and hence they borrow less and hold more unused lines of credit. Further, since the rm borrows less, the cash savings out of borrowing become less too. And this explains why the cash-to-assets ratio decreases. Table 1.5 reports the results of the counterfactual exercises. As can be seen from the second and third column of the table, conditional on the stochastic discount factor, nancing risk is still the driving force for the rm's liquidity holdings. The fourth column shows that without the stochastic discount factor, cash increases while unused lines of credit decrease. This is consistent with the above observation that risk aversion increases unused lines of credit but reduces precautionary cash. To sum up, the two take-away results are (i) a higher degree of the shareholders' risk aversion implies a relatively stronger later-borrowing motive of holding unused lines of credit but a relatively weaker pre-borrowing motive of saving precautionary cash; (ii) conditional on the stochastic discount factor, nancing risk is still the driving for rms to hold liquidity. 1.8 Empirical Evidence This section tests the key model implications using reduced form regressions. I summarize two hypotheses from the model: 45 Table 1.4: Estimation with stochastic discount factor Observed Simulated Target Moments Mean of Cash/Assets 0.189 0.129 Std of Cash/Assets 0.116 0.070 Auto of Cash/Assets 0.188 0.463 Mean of Debt/Assets 0.162 0.143 Std of Debt/Assets 0.082 0.121 Auto of Debt/Assets 0.226 0.780 Mean of Investment/Assets 0.050 0.047 Std of Investment/Assets 0.025 0.003 Auto of Investment/Assets 0.205 0.229 Mean of Payout/Assets 0.029 0.029 Std of Payout/Assets 0.027 0.019 Auto of Payout/Assets 0.136 0.226 Mean of Cash Flow/Assets 0.098 0.076 Std of Cash Flow/Assets 0.070 0.022 Auto of Cash Flow/Assets 0.297 0.230 Mean of Unused Line/Assets 0.100 0.072 Std of Unused Line/Assets 0.055 0.130 Auto of Unused Line/Assets 0.194 0.438 Calibrated Parameters Subjective discount factor, 0.97 Debt repayment rate, b 0.31 Corporate tax rate, 0.15 Risk aversion coecient, 2.0 Aggregate state, fzaH;zaLg f1:01; 0:97g Transition matrix, 0:71 0:29 0:75 0:25 Estimated Parameters The drift of productivity shock, z i 0.021 Persistence of productivity shock, z i 0.399 Volatility of productivity shock, z i 0.342 Persistence of credit shock, i 0.302 Volatility of credit shock, i 0.477 Capital depreciation rate, 0.061 Collateral rate, 0.389 Equity rigidity parameter, 0.742 Capital adjustment cost, 0.801 Price of cash, p m 0.977 46 Table 1.5: Counterfactual exercises with stochastic discount factor Benchmark Financing Productivity Without Model Shock Shock Discount Factor Target Moments Mean of Cash/Assets 0.129 0.117 0.088 0.135 Std of Cash/Assets 0.070 0.050 0.025 0.055 Auto of Cash/Assets 0.463 0.536 0.542 0.428 Mean of Debt/Assets 0.143 0.146 0.232 0.187 Std of Debt/Assets 0.121 0.122 0.050 0.089 Auto of Debt/Assets 0.780 0.844 0.870 0.715 Mean of Investment/Assets 0.047 0.047 0.049 0.045 Std of Investment/Assets 0.003 0.002 0.004 0.003 Auto of Investment/Assets 0.229 0.240 0.757 0.135 Mean of Payout/Assets 0.029 0.030 0.026 0.029 Std of Payout/Assets 0.019 0.012 0.011 0.015 Auto of Payout/Assets 0.226 0.322 0.603 0.364 Mean of Cash Flow/Assets 0.076 0.077 0.079 0.076 Std of Cash Flow/Assets 0.022 0.004 0.023 0.022 Auto of Cash Flow/Assets 0.230 0.533 0.216 0.263 Mean of Unused Line/Assets 0.072 0.069 0.024 0.041 Std of Unused Line/Assets 0.130 0.123 0.034 0.085 Auto of Unused Line/Assets 0.438 0.534 0.815 0.436 Hypothesis 1 Cash accumulation and long-term debt issuance are positively correlated, and the correlation increases in the maturity of debt. Hypothesis 2 Firms prefer cash holdings to unused lines of credit when the credit risk is high. 47 Hypothesis 1 is about the rm's nancing dynamics, and it is derived from the model simulation in which rms issue long-term debt and hold the funds in cash to hedge against future credit contractions. To test Hypothesis 1, I run the following regression: Cash it = + 1 DebtMaturity it LongDebt it + 2 LongDebt it + 3 Equity it + 4 CashFlow it + 5 Invest it + 6 Size it + i + t +" it : (1.28) The left side of equation (1.28) is net accumulation of cash, and the right side of equation represents possible sources of cash increment: net long-term debt issuance, net equity issuance, internal cash ow, and net investment. I also control for rm xed eects and year dummies in the regression. Table 1.6 shows the regression result of the determinants of cash accumulation, which conrms that the correlation between cash accumulation and debt issuance is positive, and the positive correlation increases in the maturity of debt. Hypothesis 2 tests the tradeos between cash and unused lines of credit. Based on the model simulation, rms should prefer cash to unused lines of credit when the credit risk is high. I use two measures of credit risk. The rst one is the volatility of stock prices. I argue that stock prices re ect the market price of the rm's capital assets, and therefore the true value of the rm's collateral assets. Thus, the volatility of stock prices can be a measure of credit risk. The second proxy of credit risk is a dummy of the 2008 nancial crisis. I run the following regression to test Hypothesis 2: cash it cash it +unusedlines it = + 1 Crisis it + 2 CreditVolatility it + 3 Tangibility it + 4 Leverage it + 5 CashFlow it + 6 Capex it + 7 NetWorkingCapital it + 8 Size it + i + t +" it : (1.29) 48 Table 1.6: Determinants of cash accumulation (cash it ) Debt Maturity High Low ldebtitmaturityit 0.014 (0.002) maturityit 0.001 (0.000) ldebtit 0.230 0.367 0.212 (0.012) (0.012) (0.013) equityit 0.580 0.565 0.588 (0.007) (0.011) (0.007) cashflowit 0.223 0.228 0.226 (0.008) (0.013) (0.010) investit -0.376 -0.426 -0.342 (0.010) (0.014) (0.014) sizeit -0.017 -0.014 -0.024 (0.001) (0.002) (0.002) Firm Fixed Eects Yes Yes Yes Year Dummies Yes Yes Yes Adjusted R 2 0.59 0.52 0.61 Observation 109,117 54,401 54,716 This table shows the determinants of cash accumulation. The rst column reports the result for the baseline specication based on equation (1.28), and the next two columns report the results of regressions without the interaction term, separately for high and low maturity rms. High maturity rms are those with higher than median debt maturity. The maturity of debt is dened as: maturity = (0:5dd1 + 1:5dd2 + 2:5dd3 + 3:5dd4+4:5dd5+10(dlttdd2dd3dd4dd5))=(dltt+dd1), where Compustat itemsdd1,dd2,dd3,dd4, anddd5 represent, respectively, the dollar amount of long-term debt maturing during the rst year after the annual report, during the second year after the report, and so on; item dltt represents the dollar amount of long-term debt that matures in more than one year. The data is an unbalanced panel of 14,623 Compustat rms during the period 1971-2010. The dependent variable is the cash accumulation-to-lagged assets ratio cashit = (cheL:che)=L:at, and independent variables include: net long-term debt issuance-to-lagged assets ratio ldebtit = (dltisdltr)=L:at; debt maturitymaturityit; interaction between net long-term debt issuance-to-lagged assets ratio and debt maturity ldebtitmaturityit; net equity issuance-to-lagged assets ratio equityit = (sstkprstkcdvcdvp)=L:at; cash ow-to-lagged assets ratiocashflowit =oibdp=L:at; net investment-to-lagged assets ratio investit = (capx +aqcsppesiv)=L:at; and log of lagged assets sizeit = log(L:at). Firm xed eects and year dummies are also included. Standard errors (in parentheses) are heteroskedasticity robust and clustered at the rm level, and signicance levels at 1%, 5%, and 10% are marked with superscripts , , . 49 In the regression, I also control for the rm's tangibility, nancial leverage, cash ows, capital expenditure, net working capital, and size. Table 1.7 reports the regression results, which show that rms prefer cash to unused lines of credit when the credit risk is high. Table 1.7: Determinants of cash-to-liquidity ratio ( cash it cash it +unusedlines it ) creditvolatilityit 0.030 (0.013) crisisit 0.022 (0.005) tangibilityit -0.106 -0.089 (0.017) (0.017) leverageit -0.050 -0.064 (0.015) (0.015) cashflowit 0.076 0.074 (0.019) (0.018) capexit -0.012 -0.048 (0.047) (0.046) networkingcapitalit -0.249 -0.216 (0.023) (0.023) sizeit -0.041 -0.034 (0.006) (0.005) Firm Fixed Eects Yes Yes Year Dummies Yes Yes Adjusted R 2 0.80 0.79 Observation 22,825 24,195 This table shows the determinations of cash-to-liquidity ratio, based on the equation (1.29). The data is an unbalanced panel of 3,941 rms from the Compustat and Capital IQ merged database during the period 2003-2010. The dependent variable is the cash-to-total liquidity ratio cash it cash it +unusedlines it , and independent variables include: indicator of 2008 nancial crisiscrisisit, quarterly stock prices volatilitycreditvolatilityit, physical capital-to-lagged assets ratio tangibilityit = ppegt=L:at, debt-to-lagged assets ratio leverageit = (dltt +dlc)=L:at, cash ow-to-lagged assets ratio cashflowit = oibdp=L:at, capital expenditure-to-lagged assets ratiocapexit =capx=L:at, net working capital-to-lagged assets rationetworkingcapitalit = (wcap che)=L:at, and log of lagged assets sizeit = log(L:at). Firm xed eects and year dummies are also included. Standard errors (in parentheses) are heteroskedasticity robust and clustered at the rm level, and signicance levels at 1%, 5%, and 10% are marked with superscripts , , . 50 1.9 Conclusion In this paper, I quantify a new motive of holding cash through the channel of nancing risk. I show that if the access to future credit is risky, rms may want to issue long-term debt right now and save the funds in cash, and they do so in order to secure the current credit capacity for the future. The main results are (i) the liquidity premium of holding cash is about 40bps; (ii) the value of holding cash is around 8% of shareholder value; (iii) nancing risk, instead of investment risk, is the driving force for rms to hold liquidity; (iv) increases in credit uncertainty induce rms to draw down credit lines and to hold the proceeds in cash. An interesting implication of the model is that: rms manage liquidity jointly with capital structure decisions. On the one hand, to maintain the option to issue debt in the future, rms refrain from borrowing in the current period and hold unused credit lines. On the other, to hedge the risk of losing the option to borrow in the future, rms increase leverage today and save cash for future needs. 51 Bibliography Acharya, V., H. Almeida and M. 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Journal of Finance 60, 67-103. 58 Chapter 2 Labor Liability Dynamics and Corporate Debt 1 This chapter develops a model in which rms issue self-enforcing debt contracts to external investors and oer long-term wage contracts to their employees. By paying lower wages today in exchange of higher wages in the future, long-term wage contracts provide an additional (implicit) form of nancing for the rm. In choosing the optimal composition of external nancing|standard debt and implicit borrowing from employees|rms trade o the relative costs of the two types of nancing. We estimate the model structurally and nd that a signicant fraction of the observed decrease in corporate net debt over the last ve decades can be explained by the optimal substitution of conventional debt with employees liabilities. We further decompose the impacts of long-term wage contracts on nancial leverage and nd that the stickiness of wage contracts plays a key role in crowding out nancial debt. 2.1 Introduction Labor, in the form of human or organizational capital, is becoming a more important factor of production. As shown in Figure 2.1, the contribution of human or organizational capital to production has increased dramatically over the past few decades (see also Corrado et al. 1 This chapter is co-authored with Xiaolan Zhang. 59 (2006)). During the same period, however, the net debt to total assets ratio of the corporate sector has decreased more than 70%. These two trends raise the following questions: How do rms nance the accumulation of human or organizational capital? How does the accumulation of this particular capital aect the optimal nancing decisions of rms? 1960 1970 1980 1990 2000 2010 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Year net debt 1960 1970 1980 1990 2000 2010 0.5 1 1.5 2 2.5 3 3.5 4 intangible capital net debt intangible capital Figure 2.1: Firm-level net debt ratio and organizational capital ratio In this paper we explore these questions by developing a model in which production is conducted by a single factor, human capital, which is partly portable by workers, that is, workers can carry some of the accumulated capital if they leave the rm. To retain workers, rms oer long-term contracts that allow for implicit borrowing from workers, which is obtained by paying lower wages today in exchange of higher future wages and it is in addition to a more standard channel of nancing based on corporate debt. The optimal liability structure|nancial debt versus labor liability (postponed compensation of workers)|is achieved when the marginal cost of borrowing from investors is equalized to the marginal cost of borrowing from workers. 60 The main results of the paper can be summarized as follows. First, borrowing from workers through long-term wage contracts is a sticky form of nancing but its dynamics change with the rm's nancial position. Since workers are risk-averse, they value consump- tion smoothing. Therefore, the optimal wage contract is downward rigid whenever the rm is nancially healthy. However, when the rm is nancially constrained, the motive of the rm's investment smoothing might dominate that of the workers' consumption smoothing, and therefore, wages may decrease. The second result is that the dynamics of labor liability have feedback impacts on the dynamics of nancial debt. In response to a positive productivity shock, the rm wants to accumulate human capital. To nance the investment, the rm not only raises funds from credit markets by issuing debt contracts, but also borrows, implicitly, from workers. However, since labor liability is sticky, nancial debt becomes the main source of nancing. As a result, the rm's nancial leverage increases quickly but the labor leverage responds to a lesser degree. In response to a negative productivity shock, disinvestment in human capital reduces the nancing needs. But the fact that workers are reluctant to change their wage payments induces a relatively high labor leverage. Thus, in this case, nancial leverage decreases dramatically while labor liability remains high. To sum up, the stickiness of labor liability raises the volatility of nancial debt and hence increases the rm's precautionary motives for maintaining low leverages. This is the rst channel explored in the paper through which labor liability crowds out nancial debt | the volatility eect. The third result is that labor liability also squeezes out nancial debt as a result of the accumulation of human capital at the rm level | the overhang eect. Since human capital is portable by workers, when capital accumulates, the workers' outside option increases, which creates a labor liability overhang problem. This has two implications. On the one hand, the labor leverage could alleviate the incentive of workers to leave since workers would lose the higher promised compensation if they quit. Thus, as human capital accumulates, 61 labor liability becomes a convenient form of nancing. On the other, the fact that part of the capital is portable by workers implies that the rm cannot use the capital as a `full collateral' in nancial markets. That is, the higher the labor liability, the less the rm can borrow through standard debt contracts. We evaluate the importance of labor lability dynamics by estimating the model struc- turally with data from the Compustat annual les 1960-2010. The simulated method of moments is applied to estimate the parameters concerning fundamental productivity risks, nancial market conditions, and labor market conditions over two subperiods 1960-1985 and 1985-2010. The model does a reasonable job in replicating key moments of nancial leverage and human capital investment. We nd that between the two subperiods, the workers' outside option and the rms' nancing cost increased, while the capital adjust- ment cost decreased. After the estimation, we conducted a counterfactual exercise to quantify to what extent the accumulation of labor liability can explain the decrease in net nancial leverage over the past ve decades. We rst feed the model with the estimated parameters from the rst subperiod 1960-1985, and then we replace the value of those parameters one by one using the estimates from the second subperiod 1985-2010. We calculate the explanatory power of each parameter in predicting future leverage, and nd that: the increase in labor liability explains as much as 64% of the observed decrease in net debt ratio; the fundamental risk explains around 20%; and the nancing adjustment cost contributes to another 10%. We further decompose the impact of labor liability on nancial debt into two com- ponents: the volatility eect vs. the overhang eect. We show that the volatility eect accounts for 5/8 of the total impact, while the overhang eect accounts for 3/8. This paper is related to the recently growing body of literature on understanding the increase in cash holdings and the decrease in debt capacity (e.g. Bates et al. (2009), etc.). 62 Falato et al. (2013) explores the hypothesis that the rise in intangible capital is a funda- mental driver of the secular trend in US corporate cash holdings by assuming asymmetric adjustment costs of physical capital and intangible capital. Our paper endogenizes the adjustment cost of intangible capital through the channel of implicit wage contracts. A low net debt ratio is generated because of the stickiness of labor liability. The paper also contributes to the dynamic corporate theory which emphasizes the importance of the production side. Related to the corporate theory on dynamic capital structure (Hennessy and Whited (2005), Hennessy and Whited (2007), etc.) and risk man- agement (Bolton et al. (2011), etc.), our paper studies the dynamic substitutions between nancial leverage and labor leverage by linking the joint choices of liabilities (debt versus labor) to the rm's fundamental decisions. We analyze the dynamic labor contract with limited commitment as in Thomas and Worrall (1988), Harris and Holstrom (1982), but with nancially constrained rms making human capital investment decisions. Michelacci and Quadrini (2009) study the relation- ship between rm size and wage by adopting nancial market frictions and the limited commitment of labor contracts. In our paper, however, we focus on how the investment decision of human capital aects the workers' outside option, and more importantly, on how the stickiness of labor liability crowds out nancial debt. 2.2 A Model of Wage Contract with Financial Frictions In this section, we study a model of long-term wage contract with nancial frictions. The model illustrates how the accumulation of human capital aects the nancing decisions of rms under one-sided limited commitment. Workers, who are endowed with human capital, can walk away from the wage contract whenever better outside options are available. To retain the workers, rms oer long-term wage contracts that allow for implicit borrowing 63 from workers. Firms also issue standard debt contracts to nance investment. The dynamic rent-splitting rule among the shareholders, debtholders, and workers then determines the liability allocation (nancial liability vs. labor liability) and capital structure (liability vs. equity) of the rm. 2.2.1 The Economy We consider an economy with frictional capital market and labor market. Technology Firms, owned by risk neutral shareholders, conduct production with human capital h t . The production technology is decreasing return to scale: y t = exp(z t )h t ; 0< 1; (2.1) subject to an idiosyncratic technology shock, z t Q(z t jz t1 ), where Q(z t jz t1 ) is a sta- tionary and increasing Markov transition function. The human capital is owned by the workers, but the investment decision e t , is made by the rm. The human capital evolves according to h t+1 = (1)h t + e t h t h t ; (2.2) where the function () species the capital adjustment cost which is concave in e t and decreases withh t . The concavity of() captures the idea that quick adjustment of capital stock is more costly than slow adjustment. Debt Contract Because interest payments to debt are tax deductible, rms have incen- tives to issue debt contracts. Firms issue single-period debt contracts at par b t+1 at the end of period t, with an eective interest rate R t . Since the tax shield of debt contract is 64 considered, we assume thatR t < 1 , where is the rm's subject discount factor. Further, we consider the enforcement constraint on the rm to rule out the case in which rms issue debt contracts that they cannot pay back. The enforcement constraint is as follows: b t+1 R t t E t [V t+1 ]; (2.3) where E t [V t+1 ] is dened as the discounted value of the rm's dividend ows E t P 1 s=t+1 st d t , and t is the collateral rate governed by the capital market condi- tions. The debt capacity for the rm at time t depends the rm's net present value and nancing conditions. Wage Contract Risk-averse workers are hired by the rm. Workers are endowed with preferenceu(), whereu 0 ()> 0;u 00 ()< 0, and they consume the wage each period without savings. Workers own the human capital and share the rent of human capital with the rm through a long-term wage contract. Although the human capital is invested by the rm, it is completely portable with the worker. As a result, the rm pre-commits to a long-term wage contract to retain the worker in the production. However, the worker cannot commit to the wage contract, meaning that whenever the available outside option is higher than the current wage contract, the worker can walk away. The outside option is dened by the autarky where the worker's human capital keeps constant and in each period she earns a spot wage rate a = exp(z), where the constant < 1 denotes the labor market mobility and the constant z represents the aggregate level of productivity. The worker with the level of human capital h t has the outside option as follows: !(h t ) =! 0 +E t ( 1 X s=t st u(ah t ) ) ; (2.4) 65 where the discount factor of the worker is also . Further, we assume! 0 0 to make sure that it's socially optimal to retain the workers in the rm. 2.2.2 The Firm's Optimization Problem The rm commits to a long-term wage contract that promises a complete contingent con- sumptionfc(z t )g 1 t that maximizes the total expected payo of the worker subject to the initial utility m 0 : m 0 (z t ) =E 0 ( 1 X t=0 t u(c t (z t )) ) (2.5) where z t =fz 0 ;z 1 ;:::z t g is the entire history of productivity z. In order to solve the wage contract, we need to solve for all the wage payments contingent on the entire history z t . To make the problem recursive, the worker's promised expected utility is treated as a new state variable m t = E t P 1 s=t st u(c s+1 ) (See Appendix B.1 for the equivalence of the recursive contract and the original contract). So now, the rm commits to deliver the promised utility m t today by delivering current consumption c t and a state contingent promised utility m t+1 tomorrow, which is characterized by the following promise-keeping constraint: m t =u(c t ) +E t [m t+1 ] (2.6) Since the worker has limited commitment to the wage contract, the participation constraint of the worker in any h t+1 is given by: m t+1 !(h t+1 ); 8h t+1 : (2.7) 66 The promised utility m t+1 is the labor liability which the rm commits to the worker at time t. Optimization Problem We write down the rm's optimization problemP recursively: V (h;m;b;z) = max e;c;m 0 ;b 0 d +E V 0 (h 0 ;m 0 ;b 0 ;z 0 jz) subject to: d =e z h ce + b 0 R b 0 (2.8) h 0 = (1)h + e h h (2.9) E[V 0 jz] b 0 R (2.10) m =u(c) +E[m 0 ] (2.11) m 0 w(h 0 ) (2.12) Equation (2.8) is the budget constraint with a non-negative dividend requirement. 2 The optimization takes into consideration of the interactions between debt contracts and labor contracts. The rm's optimal liability allocation depends on both the tightness of the debt enforcement constraint (2.10), which is the nancial distress of the rm, and that of the participation constraint (2.12), which is the labor-liability distress of the rm. On the top of liability allocation, the rm also choose between equity and liability optimally. The total liability is governed by the tightness of the non-negative dividend constraint (2.8). 2 We will generalize the non-negative dividend constraint to allow for equity issuance in the quantitative studies. 67 2.3 Optimal Wage Contract and Liability Allocation The model is solved numerically, but we describe the wage contract properties and the dynamic interactions between nancial liability and labor liability by deriving the rst- order equations and Euler equations. 2.3.1 Optimal Wage Contract The general properties of the wage contract is characterized in this section. Let be the multiplier on the budget constraint, ' be the multiplier on the non-negative dividend constraint, q be the multiplier on the investment constraint, be the multiplier on the debt enforcement constraint, be the multiplier on the promise-keeping constraint and be the multiplier on the participation constraint. We have the problem's rst order conditions: b 0 : =R(1 +)E[V 0 b jz] + (2.13) m 0 : =(1 +)E[V 0 m jz] (2.14) h 0 : q =(1 +)E[V 0 h jz] +zh 1 ! 0 (h 0 ) (2.15) d : = 1 +' (2.16) e : q = 0 ( e h ) (2.17) c : = u 0 (c) (2.18) 68 and the Envelope conditions: b : V b = (2.19) m : V m = (2.20) h : V h =zh 1 +q[(1) +( e h ) 0 ( e h ) e h ] (2.21) Equations (2.13)-(2.21) completely capture the rm's problem. We provide some interpretations of the Lagrangian multipliers. The variable , as the shadow price of dividend, is also the marginal cost of borrowing from the external investors. The variable , as the shadow price of wage payment, is also the marginal cost of borrowing from the workers. The variable , which governs the tightness of the enforcement constraint, is the marginal cost of nancial distress. The variable , which is the tightness of the participation constraint, captures the marginal cost of labor-liability distress. We introduce two lemmas before stating the main proposition of the paper. Lemma 1 Given the rm's optimization problem P, the shadow price of dividend 0 increases on average whenever the debt enforcement constraint (2.10) is not binding; while the shadow price 0 decreases when the enforcement constraint is tight enough: > (1R). Proof : From F.O.C (2.13) and Envelope condition (2.19), we obtain =RE[ 0 jz] (2.22) - When = 0, =RE[ 0 jz]. Thus, 0 increases on average, since R< 1. 69 - When > 0, = +RE[ 0 jz]. Thus, 0 decreases on average whenever > (1R). Lemma 1 describes the interactions between the cost of nancial distress and the shadow price of dividend. From equation (2.16), the shadow price of dividend is higher than one when the dividend is close to zero ('> 0). Because of the tax shield of holding debt, rms would choose to pay out dividend by borrowing from debtholders if the debt enforcement constraint is not binding ( = 0). However, the equity adjustment is irreversible (d 0). Issuing more debt contracts now means that the rm will be more likely to hit the non- negative dividend constraint in the future (' > 0). Thus, the shadow price of dividend 0 increases as the rm borrows more. On the other hand, when the debt enforcement constraint tightens (> (1R)), rms issue less debt and the shadow price of dividend 0 decreases. Lemma 2 Given the rm's optimization problem P, the shadow price of consump- tion/wage 0 decreases over time whenever the workers' participation constraint (2.12) is not binding; while the shadow price 0 increases when the participation constraint is tight enough: >. Proof : From F.O.C. (2.14) and Envelope condition (2.20), we obtain: = + (1 +)E[ 0 jz] (2.23) - When = 0, E[ 0 jz] = 1+ . Thus, 0 decreases on average since 0. - When > 0, E[ 0 jz] = + 1+ . Thus, 0 increases on average whenever >. Lemma 2 describes the impact of tightness of participation constraint on the marginal cost of borrowing from workers. The marginal cost of borrowing from workers is high when 70 the shadow price of consumption is high. When the workers' participation constraint is not binding = 0, the marginal cost of borrowing from workers decreases. Firms choose to borrow from workers as long as the cost of nancial distress is positive (> 0). However, when the workers' participation constraint becomes tight enough ( >), the marginal cost of borrowing from workers increases. To prepare Proposition 1, we also dene the marginal rate of substitution between dividend and consumption as the ratio of the shareholder's marginal utility of dividend and the workers' marginal utility of consumption: MRS static u 0 (c) . This ratio also captures the marginal cost of external nancing in terms of the marginal utility of workers u 0 (c). Notice that the lagrangian multiplier is marginal cost of borrowing from the workers, thus, from the rst order condition of consumption, equation (2.18), we have the static optimal liability allocation rule: u 0 (c) = (2.24) which trades o between the marginal cost of borrowing from external investors u 0 (c) and the marginal cost of borrowing from workers . Combining equation (2.14), (2.18) and (2.20), we obtain: (1 +)E[ 0 (z 0 ) u 0 (c 0 (z 0 )) jz] = + u 0 (c) : (2.25) Proposition 1 then summarizes the dynamics of the optimal liability allocation rule. Proposition 1 (Wage Contract Dynamics) Conditional on the nancial distress of the rm and the labor-liability distress , the current marginal rate of substitution between dividend and wage t u 0 (ct) is a sucient statistic of the expected marginal rate of substitution E t [ t+1 u 0 (c t+1 ) ]. 71 The expected marginal rate of substitution E t [ t+1 u 0 (c t+1 ) ] increases when the worker's participation constraint binds > 0 and the collateral constraint does not bind = 0. The expected marginal rate of substitutionE t [ t+1 u 0 (c t+1 ) ] decreases when the debt enforce- ment constraint binds > 0 and the worker's participation constraint does not bind = 0. The expected marginal rate of substitution E t [ t+1 u 0 (c t+1 ) ] keeps constant if = 0 and = 0. Undetermined changes in the direction of the expected marginal rate of substitution E t [ t+1 u 0 (c t+1 ) ] when > 0 and > 0. Proof : See Appendix B.2. This proposition characterizes the wage contract by displaying the dynamics of marginal rate of substitution. The wage contract dynamics is driven by both the nancial distress and the labor-liability distress . First, the nancial distress governs the dynamics of shadow price of dividend, i.e., the marginal cost of borrowing from debtholders. When = 0, the marginal cost of issuing debt is low. Thus, the rm borrows from the nancial market to pay out wage and dividend given the tax benet of debt. When > 0, the rm faces high nancial distress costs, and hence it borrows less from debtholders and defers wage payments by increasing labor liabilitym t+1 . As a result, a high nancial distress cost tends to drive down the marginal rate of substitution between dividend and wage. Second, the labor-liability distress governs the marginal cost of borrowing from the workers by balancing the risk-sharing motive against the employee-retention motive. When the workers' participation constraint binds > 0, it means that the rm has to commit a high promised utility m t+1 to retain the workers, and therefore the marginal cost of 72 borrowing from workers increases and the marginal rate of substitution between dividend and wage rises. When the participation constraint does not bind = 0, the dynamics of marginal rate of substitution between dividend and wage are completely driven by the tightness of debt enforcement constraint. As a result, the marginal cost of borrowing from workers decreases whenever the rm is nancially distressed (> 0). Third, the workers attain the best consumption smoothing when there is no nancial distress or labor-liability distress, that is, when = 0 and = 0. 3 The lagged marginal rate of substitution between dividend and wage t u 0 (ct) contains all information we need to predict the expected marginal rate of substitution at time t + 1. However, when there are nancial distress or labor-liability distress, the optimal dividend-wage allocation trades o between the marginal cost of nancing through labor contracts and that of debt contracts. The lagged marginal rate of substitution between dividend and wage is sucient to predict expected marginal rate of substitution only conditional on and . To sum up, our recursive wage contract with limited commitment and nancial frictions shares the common properties of the wage contract dynamics from the standard literature (Harris and Holstrom (1982), Thomas and Worrall (1988), Kocherlakota (1996), etc.), but it deviates from the literature in the following perspectives: Although the original optimal wage contract is contingent on the entire history of productivity shock z t , the recursive contract is determined only by value of human capital h t in the current period. Since in our model workers do not face any exogenous income uctuations, the relevant productivity history is remembered in the current human capital level, which determines 3 When the debt enforcement constraint or the workers' participant constraint is not binding, we can dene the slack of those constraints as precautionary liquidity buers: Firms borrow less today in order to borrow more in the future; and rms allow workers to smooth consumption today in order to leave room to distort workers' consumption in the future. 73 the workers' available outside options. 4 Thus, the optimal wage contract does not serve to provide insurance to the workers against the income uctuation, but instead, it species the optimal rent-splitting rule between the shareholders and the workers. Also, because of nancial frictions, shareholders may become more \risk averse" than workers when the cost of nancial distress is high enough. As a result, in our model the marginal rate of substitution t u 0 (ct) may decrease over time even if the worker's participant constraint is binding. This happens when the rm's nancial distress cost dominates the marginal benet of workers' consumption smoothing, that is, when > . While the above proposition summaries the risk-sharing dynamics between the share- holders and the workers, the following corollary states the overhang eect of human capital accumulation: Corollary 1 (Human Capital Overhang Eect) The expected marginal cost of bor- rowing from workers E t [ t+1 ] is increasing in the current human capital accumulation h. Further, the tightness of debt enforcement constraint is decreasing in h. Proof : Since the tightness of participant constraint is increasing inh 0 , andh 0 is increasing in h, from Lemma 2 we have E t [ t+1 ] is also increasing in h. From equation (2.22), we have is decreasing in h. The implication of Corollary 1 is very useful: since the accumulation of human capital leads to high future costs of borrowing from the workers, when the rm makes the borrowing decision today, it wants to reduce the amount of debt in order to save some debt capacity for the future. 4 The workers' outside options are invariant to the rm specic productivity zt+1 and the aggregate productivity zt+1. 74 2.3.2 Financial Eects of Long-Term Wage Contract At any period after the realization of z t , the liability capacity of the rm is xed. Under the optimality conditions, the intertemporal marginal rate of substitution of labor liability and that of debt liability are equal. Proposition 2 (Optimal Liability Allocation) The rm dynamically trades o between nancial debt and labor liability until their intertemporal marginal rates of substitution are equal. Proof : See Appendix B.3. Recall the multipliers on the debt collateral constraint (2.10) and on the participation constraint (2.12) as and , respectively. From the optimality conditions, we obtain the tradeos between the debt contract and the wage contract: R E[V 0 b jz] V b + = 1 E[V 0 m jz] V m : (2.26) The above equation illustrates the relationship between the rm's debt nancing decision (b 0 ) and the investment decision on labor (promised utility m 0 ). The intertemporal substi- tution of debt contract is the same as the intertemporal substitution of labor contract. Intuitively, the marginal rate of return on nancial debt (the marginal cost of borrowing from external investors) should be equal to the marginal rate of return on labor liability (the marginal cost of borrowing from internal workers). Proposition 3 (Liability vs. Equity) The rm's overall liability capacity (nancial debt plus employee liability) is governed by the rigidities of adjusting equity. The rm's overall liability capacity is summarized by the shadow price of adjusting equity . In the model, the rm makes two tradeos regarding its nancial structure. 75 First, given the overall liability capacity, the rm makes choices between nancial debt and labor liability as stated in Proposition 2. Second, the rm also considers the tradeos between equity and liability. Although holding debt has the tax shield, the irreversibility of equity would prevent the rm from borrowing through debt contracts. If the rm borrow too much debt currently, reducing debt in later periods could become very costly. The optimal choice between equity and debt is achieved when the tax benets of holding debt equal to the costs of adjusting equity. Similarly, although labor liability is a necessary device to retain workers, the rigidity of adjusting equity would also prevent the rm from borrowing too much through wage contracts. In other words, the optimal liability capacity bounds the wage contract from above. 2.4 Model Solution 2.4.1 Normalized Wage Contract To solve the contract numerically, we normalize the contract by assuming log utilityu(c) = log(c) and linear technologyy t = exp(z t )h t . We dene the normalized contract problem as ~ P, by using the transfer ~ m =m 1 1 log(ah),g 0 =h 0 =h, and ~ x =x=h for other variables. As in Jermann and Quadrini (2012), we also replace the non-negative dividend constraint with a smooth equity adjustment cost function '( ~ d) = ~ d +( ~ d ~ d target ) 2 , where the parameter measures the rigidities of adjusting equity, and ~ d target is a targeted dividend payout ratio calibrated to match the average dividend payout ratio in the data. When the variable ~ d< 0, it means that the rm is issuing equity. As a result, the normalized problem ~ P can be written as: 76 ~ V ( ~ m; ~ b;z) = max ~ e;~ c; ~ m 0 ; ~ b 0 ~ d +g 0 E z ~ V 0 ( ~ m 0 ; ~ b 0 ;z 0 ) subject to: '( ~ d) =z ~ c ~ e +g 0 ~ b 0 R ~ b (2.27) g 0 = (1) +(~ e) (2.28) E z [ ~ V 0 ] ~ b 0 R (2.29) ~ m = log(~ c) +E z [ ~ m 0 ] + 1 log(g 0 ) log( a) (2.30) ~ m 0 w 0 (2.31) The functional form of the capital adjustment cost is specied as (~ e) = a 1 1 ~ e 1 +a 2 , where the variable is the depreciation rate of organization capital and the value 1= is the elasticity of investment to capital ratio with respect to the marginalq. The parameters a 1 = and a 2 = 1 are set so that in the steady state capital adjustment cost is zero and the marginalq is equal to one. This adjustment cost function has been widely used in the investment and production-based asset pricing literature (Jermann (1998), etc.). Under the normalized contract, the normalized value of the workers' outside option w 0 and the normalized level of human capital accumulation h are equivalent. As a result, the overhang eect of labor liability on nancial debt is straightforward: One (normalized) unit increase in the workers' outside option w 0 reduces the rm value by units, which in turn reduces the debt capacity by units. The reduce in debt capacity then forces the rm to cut down the nancial leverage. We summarize this result in the following corollary: Corollary 2 (Overhang Eect) One unit increase in the workers' outside option w 0 reduces the rm value by units, which in turn reduces the debt capacity by units. 77 −25 −20 −15 0 0.05 0.1 0.15 0.2 0 0.1 0.2 ˜ m A. ˜ b ′ L ˜ b −25 −20 −15 0 0.1 0.2 −0.1 0 0.1 0.2 0.3 ˜ m B. ˜ b ′ H ˜ b −25 −20 −15 0 0.1 0.2 −24 −22 −20 −18 −16 −14 ˜ m C. ˜ m ′ L ˜ b −25 −20 −15 0 0.1 0.2 −24 −23 −22 −21 −20 −19 ˜ m D. ˜ m ′ H ˜ b Figure 2.2: Policy functions 2.4.2 Policy Functions Figure 2.2 plots the policy functions. Panel A and B report the debt policy implied by the model. If the current state is low z L , the next period's debt is decreasing in the current period's debt when the enforcement contract is not binding; if the current state is high z H , the next period's debt is always increasing in the current debt. In Panel A we also see the eect of labor liability on the tightness of debt enforcement constraint: The debt contract in the next period is more likely to become binding when the shareholders promise a high m to the workers in the current period. 78 Figure C and D report the policy function for the wage contract conditional on the current productivity shocks. The next period's promise utility is always increasing in the current period's debt, but not sensitive to the current period's promise utility. The rst result is because of the substitution eects between debt and labor liability, and the second is because of the stickiness of labor liability. In Panel D, the next period's promised utility may remain constant when the current debt is low. This is because that when the rm is currently experiencing high productivity shocks, the participation constraint binds as the rm wants to borrow from the workers as much as possible. 2.4.3 Impulse Response Functions To highlight the stickiness of labor liability, in this section we report the nonlinear impulse response functions after the productivity shocks. The substitution eects between nancial debt and labor liability are clearly displayed in Figure 2.3. From Panel (a), a positive productivity shock induces a high future human capital h 0 , but we do not see the moralized labor liability m 0 =h 0 responds as much as that of the moralized nancial debt b 0 =h 0 . Thus, the original labor liability m 0 should increase much slowly than that of nancial debt b 0 . On the other hand, from Panel (b), a negative productivity shock leads to a decrease in the nancial debt, but the labor liability still remains high. This is because that although the disinvestment in human capital shrinks the total nancing needs, the fact that workers are reluctant to change their wage payments induces a relatively high labor leverage. Thus, the nancial leverage decreases dramatically while the labor liability stays high. To sum up, when the productivity is low, the relative liability structure has switched to labor- liability-dominant phase. In Figure 2.4, we compare the impulse responses of debt and promise when the outside option is low to those of the case when the outside option is high. The dashed lines 79 0 10 20 30 −20 −10 0 10 20 30 40 Year percent of deviation shock z growth h′/h debt b′/h′ promise m′/h′ 0 10 20 30 −30 −25 −20 −15 −10 −5 0 5 10 15 Year percent of deviation shock z growth h′/h debt b′/h′ promise m′/h′ Figure 2.3: Impulse response functions represent the responses when the workers' outside option is low, and the solid lines represent the responses when the workers' outside option is high. As can be seen from the graph, an increase in the workers' outside option raises the sensitivity of the response of debt dramatically, while it does not change the sensitivity of the response of labor liability very much. This implies that: when the workers' outside option increases (caused by the increase in the level of human capital), nancial debt becomes relatively more volatile. 80 0 10 20 30 −0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 Year changes debt (w 0 =−25.53) debt (w 0 =−19.95) promise (w 0 =−25.53) promise (w 0 =−19.95) Figure 2.4: Stickiness of labor leverage 2.5 Structural Estimation In this section we conduct the structural estimation of the model. We start with the description of the data and then we discuss the estimation procedures and results. 2.5.1 Data All variables used in the estimation are from Compustat annual les 1960-2010. Following the literature, we exclude nancial rms and utilities with SIC codes in the intervals 4900- 4949 and 6000-6999, and rms with SIC codes greater than 9000. We also exclude rms with a missing value of sales, debt, cash, and organizational capital. All variables are winsorized at 5% and 95% percentiles to limit the impact of outliers. Nominal variables are de ated by the Production Price Index. The nal sample used in the estimation is an unbalanced panel of 17,675 rms from 1960 to 2010. We divide the sample into two subperiods 1960-1985 and 1985-2010, and conduct two separated estimations. 81 2.5.2 Simulated Method of Moments The model is solved numerically as described in Appendix B.4 and most of the model parameters are estimated through the simulated method of moments (SMM). The basic idea of SMM is to choose the parameters such that the moments generated by the model are close to those in the data. The empirical data is for a panel of heterogenous rms while the articial data is generated by simulating one rm over a number of periods. To keep consistency between the empirical data and the simulated data, we use as targets the average moments for the sample rms. More specically, we rst calculate the empirical moments for each rm in the sample and then, for each moment, we compute the average across all rms. In the current version, we use the identical (scale-adjusted) weighting matrix . The estimation procedure consists of several steps as described below: 1. For each rmi, we choose momentsh i (x it ), wherex it is a vector of variables included in the empirical data. The subscripts i and t identify, respectively, the rm and the year. 2. For each rm i we calculate the within-rm sample mean of moments as f i (x i ) = 1 T P T t=1 h i (x it ), where T is the number of years in the empirical sample. 3. The average of the within-rm sample mean is computed as f(x) = 1 N P N i=1 f i (x i ), where N is the number of rms in the data. 4. We then use the model to generate a panel of simulated data for N rms and for S periods. The vector of simulated data in period t and for rm s is denoted by y is . We set S = 100T to make sure that the representative rm ends up in all possible states at least once. 82 5. At this point we calculate the average sample mean of moments in the model as f(y;) = 1 NS P N i=1 P S s=1 h(y is ;), wherey is is the simulated data and denotes the parameters to be estimated. 6. The estimator b is the solution to min h f(x)f(y;) i 0 h f(x)f(y;) i . Model parameters are estimated with the exception of the intertemporal discount factor , the corporate tax rate , the depreciation rate , the average enforcement variable , and the worker's mobility . The discount factor is set to 0.93. We set the corporate tax rate to 30% in the rst sample period and to 20% in the second period. Given the discount factor and the corporate tax rate, the eective interest rate can be calculated as R = 1 + (1= 1) (1). The average enforcement variable = 0:5 is chosen to match the average net-debt-to-assets during the whole sample period, given the other parameters. The depreciation rate = 0:3 is set to be consistent with the depreciation rate we used in the data to construct the variable organizational capital. Since our model is partial equilibrium, the value of labor mobility cannot be identied, and we choose it to be 0.5. Finally, all those per-set parameters are xed during our two sets of estimations expect the value of the corporate tax rate. After the calibration of above parameters, we are left with 5 parameters: the persistence and volatility of the productivity shock, z and z , the workers' outside option w 0 , the nancing cost parameter, and the capital adjustment cost parameter. The productivity shock represents the fundamentals of the rm. The workers' outside option works as a direct measure of labor liability. The nancing adjustment cost parameter and the capital adjustment cost parameter captures the marginal cost of nancing and the marginal cost of investing, respectively. 83 To estimate these parameters we consider 7 moments: the mean of the ratio of net debt over total assets; the standard deviations of the ratio of net debt over total assets, the growth of sale, the growth of wage, and the growth of organizational capital; the autocorrelations of the ratio of net debt over total assets, and the growth of organizational capital. 2.5.3 Estimation Results The values of the estimated parameters are reported in the bottom section of Table 2.1. The estimated value of productivity shock is close to one in the literature (for example, DeAngelo et al. (2011)). The volatility of the shock is higher during the second sample period (1985-2010), while the persistence of the shock is higher in the rst period (1960- 1985). The estimation picks the normalized value of the workers' outside option to be -23.53 in the rst sample period, and to be -19.95 in the second sample period, which means that the labor lability did increase between the two sample periods. The another two parameters are about the nancing costs and capital adjustment costs. While the value of the nancing adjustment cost parameter increases, the value of capital adjustment cost parameter decreases. From the estimation, we are also able to quantify the changes in the tightness of nancial constraint and that of the labor liability constraint . Overtime, the workers' partici- pation constraint gets tighter, increases by 67%, while the debt enforcement constraint gets looser, decreases by 20%. By using Corollary 2, we can show that the sensitivity of the overhang eect more than doubles between the two periods: it increases from 0.08 to 0.18. The values of the moments (observed and simulated) are reported in the top section of Table 2.1. The model does a reasonable job in replicating the 7 moments used in the estimation for both sample periods. 84 Table 2.1: Moments and parameters 1960-1985 1985-2010 Target Moments Observed Simulated Observed Simulated Mean( netdebt t bookassets t ) 0.25 0.273 0.15 0.152 Std( netdebt t bookassets t ) 0.06 0.095 0.13 0.197 Std( sale t sale t1 ) 0.13 0.082 0.17 0.089 Std( wage t wage t1 ) 0.13 0.130 0.15 0.101 Std( ocapital t ocapital t1 ) 0.11 0.062 0.10 0.054 Autocor( netdebt t bookassets t ) 0.55 0.589 0.50 0.845 Autocor( ocapital t ocapital t1 ) 0.44 0.314 0.47 0.117 Pre-set Parameters Discount factor , 0.93 0.93 Corporate tax rate, 0.30 0.20 Depreciation rate, 0.30 0.30 Enforcement parameter, 0.50 0.50 Workers' mobility, 0.50 0.50 Estimated Parameters Persistence productivity shock, z 0.652 0.407 Volatility productivity shock, z 0.231 0.295 Workers' outside option, w0 -23.53 -19.95 Financing adjustment cost, 0.478 0.587 Capital adjustment cost, 0.272 0.171 Value of Multipliers Debt enforcement constraint, 69bps 55bps Workers' participant constraint, 6bps 10bps 85 2.5.4 Counterfactual Exercises The key question we would like to address in this paper is whether and to which extent the accumulation of labor liability can explain the decrease in net nancial leverage over the past few decades. To address this question we conduct the following counterfactual exercises: First, we feed the model with the estimated parameters from the period of 1960- 1985. Second, we replace the value of those parameters one by one using the estimated value from the period of 1985-2010. Third, we calculate the ratio changes in predicted leverage changes in true leverage as an indicator for the explanation power of each parameter. Table 2.2: Counterfactual: Explaining the decline in net leverage True Leverage Predicted Leverage Percent of Period 1! Period 2 Period 1! Period 2 Explanation Overall 0.25! 0.15 0.273! 0.152 121% The Role of Each Parameter Persistence of productivity shock, z 0.273!0.260 13% Volatility of productivity shock, z 0.273!0.266 7% Workers' outside option, w0 0.273!0.209 64% Financing adjustment cost, 0.273!0.263 10% Capital adjustment cost, 0.273!0.291 -18% Table 2.2 reports the results of above experiments. The observed net leverage ratio changes from 0.25 during the period of 1960-1985 to 0.15 during the period of 1985-2010, while the model-predicted leverage ratio changes from 0.273 in the rst period to 0.152 86 in the second period. Thus, overall, our model captures the changes in net leverage quite well. Further, as can be read from the bottom panel of Table 2.2, the workers' outside option plays a key role in predicting the changes in net leverage. Specically, the increase in labor liability explains as much as 64% of the decrease in the observed net leverage. The second important factor explaining the decreases in net leverage is the change of the productivity shock, which explains about 20% of the decrease in net leverage. The third is the nancing adjustment cost, which explains 10%. To sum up, our counterfactual exercises conducted with estimated model suggest that the accumulation in labor liability is the key determinant of explaining the decrease in net leverage over the past ve decades, even after controlling for the persistence and the volatility of shocks, the external nancing costs, and the capital adjustment costs. 2.5.5 Volatility Eect vs. Overhang Eect In this section, we decompose the impact of labor liability on nancial debt by distinguish- ing the volatility eect and the overhang eect. The volatility eect works through the precautionary motive of keeping low leverage, so it can be identied by examining the liq- uidity buers generated from the debt enforcement constraint. The stronger the volatility eect, the more unused debt capacity the rm holds. On the other hand, the overhang eect works through the collateral value of assets and therefore it can be identied by showing the changes in the rm's total debt capacity. In Table 2.3, we report the value of total debt capacity as well as the value of unused debt capacity for the case of low labor liability (w 0 =23:53) and the case of high labor liability (w 0 =19:95), respectively. As shown in the table, an increase in labor liability shrinks the debt capacity by the value of 0.03|the size of overhang eect, while it raises the unused debt capacity by the value of 0.05|the size of volatility eect. Thus, this 87 Table 2.3: Decompose the impact of labor liability on nancial debt w0 =23:53 w0 =19:95 Multiplier Debt enforcement constraint, 69bps 63bps Workers' participant constraint, 6bps 8bps Volatility effect Debt buers, E[V 0 ] b 0 R 0.05 0.10" Promise buers, m 0 w(h 0 ) 2.02 1.80# Overhang effect Debt capacity, E[V 0 ] 0.21 0.18# Committed promise, m 0 -19.9 -16.7" exercise suggests that the volatility eect is relatively more important than the overhang eect in understanding the impact of labor liability on nancial debt. 2.6 Conclusion We develop a model in which rms issue self-enforcing debt contracts to external investors and also oer long-term wage contracts to internal workers who have limited commitment. The long-term wage contract serves as a liability with endogenous adjustment costs. The rm dynamically trades o between nancial debt and labor liability until their intertem- poral marginal rates of substitution are equal. 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Review of Economic Studies 55 (4), 541{54. 91 Chapter 3 Credit and Hiring 1 This chapter studies an industry dynamics model where access to credit improves the bargaining position of rms with workers and increases the incentive to hire. To evaluate the importance of the bargaining channel for the hiring decisions of rms we estimate the model structurally with simulated methods of moments using data from Compustat and Capital IQ. 3.1 Introduction The idea that rms use leverage strategically to improve their bargaining position with workers is not new in the corporate nance literature. For example, Perotti and Spier (1993) developed a model where debt reduces the bargaining surplus for the negotiation of wages, allowing rms to lower the cost of labor. Recent studies by Klasa, Maxwell, and Ortiz-Molina (2009) and Matsa (2010) have tested this mechanism using rm-level data and found that more unionized rms|that is, rms where workers are likely to have more bargaining power|are characterized by higher leverage and lower holding of cash. These studies provide some evidence that the bargaining channel is relevant for deter- mining the nancial structure of rms. However, whether this channel is also important for their hiring decisions has not been fully explored in the literature. In fact, if the bar- gaining strength of workers impacts on the nancial structure of rms, the choice of the nancial structure may in turn impact on the hiring decision of rms. More specically, 1 This chapter is co-authored with Vincenzo Quadrini. 92 if higher leverage allows employers to negotiate more favorable conditions with employees, the ability to issue more debt increases the incentive to hire more workers. The goal of this paper is to study the importance of the bargaining channel for the hiring decisions of rms by estimating a dynamic model with wage bargaining and endogenous choice of nancing. 2 In the model, the compensation of workers is determined at the rm level through bargaining. Firms choose the nancial structure and employment optimally taking into account that these choices aect the cost of labor. Higher debt allows rms to negotiate lower future wages which increases the incentive to hire more workers. Higher debt, how- ever, also increases the likelihood of nancial distress. Therefore, rms face a trade-o in the choice of the nancial structure whose resolution determines the optimal nancing and employment decisions. When the nancial condition of the rm improves, the likelihood of nancial distress declines, making the debt more attractive. This, in turn, improves the bargaining position of the rm with workers, increasing the incentive to hire. It is trough this mechanism that improved rm-level access to credit generates more demand for labor. We evaluate the importance of this channel by estimating the model through simu- lated method of moments. The empirical moments are constructed using rm-level data from Compustat and Capital IQ. The rst database provides information on typical bal- ance sheet and operational variables including employment. The second database provides rm level data for unused lines of credit which is important for the identication of some key parameters. More specically, since the likelihood of nancial distress increases with leverage, rms borrow less than their credit capacity to contain the expected distress cost. 2 The importance of the bargaining channel for aggregate dynamics has been studied in Monacelli, Quadrini and Trigari (2011) but in a model with a single-worker representative rm. In the current paper, instead, we take a micro approach and explore the empirical relevance of the bargaining channel using a model with heterogeneous multi-workers rms mapped to rm-level data. 93 We interpret the dierence between the maximum debt capacity and the actual borrow- ing in the model as unused credit lines. The Capital IQ database then provides valuable information for the identication of the distress cost parameter. The paper is organized as follows. Sections 3.2 and 3.3 present the dynamic model and characterize some of the key properties. Section 3.4 describes the data and the structural estimation and Section 3.5 reports the estimation results. Section 3.7 concludes. 3.2 A Firm Dynamics Model with Bargaining To facilitate the presentation of the model and the role played by the bargaining channel, we rst describe a simplied version without nancial distress. After characterizing the properties of the simpler model, we will extend it with the addition of nancial distress. Consider a rm with production technology y t = z t N t , where z t is idiosyncratic pro- ductivity and N t is the number of workers. Employment evolves according to N t+1 = (1)N t +E t ; (3.1) where is the separation rate and E t denotes the newly hired workers. Hiring is costly. A rm with current employment N t that wishes to hire E t workers incurs the cost (E t =N t )N t , where the function (:) is strictly increasing and convex for E t > 0. The budget constraint of the rm is B t +D t +w t N t + E t N t N t =z t N t +q t B t+1 ; (3.2) where B t is the stock of bonds issued by the rm at t 1 (liabilities), D t is the equity payout, q t is the price of bonds and w t is the wage paid to each worker. 94 The issuance of debt is subject to the enforcement constraint q t B t+1 t E t S t+1 ; (3.3) where S t+1 is the net surplus of the rm as dened below. The variable t is stochastic and captures the nancial conditions of the rm, that is, its access to external credit. 3.2.1 Firm's Policies and Wages The policies of the rm, including wages, are bargained collectively with its labor force. The labor force is dened broadly and includes managers. In this way the model could also capture the agency con icts between shareholders and managers as in Jensen (1986). To derive the bargaining outcome, it will be convenient to dene few terms starting with the equity value of the rm. This can be written recursively as V t (B t ;N t ) =D t +E t V t+1 (B t+1 ;N t+1 ): (3.4) The equity value of the rm depends on two endogenous states|debt B t and employ- ment N t |in addition to the exogenous states z t and t . To simplify the notation, the dependence on the exogenous states is not shown explicitly but it is captured by the time subscript t. We will continue to use this notational convention throughout the paper. The value of an individual worker employed in a rm with liabilities B t and with N t employees is W t (B t ;N t ) =w t + (1)E t W t+1 (B t+1 ;N t+1 ) +E t U t+1 ; (3.5) where U t+1 is the value of being unemployed at t + 1. Given the partial equilibrium approach, the unemployed value is exogenous in the model. 95 The net value of the worker can be rewritten recursively as W t (B t ;N t )U t = w t U t +E t U t+1 + (1)E t W t+1 (B t+1 ;N t+1 )U t+1 (3.6) The bargaining surplus, denoted byS t (B t ;N t ), is the sum of the net values for the rm and the workers, that is, S t (B t ;N t ) =V t (B t ;N t ) + W t (B t ;N t )U t N t (3.7) We are now ready to dene the bargaining problem. Given the bargaining power of workers, the bargaining outcome is the solution to the following maximization problem max wt;Dt;Et;B t+1 W t (B t ;N t )U t N t V t (B t ;N t ) 1 ; subject to the law of motion for employment (3.1), the budget constraint (3.2), and the enforcement constraint (3.3). Dierentiating with respect to the wagew t , we obtain the well-known result that work- ers receive a fraction of the bargaining surplus while the rm receives the remaining fraction, that is, W t (B t ;N t )U t N t = S t (B t ;N t ) (3.8) V t (B t ;N t ) = (1)S t (B t ;N t ): (3.9) Next we derive the rst order conditions with respect to D t ,E t ,B t+1 . Using (3.8) and (3.9), we nd that dividend, employment and nancial policies simply maximize the net surplus S t (B t ;N t ). This property is intuitive: given that the contractual parties (rm and 96 workers) share the net surplus, it is in the interest of both parties to make the surplus as big as possible. Therefore, in characterizing the hiring and nancial policies of the rm we focus on the maximization of the net surplus which, in recursive form, can be written as S t (B t ;N t ) = max et;B t+1 ( D t + (w t u t )N t + 1 +(1) N t N t+1 E t S t+1 (B t+1 ;N t+1 ) ) subject to: D t +w t N t =z t N t E t N t N t +q t B t+1 B t q t B t+1 t E t S t+1 (B t+1 ;N t+1 ) N t+1 = (1)N t +E t : The recursive formulation is obtained by multiplying equation (3.6) byN t , summing to (3.4), and using the sharing rules (3.8) and (3.9). The termu t =U t E t U t+1 is exogenous given the partial equilibrium approach taken in this paper. 97 We now take advantage of the linearity of the model and normalize by employment N t . This allows us to rewrite the optimization problem with all variables expressed in per-worker terms, that is, s t (b t ) = max et;b t+1 d t +w t u t +(g t+1 e t )E t s t+1 (b t+1 ) subject to: d t +w t =z t (e t ) +q t g t+1 b t+1 b t t g t+1 E t s t+1 (b t+1 )q t g t+1 b t+1 g t+1 = 1 +e t : The variable s t (b t ) =S t (b t )=N t is the per-worker surplus, d t =d t =N t is the per-worker dividend, b t =B t =N t is the per-worker liabilities, e t =E t =N t are the newly hired workers per each existing employee, and g t+1 =N t+1 =N t is the gross growth rate of employment. Of special interest is the discount factor for next period (per-worker) surplus, which is equal to (g t+1 e t ). When workers do not have any bargaining power, = 0 and the discount factor reduces tog t+1 . Since the whole surplus is appropriated by investors, they will also get the next period per-worker surplus multiplied by the gross growth rate of workersg t+1 . When> 0, however, some of the next period surplus needs to be shared by investors and current workers with the new hired workers. The share going to new workers increases with their bargaining . From that the reduction in the discount factor 98 captured by the term e t . Of course, this `lower discounting' is relevant only if rms add new workers in the next period, that is, e t > 0. 3.2.2 First Order Conditions To characterize the hiring and nancial policy of the rm, we derive the rst order condi- tions with respect to e t and b t+1 . They can be written as q t b t+1 +(1)E t s t+1 (b t+1 ) = 0 (e t ); q t g t+1 +(q t+1 e t )E t @s t+1 (b t+1 ) @b t+1 + t g t+1 t E t @s t+1 (b t+1 ) @b t+1 q t = 0; where t is the lagrange multiplier for the enforcement constraint. The envelope condition provides the derivative of the surplus, which is equal to @s t (b t )=@b t =1. This implies that the normalized surplus is linear in b t . This allows us to rewrite the surplus as s t (b t ) = s t b t ; (3.10) where s t depends only on the exogenous states (shocks). The rst order conditions can then be rewritten as q t b t+1 +(1)(E t s t+1 b t+1 ) = 0 (e t ); (3.11) q t g t+1 =(g t+1 e t ) + t g t+1 ( t +q t ): (3.12) 99 3.2.3 Special Case with q t =. Since we are focusing on a partial equilibrium and we abstract from aggregate shocks, it makes sense to assume that the price of a risk-free (zero coupon) bond is equal to the discount factor, that is, q t = . Then, the rst order condition for debt, equation (3.12), becomes g t+1 = (1)g t+1 +(1) + t g t+1 (1 + t ): (3.13) The following proposition establishes an important property about the nancial policy of the rm. Proposition 3 If> 0, the rm borrows up to the limit whenevere t > 0. If = 0 and/or e t = 0, the debt is undetermined. Proof 1 If> 0, equation (3.13) implies that the lagrange multiplier t is strictly positive whenever e t = g t+1 1 + > 0. Therefore, under the condition e t > 0 the enforcement constraint is binding. When = 0 and/or e t = 0, equation (3.13) implies that t must be zero. There is a simple intuition for this property. Whenever the rm chooses to hire, that is, e t > 0, it adds new workers who will become part of the labor force starting in the next period. Therefore, the new workers will share the next period surplus of the rm. Increasing the debt today reduces the future surplus, allowing for lower compensation of the new hired workers. This increases the current surplus of the rm which is shared by shareholders and currently employed workers, but not the new hired workers. It is then in the interest of both shareholders and old workers to increase the debt of the rm. When the rm does not add new workers, however, higher borrowing does not increase the current surplus because more debt only reduces the future compensation of existing workers. In 100 this case there are no gains from borrowing. Thus, as long as the rm adds new workers, bargaining introduces a motive to borrow, breaking the irrelevance of debt of Modigliani and Miller (1958). For this property, however, the bargaining power of workers must be positive, that is, > 0. In the limiting case with = 0 the Modigliani and Miller's result continues to hold. We now turn attention to the rst order condition for hiring, equation (3.10). Under the assumption q t =, this condition can be rewritten as h b t+1 + (1)E t s t+1 i = 0 (e t ): (3.14) Together with the normalized law of motion for employment, g t+1 = 1 +e t , this equation establishes a relation between the per-worker debtb t+1 and the growth of employ- ment (which also depends on other factors aecting the surplus of the rm through the term E t s t+1 ). This relation is not linear and depends on the bargaining power of workers . Proposition 4 The hiring decision e t is strictly increasing in b t+1 if > 0 but it becomes independent of b t+1 if = 0. Proof 2 It follows directly from (3.14) given that the convexity of the cost function (:) implies that 0 (e t ) is strictly increasing in e t . Thus, the nancial structure of rms aect the hiring decision as long as workers have some bargaining power. However, when workers do not have any bargaining power|which can be interpreted as the case of a competitive labor market where the determination of wages is external to an individual rm|debt is irrelevant for the hiring decisions of rms. This is because the nancial structure becomes irrelevant as already stated in Proposition 101 3. The goal of this paper is to explore the dependence of the hiring decision from the nancial structure under the assumption that wage are negotiated and workers have some bargaining power. 3.3 Financial Distress Cost The model presented so far abstracts from the possibility of nancial distress. The variable t captures the nancial condition of a rm, that is, its access to credit. A sudden drop in this variable forces the rm to substitute debt with equity and this can be done without any direct cost. The only cost is indirect, through the impact on wages. However, the assumption that the rm has full exibility in substituting debt with equity is not very plausible, especially in the short-run: if the rm is unexpectedly forced to replace debt with equity, it may not be easy to make the substitution through regular channels and this could place the rm in a situation of nancial distress. To capture this idea, we extend the model to allow for the possibility of nancial costs associated with nancial distress. Deneb t the maximum debt that can be collateralized. This is dened by the condition b t = t s t (b t ). Since the surplus function s t (:) is strictly decreasing, the maximum debt b t is increasing in t . The rm enters the period with debt b t chosen in the previous period. Then, after the realization of t , the collateral constraint may no longer be satised, that is, b t > b t = t s t (b t ). In this case the rm will be forced to pay back the dierence b t b t before it can access the equity market or retain earnings. In order to make the payment, the rm needs to raise b t b t with alternative sources that are costly. In particular, we assume that the cost incurred to access these alternative sources of funds is (b t b t ) 2 . We call this cost `nancial distress cost' since it is paid to raise emergency funds and could also include, in 102 the extreme, the cost of bankruptcy due to the lack of liquidity. We denote this cost as ' t (b t ) = max n b t b t ; 0 o 2 . With the possibility of nancial distress, the problem of the rm becomes, s t (b t ) = max et;b t+1 d t +w t u t +(g t+1 e t )E t s t+1 (b t+1 ) (3.15) subject to: d t +w t =z t (e t ) +q t g t+1 b t+1 b t ' t (b t ) t g t+1 E t s t+1 (b t+1 )q t g t+1 b t+1 g t+1 = 1 +e t : 3.3.1 First Order Conditions The rst order conditions with respect to e t and b t+1 are, respectively, q t b t+1 +(1)E t s t+1 (b t+1 ) = 0 (e t ); (3.16) q t g t+1 +(g t+1 e t )E t @s t+1 (b t+1 ) @b t+1 + t g t+1 t E t @s t+1 (b t+1 ) @b t+1 q t = 0; (3.17) 103 where t is the lagrange multiplier for the enforcement constraint. Notice that the rst order conditions do not depend on b t . Therefore, the optimal choices of employment and next period debt are still independent of current liabilities. The envelope condition returns @s t (b t )=@b t =1' 0 t (b t ), allowing us to write the surplus function net of the distress cost as s t (b t ) = s t b t ' t (b t ): (3.18) As in the model without nancial distress, the variable s t depends only on the exogenous shocks. The surplus function, however, is no longer linear in b t . The convexity of the distress cost makes the surplus function concave, introducing a precautionary motive that discourages excessive borrowing. Eectively, the rm may choose not to borrow up to the limit and the borrowing constraint t g t+1 E t s t+1 (b t+1 ) q t g t+1 b t+1 could be only occasionally binding. We can now use the special form of the surplus function to derive expressions for the maximum collateralizable debt. First we use the condition that determines the maximum collateralizable debt, that is, b t = t s t (b t ). Substituting (3.18) we obtain b t = t [ s t b t ' t (b t )]. Since '(b t ) = 0 by denition, we can solve the last equation for b t , that is, b t = t 1 + t s t : (3.19) 104 Therefore, the collateralizable debt is only determined by the exogenous states, z t and t . Finally, the particular form of the surplus function derived in (3.18) allows us to write the rm's problem as s t = max et;b t+1 z t (e t ) +q t g t+1 b t+1 u t +(g t+1 e t ) E t h s t+1 b t+1 ' t+1 (b t+1 ) i (3.20) subject to: t g t+1 E t h s t+1 b t+1 ' t+1 (b t+1 ) i q t g t+1 b t+1 g t+1 = 1 +e t ; This problem is recursive in s t , which depends only on the exogenous shocks. Therefore, to solve for the optimal policies we do not need to keep track of the endogenous state b t . This makes the computational procedure extremely simple as we will describe below. Using the particular form of the surplus function, the rst order conditions (3.16) and (3.17) can be written as q t b t+1 +(1)E t h s t+1 b t+1 ' t+1 (b t+1 ) i = 0 (e t ); (3.21) q t g t+1 =(g t+1 e t ) 1 +E t ' 0 t+1 (b t+1 ) + t g t+1 h t 1 +E t ' 0 t+1 (b t+1 ) +q t i : (3.22) 105 Some of the properties stated in Propositions 3 and 4 also apply to the model with nancial distress. In particular, if workers do not have any bargaining power ( = 0) and q = , we can see from equation (3.22) that the enforcement constraint is never binding ( t = 0) and the expected distress cost is zero (E t ' t+1 (b t+1 ) = 0). Since debt does not provide any value to the rm when = 0, the rm prefers not to borrow to avoid the distress cost. At the same time, since the rm does not borrow and the expected distress cost is zero, the hiring decision characterized by condition (3.21) is not aected by the nancial status of the rm t . 3.3.2 Computation of the Optimal Policies The solution of the model consists of the policy functions for hiring, e t , and for borrowing, b t+1 . As shown above, these policies do not depend on the endogenous stateb t but only on the exogenous shocks. The rm's problem (3.20) is a recursive formulation in the unknown variable s t . This variable is independent of the initial state b t and depends only on the exogenous shocks z t and t . If the shocks take a discrete number of values, s t is a vector with a nite number of elements. Therefore, problem (3.20) is a Bellman's equation in the unknown vector s t . The solution can be found by iterating on the Bellman equation until we nd a xed point for s t . Denote byn z andn the discrete number of values taken, respectively, by productivity and nancial shocks. Each iteration starts with a guess for s t+1 , which is a vector with n z n elements (the combination of all possible values of the two shocks). For each combination of the two shocks in the current period and given the guess for s t+1 , we derive the optimal policies by solving the rst order conditions (3.21) and (3.22) together with the enforcement constraint reported in problem (3.20). Since the enforcement constraint could be satised with equality (in which case t > 0) or with inequality (in which case t = 0), we have to verify the Kuhn-Tucker conditions for an interior or a binding solution. 106 The policy rules for employment and borrowing allow us to determine s t (given the guess for s t+1 ), for each combinations of the shocks. The newly found s t is then used as new guess for s t+1 in the next iteration. We would like to point out that, as long as the exogenous shocks take a nite num- ber of values, the solution is exact, that is, the numerical procedure does not use any approximation (besides the assumption that the shocks take a nite number of values). 3.4 Structural Estimation In this section we conduct the structural estimation of the model. We start with the description of the data and then we discuss the estimation procedure and the identication strategy. 3.4.1 Data With the exception of unused lines of credit, all variables used in the structural estimation are from COMPUSTAT Annual. Data on unused lines of credit is not available in COM- PUSTAT and some studies collect information about credit lines from rms' SEC 10-K les (see, for example, Su (2009)). For this study, we use data from Capital IQ database which contains a large sample of unused lines of credit from 2003 to 2010. The variable unused lines of credit also refers to total undrawn credit. See Filippo and Perez (2012) for a detailed description. Following the literature, we exclude utilities and nancial rms with SIC codes in the intervals 4900-4949 and 6000-6999, and rms with SIC codes greater than 9000. We also exclude rms with a missing value of assets, sales, number of employees, debt, and unused lines of credit. To limit the impact of outliers, we also winsorize all level variables at the 2:5% and 97:5% percentiles, and growth variables at the 5% and 95% percentiles. Nominal 107 variables are de ated by the Consumer Price Index. The nal sample used in the structural estimation is a balanced panel of 1,508 rms over 8 years, from 2003 to 2010. 3.4.2 Simulated Method of Moments The model is solved numerically as described in Section 3.3.2 and most of the parameters are estimated through the simulated method of moments (SMM). The basic idea of SMM is to choose the parameters such that the moments generated by the model are close to those in the data. The empirical data is for a panel of heterogenous rms while the articial data is generated by simulating one rm over a number of periods. To keep consistency between the empirical data and the simulated data, we use target moments as the average moments for the sample rms. More specically, we rst calculate the empirical moments for each rm in the sample and then, for each moment, we compute the average across all rms. We use the bootstrap method to calculate the variance-covariance matrix associated with the target moments. The estimation procedure consists of several steps as described below: 1. For each rmi, we choose momentsh i (x it ), wherex it is a vector of variables included in the empirical data. The subscripts i and t identify, respectively, the rm and the year. 2. For each rm i we calculate the within-rm sample mean of moments as f i (x i ) = 1 T P T t=1 h i (x it ), where T is the number of years in the empirical sample. 3. The average of the within-rm sample mean is computed as f(x) = 1 N P N i=1 f i (x i ), where N is the number of rms in the data. 108 4. We then use the model to generate a panel of simulated data for N rms and for S periods. The vector of simulated data in period t and for rm s is denoted by y is . We set S = 100T to make sure that the representative rm ends up in all possible states at least once. 5. At this point we calculate the average sample mean of moments in the model as f(y;) = 1 NS P N i=1 P S s=1 h(y is ;), wherey is is the simulated data and denotes the parameters to be estimated. 6. The estimator b is the solution to min h f(x)f(y;) i 0 h f(x)f(y;) i . The weighting matrix is dened as b 1 , where b is the variance-covariance matrix associated with the average of sample mean f(x) in the data. We use the bootstrap method to calculate the variance-covariance matrix b . First, given the population of N rms in the empirical sample, we draw J random samples of size N 2 . Second, for each draw j we compute the statistics of the articial sample denoted as f(x) j . Third, we approximate the variance-covariance matrix by the variance of f(x) j , i.e., b 1 J J X j=1 2 4 f(x) j 1 J J X j=1 f(x) j 3 5 0 2 4 f(x) j 1 J J X j=1 f(x) j 3 5 : We set J=50,000 to have enough accuracy in bootstrapping. 3.4.3 Parameters and Moments In describing the model we have assumed that separation is deterministic. In reality, however, labor retention and hiring are likely to be uncertain. To capture this idea, we 109 also consider a shock to job separation. A separate shock to job creation is not necessary since this will be isomorphic to job separation shocks. Employment continues to evolve according toN t+1 = (1 t )N t +E t but t is stochastic and follows a rst order Markov process. The structure of the problem takes the same form as in (3.20). Now, however, there are three shocks that aect the rm: productivity, z t , credit, t , and separation, t . The rst order conditions are also similar. Each of the three shocks can take 9 possible values and follow independent rst order Markov chains. The only functional form that has not been specied is the hiring cost (e). We assume that this function takes the quadratic form (e t ) =e t +e 2 t , which implies two parameters, and . All model parameters are estimated with the exception of the intertemporal discount factor,, the average productivity z, the hiring parameter, and the average enforcement variable . The discount factor is set to 0.97, which implies an interest rate close to 3 percent. The average productivity z is normalized to 1. The hiring parameter is chosen so that the average growth rate of rms is zero (given the other parameters). The value of is chosen so that the available credit (used and unused) is 50 percent the total surplus of the rm. After the calibration of these four parameters, we are left with 11 parameters: the persistence and volatility of the productivity shock, z and z , the persistence and volatility of credit shock, and , the persistence and volatility of separation shock, and , the nancial distress cost, , the workers' bargaining power, , the hiring cost, , the average separation, , the unemployment ow, u. To estimate these parameters we consider 15 moments: the mean of the ratio of unused credit over total credit; the standard deviations and autocorrelations of the ratio of unused credit over total credit, employment growth, sales growth and total credit growth; the cross correlations of the ratio of unused credit over total credit, employment growth, sales growth and total credit growth. 110 3.5 Estimation Results The values of the estimated parameters are reported in the bottom section of Table 3.1. The estimation assigns a sizable bargaining power to workers with = 0:478. This is important for the bargaining channel to be relevant. Another parameter that is important for the bargaining channel is the average separation , which is estimated to be 0.399. A high separation rate implies high turnover rates and, therefore, high rates of hiring. High rates of hiring increase the importance of the bargaining channel because, as we have seen in the theoretical section, higher debt allows for lower compensation of newly hired workers. We also observe that credit and productivity shocks are quite persistent while the separation shocks are not persistent. The values of the moments (observed and simulated) are reported in the top section of Table 3.1. The model does a reasonable job in replicating the 15 moments used in the estimation. One moment for which there is a sizable divergence between the empirical and simulated moments is the autocorrelation in employment growth. In the data the autocorrelation is close to zero. The model, however, generates a positive autocorrelation of 0.200. This is a natural consequence of the particular structure of the model where the level of debt aects the growth of employment. As a result, a persistent increase in the debt level induces, through the bargaining channel, a persistent increase in the growth rate of employment. In the data, however, employment growth is not persistent while the debt level displays some persistence. This implies that the bargaining channel alone cannot replicate the absence of serial correlation in employment growth together with the persistence in debt level. The addition of separation shocks (stochastic t ) reduces the autocorrelation in employment growth because it aects the growth of employment without aecting the debt level. 111 Table 3.1: Moments and parameters Target Moments Observed Simulated Mean( unused t credit t ) 0.411 0.414 Std( unused t credit t ) 0.172 0.168 Std(employt) 0.134 0.116 Std(salest) 0.181 0.168 Std(creditt) 0.500 0.476 Autocor( unused t1 credit t1 ) 0.317 0.404 Autocor(employt1) -0.029 0.200 Autocor(salest1) 0.007 -0.024 Autocor(creditt1) -0.185 -0.108 Cor( unused t credit t ; employt) -0.067 0.099 Cor( unused t credit t ; salesit) -0.046 -0.044 Cor( unused t credit t ; creditit) -0.001 0.261 Cor(employt; salesit) 0.497 0.428 Cor(employt; creditit) 0.296 0.292 Cor(salest; creditit) 0.197 0.207 Estimated Parameters Persistence productivity shock, z 0.627 Volatility productivity shock, z 0.180 Persistence credit shock, 0.892 Volatility credit shock, 0.148 Persistence separation shock, -0.642 Volatility separation shock, 0.093 Financial distress cost, 12.736 Workers' bargaining power, 0.478 Hiring cost, 0.506 Average separation, 0.399 Unemployment ow, u 0.452 3.5.1 The Importance of the Bargaining Channel The key question we would like to address in this paper is whether the bargaining channel is quantitatively important in explaining employment uctuations at the rm level. To 112 address this question we simulate the model using the estimated parameters but with only one shock. For example, when we simulate the model with credit shocks only, we set the sequence of draws for z t and t to their unconditional means, z and respectively. Similarly, when we simulate the model with productivity shocks only, we set the sequence of draws for t and t to their unconditional means and . It is important to point out that, even if in the simulation we set the realizations of the shocks to the unconditional means, this is not anticipated by rms. They continue to assume that the two shocks follows the process dictated by the estimated parameters. Table 3.2 reports the simulation results. Table 3.2: The contribution of the three shocks Observed Benchmark Credit Productivity Separation Model Shock Shock Shock Mean( unused t credit t ) 0.411 0.414 0.421 0.481 0.483 Std( unused t credit t ) 0.172 0.168 0.163 0.023 0.030 Std(employt) 0.134 0.116 0.056 0.073 0.069 Std(salest) 0.181 0.168 0.056 0.138 0.069 Std(creditt) 0.500 0.476 0.436 0.137 0.044 Autocor( unused t1 credit t1 ) 0.317 0.404 0.431 0.522 -0.535 Autocor(employt1) -0.029 0.200 0.820 0.534 -0.536 Autocor(salest1) 0.007 -0.024 0.820 -0.021 -0.536 Autocor(creditt1) -0.185 -0.108 -0.121 -0.012 -0.182 Cor( unused t credit t ; employt) -0.067 0.099 0.218 -0.984 0.999 Cor( unused t credit t ; salesit) -0.046 -0.044 0.227 -0.802 -0.536 Cor( unused t credit t ; creditit) -0.001 0.261 0.312 -0.816 0.930 Cor(employt; salesit) 0.497 0.428 0.820 0.824 -0.536 Cor(employt; creditit) 0.296 0.292 0.161 0.832 0.928 Cor(salest; creditit) 0.197 0.207 -0.201 0.997 -0.191 113 With only credit shocks, the model generates a standard deviation of employment growth of 0.056 which is about 48 percent the empirical standard deviation of 0.116. When we simulate the model with only productivity shocks, the standard deviation of employment growth is about 0.073. Finally, with only separation shocks the model generates a standard deviation of employment growth of 0.069. Since the sum of the three standard deviations does not sum to 0.116, the transmission mechanism of each shock is not independent of the values of the other shocks. For example, when productivity is low, the impact of a positive credit shock on employment is weaker since rms do not nd convenient to hire many workers. In general, however, we can conclude that, based on the estimation, credit shocks contribute signicantly to employment uctuations. Table 3.3: The contribution of the three shocks (xed debt) Observed Experiment Credit Productivity Separation Model Shock Shock Shock Mean( unused t credit t ) 0.411 0.159 0.177 0.462 0.472 Std( unused t credit t ) 0.172 0.748 0.717 0.077 0.024 Std(employt) 0.134 0.097 0.000 0.059 0.076 Std(salest) 0.181 0.162 0.000 0.142 0.076 Std(creditt) 0.500 0.549 0.499 0.158 0.037 Autocor( unused t1 credit t1 ) 0.317 0.680 0.701 0.529 -0.534 Autocor(employt1) -0.029 -0.130 0.998 0.534 -0.536 Autocor(salest1) 0.007 -0.195 0.998 -0.100 -0.536 Autocor(creditt1) -0.185 -0.093 -0.095 -0.120 0.213 Cor( unused t credit t ; employt) -0.067 0.038 -0.062 0.992 -0.998 Cor( unused t credit t ; salesit) -0.046 0.109 -0.045 0.758 0.535 Cor( unused t credit t ; creditit) -0.001 0.222 0.213 0.731 -0.414 Cor(employt; salesit) 0.497 0.213 0.998 0.758 -0.536 Cor(employt; creditit) 0.296 0.170 -0.011 0.736 0.423 Cor(salest; creditit) 0.197 0.308 0.028 0.997 0.528 114 To further identify the impact of bargaining channel on rms' hiring decisions, we resolve and simulate the model by keeping the level of debt constant. This means that the rm cannot use debt as a strategic tool to improve its bargaining power over work- ers, and therefore the bargaining channel is completely disabled in this experiment. Table 3.3 reports the results. Without the bargaining channel, the model generates a standard deviation of employment growth of 0.097. This implies that the bargaining channel con- tributes about 16.4 percent of the standard deviation of employment growth (0.116) in the benchmark model. 3.5.2 Non-linear Impulse Response Functions Another way of showing the importance of the bargaining channel is to examine the sensi- tivity of employment growth to credit shocks with respect to dierent level of the workers' bargaining share. 0 10 20 30 40 −0.04 0 0.04 0.08 0.12 0.16 Time change of employment growth bargaining share η=0.35 bargaining share η=0.47 bargaining share η=0.59 0 10 20 30 40 −0.16 −0.12 −0.08 −0.04 0 0.04 Time change of employment growth bargaining share η=0.35 bargaining share η=0.47 bargaining share η=0.59 Figure 3.1: Change of employment growth after credit shocks The top panel of Figure 3.1 shows that after a one-standard-deviation positive credit shock, the employment growth increases by 9% when the workers' bargaining share is 0.47, while the employment growth increases by 14% when the bargaining power is 0.59. This 115 means that the higher the worker's bargaining share, the more sensitive of employment growth to credit growth. Further, the increase in employment growth is non-linear in the bargaining share: a 25% increase in bargaining share leads to a 55% increase in employment growth. Similarly, after a one-standard-deviation negative credit shock, the change of employ- ment growth is more signicant for rms who have higher workers' bargaining share. How- ever, the overall impact of negative credit shocks on the rm's employment growth is smaller than that of positive credit shocks. That is, the rm's employment growth responses asym- metrically to credit shocks. 3.6 Reduced-Form Estimation In the pervious sections, using a rm dynamics model, we have shown that there is a pos- itive relation between credit and employment growth and, more importantly, the strength of this relation increases with the bargaining power of workers. In this section, we test this key model prediction via reduced-form regressions, using rm-level data from COMPUS- TAT and Capital IQ, and also a proxy for the bargaining power of workers based on an unionization index from the Union Membership and Coverage Database. Ideally, we would like to use the unionization rate for each rm included in the sample. Unfortunately, for the most recent years, which is the focus of this paper, large-sample unionization data is only available at the industry level. 3 Therefore, we are forced to proxy the bargaining power of workers of a rm with the average unionization index of the 3 One consideration that makes the use of the industry index a good proxy for the bargaining power of workers at the rm level is that labor mobility and competitive pressure tends to be higher within the industry rather than across industries. This implies that, even if a rm do not have unionized workers, it will face higher competitive pressure from other rms if the industry is highly unionized. 116 industry in which the rm operates. 4 As a robust test, we also randomly sample 300 rms and manually collect rm-level unionization rate from the SEC 10k lings. 3.6.1 Unionization Data We rst obtain rm-level employment and balance sheet variables from the Compustat Annual Industrial Files for the period 2003-2010. We then merge the variables with the industry unionization rates for the same period. We collect industry unionization rates from the Union Membership and Coverage Database. The Union Membership and Coverage Database is maintained by Barry Hirsch and David Macpherson and is publicly available at http://www.unionstats.com. It compiles industry union coverage annually from the Current Population Survey (CPS). 3.6.2 Regression Equation To test the hypothesis that the relation between employment growth and credit growth increases with the workers' bargaining power, we specify the following regression equation: employ it = + 1 union cic;t credit it + 2 union cic;t + 3 credit it + 4 credit it1 + 5 log(employ it1 ) + 6 Q it + 7 cashflow it + i + t +" it : (3.23) The dependent variable is employment growth, employ it , and the main independent variable is the interaction term between industry unionization rate and credit growth, union cic;t credit it , where we use unionization rate union cic;t to approximate the bar- gaining power of workers. We control for the lagged credit-to-asset ratio credit it1 and 4 This is also the approach used by Klasa, Maxwell, and Ortiz-Molina (2009) to study the relation between cash holdings and bargaining power of workers. 117 the lagged log-employment log(employ) it1 in the regression. Following the investment literature, 5 we also include market-to-book ratio Q it , cash ow-to-asset ratio, cashflow it , rm-level xed eects, i , and year xed eects, t . The primary interest is in the interaction term between credit growth and unionization rate, union cic;t credit it . We expect that this interaction term has a positive eect on employment growth, that is, 1 > 0. This is in addition to the direct eect of credit growth captured by the parameter 3 . The rst column of Table 3.4 reports the estimation results for the baseline specication of the regression equation (3.23). The coecient for the interaction term is 0.088 and it is statistically signicant at 1% level. Therefore, the growth of credit in rms with more unionized labor is associated with higher growth rate of employment. However, these results should be taken with caution since we use industry level unionization rate to proxy for the bargaining power of workers employed by a particular rm. Furthermore, in conducting the estimation we are not testing for causality. We are only estimating conditional correlations. Turning to the control variables, the rst column of Table 3.4 shows that employment growth is negatively related to the lagged number of employment, and positively related to lagged credit-to-asset ratio, market-to-book value and cash ow-to-asset ratio. An alternative way of testing the importance of unionization is by estimating equation (3.23) without the interaction term, separately for high and low unionization rms. The high unionization group includes rms that operate in industries with higher than median unionization rate. The estimation results are reported in the last two columns of Table 3.4. The coecient of credit it , is larger for rms with high unionization rates. Thus, this estimation also conrms that the relation between employment growth and credit growth increases with the bargaining power of workers, consistent with the theory. 5 Under the assumption that employment and investment are complements. 118 Table 3.4: Employment growth regression. Baseline regression Unionization Rate High Low union cic;t credit it 0.088 (0.034) union cic;t -0.045 (0.054) credit it 0.043 0.060 0.042 (0.004) (0.005) (0.004) credit it1 0.048 0.052 0.044 (0.015) (0.023) (0.022) log(employ t1 ) -0.153 -0.158 -0.151 (0.009) (0.010) (0.014) Q it 0.019 0.024 0.017 (0.004) (0.006) (0.005) cashflow it 0.218 0.258 0.190 (0.021) (0.035) (0.028) Firm Fixed Eects Yes Yes Yes Year Dummies Yes Yes Yes Adjusted R 2 0.35 0.35 0.34 Observation 19,656 9,658 9,998 The rst column reports the results for the baseline specication based on industry-level unionization. The next two columns report the results of regressions without the interaction term, separately for high and low unionization rms. High unionization rms are those located in industries with higher than median unionization rate. The sample is an unbalanced panel of the period 2003 to 2010. The dependent variable is employment growth, employit, and independent variables include: interaction between industry unionization rate and credit growth, unioncic;t creditit, industry unionization rate unioncic;t, credit growth, creditit, lagged credit-to-asset ratio,creditit1, lagged log-employment, log(employ)it1, market- to-book ratio, Qit, cash ow-to-asset ratio, cashflowit. Firm xed eects and year dummies are also included. Standard errors (in parentheses) are heteroskedasticity robust and clustered at the rm level, and signicance levels at 1%, 5%, and 10% are marked with superscripts , , . 3.6.3 Robust Test Table 3.5 reports the estimation results when we replace the industry-level unionization index with a rm-level index from a random sample of 300 rms. In the data, we only 119 Table 3.5: Employment growth regression. Firm-level unionization Unionization Rate High Low union i;t credit it 0.238 (0.046) union i;t credit it 0.058 0.136 0.054 (0.008) (0.019) (0.008) credit it1 0.063 0.067 0.071 (0.042) (0.062) (0.051) log(employ t1 ) -0.130 -0.134 -0.130 (0.017) (0.027) (0.020) Q it 0.013 -0.056 0.022 (0.011) (0.039) (0.010) cashflow it 0.241 0.266 0.249 (0.063) (0.154) (0.067) Firm Fixed Eects Yes Yes Yes Year Dummies Yes Yes Yes Adjusted R 2 0.38 0.38 0.38 Observation 2,084 673 1,411 This table reports the regression results using the randomly sampled rm-level unionization data. We randomly sample 300 rms from the unbalanced panel of the baseline regression and then manually collect the unionization data from the 10k lings. Within the 300 rms, 93 rms have at least some collective bargaining coverage, and 207 rms do not have any union coverage. High unionization rms are those with higher than median unionization rate (which is zero), and therefore they are also the rms having at least some collective bargaining coverage. Standard errors (in parentheses) are heteroskedasticity robust and clustered at the rm level, and signicance levels at 1%, 5%, and 10% are marked with superscripts , , . collect one constant unionization rate for each rm, and we make the assumption that rms retain the same unionization rate during the sample period. Thus, any variation in the strength of the relation between employment growth and debt growth would come from the cross-section variation of the unionization rate among rms. 120 Within the 300 randomly sampled rms, 93 rms report they have at least some collec- tive bargaining coverage. The average unionization rate is 0:08, 6 and the standard deviation is 0:17. Among the 93 rms with non-zero unionization rate, the average unionization rate is 0:26, and the standard deviation is 0:21. As can be seen in the rst column of Table 3.5, the coecient of interaction term union i;t credit it is positive and statistically signicant at 1% level. The unionization rate union i;t , without interaction, is dropped from the regression because it is constant during the sample period. The next two columns of Table 3.5 reports the results of estimating equation (3.23) without the interaction terms, separately for high and low unionization rms. Similar to those obtained with the industry-level unionization index (Table 3.4), the coecient of credit it is larger for high unionization rms. 3.7 Conclusion There is a well-established literature in corporate nance exploring the use of debt as a strategic mechanism to improve the bargaining position of rms with workers. Less attention has been devoted to studying whether this mechanism is also important for the hiring decision of rms. In this paper we have investigated the theoretical and empirical relevance of the bargaining channel for hiring. Using a rm dynamics model, we have shown that there is a positive relation between the level of debt and the growth of employment, and the strength of this relation increases with the bargaining power of workers. The estimation results show that the bargaining channel is important for the employment uctuation of rms. This mechanism could also 6 This number is very close to the average of industry unionization rate. 121 be important for the long-term dynamics of the rm in the sense that greater uncertainty about the rm's access to credit could have sizable negative eects on its long-term growth. 122 Bibliography Almeida, H., M. Campello, B. Laranjeira, and S. Weisbenner (2012). Corporate debt maturity and the real eects of the 2007 credit crisis. Critical Finance Review 1, 3-58. Benmelech, E. N. K. Bergman, and A. Seru (2010). Financing labor. Unpublished manuscript, Harvard University. Eschuk, C. A. (2001). Unions and rm behavior: prots, investment, and share prices. Ph. D. thesis, University of Notre Dame. Hirsch, B. T. (2010). Unions, dynamism, and economic performance. Andrew Young School of Policy Studies Research Paper Series No. 10-08. Jensen, M. (1986). The agency cost of free cash ow: Corporate nance and takeovers. American Economic Review, 76(2), 323-30. Klasa, S. W. F. Maxwell, and H. Ortiz-Molina (2009). The strategic use of corporate cash holdings in collective bargaining with labor unions. Journal of Financial Economics, 92(3), 421-442. Matsa D. A. (2010). Capital structure as strategic variable: Evidence from collective bargaining, Journal of Finance, 65(3), 1197-1232. Mian, A and A. Su (2011). What explains high unemployment? The deleveraging- aggregate demand hypothesis. Unpublished manuscript, University of Chicago. Modigliani, F., and M. H. Miller (1958). The cost of capital, corporate nance and the theory of investment. American Economic Review, 48(3), 261-97. 123 Monacelli, T., V. Quadrini, and A. Trigari (2011). Financial markets and unemployment. NBER Working Paper No. 17389. Ippolito, F., and A. Perez (2012). Credit Lines: The other side of corporate liquidity. Working Paper, Barcelona GSE. Perotti, E. C. and K. E. Spier (1993). Capital structure as a bargaining tool: The role of leverage in contract renegotiation. American Economic Review, 83(5), 1131-41. Su, A. (2009). Bank lines of credit in corporate nance: An empirical analysis. Review of Financial Studies 22, 1057-1088. 124 Appendix A Appendix to Chapter 1 A.1 A Micro-Interpretation of the Enforcement Constraint In this appendix, I provide a micro-interpretation of the enforcement constraint (1.4) used in Section 1.3.3: p t b t+1 max n t k t+1 ; (1 b )p t b t o : I will keep the variable t as a constant collateral rate and introduce a new variable t to capture the credit risk. I assume that rms need to search for lenders when they decide to tap the credit market. The probability of nding a lender depends on the nancing condition. When the nancing condition is t , the rm can nd a lender with probability t , and with probability 1 t the rm cannot get nanced. Here, the inverse of the nancing condition 1= t can be interpreted as a measure of credit market tightness. Thus, the probability of nding a lender decreases in the credit market tightness. The variable t can also be interpreted as a measure of the lender's nancial health. In the case that the rm nds a lender, it can issue new debt. However, due to the rm's limited commitment on its debt obligations, the issuances of debt are subject to collateral constraints: when the lender provides loans to the rm in the current period, it wants to make sure that in the next period the liquidation value of the rm's assets is larger than the value of the rm's outstanding debt so that the rm does not default. To be specic, if the rm has capital assets k t+1 at the end of period t, its total credit limit during periodt would bek t+1 , in which I assume that the assets in place (1)k t and the 125 new investmentsi t have the same collateral rate. As a result, the rm's debt outstanding b t+1 at the end of period t should satisfy: p t b t+1 k t+1 . The value of total debt should be less than or equal to the value of collateral assets. In the case that the rm does not nd a lender, it cannot issue new debt. However, according to the arrangement of long-term debt, the lender cannot force the rm to repay more than b percent of its debt outstanding, without regard to the nancing conditions. In this case, the borrowing constraint would be p t b t+1 (1 b )p t b t , where (1 b )p t b t is the value of non-paid debt. To sum up, during the periodt the rm is subject to the following revised enforcement constraint, which is a stochastic version of the constraint (1.4): p t b t+1 ! t+1 ; (A.1) where p t b t+1 is the value of debt outstanding and ! t+1 is the rm's total debt capacity as follow: ! t+1 |{z} debt capacities = t |{z} renancing prob. k t+1 |{z} collateral assets + (1 t )(1 b )p t b t | {z } non-paid debt : (A.2) The rm's debt capacity depends on the nancing condition t , the value of collateral assets k t+1 , and the value of non-paid debt (1 b )p t b t . Accordingly, the rm's unused lines of credit during period t would be dened as: l t = t k t+1 + (1 t )(1 b )p t b t p t b t+1 : (A.3) There are three remarks on the enforcement constraint (A.1). First, as can be seen from equation (A.2), a better nancing condition t eases the enforcement constraint, a lower repayment rate b relaxes the enforcement constraint, and a larger the last period's debt outstanding b t relaxes the current period's enforcement constraint. 126 Second, if the repayment rate b = 1, the enforcement constraint (A.1) becomesp t b t+1 t k t+1 . In this case, consider the constraint in periodt+1: p t+1 b t+2 t+1 k t+2 . Suppose there is a decline of the nancing opportunity t+1 . Then, as a result, the rm has to reduce its debt outstanding b t+2 , which in turn forces the rm to cut either investment or dividend. Thus, if it is costly for the rm to adjust capital or equity quickly within a period, concerns about period t + 1's credit contractions would induce the rm to borrow less and save unused debt capacity in period t. Third, if the repayment rate b < 1, the second term (1 t )(1 b )p t b t on the right side of equation (A.2) comes up. In this case, the rm would have incentives to borrow more to hedge against future credit contractions. This is because an additional unit of borrowing b t in periodt1 would relax the enforcement constraint in periodt by (1 t )(1 b )p t b t dollars. Further, if it is costly to adjust capital or equity quickly, the rm would temporally save the funds from the long-term borrowing in cash. Let's compare the eciency of cash and unused lines of credit in providing future liquidity. Denote the price of cash at period t as p m t , then one additional dollar of cash in periodt 1 leads to 1 p m t1 dollars of available funds in periodt. Similarly, suppose the price of debt at periodt isp t , then one additional dollar of unused lines of credit in period t 1 leads to t(1 b )pt+ b p t1 dollars of available funds in period t. The term t(1 b )pt+ b p t1 depends on the credit market condition t , and it contains two parts. The rst part t(1 b )pt p t1 represents the increase in debt issuance, and the second part b p t1 is the reduction in debt repayment. The rm makes a trade-o between low-return cash 1 p m t1 and contingent unused lines of credit t(1 b )pt+ b p t1 . And this trade-o depends on the maturity of debt ( 1 b ), the oppor- tunity cost of holding cash (p m t1 p t1 ), and the future nancing condition ( t ). If b = 1, t(1 b )pt+ b p t1 = 1 p t1 > 1 p m t1 , which means that unused lines of credit are less costly than cash holdings in providing liquidity. However, if b < 1, unused lines of 127 credit become contingent, and cash can be more ecient than credit lines in accumulating liquidity in some states, particularly when future credit market conditions become worse: it is more likely that 1 p m t1 > t(1 b )pt+ b p t1 when t becomes smaller. The above results can also be explained by the features of long-term debt. With long- term debt, one unit of debt issuance in periodt1 not only brings inp t1 dollars of proceeds in period t 1, but also relaxes the period t's enforcement constraint by (1 t )(1 b )p t dollars. The relaxation of enforcement constraint then increases the available credit the rm can use in period t. On the other hand, one unit of debt retirement in period t 1 only leads to t (1 b )p t + b dollars of available funds in period t. This is because that the nancing opportunity is stochastic, if the rm does not borrow now, it may lose the chance to borrow in the future. A.2 Proofs The rm's problem after detrending is (I remove the tilde on the detrended variables): V (m;b;s) = max g 0 ;m 0 ;b 0 ;d d +g 0 E[( z 0 a z a ) V (m 0 ;b 0 ;s 0 )] subject to: p m m 0 g 0 z i z a (A.4) z i z a +m +pn =p m m 0 g 0 + b b +i +'(d) (A.5) g 0 = (1) +(i) (A.6) pb 0 g 0 = (1 b )pb +pn (A.7) pn 0 (A.8) pn[g 0 (1 b )pb] (A.9) 128 Let be the multiplier on the cash-in-advance constraint (A.4), 0 be the multiplier on the budget constraint (A.5), q be the multiplier on the investment equation (A.6), 1 be the multiplier on the debt dynamics equation (A.7), 2 be the multiplier on non-negative debt issuance constraint (A.8), and 3 be the multiplier on the enforcement constraint (A.9). The Lagrangian equation is: L =d +g 0 E[( z 0 a z a ) V (m 0 ;b 0 ;s 0 )] + p m m 0 g 0 z i z a + 0 z i z a +m +pnp m m 0 g 0 b bi'(d) +q 1 +(i)g 0 + 1 p b 0 g 0 (1 b )bn + 2 pn + 3 [g 0 (1 b )pb]pn where 2 0 and is the probability of having a nancing opportunity. 129 First Order Conditions for d, i, m 0 , b 0 , g 0 , n are: 0 1 ' 0 (d) = 0 q 0 0 (i) = 0 g 0 E[( z 0 a z a ) V 0 m 0] 0 p m g 0 +p m g 0 = 0 g 0 E[( z 0 a z a ) V 0 b 0] + 1 pg 0 = 0 E[( z 0 a z a ) V 0 ] +p m m 0 0 p m m 0 q + 1 pb 0 + 3 = 0 0 p 1 p + 2 p 3 p = 0 Envelope Conditions are: V m = 0 V b = 0 b 1 (1 b )p 3 (1 b )p Proof of Proposition 3.1: If b = 1, then = 0 1 p p m > 0, by using 0 1 = 3 0 and p m >p. Thus, the cash-in-advance constraint is always binding. Proof of Proposition 3.2: When b < 1, = 0 p p m 1 b +(1 b )p + p p m E s h ( z 0 a za ) (1)(1 b ) 0 1 b +(1 b )p i . The size of lagrangian multiplier depends on the state s. Thus, it is possible that in some states = 0 and therefore the cash-in-advance constraint can be occasionally non-binding. Appendix A.3.2 demonstrates all the possible cases of non-binding constraints. 130 A.3 Numerical Methods After writing down the rst-order conditions and the envelope conditions, the rm's prob- lem can be summarized by a system of non-linear equations associated with three expec- tation terms. Thus, by solving the non-linear equations, I get the solution of the rm's problem. The numerical solution takes three steps. First, I approximate the three conditional expectation functions as follows: V (m;b;s) =E s (z 0 a ) V (m 0 ;b 0 ;s 0 ) m (m;b;s) =E s (z 0 a ) V m 0(m 0 ;b 0 ;s 0 ) b (m;b;s) =E s (z 0 a ) V b 0(m 0 ;b 0 ;s 0 ) Second, given the parameterized expectations, I solve the system of non-linear equations on each grid. I discreterize each shock on ve grid points and each state variable on ten grid points. I also do robust check by increasing the number of grids. I interpolate linearly between grids when calculating the expectations. Finally, I iterate on the approximation functions until convergence. A.3.1 Main Programming Routine The main numerical routine contains two loops: The outside loop: given states (m;b;s), solve policies (m 0 ;b 0 ) and update the approx- imation functions ( V ; m ; b ). The inside loop: solve a non-linear equation system with four unknowns. 131 The four unknowns are: m 0 , b 0 , i, V , and the four equations are: EQ1 :(p m m 0 g 0 z i z a ) = 0 EQ2 : 2 pn = 0 EQ3 : 3 g 0 (1 b )pb pn = 0 EQ4 :d +g 0 (z a ) V V = 0 where, g 0 = (1) +(i) n =b 0 g 0 (1 b )b d =' 1 (z i z a +m +pnp m m 0 g 0 b bi) 0 = 1 ' 0 (d) q = 0 0 (i) 1 = (z a ) b p = 0 (z a ) m p m 3 = 0 p m m 0 +q 1 pb 0 p m m 0 (z a ) V 2 = 3 0 + 1 A.3.2 Occasionally Binding Constraints I rst solve the equation system by assuming that the two constraints (A.4) and (A.9) are both binding, and then check the Lagrangian multipliers and 3 . According to the sign of and 3 , I specify four cases and resolve the system case by case. 132 Case A, both binding, neither precautionary cash nor unused lines of credit: EQ1 : g 0 (1 b )pb pn = 0 EQ3 :p m m 0 g 0 z i z a = 0 Case B, one non-binding, only has precautionary cash: EQ1 : g 0 (1 b )pb pn = 0 EQ3 :p m m 0 g 0 z i z a > 0 Case C, one non-binding, only has unused lines of credit: EQ1 : g 0 (1 b )pb pn> 0 EQ3 :p m m 0 g 0 z i z a = 0 Case D, both non-binding, precautionary cash coexists with unused lines of credit: EQ1 : g 0 (1 b )pb pn> 0 EQ3 :p m m 0 g 0 z i z a > 0 133 A.4 Simulated Method of Moments The choice of model parameters is done by the simulated method of moments (SMM). The basic idea of SMM is to choose the model parameters such that the moments generated by the model are as close as possible to the corresponding real data moments. The real data is a panel of heterogenous rms, but the simulated data is generated by a representative rm. To keep consistency between the actual data and the simulated data, I estimate the parameters of an average rm in the data. To be specic, given the panel structure of the data, I rst calculate moments for each rm, and then compute the average of moments across rms and use it as the target moment. I use the bootstrap method to calculate the variance-covariance matrix associated with the target moments. The estimation procedure is as follows. 1 First, for each rmi, I choose momentsh i (x it ), wherex it is a vector representing variables in the actual data, and subscripti andt indicates rm and year respectively. Second, for each rmi, I calculate the within-rm sample mean of moments as f i (x i ) = 1 T T P t=1 h i (x it ), where T is the number of scal years in the data. Third, I compute the average of the within-rm sample mean as f(x) = 1 N N P i=1 f i (x i ), where N is the number of rms in the data. Correspondingly, I use the model to simulate a panel data of N number of rms and S periods. I set S = 100T to make sure that the representative rm would visit all the states in the model. I calculate the average sample mean of moments in the model as f(y;) = 1 NS N P i=1 S P s=1 h(y is ;), where y is is the simulated data from the model, and represents the parameters to be estimated. The estimator b is the solution to min : [f(x)f(y;)] T [f(x)f(y;)]. 1 I also use the estimation procedure described in DeAngelo, DeAngelo, and Whited (2011), and the estimation results are robust. 134 The weighting matrix is dened as b 1 , where b is the variance-covariance matrix associated with the average of sample mean f(x) in the data. I use the bootstrap method to calculate the variance-covariance matrix b . First, given the population of N number of rms from the real data, I draw J random samples with size N 2 . Sec- ond, for each draw j, I compute the statistics of the drawn sample, denote by f(x) j . Third, I approximate the variance-covariance matrix by the variance of f(x) j , i.e., b 1 J J P j=1 f(x) j 1 J J P j=1 f(x) j T f(x) j 1 J J P j=1 f(x) j . Finally, I set J=50,000 to have enough accuracy of the bootstrap method. In the estimation, parameters are jointly identied by moments, and the number of moments is larger than the number of parameters. Thus, there is no one-to-one mapping between moments and parameters. To have a clear idea about the identication of the model parameters, I conduct comparative statics exercises to nd out the relationship between the target moments and the model parameters. In the comparative statics study, I rst use the estimated parameters as benchmark parameters to compute the moments. Then, I adjust the parameters one by one to examine the sensitivity of each moment with respect to the change of parameters. Table A.1 reports the results of the comparative statics exercises. According to the comparative statics exercises, the main identication of parameters is as follows. First, consider the identication of two shocks in the model. The drift of productivity shock z can be identied by the mean of investment. This is because increases in z raise the marginal prot of investment, and therefore the level of investment. The persistence of productivity shock z is mainly identied by the autocorrelation of cash ows, and the standard deviation z is identied by the standard deviation of cash ows. Similarly, the persistence of the credit shock is mainly identied by the autocorrelation of cash, and the standard deviation of credit shock is identied by the standard deviation of debt. 135 The change of capital deprecation rate aects the level of cash, the level of debt, the level of investment, and the level of cash ows, and therefore the parameter is pinned down by those four moments. The collateral rate is mainly identied by the level of debt since increases in raise the level of debt uniquely. The next set of parameters are about frictions. The equity rigidity parameter mea- sures the rigidities of adjusting equity. It is mainly identied by the standard deviation of payout. The second friction parameter, the capital adjustment cost parameter , is identied by autocorrelation of investment. The price of cash p m measures the opportunity cost of holding cash. Increases in the price of cash reduces the level of cash, but raise the level of unused lines. Thus, the parameter p m can be jointly identied by two moments: the level of cash and the level of unused lines. Table A.1: Comparative statics of estimated parameters Bench z z z p m Mean of Cash/Assets 0.154 0.156 0.149 0.147 0.156 0.172 0.173 0.168 0.152 0.155 0.107 Mean of Unused Line/Assets 0.047 0.044 0.044 0.049 0.053 0.066 0.045 0.068 0.061 0.047 0.129 Mean of Debt/Assets 0.184 0.189 0.184 0.180 0.170 0.146 0.179 0.229 0.167 0.184 0.088 Mean of Investment/Assets 0.053 0.056 0.040 0.052 0.052 0.052 0.067 0.052 0.053 0.056 0.055 Mean of Payout/Assets 0.041 0.038 0.044 0.045 0.041 0.044 0.046 0.040 0.041 0.038 0.046 Mean of Cash Flow/Assets 0.093 0.093 0.088 0.086 0.092 0.091 0.112 0.091 0.094 0.092 0.098 Std of Cash/Assets 0.046 0.047 0.046 0.046 0.046 0.056 0.045 0.054 0.042 0.046 0.032 Std of Unused Line/Assets 0.074 0.073 0.073 0.078 0.085 0.105 0.074 0.102 0.086 0.075 0.124 Std of Debt/Assets 0.091 0.093 0.092 0.093 0.103 0.128 0.090 0.112 0.089 0.093 0.071 Std of Payout/Assets 0.025 0.024 0.027 0.027 0.026 0.029 0.026 0.026 0.022 0.024 0.025 Std of Cash Flow/Assets 0.033 0.034 0.035 0.041 0.033 0.033 0.040 0.033 0.034 0.034 0.035 Auto of Cash/Assets 0.191 0.199 0.219 0.174 0.256 0.174 0.172 0.185 0.175 0.191 0.146 Auto of Investment/Assets 0.220 0.213 0.393 0.257 0.264 0.164 0.249 0.203 0.280 0.190 0.095 Auto of Cash Flow/Assets 0.315 0.312 0.445 0.304 0.310 0.292 0.292 0.317 0.305 0.309 0.262 This table shows the results of comparative statics exercises of the estimated parameters. The rst column lists the benchmark moments simulated by the parameters estimated in Table 1.1. The second to the twelfth column shows the results of the sensitivity test by changing the value of one parameter each time. The parameters are: the drift of productivity shock z , the persistence of productivity shock z , the volatility of productivity shock z , the persistence of credit shock , the volatility of credit shock , the capital depreciation rate , the collateral rate , the equity rigidity parameter , the capital adjustment cost , and the price of cash p m . I increase each parameter by 33% to test its sensitivity, except increasing price of cash p m from 0:975 to 0:98. 136 A.5 Variable Denitions in the Structural Estimation Table A.2: Variable denitions in the structural estimation Variable Model Detrended Model Data Cash/Assets p m m t+1 k t +m t p m ~ m t+1 g t+1 1+ ~ m t (Cash and Short-Term Investments (CHEt) Debt in Current Liabilities-Total (DLCt)) / Assets-Total (ATt1). From Compustat. Debt/Assets p t b t+1 k t +m t p t ~ b t+1 g t+1 1+ ~ m t Long-Term Debt-Total (DLTTt) / Assets-Total (ATt1). From Compustat. Investment/Assets i t k t +m t ~ i t 1+ ~ m t Capital Expenditures (CAPXt) / Assets-Total (ATt1). From Compustat. Payout/Assets d t :d t >0 k t +m t ~ d t : ~ d t >0 1+ ~ m t (Purchase of Common and Preferred Stock (PRSTKCt) + Dividends-Preferred/Preference (DVPt) + Dividends Common/Ordinary (DVCt) ) / Assets-Total (ATt1). From Compustat. Cash Flow/Assets z t k t k t +m t z t 1+ ~ m t Operating Income Before Depreciation (OIBDPt) / Assets-Total (ATt1). From Compustat. Unused Line/Assets l t k t +m t ~ l t 1+ ~ m t Total Undrawn Creditt / Assets-Total (ATt1). From Capital IQ and Compustat. 137 Appendix B Appendix to Chapter 2 B.1 Equivalence of the Recursive Problem and the Original Problem We can write down the rm's problem as follows: V 0 = max fet;ct;b t+1 g 1 t=0 :E 0 1 X t=0 t d t subject to: d t =z t h t c t e t + b t+1 R t b t 0 (B.1) h t+1 = (1)h t +(e t =h t )h t (B.2) t E t 1 X n=0 n d t+1+n b t+1 R t (B.3) E t 1 X n=0 n u(c t+1+n )w(h t+1 ) (B.4) Equation (B.1) is the budget constraint, and equation (B.2) is the law of motion of organi- zational capital h. Equation (B.3) is the debt enforcement constraint, and equation (B.4) is the worker's participation constraint, at the end of period t. 138 Dene m t+1 (z t+1 ;h t+1 ) = E t+1 1 P n=0 n u(c t+1+n ), then equation (B.4) is equivalent to the following recursive form: m t =u(c t ) +E t [m t+1 ] (B.5) (z t+1 jz t )m t+1 (z t+1 ;h t+1 )(z t+1 jz t )w(h t+1 ),8z t+1 ;8h t+1 (B.6) where equation (B.5) is the promise-keeping constraint and equation (B.6) is the partic- ipation constraint. Since the outside option of workers w(h t+1 ) is independent of z t+1 , substituting equation (B.4) with (B.5) and (B.6), we obtain the recursive problemP. B.2 Proof of Proposition 1 Let be the multiplier on the budget constraint, ' be the multiplier on the non-negative dividend constraint, q is the multiplier on the investment constraint, is the multiplier on the collateral constraint (enforcement constraint), is the multiplier on the promise- keeping constraint and is the multiplier on the participation constraint. Write down the Lagrangian of the problemP: L = d +E[V (m 0 ;b 0 ;h 0 ;z 0 )jz] + zh ce + b 0 R bd +'d +q (1)h +( e h )hh 0 + E[V (m 0 ;b 0 ;h 0 ;z 0 )jz] b 0 R + log(c) +E[m 0 ]m + m 0 !(h 0 ) 139 Solve to obtain the problem's rst order conditions: b 0 : =R(1 +)E[V 0 b jz] + (B.7) m 0 : =(1 +)E[V 0 m jz] (B.8) h 0 : q =(1 +)E[V 0 h jz] +zh 1 ! 0 (h 0 ) (B.9) d : = 1 +' (B.10) e : q = 0 ( e h ) (B.11) c : = u 0 (c) (B.12) and the Envelope conditions: b : V b = (B.13) m : V m = (B.14) h : V h =zh 1 +q[(1) +( e h ) 0 ( e h ) e h ] (B.15) (B.7)-(B.15) completely capture the system. Lemma 1 From F.O.C (B.7) and Envelope condition (B.13), we obtain =RE[ 0 jz] (B.16) - When = 0, =RE[ 0 jz]. Thus, 0 increases on average, since R< 1. - When > 0, = +RE[ 0 jz]. Thus, 0 decreases on average whenever > (1R). 140 Lemma 2 From F.O.C. (B.8) and Envelope condition (B.14), we obtain: = + (1 +)E[ 0 jz] (B.17) - When = 0, E[ 0 jz] = 1+ . Thus, 0 decreases on average since 0. - When > 0, E[ 0 jz] = + 1+ . Thus, 0 increases on average whenever >. Dene the marginal rate of substitution between dividend and worker's consumption as u 0 (c) . Proposition 1 Combining equation (B.8), (B.12) and (B.14) to obtain (1 +)E[ 0 (z 0 ) u 0 (c 0 (z 0 )) jz] = + u 0 (c) (B.18) The following statements say that the expected marginal rate of substitution can be predicted by the last period marginal rate of substitution conditional on and . 1. If > 0; = 0, (1 +)E[ 0 (z 0 ) u 0 (c 0 (z 0 )) jz] = u 0 (c) , hence E[ 0 (z 0 ) u 0 (c 0 (z 0 )) jz]< u 0 (c) . 2. If = 0; = 0, E[ 0 (z 0 ) u 0 (c 0 (z 0 )) jz] = u 0 (c) . 3. If > 0; > 0, (1 +)E[ 0 (z 0 ) u 0 (c 0 (z 0 )) jz] = u 0 (c) + > u 0 (c) . 4. If = 0; > 0, E[ 0 (z 0 ) u 0 (c 0 (z 0 )) ] = u 0 (c) + > u 0 (c) . 141 B.3 Proof of Proposition 2 Recall the systems of optimality conditions (B.7)-(B.15). Rearrange to obtain Euler equa- tions for promised utility m and debt capacity b: m : V m =(1 +)E[V 0 m jz] (B.19) b : +V b =R(1 +)E[V 0 b jz] (B.20) Combining two equations (B.19) and (B.20) and substituting out 1 +, we obtain: 1 E[V 0 m jz] V m =R E[V 0 b jz] V b + (B.21) 1 E[V 0 m jz] Vm is dened as the rate of return on borrowing from the workersm, andR E[V 0 b jz] V b + is dened as the rate of return on borrowing from the creditorsb. SinceV 0 m < 0 andV 0 b < 0. The rm equalizes the marginal rate of return on m 0 and b 0 by rising one while reducing the other. 1 E[V 0 m jz] V m 1 E[V 0 m jz] V m =R E[V 0 b jz] V b + R E[V 0 b jz] V b 1. > 0: the rm increases m 0 or decrease the debt level b 0 . 2. > 0: the rm decrease the the debt level b 0 or increases m 0 . B.4 Numerical Procedure We solve the contract numerically using the projection method. After writing down the rst-order conditions and the envelope conditions, the rm's problem can be summarized by a system of non-linear equations associated with two expectation terms. Thus, by solving the non-linear equations (B.7)-(B.15), we get the solution of the rm's problem. 142 The numerical procedure takes three steps. First, we parameterize the two expectation terms. Second, given the parameterized expectations, we solve the system of non-linear equations on each grid. We discreterize the productivity shock on seven grid points and each state variable on ten grid points. We also do robust check by increasing the number of grids. We interpolate linearly between grids when calculating the expectations. Third, we iterate on the approximated expectations until convergence. B.5 Sensitivity Test Table B.1: Sensitivity Benchmark z z w0 Mean( netdebt t bookassets t ) 0.273 0.260 0.266 0.209# 0.263 0.291 Std( netdebt t bookassets t ) 0.095 0.083 0.106 0.167" 0.104 0.086 Std( sale t sale t1 ) 0.082 0.069 0.106 0.081 0.081 0.082 Std( wage t wage t1 ) 0.130 0.058 0.131 0.113# 0.130 0.163 Std( ocapital t ocapital t1 ) 0.062 0.031 0.079 0.061 0.065 0.087 Autocor( netdebt t bookassets t ) 0.589 0.778 0.667 0.742 0.656 0.421 Autocor( ocapital t ocapital t1 ) 0.314 0.179 0.304 0.298 0.353 0.284 The rst column reports the moments generated by the simulation of the model under the estimated param- eters of the period 1960-1985. The remaining columns report the simulated moments after changing the value of the specic parameter into the estimated parameters of the period 1985-2010. The ve parameters are: the persistence and volatility of the productivity shock, z andz, the workers' outside optionw0, the nancing cost parameter , and the capital adjustment cost parameter . 143 Appendix C Appendix to Chapter 3 C.1 Variables Used in the Structural Estimation unused it credit it : Ratio of unused lines of credit to total credit (debt + unused lines of credit) at time t. The variable \debt" is from COMPUSTAT, dlc +dltt; and the variable \unused lines of credit" is from Capital IQ, undrawn. credit it : Percentage change in total credit fromt 1 tot. Calculated from Capital IQ and COMPUSTAT. employ it : Percentage change in the number of employees from t 1 to t. From COMPUSTAT, emp. sale it : Percentage change in sales from t 1 to t. From COMPUSTAT, sale. C.2 Additional Variables Used in the Reduced-Form Esti- mation union cic;t : Industry unionization rate is dened as percent of employed workers who are covered by a collective bargaining agreement in an industry. From Union Mem- bership and Coverage Database. credit it : Total credit to assets ratio at time t. From COMPUSTAT and Captial IQ, (dltt +dlc +undrawn)=at. 144 cashflow it : Operating income before depreciation over assets at timet. From COM- PUSTAT, oibdp=at. Q it : Book value of assets plus the market value of equity minus the book value of equity and deferred taxes, over the book value of assets. From COMPUSTAT, (at +cshoprcc fceqtxdb)=(0:9at + 0:1 (at +cshoprcc fceqtxdb)). 145

Abstract (if available)

Abstract This dissertation studies how firms make investment and employment decisions when they face frictions in capital and labor markets. Specifically, I study (i) how firms manage liquidity under uncertain financing conditions

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Creator Sun, Qi (author)

Core Title Essays in financial economics

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 04/28/2014

Defense Date 03/11/2014

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Advisor Quadrini, Vincenzo (committee chair), DeAngelo, Harry C. (committee member), Dekle, Robert (committee member), Michaux, Michael (committee member)

Creator Email qisun@usc.edu,qisun2013@gmail.com

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