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Risks, returns, and regulations in real estate markets

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Risks, returns, and regulations in real estate markets

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Content Risks, Returns, and Regulations in Real Estate Markets by Anthony W. Orlando A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY PUBLIC POLICY AND MANAGEMENT May 2018 Contents Introduction 6 1 An Econometric Analysis of Housing Supply Dynamics in the United States, 1959-2015 10 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Three Measures of Housing Quantity: Data and Trends . . . . . . . . . . . . . . . . 12 1.2.1 Permits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.2 Starts and Completions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.3 Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 Estimating Lags in Housing Production . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Reduced-Form VAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 Unit Root Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4 Cointegration and Errors Over Time . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.1 Vector Error Correction Model . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.2 Cointegrating Relationships Over Time . . . . . . . . . . . . . . . . . . . . . 19 1.4.3 Prediction Errors Over Time . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5 Forecasting Future Production and Risks . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5.1 Forecasting Short-Term Production . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5.2 Forecasting Long-Term Production . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5.3 Predicting Recession Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.6 A New Methodology for Housing Supply . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2 Asset Markets, Credit Markets, and Inequality: Distributional Changes in Hous- ing, 1970-2016 47 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.2 Theoretical Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.2.1 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.2.2 Credit Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.3 Data: The Housing Price Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.3.1 Home Price Quantiles Over Time . . . . . . . . . . . . . . . . . . . . . . . . . 55 1 2.3.2 Home Characteristics Over Time . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.4 Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.4.1 The In uence Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.4.2 The RIF Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.4.3 Estimating the Unconditional Quantile Partial Eect of Monetary Policy . . 59 2.4.4 Estimating the Unconditional Quantile Partial Eect of Credit Supply . . . . 61 2.5 Main Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.5.1 Basic Hedonic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.5.2 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.5.3 Credit Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.6.1 Price Eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.6.2 Wealth Eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.6.3 A Simulation of the Housing \Bubble" . . . . . . . . . . . . . . . . . . . . . . 68 2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3 What's Lost in the Aggregate: Lessons from a Local Index of Housing Supply Elasticities 93 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.2 Motivating Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.3 Local Housing Prices and Quantities: Data and Trends . . . . . . . . . . . . . . . . . 96 3.3.1 Local Housing Price Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.3.2 Local Housing Quantity Index . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.4 Calculating Housing Supply Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.4.1 Sign-Restricted Vector Autoregression Model . . . . . . . . . . . . . . . . . . 100 3.4.2 Sign-Restricted VAR(2) Results . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.5 Cross-Sectional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 A Robustness Tests for VAR/VEC Lag Structure 114 A.1 Selection-Order Criteria for VAR Models . . . . . . . . . . . . . . . . . . . . . . . . . 114 A.2 Eigenvalue Stability Condition for VAR and VEC Models . . . . . . . . . . . . . . . 116 B Robustness Tests for Unconditional Quantile Regressions 119 B.1 National GDP vs. State GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 B.2 County vs. Tract Fixed Eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 2 List of Tables 1.1 Annual Lags: VAR(2) Model at National and Regional Levels, 1970-2015 . . . . . . 26 1.2 Monthly Lags: VAR(4) Model at National and Regional Levels . . . . . . . . . . . . 27 1.3 ADF Test for Unit Root in Annual VAR(2) Models: p-Values . . . . . . . . . . . . . 28 1.4 ADF Test for Unit Root in Monthly VAR(4) Models: p-Values . . . . . . . . . . . . 28 1.5 Johansen Tests for Cointegration in Annual Model with Two Lags . . . . . . . . . . 28 1.6 Johansen Tests for Cointegration in Monthly Model with Four Lags . . . . . . . . . 29 1.7 Annual Lags with Cointegrating Equation: National and Regional VECM, 1970-2015 29 1.8 VECM Residual Variation Across the Business Cycle . . . . . . . . . . . . . . . . . . 30 1.9 Comparing One-Year Forecasts: Area Under the ROC Curve . . . . . . . . . . . . . 30 2.1 Eect of Monetary Policy Shocks on Housing Price Distribution . . . . . . . . . . . . 70 2.2 Eect of State-Level Credit Supply on Housing Price Distribution . . . . . . . . . . 71 2.3 Simulation of Monetary Policy Shock on Housing Price Distribution . . . . . . . . . 71 2.4 Simulation of Credit Supply Shock on Housing Price Distribution . . . . . . . . . . . 72 3.1 Short-Run SVAR(2) Elasticities, 1996-2015 . . . . . . . . . . . . . . . . . . . . . . . 105 3.2 Long-Run SVAR(2) Elasticities, 1996-2015 . . . . . . . . . . . . . . . . . . . . . . . . 106 3.3 Cross-Sectional Analysis of Short-Run Supply Elasticities in LA County . . . . . . . 107 3 List of Figures 1.1 U.S. Permits vs. Starts vs. Completions, 1959-2015 . . . . . . . . . . . . . . . . . . . 31 1.2 Annual Permits, Starts, and Completions Ratios, 1968-2015 . . . . . . . . . . . . . . 32 1.3 Regional Permits vs. Starts vs. Completions, 1968-2015 . . . . . . . . . . . . . . . . 33 1.4 Cointegrating Relationship for National VECM, 1968-2015 . . . . . . . . . . . . . . . 34 1.5 Cointegrating Relationship for Regional VECMs, 1968-2015 . . . . . . . . . . . . . . 35 1.6 Residuals for National VECM, 1970-2015 . . . . . . . . . . . . . . . . . . . . . . . . 36 1.7 Absolute Residual Size for National VECM, 1970-2015 . . . . . . . . . . . . . . . . . 37 1.8 Residuals for Completions Equation in Regional VECMs, 1970-2015 . . . . . . . . . 38 1.9 Absolute Residual Size for Completions Equation in Regional VECMs, 1970-2015 . . 39 1.10 Residuals for Completions Equation in Monthly VAR(4), 1968-2016 . . . . . . . . . 40 1.11 \Out-of-Sample" Forecasts of 2016 Using Monthly VAR(4) Model . . . . . . . . . . . 41 1.12 \Out-of-Sample" Forecasts of Great Recession Using Annual VECM . . . . . . . . . 42 1.13 \Out-of-Sample" Forecasts of Housing Recovery Using Annual VECM . . . . . . . . 43 1.14 Recession Risk Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.15 ROC Curve for Recession Risk Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.16 Permits vs. Completions vs. Permit-Imputed Completions, 1959-2015 . . . . . . . . 46 2.1 Total U.S. Housing Starts, 1959-2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.2 Average 30-Year Mortgage Rate and Federal Funds Rate . . . . . . . . . . . . . . . . 73 2.3 Nominal Single-Family Home Transaction Prices in California, 1970-2016 . . . . . . 74 2.4 Real Single-Family Home Transaction Prices in California, 1970-2016 . . . . . . . . . 75 2.5 Logged Single-Family Home Transaction Prices in California, 1970-2016 . . . . . . . 76 2.6 Single-Family Home Sizes in California, 1970-2016 . . . . . . . . . . . . . . . . . . . 77 2.7 Single-Family Lot Sizes in California, 1970-2016 . . . . . . . . . . . . . . . . . . . . . 78 2.8 Single-Family Lot Sizes in California, 1970-2016 . . . . . . . . . . . . . . . . . . . . . 79 2.9 Eective Federal Funds Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.10 Unexpected Monetary Policy Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.11 Change in Actual Federal Funds Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.12 Mortgage Originations in California, 1990-2015 . . . . . . . . . . . . . . . . . . . . . 83 2.13 Eect of Hedonic Characteristics on Housing Price Distribution . . . . . . . . . . . . 84 2.14 Eect of Monetary Policy Shocks on Housing Price Distribution . . . . . . . . . . . . 85 4 2.15 Eect of Monetary Policy Shocks on Housing Price Distribution by Decade . . . . . 86 2.16 Eect of Loan Volume on Housing Price Distribution . . . . . . . . . . . . . . . . . . 87 2.17 Eect of Loan Volume on Housing Price Distribution by Subperiod . . . . . . . . . . 88 2.18 Eect of County-Level IV for Lending on Housing Price Distribution . . . . . . . . . 89 2.19 Distribution of Annual Monetary Policy Shocks . . . . . . . . . . . . . . . . . . . . . 90 2.20 Distribution of State-Level Changes in Loan Volume . . . . . . . . . . . . . . . . . . 91 2.21 Simulated Housing Prices, 2000-2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.1 Municipal Housing Unit Growth in Los Angeles County, 2000-2012 . . . . . . . . . . 108 3.2 Los Angeles County Permits vs. Prices, 1988-2012 . . . . . . . . . . . . . . . . . . . 109 3.3 SVAR Impulse Responses: City of Los Angeles . . . . . . . . . . . . . . . . . . . . . 110 3.4 SVAR Impulse Responses: City of Calabasas . . . . . . . . . . . . . . . . . . . . . . 111 3.5 Long-Run vs. Short-Run Elasticity by City, 1996-2015 . . . . . . . . . . . . . . . . . 112 3.6 Municipal Housing Supply Elasticity Distributions in Los Angeles County, 1996-2015 112 3.7 Municipal Housing Supply Elasticities in Los Angeles County, 1996-2015 . . . . . . . 113 B.1 Unconditional Quantile Partial Eects, Controlling for State GDP . . . . . . . . . . 121 B.2 Eect of Loan Volume on Housing Price Distribution with Tract Fixed Eects . . . 122 5 Introduction People are moving back into the cities (Baum-Snow and Hartley 2017, Couture and Handbury 2017). It's an urban renaissance, and housing is not being built fast enough (Morrow 2013, Taylor 2015). This dissertation explores where it is being built, how to predict construction activity with early development indicators, what is holding it back in tight markets, how local regulations drive the choice of where to build, and how dierent homes across the distribution are aected by economic factors suggested by theory. It categorizes these research questions into \the three R's of real estate": risks, returns, and regulations. The initial inspiration for this research came a little over a decade ago, when the U.S. housing market began to depreciate. At rst, it seemed like one of many cycles that investors had ex- perienced before, and then, suddenly, it was a new and frightening experience. 1 Fear gripped the market, and it did not let go until it had wrung trillions of dollars of wealth out of the system. Even today, with economic growth persistently low, we are living through the disastrous consequences (Blanchard and Summers 2017, Fat as and Summers 2018). This experience has revealed important gaps in our understanding of real estate markets: First, what risks do real estate markets pose for the macroeconomy? Can we predict them? Can we insure against them? Second, how much do credit markets drive returns on investment in housing? How are dierent households aected? How is wealth inequality aected? Third, how much do housing regulations restrain the market at a local level? How much do they dier across the metropolitan area? How much do they change the allocation of housing? The chapters in this dissertation begin to answer these questions|and by extension, to ll these gaps in the literature. The resulting policy implications can help to avoid a recurrence of the Great Recession and to put homebuilding on a more sustainable footing in this new urban resurgence around the globe. Chapter One begins at the macroeconomic level with a dynamic time-series analysis of the housing production process. It breaks this process down to the three stages at which we have national and regional data: building permits, housing starts, and completed units. It shows how cointegrated these three series are and how well they can be used to predict future production. It 1 Sitting in the classroom at Wharton, I remember the utter disbelief of my professors. 6 reveals how this relationship diers across time and space, how it can be used to improve estimates of housing supply for dierent research purposes, and how it helps to forecast recessions, thus tying risks in real estate markets directly to the macroeconomy as forecasters failed to do in the run-up to the Great Recession. This analysis applies two methodologies in new ways. First, it uses a vector autoregression (VAR) model to estimate the lag structure among these three variables over time. Due to their cointegration, it employs a vector error correction (VEC) technique to the annual data. While these methods have been used to estimate house price trends and supply elasticities, this is the rst application to forecast future production. It is accurate in most \normal" time periods, but importantly, it fails to predict the full trajectory of the 2000-2006 boom and 2007-2009 bust, suggesting that these experiences were atypical compared to past cycles. It is not surprising, based on these data, that most market participants failed to foresee the true severity of these market movements. Second, this chapter uses a receiver operating characteristic (ROC) curve to compare the accuracy of its forecasts to other models in the literature. The macroeconomics literature has only recently borrowed this methodology from statistics. This is the rst application to housing variables, and it reveals that they are more successful in forecasting recessions than any other variables identied by previous research. Chapter Two unpacks these macroeconomic changes across the housing distribution. It identies the eect of two nancial shocks that have been blamed for the recent \housing bubble"|monetary policy and credit supply|on the entire unconditional distribution of housing prices in California using transaction-level data from 1970 to 2016. It nds that unexpected increases in the federal funds rate lead to increases in home prices for most of the distribution, with higher increases for higher-priced homes, widening the dispersion in the home price distribution. This evidence supports new macroeconomic theories arguing that the positive psychological signal of tight monetary policy can outweigh the negative nancial eect on the ability to borrow, except for the most constrained households at the bottom of the distribution where there is some evidence of a decrease in home prices. This chapter also nds that increases in mortgage lending volume lead to increases in home prices for the entire distribution, but the percentage increase is greatest for mid-priced homes. Importantly, however, the dynamic changes during the 2000-2006 \bubble" period, when low-priced homes experience the biggest boost from mortgage lending, shedding new light in the debate in the literature about which households were borrowing the most and driving the unsustainable price appreciation. This analysis applies three methodologies in new ways. First, it uses the \recentered in uence function" (RIF) borrowed from the robust statistics literature by Firpo, Fortin, and Lemieux (2009) to estimate an unconditional quantile regression of credit market shocks on the housing price distribution. Unlike previous conditional quantile regression methodologies, RIF regressions can show how the entire distribution changes over time, revealing important heterogeneity that is masked by average treatment eects in the literature. Second, this chapter uses the residual from regressions of Federal Open Market Committee (FOMC) decisions on publicly available information 7 to reveal unexpected changes in the federal funds rate, as proposed by Romer and Romer (2004), to create a plausibly exogenous treatment variable for monetary policy. This variable has been useful in identifying the eect of monetary policy on output and in ation, but until now, it has not been applied to housing market outcomes. Third, this analysis uses a shift-share instrument for county-level lending, as proposed by Greenstone, Mas, and Nguyen (2018), to create a plausibly exogenous treatment variable for credit supply. While the authors originally used this approach to estimate the eect of small business lending, this dissertation is the rst application to mortgage lending. Chapter Three drills down to the local level, where homebuilding actually occurs and is reg- ulated, to create the rst city-level index of housing supply elasticities. It estimates the eect of a positive demand shock|identied as a simultaneous increase in prices and quantities in a VAR system of equations|on prices and quantities over time to reveal how the supply curve responds. The resulting elasticities are very low|in the 0 to 0.2 range|consistent with similar estimates in other markets where investments are large, lumpy, and costly to reverse. They suggest that pre- vious research signicantly overestimated the slope of the housing supply curve, partly due to less accurate data and partly because of endogeneity bias. This research improves on both dimensions. It shows that elasticities vary greatly across the metropolitan area, with less elastic housing supply in higher-density, lower-income municipalities located in the core, pushing construction activity out to the periphery. These ndings are striking new evidence of urban sprawl resulting in longer commute times, less agglomeration, and suboptimal allocation of housing. This analysis applies one nal methodology in a new way. It uses a structural VAR model with sign restrictions to identify demand shocks and reveal responses of prices and quantities along the supply curve. This method has been used to estimate elasticities in oil markets, but it has not been applied to housing and land markets to date (Kilian 2009, Kilian and Murphy 2012, Baumeister and Hamilton 2015). Its structural identication allows for causal inference in a way that previous studies have been unable to achieve. Taken together, these chapters give a rich new portrait of real economic risks in real estate markets that can be forecast with a high degree of accuracy, investment returns at dierent quantiles of the housing price distribution that can be driven by credit market shocks, and the spatial pattern of local regulations that can be implied from housing supply elasticities. These \three R's of real estate" form a useful framework for future research and public policy. As urban populations and housing prices continue to grow, we can use the ndings in these three chapters to (1) forecast cyclical risk, (2) target monetary and credit market policies to the appropriate households, and (3) achieve a more productive balance of construction activity across the urban landscape. These advances have the potential to contribute positively to the welfare of our society, but they also raise important new questions that have even greater potential in the long run: Once we can forecast risks, how can we prevent them or at least safeguard society from their most damaging eects? Once we understand how credit policies have historically aected the distribution of homes, how should we change them to make future eects more benecial and more equitable? Once we see 8 the disproportionate allocation of housing supply across the metro area, what regulations can we amend or eliminate to improve the welfare of the city and its residents? These next steps stretch out before us, daring researchers and policymakers alike to reach out and grasp at their tantalizing possibility. It is the dual possibility of economic growth and social justice, and it has made this dissertation well worth writing. 9 Chapter 1 An Econometric Analysis of Housing Supply Dynamics in the United States, 1959-2015 1.1 Introduction This chapter addresses a fundamental tension in the study of \housing supply": the use of various divergent measures of quantity. Most of the literature refers interchangeably to three distinct phases in the construction process: building permits, housing starts, and completed units. They are not the same thing. A building permit signals an intent to build, but a new housing unit does not actually exist yet. It may never exist|or if it does, it may be completed long after the permit was issued. The same problem, to a lesser extent, aicts housing starts. Studies that use these variables to measure the quantity of housing units may err signicantly. In this chapter, I investigate how closely related permits and starts are to the quantity of units actually supplied. I use national and regional counts at each phase of the construction process to determine how cointegrated the three variables are, how their relationship has changed over time, and how their relationship diers across regions. I use this relationship to identify regulatory and nancial barriers to construction. I hypothesize that permits predict completions better in less regulated markets and submarkets|and at less nancially constrained points in the business cycle. I use a vector autoregression (VAR) model to test these hypotheses by comparing the lag structures in each region. Unlike previous chapters in the literature, this test dierentiates between dierent types of restrictions on housing supply. Specically, it can assess the extent to which the cross-sectional variation in housing unit growth is related to permitting versus construction. This novel distinction is useful both to developers and policymakers in these localities. From this VAR model, I can plot the errors over time to reveal systematic variation in housing supply restrictions over the business cycle. I show that all cycles are not equal. Importantly, I show the extent to which forecasters would have mistakenly predicted the trajectory of the 2000-06 10 boom based on the lag structures they observed in previous cycles. I quantify the extent to which these expectations can explain seemingly \irrational" behavior during this recent \bubble." Despite these dierences, I detect a common trend, or cointegrating factor, among the three variables at all geographic levels over time. This factor allows me to make two further contribu- tions. First, I use it to impute the quantity of new housing units completed in real-time from the permit data that are available at a higher frequency than starts or completions. This imputation signicantly improves the measurement of \quantity" in the housing market, providing a more accurate way for researchers to study housing supply dynamics. Second, I use it to create a simple forecasting model that can be used in real time to project housing production at each stage of the real estate cycle. To my knowledge, Wheaton, Chervachidze, and Nechayev (2014) is the only other paper to apply a VAR model to housing quantity, but like the rest of the literature, they do not dierentiate between the three measures of quantity. On the contrary, they add annual building permits to decennial housing units to calculate the change in housing quantity, and then they use this series to estimate supply elasticities with a vector error correction model. Mine is the rst analysis to apply a VAR model to the relationship between these three measures and create a more accurate estimate of the quantity supplied. 1 Elsewhere in the literature, VAR models have proven to be useful in analyzing housing prices. Most recently, Cohen, Ioannides, and Thanapisitikul (2016) use a VAR to show that lagged house prices at the metropolitan statistical area (MSA) level aect house prices in contiguous MSAs. This work follows the spatial VAR literature pioneered by Beenstock and Felsenstein (2007) and applied by Holly, Pesaran, and Yamagata (2010) and Kuethe and Pede (2011). To my knowledge, this is the rst attempt to apply this approach to housing quantity, showing similar but distinct spatial relationships in permitting and construction. By focusing on these three phases in housing production, I can also contribute to the literature on \time-to-build," an important component in structural macroeconomic models that try to ac- count for the lag between real output and residential investment. Montgomery (1995) provided one of the rst estimates of the average time-to-build using government survey data. Unfortunately, his estimates tell us nothing about the period after 1991, when land values have appreciated con- siderably and the development process has become signicantly more complicated. Moreover, the average time-to-build alone cannot predict the dynamics of housing supply in the aggregate, espe- cially with systematic variation over the business cycle. Jung (2013) attempts to draw a connection between levels of aggregation by inferring time-to-build from a structural model, but as with all such models, this conclusion requires tenuous structural assumptions. I estimate these parameters directly. Furthermore, by studying the dynamics of permitting and construction simultaneously, we can connect these \time-to-build" lags with the preceding \time-to-plan" lags that Miller, Oliner, and Sichel (2016) identify in pre-construction development. 1 Also, it is important to note that Wheaton, Chervachidze, and Nechayev (2014) are not forecasting. They are estimating supply elasticities, which is a slightly dierent goal than this chapter's. 11 The ultimate result of this research is the most accurate measurement of housing quantity in the literature to date. Until now, the \housing supply" literature has not followed a consistent ap- proach to these data. Quigley and Raphael (2005), Wheaton, Chervachidze, and Nechayev (2014), and Nathanson and Zwick (2016) all use a combination of building permits and completed units, implying the two are additively equivalent. Green, Malpezzi, and Mayo (2005), Glaeser, Gyourko, and Saiz (2008), Glaeser and Ward (2009), Schuetz (2009), and Kahn (2011) use building permits; Guttentag (1961), Alberts (1962), Maisel (1963), and Mayer and Somerville (2000a) use housing starts; Davido (2013) and Gyourko, Mayer, and Sinai (2013) use completed units; and Malpezzi and Maclennan (2001) use housing starts and completed units. Yet none of these chapters justies their use of one measure over the others from a theoretical perspective. I provide a framework for future researchers to use the optimal measure in each context. This new imputation can improve predictions of housing production and therefore contribute to the literature on forecasting risks in nancial markets and the real economy. Nicol o and Lucchetta (2016) demonstrate the utility of VAR models in forecasting tail risks. I extend this approach to the housing market, where some of the most signicant tail risks can arise, and I show that this targeted approach can identify risks that previous models miss. Using the "receiver operating characteristic" (ROC) curve methodology newly introduced to the economics literature, I nd that this model is more accurate in forecasting recessions than any of the leading indicators that have been used in previous research to date. The remainder of the chapter is organized as follows. Section 1.2 describes the three measures of housing quantity and their evolution over time. In Section 1.3, I estimate a VAR model at each geographic level and compare the lag structures across regions. Section 1.4 estimates the cointegrating factor between the variables and plots the errors over time to identify systematic variance over the business cycle. Section 1.5 forecasts out-of-sample to identify future production and risks. Section 1.6 suggests a new methodology for measuring quantity in \housing supply" research. Section 1.7 concludes. 1.2 Three Measures of Housing Quantity: Data and Trends The most direct measure of the housing stock is completed units, but these data are not always suitable for analysis for two reasons. First, they are not as readily available at a local level. The Census Bureau does not release a measure of completions for individual cities or counties, restricting any analysis of municipal housing supply. Second, housing units typically take several months to build, making them a poor leading indicator of the economy. A completion is the end, rather than the beginning, of an economic activity. We can partially resolve these issues by working backwards in the construction process. Before a housing unit is completed, it must be started, and housing \starts" are measured in the same survey that measures completions. Unfortunately, they too are only released at national and regional levels. So we go one step further backward to the moment when the local government gave 12 the builder permission to put a house in that location. This \building permit" is measured by a separate Census survey, and it is released at a local level. It is the earliest measure we have of construction activity, making it a useful forecasting tool. If our forecasting is reasonably accurate, we can use permits to predict how many starts and completions will occur not only at a national and regional level but at a local level as well, resolving the initial constraint on measuring housing quantity at a local level. 2 In this section, I describe each of these datasets, explain how they were collected and calculated, and compare them visually over time. 3 1.2.1 Permits Every month, the Census Bureau surveys local ocials in 9,000 \permit-issuing places," mostly municipalities with a smattering of counties, townships, and other towns. Each permit oce is asked to ll out a form indicating the number of new privately-owned single-family houses and two-unit, three- and four-unit, and ve-unit residential buildings, with the corresponding number of housing units, as well as the total dollar value of construction. The Building Permit Survey additionally asks for a description and owner or builder information for permits valued at $1 million or more. In addition to the monthly responses, the Census Bureau sends annual forms to another 11,000 permit oces. 4 The Census Bureau then imputes the number of new housing units permitted in places that do not respond to this Building Permits Survey, based on the assumption that the non-reporting places issued permits at the same rate as the reporting places, relative to the previous year. In 2015, they imputed 19% of the monthly housing units and 7% of the annual units. 1.2.2 Starts and Completions Every month, the Census Bureau chooses approximately 900 permit-issuing places, where they select a sample of residential permits. 5 They also drive around land areas that do not issue permits, and they look for new buildings that have recently been started. In both cases, they contact the owner or the builder each month until the project is completed or abandoned. This Survey of Construction allows the Census Bureau to estimate both starts and completions, since they track 2 The United States is one of the few countries where this kind of exercise is possible. In Europe, for example, the vast majority of countries only release one or two of these three datasets (Eurostat 2012). 3 The U.S. Census Bureau releases data on three distinct phases of the housing production process: \authorized by building permits," \started," and \completed." They also track intermediate series, such as \under construction," which are derivative of the rst three. Since we can infer these latter series if need be, there is no reason to include them as separate variables. To download any of these series, visit the \New Residential Construction" section of the Census website at https://www.census.gov/construction/nrc/historical_data/index.html. 4 This population size has doubled since the survey's inception in 1959. From this population, the Census Bureau selects the monthly sample with a stratied sampling methodology that selects places with the most housing units with certainty and other places at a rate of 1 in 10. The national monthly estimate and relative standard errors are imputed from the data collected using this sampling approach. 5 They sample approximately 1 in 50 one-to-four unit buildings permitted, and they select all permits for buildings with ve or more units. 13 each start until completion. Due to the smaller sample size, however, these data are only available at the national and regional levels, unlike permit data, which are available at a metropolitan (and sometimes, municipality) level. As a result, this chapter will focus on the national and regional levels, where all three data are available, allowing us to study the relationship between them. 1.2.3 Trends Figure 1.1 shows the three housing supply variables at the national level annually from 1959 to 2015. The cyclicality is striking. In most business cycles, they increase approximately 100% trough- to-peak before retreating to where they started. The lone exception appears to be the most recent cycle, when they fell so much further that they bottomed out at 50% of their previous trough. Over the history that these records have been collected, the Great Recession was an unprecedented crisis. In all these cases, however, the short-term trends appear to last for several years. This \momentum" is one of the motivating observations of the chapter, as it suggests that the time series do not follow a random walk, but rather exhibit some predictability that can be captured with an autoregressive model. The second striking feature is the comovement of the variables. This may not be surprising considering the fact that they are chronological steps of the same production process, but the tightness of the relationship is interesting considering (a) there is a lag between these steps, and these variables are shown contemporaneously; and (b) not all housing units ultimately progress through all three steps. This real-time correlation is another motivating observation of this chapter, as it suggests that the variables might be cointegrated, and therefore previous attempts to study them without cointegration techniques can be improved upon. The third noteworthy feature of these variables is the lack of a long-term deterministic trend. 6 Unlike many macroeconomic series, these variables do not follow an upward trend over time, despite good reason to expect that they should. Consider, for example, the fact that the population grew by 50% more people in the 1990s than it did in the 1980s, yet the number of housing units added each year is approximately the same in levels in both decades (Mackun and Wilson 2011). Even during the \bubble" of the early-to-mid 2000s, housing unit growth remained lower than it was in the early 1970s. On the one hand, this evidence seems to contradict the claim by some observers that the depth and length of the ensuing recession can be explained by the overhang from unprecedented overbuilding. 7 On the other hand, the fact that construction was historically above average throughout the \bubble" seems to contradict the claim by other observers that it was largely driven by supply restrictions. 8 Construction activity during this period was neither unprecedented nor visibly restrained. Figure 1.2 shows the relationship between the variables by computing ratios from 1968 to 2015 when all three variables are available. The permits/starts ratio, for example, shows whether more 6 This does not preclude the possibility of a stochastic trend, for which I explicitly test later in the chapter. 7 See, for example, Haughwout, Peach, Sporn, and Tracy (2013) and Rognlie, Shleifer, and Simsek (2018). 8 See, for example, Glaeser, Gyourko, and Saiz (2008) and Huang and Tang (2012). 14 permits or starts are recorded in a given year. It reveals very little cyclicality in this particular relationship but an increasing trend over time. In the early years, it appears that more units were being built than were permitted. To my knowledge, this is the rst chapter to point out this discrepancy, which suggests that building permit data were undercounting the actual housing stock being built in the 1970s and 1980s. 9 This is no longer the case, but it presents a potential problem for research conducted with these data in the past. Now, however, permits seem to be perennially exceeding starts, suggesting that a nontrivial fraction of permitted units are not getting built. The starts/completions ratio tells a much dierent story. It is very cyclical, taking a dive immediately before every recession. This results in the same dynamic in the permits/completions ratio, which is essentially a combination of the rst two ratios. The conclusion is that the rst two stages of the production process|permits and starts|slow down before the nal stage, probably because contractors try to nish projects-in-progress before the recession fully hits. This ratio appears to be a reliable leading indicator of the cycle. It forms another motivating observation of the chapter, as it suggests that we can use the cointegrating relationship between these variables to predict future production and risks at dierent stages of the business cycle. Finally, there is signicant heterogeneity across regions. Figure 1.3 shows normalized permits, starts, and completions in the Midwest, Northeast, South, and West from 1968 to 2015. Each series has been indexed to 100 in 1968 to show growth over time. They clearly reveal more accelerated housing production in the South and the West|a distinction that has been wide and persistent since 1990, though it was true for most years before then as well. This nal motivating observation suggests that each region might follow dierent growth paths and therefore require dierent models to understand and predict their housing production. 1.3 Estimating Lags in Housing Production 1.3.1 Reduced-Form VAR I begin by estimating a three-variable reduced-form VAR(2) model on the annual data series: 2 6 4 Permits t Starts t Completions t 3 7 5 = 2 6 4 P S C 3 7 5 + 2 6 4 P P;1 P S;1 P C;1 S P;1 S S;1 S C;1 C P;1 C S;1 C C;1 3 7 5 2 6 4 Permits t1 Starts t1 Completions t1 3 7 5 + 2 6 4 P P;2 P S;2 P C;2 S P;2 S S;2 S C;2 C P;2 C S;2 C C;2 3 7 5 2 6 4 Permits t2 Starts t2 Completions t2 3 7 5 + 2 6 4 " P;t " S;t " C;t 3 7 5; or Y t = A + B 1 Y t1 + B 2 Y t2 + E t ; 9 The discrepancy lasts too long to be explained by a \catch-up" phase for earlier permits that had not been executed. 15 where the two-lag structure has been chosen because it minimizes the information criteria more often than alternative specications. 10 Since I am estimating 21 coecients with only 46 observations, I apply a small-sample degrees-of-freedom adjustment to calculate t-statistics. Table 1.1 reports the estimated coecients for each equation in vertical succession. 11 At the national level, permits exhibit medium-term momentum, with this year's permits tending to be higher than last year's permits, but long-term mean reversion, with this year's permits tending to be lower than permits were two years ago. These permits then signicantly predict starts and completions, though again there is reversion to the mean. Higher permits this year lead to higher starts and completions next year but lower starts and completions the following year. The relationship is not signicant in the other direction. Starts and completions do not predict permits, nor do they exhibit signicant autocorrelation after controlling for permits. It appears that construction does not generate its own momentum independent from the permitting process. Equally interesting, starts do not predict completions after controlling for permits, even though we know that they are related over time. Permits seem to be sucient to predict how starts will turn into completions. This will be useful for my forecasting exercise later on. 12 At the regional level, this predictive power is not always as strong. The Midwest and Northeast follow the same pattern as the nation as a whole, but the South and West do not. In the South, higher permits lead to higher starts and completions after one year and lower starts and completions after two years, but the eect is signicantly weaker. In the West, there is very little signicance at all. This is somewhat surprising. The literature suggests that the South is the least regulated and therefore should have the tightest and most predictable permitting and construction processes. Conversely, the Northeast is considered to have fairly stringent regulations and therefore should be more uncertain. It does not appear that these reputations translate as directly into housing production as previous research might suggest. 13 To better understand this variation, I replicate this exercise with the seasonally-adjusted monthly data, where I nd that a VAR(4) minimizes the information criteria most often. 14 With signif- icantly more degrees of freedom, we do not need to use a small-sample adjustment to calculate t-statistics. Table 1.2 displays the estimated coecients. They tell a very dierent story than the annual coecients. At the national level, permits, starts, and completions all exhibit short-term momentum, with 10 See Appendix A.1 for the selection-order criteria of dierent lag structures at the national and regional levels. 11 The intercepts are not reported, but they were included in the regressions. 12 This interpretation|that a coecient represents a response to a shock in a given variable|relies on the assump- tion that the VAR is stable. We can test this assumption by calculating the roots of the companion matrix. If the eigenvalues lie inside the unit circle, the VAR satises the stability condition. Appendix A.2 graphs these eigenvalues, all of which satisfy this condition. 13 Edward L. Glaeser has been the most vocal proponent of this view. See, for example, Glaeser (2004) and Glaeser and Tobio (2008). 14 The Census seasonally adjusts the monthly data using their own software program called X-13ARIMA-SEATS. (For more details, see https://www.census.gov/construction/bps/faqs/faqs_seas.html.) I use the seasonally- adjusted data for two reasons. First, they are the most widely reported data, so it allows an easier comparison with the news people are actually hearing in real-time. Second, the seasonal adjustment removes seasonal outliers and temporary level shifts, both of which can reduce the reliability of a VAR model. 16 anywhere from two- to four-month lags predicting the current month. There is no mean reversion for these individual variables within this timeframe. Like the annual data, higher permits lead to higher starts and higher completions, and both of these relationships exhibit mean reversion after four months. Finally, starts predict completions at a four-month lag. These results suggest that the short-term dynamic of housing production is slightly dierent from the medium- and long-term dynamics, with more momentum within each variable and less clear predictive power from one variable to the next. Most of these results hold at the regional level. Permits and completions reliably exhibit au- tocorrelation; starts less so. Higher permits reliably lead to higher starts with a one-month lag and revert to the mean after four months, though the mean reversion has less statistical signi- cance. Higher starts also lead to higher completions with a four-month lag with varying degrees of signicance. 1.3.2 Unit Root Tests VAR models face well-known problems when the endogenous variables are nonstationary, partic- ularly if they are independent random walk processes (Granger and Newbold 1974). Formally, \stationarity" requires the probability distribution of a random variable not to change over time. If a series is nonstationary, we cannot expect the historical relationship to predict the future, as the relationship itself is dependent on time. We can test for this possibility by computing augmented Dickey-Fuller (ADF) statistics to detect unit roots. Following Dickey and Fuller (1979), I run a two-lag autoregression on the rst-dierences of each annual time series, Y t = 0 +Y t1 + 1 Y t1 + 2 Y t2 +u t ; with a stochastic trend, Y t1 . The ADF statistic tests the null hypothesis that this trend is not signicantly dierent from zero. Table 1.3 reports the p-values, which have been computed using the approximate asymptotic distributions in MacKinnon (1994). At a 5% signicance level, we cannot reject the null hypothesis of a unit root for most of the variables. At a 1% signicance level, we cannot reject the null for any of the variables. Interestingly, the evidence for a stochastic trend seems to be strongest for completions and weakest for permits|and following the predictive power of the VAR model, the p-values are highest in the Midwest and the Northeast and lowest in the West. This is not surprising, as a stochastic trend suggests that current values of the variable are more closely related to previous values. I also calculate ADF statistics for each of the monthly time series, only this time using a four-lag autoregression to match the lag structure of our VAR model. Table 1.4 reports the p-values, again using the distributions from MacKinnon. Here, none of the statistics reject the null hypothesis of a unit root|at a 5% or 1% signicance level. This nding is consistent with our VAR coecients showing signicant autocorrelation for each variable at all four lags. Current values are strongly related to previous values. Taken together, these two sets of tests suggest that a VAR model is not 17 sucient alone. 1.4 Cointegration and Errors Over Time 1.4.1 Vector Error Correction Model Engle and Granger (1987) show that VAR models do not capture long-run co-movements in two or more nonstationary time series. Because series with unit roots are integrated of order one, their rst dierences can be stationary together if the series of equations includes one or more lagged error-correction terms that capture the stationary linear combinations of the variables over time: Y t = A + Y Y t1 + p1 X i=1 i Y ti + E t ; where Q = P j=p j=1 B j I k is the cointegrating relationship for p lags of k variables, and i = P j=p j=i+1 B j is the sum of the matrices of coecients on the lagged variables. Estimating this model requires us to specify the rank of Q , which indicates the degree of cointegration. We test for this degree with the maximum likelihood framework formulated by Johansen (1995). We calculate a likelihood ratio \trace statistic," LR(r 0 ;k) =T k X i=r 0 +1 ln(1 i ) ; (1.1) testing the null hypothesis that rank r =r 0 against the alternative hypothesis that r >r 0 . If the null hypothesis is rejected, we proceed to r = r 0 + 1 and continue until we nd a null that is not rejected|or until we reach r = k, the number of variables in the VEC model, at which point we conclude that Q has full rank and there are no cointegrating vectors. Table 1.5 lists the trace statistic (and critical value in parentheses) for the hypotheses testing a maximum rank of zero and one with the annual data series. At each level of geography, the trace statistic exceeds the critical value for a maximum rank of zero|and therefore the null hypothesis is rejected. We therefore conclude that the variables cointegrated. The trace statistic does not exceed the critical value for a maximum rank of one, leading us to conclude that the rank of Q is 1. Similarly, Table 1.6 lists the the trace statistics and critical values for the monthly data series. In this case, however, the null hypothesis is rejected for r = 0 and r = 1|and for every geography except the Midwest, it is rejected for r = 2 as well. The only remaining possibility is that Q has full rank, which means the variables do not have unit roots after all. They are stationary. Given these results, I estimate a vector error correction model (VECM) with two lags of levels (or one lag of rst dierences) and a rank of one on each of the annual datasets. 15 Table 1.7 lists the coecients for each of the three equations at each level of geography: the lagged cointegrating 15 Again, I make a small-sample adjustment to the variance-covariance matrix estimator by subtracting the degrees of freedom from the number of observations in the calculation, per Johansen (1995). 18 equation, followed by the lagged rst dierence of each variable, respectively. The national results indicate that the change in permits between t =2 and t =1 positively predicts the change in permits, starts, and completions between t =1 and t = 0. The change in starts, on the other hand, does not have much eect. Finally, the change in completions negatively predicts the change in permits, starts, and completions, suggesting that the market slows down after construction is completed and the new units are ocially supplied. This dynamic response is exactly the equi- libriating force we would expect from an increase in supply with a lag. The regional results are similar but stronger in the Midwest and Northeast, as was true of the VAR model. Higher permit growth leads to higher permit, start, and completion growth, which are all then tempered in future states as those units are completed. The permit eect is consistent with the VAR model, but the completions eect is new|suggesting the importance of controlling for the common stochastic trend to detect this latent response. 1.4.2 Cointegrating Relationships Over Time The cointegrating relationship itself, which is not reported in Table 1.7, can tell us how the variables' relationship has changed over time. Figure 1.4 plots the in-sample values of the cointegrating equation for national data from 1968 to 2015. From an econometric standpoint, the important takeaway is that this relationship appears to be stationary. There is no need to include a trend in the VECM. 16 The regional cointegrating relationships, shown in Figure 1.5, yield the same conclusion. More generally, Figure 1.4 shows that the relationship was much more volatile in the early years prior to the 1980s. Since then, it has become more stable. This stability is consistent with the \Great Moderation" observed in other macroeconomic data over the same time period (Lucas 2003, Stock and Watson 2003, Bernanke 2004). Similar to those series, the stability in this relationship disappears in 2006, when the housing \bubble" begins to de ate. At this time, the re- lationship becomes largely positive, which indicates that starts are declining relative to permits and completions. This pattern appears to repeat during every recession to dierent degrees. Figure 1.5 shows the same pattern in each region across the country. 17 This is an original and interesting nding. It is most likely driven by starts and completions, which are more heavily weighted than permits in the equation. Given that assumption, it suggests that starts decline before completions|and therefore, new units continue to enter market after the demand for them has dried up. This is consistent with reports of empty homes and high vacancy rates during downturns (Clark 2009). It also suggests that researchers and forecasters who are using permits to understand the dynamics of housing supply are underestimating the growth of housing 16 As a robustness check, I include a trend in both the cointegrating equation and in the VECM more generally. They are not statistically signicant, and they do not substantively change any of our conclusions. I also calculate the roots of the companion matrix. Appendix A.2 graphs the eigenvalues, which all lie inside the unit circle. The VECM satises the stability condition. 17 The South may appear to tell the opposite story, but note the cointegrating equation. The sign ips on starts and completions, so the story is actually the same. 19 units in the early stages of a downturn, as the decline in starts likely re ects a slowdown in new projects more generally while existing projects continue being completed. Similarly, it appears that the reverse is true throughout much of the recovery: The cointegrating relationship is persistently negative, with starts picking up and completions lagging behind. Using permits (which lead to those starts) to measure the growth in housing units is likely not accounting for the lag until those units are actually supplied to the market. 1.4.3 Prediction Errors Over Time How accurate is this model over time? Some research suggests that the housing production process has become more complicated and lengthy over time (Glaeser, Gyourko, and Saks 2005, Miller, Oliner, and Sichel 2016). If this is the case, we should expect to see the errors of the model growing. Similarly, Rajan, Seru, and Vig (2015) show that nancial models became increasingly inaccurate as the market was overtaken by private-label securitization. Do we see the same eect in housing supply? Gerardi, Lehnert, Sherlund, and Willen (2008) argue against this view, suggesting that market participants could have predicted the severity of the bust|but failed because they had irrationally positive expectations throughout the boom. We can assess this claim given what rational participants would have learned from past housing supply dynamics. Figure 1.6 plots the residuals from the three equations in the national VECM over time. The uctuations are remarkably well-behaved. They do not appear to grow over time or to exhibit many outliers. The 2001-2006 period is boringly average, giving us little reason to believe that the behavior of housing supply during the \bubble" period was unusually unpredictable. On the contrary, it seems that the model would perform at least as well during this time period as during any other historically. The Great Recession, on the other hand, exhibits sharp negative residuals, suggesting that the model is predicting higher housing quantity growth than what was actually observed. Even these in-sample predictions cannot fully capture the severity of that downturn. Purely from a supply perspective, market participants could not have predicted the severity of the bust. Table 1.8 conrms this nding. Not only are some of the errors signicantly more negative in the Great Recession, but they are signicantly more negative in all recessions|doubly so (in magnitude) for the Great Recession. Figure 1.7 addresses the larger issue of the model's accuracy over time by plotting the residuals in absolute value. They are clearly not increasing over time, though they do tick up during the Great Recession, as they have done during previous recessions. There is no evidence, however, that the increasing complexity of the housing production process has made it more dicult to model the relationship between these three variables. Figures 1.8 and 1.9 tell the same story from a regional perspective. In all four regions, the model errs signicantly negative during the Great Recession, underestimating how bad the downturn would be, but there is no trend over time, either in raw levels or absolute values. It does appear, however, that the errors are higher for the South and the West, consistent with our ndings in earlier sections that the variables are less predictive of each other in these regions. 20 Finally, we consider the VAR(4) model applied to the national monthly data, as in Section 1.3. Figure 1.10 shows almost perfect white noise. It is clear|and unsurprising|that this model, which predicts four months in advance, is no more or less predictive during recessions, as it is not designed to detect such lengthy parts of the cycle. The unpredictability of, say, the Great Recession was not how it evolved from month to month, but rather over the long run. When we use these models to forecast out-of-sample, we must take care to dierentiate based on the length of the period we intend to predict. 1.5 Forecasting Future Production and Risks How useful is this model for market participants and policymakers? Ideally, an autoregressive model should have signicant predictive power out-of-sample, assuming past relationships hold between the variables. In this section, I consider three such forecasts: short-term using the monthly VAR(4) model, long-term using the VECM, and using housing production to predict the probability of a recession. 1.5.1 Forecasting Short-Term Production Figure 1.11 shows \out-of-sample" forecasts for permits, starts, and completions for the last year of data, 2016. I estimate the monthly VAR(4) model with all months up to November 2015, and then I compute an iterated forecast over the following twelve months up to November 2016. The solid blue line shows the actual observed outcomes, while the solid orange line projects our forecast over the same time period. The dashed orange lines indicate the upper and lower bounds for a 95% condence interval. The results are mixed. The good news is that all the observed values fall within the condence interval. The bad news is that the point estimates persistently overestimate all three series. This could simply be an unusual trend in this particular year, a permanent change in the relationship between the variables, or a statistical artifact. It seems unlikely that it is a permanent change, however, given the accuracy of the condence interval and the fact that completions are almost exactly accurate in multiple months. The general conclusion appears to be that it is dicult to predict any given month|as one would expect, considering how noisy the data are at this frequency|but that the condence intervals give a reliable range for market participants to use as the distribution of likely outcomes in their objective functions. 1.5.2 Forecasting Long-Term Production How dierent was the recent housing boom-and-bust from past experience? We can partly answer this question by forecasting the VECM at critical turning points. Figure 1.12 shows out-of-sample forecasts of the Great Recession, for example. I estimate the VECM with all years up to 2006, and then I compute an iterated forecast over the following four years up to 2010. Again, the solid blue 21 line shows the actual observed outcomes, the solid orange line projects my forecast, and the dashed orange lines indicate the upper and lower bounds for a 95% condence interval. These results tell an interesting story in their evolution. For the rst year, the point estimates are almost identical to the observed values. After that, the forecasts diverge sharply from the actual observations. The VECM predicts a market turnaround, while in reality the market continued declining for another two to three years. The lower bounds capture the possibility of another two years but not a third|and not as severe as the bust became in all three series. The Great Recession truly was an atypical experience. Still, the accuracy of the rst year of the forecast gives us condence that the model might apply in more normal times. Figure 1.13 shows out-of-sample forecasts of the recovery after the Great Recession. I estimate the VECM with all years up to 2009, and then I compute an iterated forecast over the following four years up to 2013. This time, the point estimates are much more accurate. In most years, they slightly underestimate the recovery, but in several years they are almost exactly identical. The standard errors add a note of caution, however, as the previous experience of the Great Recession was so atypical that it drastically increased the condence interval. Market participants who felt unusually uncertain in 2009 clearly had good reason: Recent experience was so far outside the norm that they could not know whether the future would revert to familiar dynamics. 18 The point estimates suggest, however, that the market did revert to familiar dynamics. 1.5.3 Predicting Recession Risk The model appears to be useful for forecasting, particularly one year ahead. Given this fact|and the stability in housing supply dynamics that it implies|I attempt to use these three time series to forecast a fourth variable: the probability of a recession. I dene a \recession" as the years when the Business Cycle Dating Committee at the National Bureau of Economic Research has ocially declared that the United States spent any part of that year in a \contraction" retrospectively. 19 I take the predictive variables from the VECM and use them in a probit model that predicts the probability of a recession in the year following the nal lag, specically: Pr (recession t = 1) =F ( + P;1 Permits t1 + S;1 Starts t1 + C;1 Completions t1 + P;2 Permits t2 + S;2 Starts t2 + C;2 Completions t2 +" t ) : Figure 1.14 shows the resulting \Recession Risk Index" over time. To assess the accuracy of this index, I use the \receiver operating characteristic" (ROC) curve developed by Peterson and Birdsall (1953) to compare diagnostic tests in the statistics literature, where it went unnoticed by economists until a few years ago. It is useful in situations like re- cession forecasting, where the outcome is binary but the forecast is continuous. First, the ROC 18 Of course, it it always true that we do not know if the future will follow familiar dynamics, but some events cast more doubt than others. 19 The Committee's process is described at http://www.nber.org/cycles/recessions.html, and the months of each \contraction" are listed at http://www.nber.org/cycles.html. 22 methodology determines an appropriate threshold that the continuous forecast must meet in order to be considered signicantly close to the correct binary outcome. Then, the ROC curve graphs the fraction of positive cases that the forecast correctly predicts (a.k.a. \sensitivity") on the y-axis versus the fraction of negative cases that the forecast correctly predicts (a.k.a. \1 - specicity") on the x-axis. The greater the area under the ROC curve (AUC), the more accurate the forecast. Figure 1.15 shows this curve for the Recession Risk Index. Liu and Moench (2016) provide the most comprehensive comparison of AUCs for the leading variables that economists have identied to forecast recessions. They nd that the Treasury term spread (i.e. the yield curve) is the single most successful leading indicator, but the forecast improves signicantly with several other variables. Table 1.9 compares their one-year-ahead forecasts to my Recession Risk Index. They nd an AUC of 0.869 with only the term spread, and it increases to a maximum of 0.912 when adding the 5-year spread between the Treasury yield and the federal funds rate. Using the nonparametric estimation proposed by Pepe (2003), my index yields an AUC of 0.974. Liu and Moench (2016) do not indicate the standard error for their AUCs, but mine is 0.022, suggesting that it is signicantly better than the point estimate for their best forecast. It appears that this Recession Risk Index outperforms the best forecasting models in the literature today. This is consistent with Leamer's (2015) evidence that housing is a critical factor in the business cycle. 1.6 A New Methodology for Housing Supply A large literature relies on annual building permits to study housing supply dynamics for the simple reason that they are the only data available at a local level in between the decadal Censuses, when completed housing units are actually counted. 20 In some cases, this may be sucient, particularly if the researchers are trying to study developers' intent rather than their impact. To study the actual eect on the housing supply, however, the ideal measure is completed units|and as we have shown here, completions lag signicantly behind permits. Moreover, I have shown that this relationship changes signicantly over the business cycle. Permits underestimate the growth of housing units after the peak of the cycle, and they overestimate the change in the actual quantity of housing units after the trough. Unfortunately, I cannot directly use my model to correct this disparity because my model relies on the previous two years of starts and completions, which are not available at an annual frequency at a local level. Instead, I simply estimate the linear relationship between current completions and past and current permits|and then use that model to \predict" completions in real-time. Specically, I simplify the VECM to a single-equation lagged model: Completions t = + 0 Permits t + 1 Permits t1 + 2 Permits t2 +" t : 20 See, for example, Green, Malpezzi, and Mayo (2005), Quigley and Raphael (2005), Glaeser, Gyourko, and Saiz (2008), Glaeser and Ward (2009), Schuetz (2009), Kahn (2011), Wheaton, Chervachidze, and Nechayev (2014), and Nathanson and Zwick (2016). 23 Figure 1.16 shows the in-sample \predicted" values of this model, compared to permits and completions. The new series, which I call \Permit-Imputed New Housing Units," appears to hew closer to completions than permits does, as intended. On average, the new measure reduces the gap between permits and completions by over 56,000 units per year, or 40% of the original gap. 21 Though this model operates at the national level, it oers a useful methodology to test the robust- ness of results at the local level. 1.7 Conclusion In this chapter, I study three stages of the \housing supply" process: the intent to build, construc- tion activity, and units nally supplied to the market. I nd that they are very cyclical (more so than the overall economy), that they are tightly correlated despite the lag between them, and that they have not exhibited any long-term deterministic trend from 1959 to 2016. I show that permits have become more numerous than starts over time and that completions tend to lag behind permits and starts at turning points in the cycle. Throughout all these observations, I note that housing production has been more accelerated and more dicult to predict in the South and the West than in the Midwest and the Northeast. This study uses vector autoregressive models to understand and extrapolate from these motivat- ing observations. A VAR(2) model reveals medium-term momentum and long-term mean reversion in annual permits, as well as permits signicantly and positively predicting future starts and com- pletions. A VAR(4) model reveals short-term momentum in all three monthly variables, but no mean reversion in this brief time period. Again, permits predict starts and completions, and again, the relationship diminishes over time. The monthly VAR(4) model appears to be stationary, but the annual VAR(2) model exhibits unit roots, or nonstationarity, leading us to estimate a vector error correction model. This VECM uncovers one cointegrating relationship between the variables, which appears stable during the \Great Moderation" but discontinuously volatile during the Great Recession. It suggests that permits and starts decline before completions, leading to oversupply during the downturn, as well as the reverse during the initial upswing. Controlling for this cointegrating vector, the VECM conrms the ndings from the VAR(2) model but also shows that the change in completions negatively predicts the change in permits, starts, and completions, suggesting a dynamic response where the market pulls back after the market has been excessively supplied with a lag. By plotting the residuals over time, I show that the past behavior of housing supply was insucient to predict the severity of the Great Recession, but the \bubble" itself was not as unpredictable as many accounts have alleged. Overall, these errors do not increase in absolute value over time, giving no evidence to support claims that the housing production process has become increasingly complicated and uncertain. 21 Specically, I calculate the absolute value of the dierence between permits and completions. Then, I calculate the absolute value of the dierence between permits and \permit-imputed completions." Finally, I average the two and divide the latter by the former to obtain the percent of the gap that is closed on average. 24 This VECM becomes very useful in forecasting future production. In the short run, the con- dence interval appears to capture the full range of possible outcomes, though the point estimates are often inaccurate. In the long run, the model predicted the recovery but not the depth of the Great Recession, suggesting that it is useful in normal times but not during these extraordinary few years. The same variables are then shown to be extremely accurate in predicting the risk of recession using a probit model. This model outperforms all previous forecasting models along the dimensions measured by the newly applied ROC curve methodology. This new \Recession Risk Index" may be benecial to both investors and policymakers trying to manage the business cycle. Finally, the relationship we uncover is useful in helping researchers improve their estimates of local housing growth at an annual frequency. Since permits are typically the only variable available, I estimate a model that \predicts" completions using past and current permits, and I nd that my new \Permit-Imputed New Housing Units" measure is 40% more accurate for measuring completions than using permits alone. This is an important contribution to the literature on housing supply and calls into question the accuracy of previous papers that relied on permits without this correction. Overall, this study reveals that the relationship between the stages of the housing production process are important, somewhat predictable, and useful to identify market changes both over time and across geographic regions. Future work can build upon these ndings with increasingly sophisticated models. One approach, for example, might allow for Bayesian learning as market participants absorb increasing amounts of information about housing markets and change their behavior over time. Another approach might enable the model to switch between states of the world to better capture tail risks such as the Great Recession, improving one of the weaknesses of the VAR model in this chapter. Additionally, researchers might be able to use the changes in the production process over time to infer the real option value of waiting to apply for a permit in an uncertain world or waiting to start production while holding a permit depending on the risk of an impending shift in the direction of the market. More generally, this model can be incorporated into a wider forecasting exercise involving other economic variables to determine how interlinked housing is with other markets and how important this interdependence is to changes in economic activity overall. Finally, all these analyses can be compared across countries to determine whether these results in the United States generalize to all economic environments|or whether we learn dierent lessons from the housing production processes in other countries. 22 Earlier research and recent experience showed that housing is important to economic growth and the business cycle, but this chapter has begun to illuminate the extent to which that importance can be leveraged to learn more and predict better in these great macroeconomic elds. 22 As of 2011, only 6 of 32 surveyed European countries released all three data series. Over one-third of the countries only release building permits (Eurostat 2012). In this way, the United States may be one of the few countries where this kind of comprehensive analysis is possible, but it appears that there are some available comparisons. 25 Table 1.1: Annual Lags: VAR(2) Model at National and Regional Levels, 1970-2015 (1) (2) (3) (4) (5) US Midwest Northeast South West Permits L.Permits 3:0670 2:4736 1:7490 2:2455 1:5619 L2.Permits 2:4581 1:7781 1:0892 1:4815 0:7146 L.Starts 1:6112 1:3563 0:0371 0:8770 0:0255 L2.Starts 1:2789 0:5546 0:2343 0:1876 0:2977 L.Completions 0:0175 0:7093 0:5273 0:2039 0:2940 L2.Completions 0:5055 0:2923 0:4955 0:4939 0:4705 Starts L.Permits 2:2024 1:9416 1:4882 1:3979 1:3816 L2.Permits 2:5020 2:0328 1:4694 1:5870 1:0769 L.Starts 0:6018 0:7724 0:0278 0:0498 0:1515 L2.Starts 1:2888 0:8302 0:5186 0:2014 0:1015 L.Completions 0:2072 0:6903 0:0864 0:2600 0:2484 L2.Completions 0:6531 0:2763 0:4266 0:5595 0:4462 Completions L.Permits 1:2245 0:8492 0:6355 0:8317 0:8321 L2.Permits 1:3881 0:8991 0:6983 0:9081 0:5822 L.Starts 0:0334 0:2473 0:3959 0:1962 0:3095 L2.Starts 0:9332 0:5457 0:2893 0:3750 0:2232 L.Completions 0:2124 0:0158 0:0416 0:0969 0:1598 L2.Completions 0:3910 0:2040 0:2938 0:3003 0:2443 N 46 46 46 46 46 Notes: Vector autoregression (VAR) model with two lags for United States and four Census regions from 1970 to 2015: Yt = A + B1Yt1 + B2Yt2 + Et, where Yt = Permitst;Startst;Completionst . Annual building permits collected by the U.S. Census bu- reau in the Building Permit Survey; annual housing starts and completions collected in the Survey of Construction. Statistical signicance: p< 0:05; p< 0:01; p< 0:001. 26 Table 1.2: Monthly Lags: VAR(4) Model at National and Regional Levels (1) (2) (3) (4) (5) US Midwest Northeast South West Permits L.Permits 0:8484 0:5468 0:5139 0:6806 0:5730 L2.Permits 0:1738 0:2114 0:0630 0:1799 0:1303 L3.Permits 0:0255 0:1935 0:0749 0:0958 0:0673 L4.Permits 0:0403 0:0732 0:0754 0:0234 0:0314 L.Starts 0:0371 0:0851 0:1163 0:0435 0:2278 L2.Starts 0:0330 0:0046 0:0676 0:0615 0:0461 L3.Starts 0:0777 0:0929 0:0088 0:0113 0:0487 L4.Starts 0:0100 0:0348 0:0815 0:0516 0:1540 L.Completions 0:0635 0:0937 0:1351 0:0061 0:0344 L2.Completions 0:0316 0:0644 0:0834 0:0868 0:0329 L3.Completions 0:0448 0:0266 0:0544 0:0117 0:0171 L4.Completions 0:0587 0:0430 0:0265 0:0086 0:0192 Starts L.Permits 0:6498 0:5286 0:4998 0:5445 0:4620 L2.Permits 0:1268 0:0376 0:0137 0:0852 0:2252 L3.Permits 0:0722 0:1067 0:0301 0:0194 0:0126 L4.Permits 0:3448 0:1629 0:0202 0:2330 0:1656 L.Starts 0:2454 0:1217 0:0994 0:1946 0:1276 L2.Starts 0:2148 0:1454 0:0587 0:2773 0:0606 L3.Starts 0:2581 0:0489 0:1015 0:2115 0:1120 L4.Starts 0:1979 0:1026 0:1295 0:0718 0:1726 L.Completions 0:0050 0:0537 0:0533 0:0238 0:0397 L2.Completions 0:0374 0:0458 0:0269 0:0319 0:0184 L3.Completions 0:0320 0:0017 0:0196 0:1393 0:0320 L4.Completions 0:0345 0:0702 0:0637 0:1247 0:0209 Completions L.Permits 0:1207 0:0367 0:0835 0:0935 0:1792 L2.Permits 0:0532 0:0913 0:0753 0:0187 0:0260 L3.Permits 0:0612 0:1107 0:0880 0:0460 0:0468 L4.Permits 0:1309 0:1201 0:0398 0:0847 0:0009 L.Starts 0:0225 0:0338 0:0849 0:0042 0:0274 L2.Starts 0:0175 0:1493 0:1552 0:0205 0:0041 L3.Starts 0:0647 0:1148 0:0686 0:0901 0:0932 L4.Starts 0:1453 0:1238 0:0107 0:1502 0:0967 L.Completions 0:2471 0:1045 0:1407 0:2608 0:1246 L2.Completions 0:2030 0:1928 0:1415 0:1475 0:1634 L3.Completions 0:1113 0:1657 0:1630 0:0963 0:1841 L4.Completions 0:1776 0:1642 0:2440 0:1893 0:1946 N 583 451 451 451 451 Notes: Vector autoregression (VAR) model with four lags for United States and four Census regions from 1970 to 2015: Yt = A +B1Yt1 +B2Yt2 +B3Yt3 +B4Yt4 +Et, where Yt = Permitst;Startst;Completionst . Monthly building permits collected by the U.S. Census bureau in the Building Permit Survey; monthly housing starts and completions collected in the Survey of Construction. Statistical signicance: p< 0:05; p< 0:01; p< 0:001. 27 Table 1.3: ADF Test for Unit Root in Annual VAR(2) Models: p-Values (1) (2) (3) (4) (5) US Midwest Northeast South West Permits 0:0328 0:2071 0:0544 0:0456 0:0189 Starts 0:0575 0:2278 0:0783 0:0370 0:0143 Completions 0:1401 0:2948 0:3395 0:0739 0:0475 Notes: Augmented Dickey-Fuller (ADF) two-lag autoregression model on the rst-dierences of three annual time series (permits, starts, and completions) with a stochastic trend for United States and four Census regions from 1970 to 2015: Yt =0 +Yt1 + 1Yt1 + 2Yt2 + ut. p-values calculated using the approximate asymptotic distributions in MacKinnon (1994). Statistical signicance: p< 0:05; p< 0:01; p< 0:001. Table 1.4: ADF Test for Unit Root in Monthly VAR(4) Models: p-Values (1) (2) (3) (4) (5) US Midwest Northeast South West Permits 0:0727 0:1414 0:1442 0:0882 0:0911 Starts 0:1029 0:1060 0:1421 0:0775 0:1260 Completions 0:4270 0:1147 0:3545 0:5300 0:3618 Notes: Augmented Dickey-Fuller (ADF) four-lag autoregression model on the rst-dierences of three monthly time series (permits, starts, and completions) with a stochastic trend for United States and four Census regions from 1970 to 2015: Yt =0 +Yt1 + 1Yt1 + 2Yt2 + 3Yt3 + 4Yt4 +ut. p-values calculated using the approximate asymptotic distributions in MacKinnon (1994). Statistical signicance: p< 0:05; p< 0:01; p< 0:001. Table 1.5: Johansen Tests for Cointegration in Annual Model with Two Lags (1) (2) (3) (4) (5) US Midwest Northeast South West r = 0 61:14 64:21 50:30 53:71 62:35 Critical Value: 29.68 r = 1 9:54 7:20 11:60 8:21 14:25 Critical Value: 15.41 Notes: Likelihood ratio \trace statistics" testing the null hypothesis that rank r = r0 against the alternative hypothesis thatr>r0 for annual permits, starts, and completions in the United States and four Census regions from 1970 to 2015. Following the model formulated by Johansen (1995): LR(r0;k) =T P k i=r 0 +1 ln(1i). Critical values in parentheses: p< 0:05. 28 Table 1.6: Johansen Tests for Cointegration in Monthly Model with Four Lags (1) (2) (3) (4) (5) US Midwest Northeast South West r = 0 185:86 211:85 268:54 148:32 281:27 Critical Value: 29.68 r = 1 27:11 61:83 77:53 61:96 75:08 Critical Value: 15.41 r = 2 9:27 3:73 7:16 5:16 5:95 Critical Value: 3.76 Notes: Likelihood ratio \trace statistics" testing the null hypothesis that rank r = r0 against the alternative hypothesis that r > r0 for monthly permits, starts, and com- pletions in the United States and four Census regions from 1970 to 2015. Following the model formulated by Johansen (1995): LR(r0;k) =T P k i=r 0 +1 ln(1i). Critical values in parentheses: p< 0:05. Table 1.7: Annual Lags with Cointegrating Equation: National and Regional VECM, 1970-2015 (1) (2) (3) (4) (5) US Midwest Northeast South West D Permits L. ce1 0:0174 0:0295 0:0785 0:0098 0:0197 LD.Permits 2:4496 1:7175 1:1071 1:5813 0:8156 LD.Starts 0:9838 0:3169 0:0045 0:0129 0:5953 LD.Completions 0:7943 0:4615 0:8297 0:7855 0:8899 D Starts L. ce1 0:0147 0:0266 0:1508 0:0108 0:0198 LD.Permits 2:5088 2:0590 1:5407 1:7031 1:4025 LD.Starts 1:0551 0:7237 0:4380 0:0246 0:0482 LD.Completions 0:8942 0:3965 0:6122 0:8416 0:8365 D Completions L. ce1 0:0126 0:0159 0:1820 0:0037 0:0205 LD.Permits 1:3928 0:9257 0:7771 0:9697 0:8202 LD.Starts 0:8203 0:5059 0:3442 0:2909 0:2514 LD.Completions 0:5088 0:2629 0:3013 0:4403 0:4583 N 46 46 46 46 46 Notes: Vector error correction model (VECM) with two lags for United States and four Cen- sus regions from 1970 to 2015: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions collected in the Survey of Con- struction. Statistical signicance: p< 0:05; p< 0:01; p< 0:001. 29 Table 1.8: VECM Residual Variation Across the Business Cycle (1) (2) (3) (4) (5) (6) Permits Starts Completions Permits Starts Completions Recession 102:859 99:708 61:360 (1:81) (1:81) (2:19) GreatRecession 190:100182:286 126:669 (1:85) (1:81) (2:52) N 46 46 46 46 46 46 R 2 0:070 0:069 0:098 0:072 0:070 0:126 F 3:289 3:268 4:793 3:419 3:286 6:336 Notes: Coecients reported for dummy variables for all recession years and Great Recession years, respectively, added to vector error correction model (VECM) with two lags for United States and four Census regions from 1970 to 2015: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions collected in the Survey of Construction. t statistics in parentheses: p< 0:05; p< 0:01; p< 0:001. Table 1.9: Comparing One-Year Forecasts: Area Under the ROC Curve (1) (2) (3) AUC Standard Error Source Spread(t) only 0.869 N/A (Liu and Moench 2016) Spread(t) + spread(t 6) 0.886 N/A (Liu and Moench 2016) 10 yr-FF spread 0.907 N/A (Liu and Moench 2016) 1 yr-FF spread 0.909 N/A (Liu and Moench 2016) 5 yr-FF spread 0.912 N/A (Liu and Moench 2016) Recession Risk Index 0.974 0.022 this chapter Notes: Area under the receiver operating characteristic curve (AUC) calculated for Reces- sion Risk Index in Figure 1.14 using nonparametric estimation methodology in Pepe (2003). Compared to AUCs calculated by Liu and Moench (2016) for leading indicators to forecast U.S. recessions in the literature. Higher AUCs indicate more accurate forecasts, combining two dimensions: higher fraction of accurately identifying positive outcomes and higher frac- tion of accurately identifying negative outcomes. \Spread" indicates Treasury term spread (i.e. yield curve). All Liu and Moench (2016) forecasts include this term spread plus any other variables indicated. All \FF spreads" indicate the dierence between the Treasury yield of a given maturity and the federal funds rate. All forecasts are conducted in-sample one-year-ahead. 30 Figure 1.1: U.S. Permits vs. Starts vs. Completions, 1959-2015 0 500 1000 1500 2000 2500 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 Permits Starts Completions Notes: Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 31 Figure 1.2: Annual Permits, Starts, and Completions Ratios, 1968-2015 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 (a) Permits/Starts Ratio 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 (b) Starts/Completions Ratio 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 (c) Permits/Completions Ratio Notes: Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 32 Figure 1.3: Regional Permits vs. Starts vs. Completions, 1968-2015 0 50 100 150 200 250 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Midwest Northeast South West (a) Permits 0 50 100 150 200 250 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Midwest Northeast South West (b) Starts 0 50 100 150 200 250 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Midwest Northeast South West (c) Completions Notes: Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 33 Figure 1.4: Cointegrating Relationship for National VECM, 1968-2015 -20000 -15000 -10000 -5000 0 5000 10000 15000 20000 25000 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Cointegrating equation: Permits t 138:3Starts t + 138:0Completions t Notes: Cointegrating relationship, Q Yt1, from vector error correction model (VECM) with two lags for United States from 1968 to 2015: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 34 Figure 1.5: Cointegrating Relationship for Regional VECMs, 1968-2015 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 (a) Midwest Permitst 44:2Startst + 44:4Completionst -150 -100 -50 0 50 100 150 200 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 (b) Northeast Permitst 4:4Startst + 3:5Completionst -30000 -20000 -10000 0 10000 20000 30000 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 (c) South Permitst + 110:9Startst 111:9Completionst -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 (d) West Permitst 33:7Startst + 32:5Completionst Notes: Cointegrating relationships, Q Yt1, from vector error correction models (VECMs) with two lags for four Census regions from 1968 to 2015: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 35 Figure 1.6: Residuals for National VECM, 1970-2015 -600 -400 -200 0 200 400 600 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Permit Errors Start Errors Completion Errors Notes: Residuals, Et, from vector error correction model (VECM) with two lags for four Census regions from 1968 to 2015: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 36 Figure 1.7: Absolute Residual Size for National VECM, 1970-2015 0 100 200 300 400 500 600 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Permit Errors Start Errors Completion Errors Notes: Absolute value of residuals,jEtj, from vector error correction models (VECMs) with two lags for four Census regions from 1968 to 2015: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 37 Figure 1.8: Residuals for Completions Equation in Regional VECMs, 1970-2015 -100 -50 0 50 100 150 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Midwest Northeast South West Notes: Residuals, Et, from completions equation in vector error correction model (VECM) with two lags for four Census regions from 1968 to 2015: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 38 Figure 1.9: Absolute Residual Size for Completions Equation in Regional VECMs, 1970-2015 0 20 40 60 80 100 120 140 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Midwest Northeast South West Notes: Absolute value of residuals,jEtj, from completions equation in vector error correction models (VECMs) with two lags for four Census regions from 1968 to 2015: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 39 Figure 1.10: Residuals for Completions Equation in Monthly VAR(4), 1968-2016 -300 -200 -100 0 100 200 300 400 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Notes: Residuals, Et, from completions equation in vector autoregression (VAR) model with four lags for the United States from 1968 to 2015: Yt = A + B1Yt1 + B2Yt2 + B3Yt3 + B4Yt4 + Et, where Yt = Permitst;Startst;Completionst . Monthly building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; monthly housing starts and completions (in thousands) collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 40 Figure 1.11: \Out-of-Sample" Forecasts of 2016 Using Monthly VAR(4) Model 0 200 400 600 800 1000 1200 1400 1600 1800 2000 (a) Permits 0 200 400 600 800 1000 1200 1400 1600 1800 2000 (b) Starts 0 200 400 600 800 1000 1200 1400 1600 (c) Completions Notes: Forecasts of monthly permits, starts, and completions (in thousands) in 2016 using vector autoregression (VAR) model with four lags for the United States from 1970 to 2015: Yt = A + B1Yt1 + B2Yt2 + B3Yt3 + B4Yt4 + Et, where Yt = Permitst;Startst;Completionst . Monthly building permits collected by the U.S. Census bureau in the Building Permit Survey; monthly housing starts and completions collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 41 Figure 1.12: \Out-of-Sample" Forecasts of Great Recession Using Annual VECM 0 500 1000 1500 2000 2500 3000 3500 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 (a) Permits 0 500 1000 1500 2000 2500 3000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 (b) Starts 0 500 1000 1500 2000 2500 3000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 (c) Completions Notes: Forecasts of annual permits, starts, and completions (in thousands) from 2007 to 2010 using vector error correction model (VECM) with two lags for the United States from 1970 to 2006: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 42 Figure 1.13: \Out-of-Sample" Forecasts of Housing Recovery Using Annual VECM -500 0 500 1000 1500 2000 2500 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 (a) Permits -500 0 500 1000 1500 2000 2500 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 (b) Starts -500 0 500 1000 1500 2000 2500 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 (c) Completions Notes: Forecasts of annual permits, starts, and completions (in thousands) from 2010 to 2013 using vector error correction model (VECM) with two lags for the United States from 1970 to 2009: Yt = A + Q Yt1 + P p1 i=1 i Yti + Et, where Yt = Permitst;Startst;Completionst . Annual building permits collected by the U.S. Census bureau in the Building Permit Survey; annual housing starts and completions collected in the Survey of Construction. Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 43 Figure 1.14: Recession Risk Index 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Notes: Recession risk predicted from probit regression of annual binary recession variable on lagged permits, starts, and completions for the United States from 1970 to 2015: Pr (recessiont = 1) =F ( +P;1Permitst1 + S;1Startst1 +C;1Completionst1 +P;2Permitst2 +S;2Startst2 +C;2Completionst2 +"t). Recession years are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 44 Figure 1.15: ROC Curve for Recession Risk Index 0.00 0.25 0.50 0.75 1.00 Sensitivity 0.00 0.25 0.50 0.75 1.00 1 - Specificity Area under ROC curve = 0.9744 Notes: Receiver operating characteristic (ROC) curve calculated for Recession Risk Index in Figure 1.14 using nonparametric estimation methodology in Pepe (2003). On the y-axis, \sensitivity" indicates the fraction of accurately identifying positive outcomes. On the x-axis, \1 - specicity" indicates the fraction of accurately identifying negative outcomes. Forecast is conducted in-sample one-year-ahead. 45 Figure 1.16: Permits vs. Completions vs. Permit-Imputed Completions, 1959-2015 0 500 1000 1500 2000 2500 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 Permits Completions Permit-Imputed Completions Notes: Imputed \missing" completions calculated from in-sample prediction of ordinary least-squares regression of completions on current permits and two lags for the United States from 1970 to 2015: PermitImputedCompletionst = 34:92 + 0:50Permitst + 0:34Permitst1 + 0:16Permitst2. Annual building permits (in thousands) collected by the U.S. Census bureau in the Building Permit Survey; annual housing completions (in thousands) collected in the Survey of Construction. 46 Chapter 2 Asset Markets, Credit Markets, and Inequality: Distributional Changes in Housing, 1970-2016 2.1 Introduction The distribution of housing prices, like the distribution of wealth more generally, has changed considerably in the past half century. How much are nancial markets to blame? This chapter unpacks two key components of housing nance|the federal funds rate targeted by the Federal Reserve and the supply of credit issued by mortgage lenders|and their contribution to this changing dispersion in the housing market. Using a private database of millions of housing transactions from Zillow, I test how monetary policy and credit supply aect the distribution of house prices in California from 1970 to 2016, controlling for structural housing characteristics and locational xed eects. I nd that tight monetary policy tends to increase dispersion, beneting high-priced homes more than low-priced homes. I also nd that an increase in mortgage lending tends to boost middle- priced homes more than low- and high-priced homes. As a result, I nd that mortgage lending can explain some of the 2000-2006 \bubble" in housing prices, but monetary policy cannot. Until recently, econometricians have been unable to recover these marginal eects on the un- conditional distribution. Previous methodologies revealed the eect of treatment variables within categories, but the resulting change in the entire distribution was not well-understood. For exam- ple, conditional quantile regressions can only estimate the eects of a treatment variable within increments of the covariates, and binned OLS regressions only estimate eects within increments of the distribution of the outcome variable. Neither methodology shows how the overall dispersion of the Y distribution changes (Bento, Gillingham, and Roth 2017). In this chapter, I apply the unconditional quantile regression method pioneered by Firpo, Fortin, and Lemieux (2009) to reveal how the distribution of house prices shifts over time in response to monetary policy and credit supply. I focus especially on the 2000-2006 period, when both of these factors were blamed for the 47 \bubble" in housing prices. Do these factors aect all house prices equally? Or do they aect some quantiles more than others? Who is experiencing these shocks most acutely? I answer these questions in three steps. First, I estimate the eect of monetary policy shocks on the home price distribution, controlling for hedonic characteristics as well as the lagged natural log of GDP and a quadratic time trend. To identify the causal eect of monetary policy, I use the methodology developed by Romer and Romer (2004) to estimate \unexpected" changes in the federal funds rate from 1970 to 2007. This measure of monetary policy is positive when the Federal Reserve unexpectedly raises interest rates and negative when they unexpectedly decrease. I nd that it has a positive association with most of the housing price distribution, suggesting that tight monetary policy tends to increase most home prices. Moreover, this eect increases at higher quantiles, suggesting that tight monetary policy increases dispersion in the distribution as higher-priced homes appreciate more. The eect only appears to be negative for the very bottom of the distribution where potential homeowners are the most nancially constrained. These eects hold when I add county-level xed eects, though they lose signicance for the low-priced homes. To address questions about the recent boom-and-bust more directly, I run a specication with interaction eects for each decade. In the 2000s, the eect was positive for most of the housing price distribution. This evidence suggests that, contrary to critics' claims, articially low interest rates were not to blame for the \bubble" in housing prices at that time. In the 1970s and 1980s, the eect was positive but approximately equal across most of the distribution. In fact, tight monetary policy may have compressed much of the distribution during this time. In the 1990s, the eect was negative. Second, I estimate the eect of credit supply on the home price distribution. By credit supply, I mean the loan volume reported under the Home Mortgage Disclosure Act (HMDA). Although it is not exogenous, lagged HMDA data have predictive \Granger causality." Again, I control for hedonic characteristics, the lagged log of GDP, and a time trend. In all estimations from 1990 to 2015, credit supply has a positive eect across the distribution, but it has a stronger eect on the middle-priced homes than the low- and high-priced homes. To infer causality, I use the new methodology developed by Greenstone, Mas, and Nguyen (2018) to create a plausibly exogenous instrumental variable for lending. This IV conrms that mortgage lending leads to larger price increases for middle-priced homes than for low- or high-priced homes. Again, I break this eect down by subperiod. In the 1990s, or \pre-bubble" period, the results from the full estimation hold, with the middle-priced homes experiencing a bigger increase from credit supply than the low and high end. From 2000 to 2006, the \bubble" period, however, the story changes: Now, the low-priced homes are receiving the biggest boost, consistent with researchers like Mian and Su (2009) who pinpoint the subprime mortgage boom as a key culprit. In the \bust" (2007-2010) and \recovery" (2011-2015) periods, the eect turns negative, suggesting that credit supply has not been benecial to housing values since the Great Recession began. Finally, I convert these estimated eects into economic magnitudes and simulate their overall 48 eect on the wealth gap across the distribution of U.S. households. I nd that these eects are sizable and have nontrivial eects on wealth inequality. These ndings contribute to the long literature in urban economics that explores the dierences in prices across the distribution. Gyourko and Tracy (1999) set the stage for this research by com- puting quantile indices over time, both in real terms and in constant-quality terms, to understand why housing has become unaordable for owners at the bottom of the distribution. They primarily focus on structural characteristics of the building itself. Similarly, McMillen (2008) runs hedonic regressions in Chicago and shows that home price appreciation was higher for more expensive homes from 1995 to 2005, largely due to increases in the regression coecients, not increases in the he- donic characteristics themselves. This chapter builds on these ndings using a longer time period, a larger geography, and a newer methodology. 1 This unconditional quantile regression approach is also distinct from the structural model used by Nieuwerburgh and Weill (2010), which shows how increases in productivity dispersion can translate into even larger increases in housing price dispersion. While this theory is consistent with the data, it is not the only possible mechanism. The authors do not consider the role of credit markets, which we will explore here. Finally, the most extensive exploration of housing price variation comes from Bogin, Doerner, and Larson (2018), who use federal housing data to calculate real home price indices at city, county, and ZIP code level from 1975 to 2015. While they are able to show interesting variation across location, they do not illuminate the distributional question asked here. Moreover, their data are not representative of the population, as they only include transactions that were nanced by a loan purchased or guaranteed by Fannie Mae or Freddie Mac. These ndings also contribute to a newer literature in nancial economics that seeks to identify the causes of the housing \bubble" and subsequent nancial crisis. Mian and Su (2009) initiated this eld by showing that credit growth was not correlated with income growth at a ZIP code level, suggesting that price growth was being driven by credit given to subprime borrowers. Adelino, Schoar, and Severino (2016) challenge this result by showing that it does not hold at an individual loan level. They argue, instead, that credit growth was most prevalent at the middle-income level. Mian and Su (2017) respond by suggesting that individual loans were contaminated by income overstatement fraud, making income-credit comparisons unreliable at a loan level. Foote, Loewenstein, and Willen (2016) challenge their underlying premise of using the number of loans by showing that the total dollar value of loans did not change its distribution during this period. To our knowledge, however, none of these authors have explicitly made their case based on the eect of credit markets on housing prices, which is the outcome that they are all ultimately trying to understand. Landvoigt, Piazzesi, and Schneider (2015) are one exception, as they show that low-priced homes in 2000 appreciated the most between 2000 and 2005. Their ndings are limited, however, by the facts that (1) they are only studying San Diego, (2) they are only looking at properties that transacted more than once, and (3) they are looking at a very short and unusual 1 Nicodemo and Raya (2012) and Villar and Raya (2015) apply a similar approach to McMillen's in multiple cities, though they are a European context (and in the latter case, use less reliable appraisal data). 49 time period, masking any long-term context in how housing markets traditionally operate that would be necessary to determine whether the \bubble" period was actually dierent or part of a secular trend in housing price dispersion. This chapter improves on all three fronts. The chapter is organized as follows. Section 2.2 discusses the tension in the literature that leads to contradictory theoretical predictions for the eects of capital markets on the housing price distribution. Section 2.3 describes the data I will use to test these predictions. Section 2.4 derives the new methodology that allows us to estimate these marginal eects on the entire distribution of housing prices over time. Section 2.5 presents my empirical results, and Section 2.6 uses these reduced-form results to simulate the impacts of credit market shocks on the housing price and wealth distributions. Section 2.7 concludes. 2.2 Theoretical Predictions It is useful to categorize the theories of housing cycles based on the fundamental formula that governs housing value, the user cost of owner-occupied housing: C = (1t)(i +h) +dg v; (2.1) wheret is the income tax rate of the homeowner,i denotes the interest rate,h refers to the property tax rate, d accounts for depreciation, g is the annual growth rate of the property's value, and v is the purchase price per unit of housing. Assuming h do not change in the short run, a cycle in property value must occur via either the interest rate and/or the expectation of changing capital gains. 2 This chapter focuses on the interest rate side of the equation, which we can model as a function of the short-term risk-free rate of borrowing and the risk premium, or \spread," that compensates the lender for prepayment and default risk, 3 i =r f + ; (2.2) wherer f is set by the Federal Reserve through its federal funds rate target and is determined in equilibrium by the supply of and demand for credit. Because we are interested here in the eect of credit markets on asset markets and not vice versa, we will conne our investigation to the supply side. 2.2.1 Monetary Policy The Federal Reserve has been a target for business cycle researchers as long as it has existed. Friedman and Schwartz (1963) made the most in uential critique of Fed behavior, showing that the worst contractions in the Great Depression followed almost immediately after the Fed raised 2 Hendershott and Slemrod (1983) and Poterba (1991) originally developed this formula. 3 This is a standard general asset pricing formula that serves useful in a variety of housing nance models. See, for example, Campbell and ao F. Cocco (2015). 50 the discount rate or reserve requirements. In each case, the money supply shrank signicantly. Had it continued to grow at a consistent rate, they argued, the economy would have continued on its upward trend. From this argument, they extrapolated that consistent money supply growth was the key to stable economic growth. It \would be dicult to overstate" the in uence of this prescription, said Bernanke (2002) on Friedman's 90th birthday. Taken literally, it was probably too simplistic. The money supply only matters insomuch as it generates consumption and investment, and the historical record suggests that that relationship|i.e. the \velocity" of money|varies over time (Tobin 1965). The sentiment, however, inspired a generation of monetary economists to specify a monetary policy that would maintain stable growth without accelerating in ation. The most famous attempt was the \Taylor rule," proposed in 1993 as a way to calculate the optimal interest rate i, using the equilibrium real interest rate r t , the rate of in ation p t , the desired rate of in ation p t , and the logarithms of real GDP y t and potential GDP y t : i t =p t +r t +a p (p t p t ) +a y (y t y t ): (2.3) Using the parameters that t the historically stable period known as the \Great Moderation," Taylor (2009) shows that the Fed deviated from his rule in the expansion that preceded the Great Recession. He then regresses interest rates on housing starts and uses the coecient to simulate what the housing cycle would have looked like if the Fed had followed the Taylor rule|and critically, if the relationship had remained the same over time, i.e. if the coecient were time-invariant. It is important to highlight this assumption because we have known since Lucas (1976) that economic relationships tend to change signicantly over time, such that a given policy might have drastically dierent eects under one set of parameters than another. Bernanke (2015) criticizes this simulation on two grounds. First, the Fed has not followed the Taylor rule for most of the years since Taylor proposed it, and the results have not been nearly as negative as Taylor would have us believe. 4 Second, the original Taylor rule uses the GDP de ator as its measure of in ation, whereas the Fed uses core PCE in ation, which has been shown to be a more stable and reliable guide to the future path of consumer prices. Additionally, in ation tends to be more stable than economic output, which means the Fed should not use the same coecient for both components of the equation. Making these adjustments, Bernanke nds that the Fed has followed the Taylor rule almost exactly|until the end of the Great Recession when it became constrained by the zero lower bound. The problem with Taylor's critique runs deeper, however, than the econometrics. First, consider Figure 2.1. This graph extends housing starts back to 1959, when the Fed starts tracking them. Does the so-called \boom" in Taylor's story seem so extreme in this context? On the contrary, 4 For example, the Fed consistently undershot the Taylor rule throughout most of the 1990s. If the rule ought to be followed precisely, then the Fed was generating excess unemployment throughout most of this period. This conclusion seems hard to square with the booming economy of the 1990s that most economists consider to have approximated full employment. Similarly, the Fed consistently undershot the Taylor rule during the Great Recession, yet no housing bubble formed at that time. 51 it appears to be the natural, linear continuation of growth that began in 1991, and it appears consistent with the height of cycles in 1973, 1978, and 1984. These swings do not line up with the history of loose monetary policy as most economists would tell it. Why the divergence? Perhaps it is because Taylor has chosen an unusual measure of the housing cycle. Most nancial economists would use a denition that includes housing prices; and most urban economists would argue that prices tend to appreciate the most when housing starts do not grow rapidly|that is, when housing supply is inelastic, funneling most of the demand into prices. Second, the average thirty-year mortgage rate often does not move in tandem with the federal funds rate. Figure 2.2a shows the two rates at a weekly frequency, and there are many clear instances where they diverge. How large is this divergence? On the one hand, they have a high correlation exceeding 0.9. On the other hand, Figure 2.2b shows the spread between the two rates, and it is volatile and varies from -5 to +7 percentage points. Whether this volatility and range is enough to mute the transmission of monetary policy to housing prices is an open empirical question that this chapter will tackle. What, then, can we say about the eect of monetary policy on housing prices? Jord a, Schularick, and Taylor (2015) use a novel instrumental variable strategy to identify the causal eect, which has been notoriously dicult to pin down for the reasons Lucas (1976) elucidated. They look at episodes when countries with a xed exchange rate experienced a loosening of monetary policy because they were pegged to the currency of a foreign central bank, whose actions were plausibly exogenous to any country other than their own. In such cases, monetary loosening had a signicant positive eect on house prices. Of course, this nding does not apply directly to the United States, which has never pegged the dollar to a foreign currency, but it suggests that low interest rates do matter. Whether they have historically been signicant drivers of U.S. housing prices|where Bernanke's evidence suggests that they were not articially low in the latest cycle|is therefore a fruitful question for this chapter to explore. Theoretically, the eect of monetary policy on housing prices is even less clear. Bernanke and Gertler (1995) famously argued that housing plays an important role in the transmission of monetary policy via the credit channel. Higher interest rates increase the burden of mortgage payment, thus depressing the demand for housing. Black, Hancock, and Passmore (2010) show that deposit-constrained and capital-constrained banks tend to shift away from lending in high- cost subprime communities after monetary contractions because they have to nd funding from uninsured market debt, where the borrowers charge a high external nance premium if they engage in such risky lending. They do not show how much this marginal change matters for housing prices, however; nor do they nd that monetary contractions have any eect on banks that are not facing these imminent constraints. An alternate channel exists: What if the higher interest rates signal to the market that the econ- omy is improving, triggering an increase in in ation expectations? Such a transmission mechanism could have the opposite eect, increasing housing prices as well as consumer prices more generally. This eect would contradict most of mainstream macroeconomic theory, but it is not so far-fetched. 52 A new strand of the literature, led by Kocherlakota (2016), Cochrane (2017), Garriga, Kydland, and Sustek (2017), and Schmitt-Groh e and Uribe (2017), suggests a \neo-Fisherian" relationship, building on Fisher's (1930) classic equation, i t =r t +E t t+1 ; (2.4) wherei t is the nominal interest rate at time t,r t is the real interest rate, andE t t+1 is the expected rate of in ation. If we make the (critical) assumption that r t reaches a stable equilibrium in the long run, then a change in i t by the Federal Reserve translates directly into a change in E t t+1 . To use the example that motivated this literature: If in ation is stable at the zero lower bound, perhaps it re ects a stability in real interest rates, in which case an increase in the federal funds rate will lead to an increase, rather than a decrease, in in ation|and by extension, in housing prices. Though this theory is relatively new, it has much empirical evidence to support it. While vector autoregression (VAR) models have consistently shown that monetary policy shocks have a negative eect on output, they tend to show a zero-to-positive eect on in ation in the short and medium run. It is only after six quarters that the eect seems to turn negative, a phenomenon known as the \price puzzle" in the literature. 5 When Vargas-Silva (2008) applies the VAR methodology to housing starts and residential investment, he too nds weak evidence. Though these variables respond negatively to contractionary monetary policy, the results are sensitive to the horizon choice, and as in the case of Taylor (2009), they do not map directly onto housing prices. This latter eect is very much an open question for empirical investigation. When the Federal Reserve raises interest rates, which matters more: the nancial burden on borrowers or the psychological boost of condence in future growth? 2.2.2 Credit Supply Whether or not monetary policy is an important driver, there is strong evidence suggesting that credit supply matters. The latest housing cycle was characterized by a drastic rise and fall in mortgage debt, relative to the size of the economy (Emmons and Noeth 2013). While this correlation alone does not establish causality|it is certainly possible that credit rose to keep up with price expectations|it merits the large literature that has developed to explain it. Mian and Su (2009) are among the rst to show the linkage between debt, house prices, and subsequent foreclosures in the most recent cycle. Using Home Mortgage Disclosure Act (HMDA) data, they nd that ZIP codes with a higher share of subprime borrowers (with a credit score under 660) experienced faster credit growth despite exhibiting lower income growth than ZIP codes with a higher share of prime borrowers. This negative correlation only appears in their data from 2002 to 2005, a truly extraordinary period in the history of mortgage lending. This evidence is only 5 Even in the extreme case that Friedman and Schwartz identied, recent empirical work by Amir-Ahmadi and Ritschl (2009) and Amaral and MacGee (2017) suggest that monetary policy played a minor role at best in the Great Depression. 53 suggestive, but what it suggests comports with many anecdotal accounts of the lending industry at the time: namely, that underwriting standards were loosened, loans were increasingly supplied to less creditworthy borrowers, and these borrowers were predictably unable to keep up with the payments, resulting in the higher foreclosure rates that Mian and Su observe in these ZIP codes (Levitin and Wachter 2012, Bostic and Orlando 2017). Adelino, Schoar, and Severino (2016) dispute this account. They augment Mian and Su's HMDA data with income data from the IRS, as well as a 5% random sample of all loans from Lender Processing Services. As a result, they can look at individual borrowers, not just ZIP codes. They nd that lenders actually issued more debt to middle- and high-income borrowers than low- income borrowers from 2002 to 2006, and these prime borrowers then accounted for a growing share of mortgage debt defaulted on, relative to subprime borrowers. The key dierence here is that they are measuring total dollar value of debt, while Mian and Su are measuring the number of originations. The lenders seem to be originating an increasing number of mortgages in low-income communities, but the average mortgage size is small enough that the middle- and high-income borrowers still account for the majority of the capital. Adelino, Schoar, and Severino then make a surprising leap of logic. They conclude that home price appreciation must have been driven by the expectation of rising prices and not by an increase in credit supply. 6 While their evidence changes the nature of our understanding about credit growth, it does not prove anything about causation. For that, we will have to turn to research with more careful identication strategies. As early as the 1920s, we have evidence that the credit supply can drive real estate prices. Rajan and Ramcharan (2015) use dierences in bank regulations to identify which regions had greater exogenous access to credit during the cycle in agricultural commodity prices from 1917 to 1920. Because some areas were more dependent on these commodities than others, they have a second dierence that allows them to tease out the channels through which credit availability operates. They nd that credit availability signicantly increased land prices, especially but not exclusively in counties that were more exposed to the booming commodities. Similarly, they nd that these same regions experienced the most bank failures when prices declined, with repercussions that lasted for many years after. Favara and Imbs (2015) apply a similar methodology to the latest housing cycle, using state regulations as exogenous sources of variation from 1994 to 2005, when they were allowed to limit interstate branching. When states removed these restrictions, commercial banks issued more loans, a greater volume of debt, and riskier loans, as measured by debt-to-income. The entire change seems to have come from out-of-state banks that opened new branches, underscoring that it truly was caused by the deregulation. This increase in lending led directly to greater activity in the housing market. In areas where it was easier to build (i.e. more elastic housing supply), the housing stock grew more after deregulation. In areas with less elastic supply, prices increased. As a result, the 6 As mentioned above, we will not be addressing expectations in this chapter, as they are important and complicated enough to deserve separate treatment. 54 authors nd that deregulation can account for one-half to two-thirds of the increase in lending and one-third to one-half of the increase in prices. This is one of the most robust ndings to date, but it still does not answer the question that Mian and Su pose and that this chapter addresses directly: Who exactly experiences the price eects of this lending, and how large are the eects that they experience? 2.3 Data: The Housing Price Distribution Until recently, it would have been dicult, it not impossible, to estimate the eect of credit market shocks on the entire distribution of housing prices because there was no comprehensive database of housing transactions over an extended period of time. Now, such databases exist. This chapter uses a dataset of publicly recorded single-family home transactions throughout the state of California from 1970 to 2016. 7 For each observation, the dataset contains variables for transaction value ($), transaction date, number of bedrooms, number of bathrooms, building size (square feet), lot size (square feet), latitude, longitude, address, city, and ZIP code. I truncated the data by dropping all transactions with prices of $0, which typically signify transactions that are not arm's length and therefore do not represent true market value. I also dropped all transactions with prices greater than $100 million for two reasons: their extreme values make them dicult to compare to the rest of the market, and such high numbers might re ect miscoding. In total, the truncated dataset contained 12,443,500 observations. I need richer geographic detail in order to conduct some of the specications of my models. For example, I run specications with county xed eects to control for local heterogeneity that aected housing prices in a way that might bias the coecients from capital market shocks. As a result, I used the geocoding of the housing price data to match them with Census tracts and counties using GIS mapping. 75% of the observations were able to be matched. When running regressions with geographic controls, we therefore have N 9:3 million. 2.3.1 Home Price Quantiles Over Time Figure 2.3 shows the mean, as well as the 10th, 25th, 50th, 75th, and 90th quantile, of housing prices in each year that they transacted from 1970 to 2016. In 1970, single-family homes in California sold for $25,423 on average. Almost half a century later, in 2016, the average was $589,461, down from a peak of $645,097 in 2005. In this 47-year range, the average home price followed two distinct boom-and-bust cycles and several smaller ups-and-downs along the way, as shown by the dotted black line. As shown by the solid lines, however, the average is certainly not the experience of the majority. In fact, it roughly follows the 75th percentile, suggesting that there is signicant skewness, with a small minority of very high-priced homes pushing the mean far above the median. Because not every house transacts in every year, we cannot literally conclude that only 25% of houses experienced the average appreciation or better, but we can say with condence that any 7 It was privately obtained through a restricted-use agreement with Zillow. 55 studies reporting \average" eects are in danger of failing to capture most of the distribution. We can also conclude that regressions should use the natural logarithm of prices to reduce some of the skewness and bring the distribution closer to normality. The severity of the two boom-and-bust cycles is striking, as is the dierence in experience across the distribution. From 1970 to 2000, the 10th percentile experienced very little appreciation, and then after the unprecedented boom from 2000 to 2006, prices swiftly plummeted back almost to their original levels. By contrast, the 90th percentile lost less than a third of its value|and unlike the bottom half of the distribution, it has already surged past its original peak. We might be concerned that in ation is driving much of this variation over time. Figure 2.4 reports in ation-adjusted prices in constant 1970 dollars using the core PCE index to de ate the series in Figure 2.3. The story remains the same. If anything, the boom-and-bust periods appear even more extreme. We might also be concerned that changes in absolute values masks the dierence in growth rates, as even the same growth rate would increase absolute values more at the top than the bottom. Figure 2.5 reports the natural logarithm of nominal housing prices. This picture is more nuanced. The top and bottom of the distribution appear to have grown at roughly the same rates, as the gap between them has not changed noticeably, but the median has drifted down toward the bottom, suggesting that the middle of the distribution is growing slower. This trend parallels income and wealth inequality, where there has been a so-called \disappearing" middle class (Orlando 2013). Why has this distribution changed in dispersion? And why were some homes more sensitive to the cycle than others? To answer those questions, it is natural to begin with the characteristics of the homes themselves. 2.3.2 Home Characteristics Over Time According to economic theory, homes with more valuable features should be worth more money, holding all else constant. If this theory is correct|and we have ample evidence that it is|we might expect that changes in the homes themselves might explain some of the changes in the price distribution. For example, if the most expensive 10% of houses have become larger relative to the rest of the market, they should become more expensive, explaining part of their outsized appreciation in Figures 2.3 and 2.4. This does not appear to be the case. According to Figure 2.6, the 90th percentile of the home size distribution increased slightly from the mid-1990s to the mid-2000s, but it is nowhere near the increase in prices. Moreover, it does not appear to have increased before or after that period, contradicting the experience of the price distribution. Further, the mean building size is well below the 75th percentile and not too far from the median, suggesting that the skewness of the size distribution is far less than that of the price distribution. Lot size tells a very dierent story, but it also does not appear to explain the change in prices. First, lot size is far more skewed than prices, so much so that Figure 2.7 makes it dicult to see 90% of the distribution relative to the mean. To get a better sense of the rest of the distribution, Figure 2.8 drops the mean. Even within this 90-10 range, there is signicant skewness. Large plots 56 seem to be getting larger over time, though the timing does not coincide with the \bubble" growth period at all, and the rest of the distribution has remained roughly the same during the entire period. The bottom of the distribution has actually fallen, suggesting that small lots are getting even smaller. Bedrooms and bathrooms do not merit a graph because they have not changed at all. Homes have roughly the same allocation of these types of rooms as they have had for several decades. This evidence is consistent with McMillen (2008), who found that a change in structural characteristics did not explain most of the appreciation or increased dispersion in home prices in Chicago. This conclusion suggests that other factors, such as credit market shocks, may explain some of these changes over time. 2.4 Empirical Approach Our goal is to estimate the impact of marginal changes in monetary policy and credit supply on the unconditional distribution of housing prices. Let us begin with familiar representations for our outcome variable (housing prices), Y , and explanatory variables (monetary policy and credit supply), X. We want to estimate the impact of marginal changes in X on the unconditional distribution of Y . We will estimate this eect at each quantile of Y individually. Let us represent each quantile with. SinceX andY are observed together, we assume they have a joint cumulative distribution F Y;X . First, we need the unconditional distribution function of Y, F Y (y) = Z F YjX yjX =x dF X (x); (2.5) which sums over all the conditional distribution functions, F YjX (yjX =x) = Pr Y >yjX =x : (2.6) Second, we need a method to estimate the impact of innitesimal (marginal) changes on nonpara- metric statistics, such as quantiles, of a function. This method is called the \in uence function." In this section, I describe the basic theory behind the in uence function and the methodology developed by Firpo, Fortin, and Lemieux (2009) to use it in regression analysis. Then, I explain how I apply this type of regression to quantiles of the housing price distribution with respect to changes in credit markets. 2.4.1 The In uence Function In uence functions hail from the eld of robust statistics, where they are used to understand the stability of statistical procedures (Hampel 2001). They begin with a statistical functional, which is a function of the distribution function itself, =T (F Y ): (2.7) 57 For example, we are interested in the quantile functional, T (F Y ) =F 1 Y (): (2.8) We want to infer the marginal eect of a change in the distribution of X on this functional. Let us denote G Y (y) as the counterfactual distribution function of Y due to this change in the distribution of X, G Y (y) = Z F YjX (yjX =x) dG X (x): (2.9) Fortunately, the formula for the G^ ateaux derivative yields the rate of change of the functional T from a small amount of contamination that moves the distribution function F Y in the direction of G Y , L T;F Y (G Y ) = lim !0 " T (1)F Y +G Y T (F Y ) # : (2.10) The trick to estimating the in uence function is to pick one y at a time out of the distribution of Y . In other words, we use a probability measure y that assigns the point mass 1 to y, y (u) = 8 < : 0 if u<y 1 if uy ; (2.11) which nally yields the equation of the in uence function, IF T;F Y (y) = lim !0 " T (1)F Y + y T (F Y ) # : (2.12) It is worth pausing to appreciate why Hampel (1974) rst proposed this function for robust statis- tics. It is, in his words, \essentially the rst derivative of" the functional T at the distribution F Y . As such, it tells us how the statistic in question changes if we add an additional observation at y. The \in uence" of this \contamination" reveals the stability of the estimate T ( ^ F Y ) for that statistic based on our sample. The in uence function only reveals this in uence at y, however. It is, in a sense, a partial derivative. To reveal how the functional T changes, we have to sum over these innite partial derivatives, T (G Y )T (F Y ) = Z IF T;F Y (y) dG Y (y): (2.13) The in uence function therefore acts like a residual between the original functional and the new, counterfactual functional that we are trying to estimate (Borah and Basu 2013). Our goal, remem- ber, is to run a regression of this new functional on X, and therefore we need to add T (F Y ) back to the in uence function to create a \recentered" in uence function (RIF), RIF T;F Y (y) =T (F Y ) + IF T;F Y (y); (2.14) 58 which can now serve as the dependent variable in our regression. 2.4.2 The RIF Regression What makes RIFs well suited for regression analysis? It is the fact that their conditional expectation with respect to the distribution ofX is the exact functional we want to use as our outcome variable, T (F Y ) = Z E RIF T;F Y (Y )jX =x dF X (x): (2.15) This convenient fact is what motivates Firpo, Fortin, and Lemieux (2009) to create the RIF and to use it as the dependent variable in an ordinary least squares (OLS) regression, yielding the \unconditional partial eect" of X on T (F Y ), T = Z dE RIF T (Y )jX =x dx dF (x): (2.16) We want to estimate this eect for theth quantile,T (F Y ) =q . First, we combine equations 2.5 and 2.8 to create the IF for q , IF q (y) = 1fyq g f Y (q ) ; (2.17) where f Y (q ) is the density of Y at q . Next, we insert the IF into equation 2.14 to calculate the RIF, RIF q (y) =q + 1fyq g f Y (q ) : (2.18) Finally, we take the expectation, conditional on the distribution of X, E RIF q (Y )jX =x =q + Pr Y >q jX =x f Y (q ) : (2.19) Now, we have a dependent variable for the RIF-OLS regression, which I will refer to as an \unconditional quantile regression," following Firpo, Fortin, and Lemieux (2009). Plugging this formula into equation 2.16 yields the \unconditional quantile partial eect," =f 1 Y (q ) Z d Pr Y >q jX =x dx dF X (x); (2.20) which is the eect of X on the th quantile of the unconditional distribution of Y , our ultimate goal. 2.4.3 Estimating the Unconditional Quantile Partial Eect of Monetary Policy Now that we have a methodology with an appropriate outcome variable, we need a treatment variable for monetary policy shocks that is plausibly exogenous. The most direct measure is the federal funds rate that the Federal Reserve targets with its open market operations. As Figure 2.9 59 shows, however, this measure is endogenous to the macroeconomy|and by extension, the housing market|tending to rise in good times and fall in bad times as a reaction to good and bad news, respectively. This positive correlation would fail to capture any countercyclical eect that the federal funds rate may have on the economy. Even a lagged federal funds rate may fail to capture the eect of monetary policy shocks, as the Fed may anticipate future movements in the economy and move their target accordingly. Romer and Romer (2004) resolve these endogeneity issues with a new measure of monetary policy shocks that controls for the Fed's forecasts and the market's expectations. The resulting variable is plausibly exogenous because it is not made in response to any observable macroeconomic trends and therefore it is truly unexpected. Specically, they estimate an OLS regression using the change in the federal funds rate target, ff m , after each Federal Open Market Committee (FOMC) meeting, m, ff m = +ffb m + 2 X i=1 i ~ y m;i + 2 X i=1 i (~ y m;i ~ y m1;i ) (2.21) + 2 X i=1 ' i ~ m;i + 2 X i=1 i (~ m;i ~ m1;i ) +~ u m;0 +" m ; with ffb m as the intended federal funds rate target before the meeting, and with ~ y, ~ , and ~ u representing forecasted output, in ation, and unemployment, respectively. Romer and Romer infer ffb m by reading the Record of Policy Actions of the Federal Open Market Committee, and they use the Fed's own forecasts for ~ y, ~ , and ~ u from the \Greenbook" prepared by the Fed's sta before each meeting. 8 The residual " m is their new monetary policy shock variable, as it represents the amount of ff m that could not have been predicted based on the Fed's own prior intentions and forecasts. It is truly an unexpected shock to the market. I will therefore use it as my treatment variable to estimate the eect of monetary policy shocks on the housing price distribution. The original Romer and Romer series covers the period from 1969 to 1996. I replicate their results and extend them to 2007, giving 39 years for my treatment variable. Figure 2.10 shows the time series at a monthly frequency. 9 It appears to have become slightly less volatile after the early 1980s, consistent with the \Great Moderation" narrative in the macroeconomic literature (Gal and Gambetti 2009). Also consistent with widely accepted history of this period, it shows the \Volcker disin ation" of 1980-82 to be an extraordinary episode, with large unexpected shocks designed to change the expectations embedded in the Phillips curve (Orlando 2013). While certainly not denitive evidence, the later years appear to register consistently negative, as Taylor (2009) alleges. This chapter will determine whether these negative shocks translated into unusually high house price growth. Compare these shocks to the actual change in the federal funds rate, shown in Figure 2.11. From 8 They nd these forecasts to be superior to private forecasts, as well as forecasts made by individual FOMC members. 9 In months where there was more than one FOMC decision, the residuals are summed over the month. 60 this measure, it is dicult to identify the period that Taylor refers to, aside from the fact that it is unusually static. It would be dicult to judge it without the context of the market's expectations. The story of the Great Moderation and the Volcker disin ation, in contrast, are as clear in this graph as they were in the last. It may not be clear from this graph, however, that the Fed tended to surprise on the positive side more often than the negative during the Great Moderation, keeping rates higher than expected, even when the actual rate was at or falling. Romer and Romer nd that this new measure is a signicant predictor of output and prices. Consistent with standard New Keynesian theory, an unexpected increase in interest rates has a negative eect that lasts at least two years|and is sizably larger than the eect estimated with the actual change in the federal funds rate. Their results suggest that previous empirical studies may have had diculty revealing the predicted relationship because they were confounded by the omitted variable of the market's expectations. The robust association between this measure of monetary policy shocks and economic theory gives us condence to use it as a plausibly exogenous treatment variable. With this treatment variable, we can nally estimate an unconditional quantile regression, E RIF q (lnp i;t )jM t1 ;X i;t = M t1 +X 0 i;t ; (2.22) with M as the \exogenous" monetary policy shock modeled after Romer and Romer (2004) and X as a matrix of controls to eliminate omitted variable bias, including hedonic characteristics such as the number of bedrooms, bathrooms, building size, and lot size, as well as the lagged natural log of GDP and a quadratic time trend. 10 This specication follows Bento, Gillingham, and Roth (2017) in treating the RIF regression like a time series relationship where the treatment aects all individuals in the sample, thus precluding the possibility of a dierence-in-dierence approach with a control group. I aggregate the monetary policy shocks by summing over each year to estimate t at an annual frequency. 11 It is well known that housing markets take longer than stock or bond markets to incorporate news into valuations, making it unlikely that a monthly frequency is appropriate (Case and Shiller 1989, Case and Shiller 1990). 2.4.4 Estimating the Unconditional Quantile Partial Eect of Credit Supply Like monetary policy, credit supply is arguably endogenous to housing prices, requiring us to identify an exogenous component for causal inference. Some studies have used state-level policies as exogenous changes in availability of credit, but these policies do not allow us to identify causality within one state where there is no control group. I will therefore use a similar time series approach as I did for monetary policy. I will also attempt to predict loan volume with a shift-share approach similar to the method developed by Bartik (1991) to predict housing demand. I will not be able to estimate the local average treatment eect, however, because an instrumental variable version 10 In Appendix B.1, I estimate this equation with state GDP instead of national GDP, and the conclusions do not change. 11 I test the robustness of my results by summing over each quarter. 61 of unconditional quantile regressions does not currently exist for continuous variables. 12 Instead, I will estimate the reduced form eect of the \instrument" directly on the quantiles of the housing price distribution. The Home Mortgage Disclosure Act of 1975 (HMDA) empowered the government to collect the data we need to estimate this eect. It required depository institutions (and subsidiaries in which they held a majority stake) to create a \loan/application register" in which they record each mortgage application and report it to the Federal Reserve. 13 Institutions were exempt if they were smaller than an asset threshold set by the Fed. Over the years, the rules were amended to cover nondepository institutions and to raise the asset threshold. In 2016, for example, depository institutions were exempt if they had less than $44 million in assets, and nondepository institutions were exempt if they had less than $10 million in assets or originated less than 100 home purchase loans. 14 Figure 2.12 shows the total mortgage volume in California from 1990 to 2016, both in dollars and in number of loans originated. The most striking feature is the so-called \bubble period." Loan originations spike at exponential rates from 2000 to 2003 and then remain at that unusually high level through 2005. The unusual nature of this period is far more apparent in this graph than in any of the monetary policy graphs. Also interesting is the fact that loan originations have been higher in the post-recession era than the pre-recession era, suggesting that the market for home lending has not been persistently squelched by the Great Recession. With this time series as the treatment variable, we can estimate an unconditional quantile regression following the same approach as we used for monetary policy, E RIF q (lnp i;t )j lnL t1 ;X i;t = lnL t1 +X 0 i;t ; (2.23) where L is the loan volume for the state of California from the HMDA dataset and X is the same matrix of controls as we used in equation 2.22. 15 The lag of the treatment variable establishes causality in the predictive Granger (1969) sense, but it does not elucidate the underlying mechanism. For that, we need a more plausibly exogenous instrument. Greenstone, Mas, and Nguyen (2018) create a county-level instrument for bank lending to small businesses that we can apply to mortgage lending. They construct this instrument in two steps. First, they regress their lending variable on county and bank xed eects, lnL i;j =c i +b j +e i;j ; (2.24) 12 Fr olich and Melly (2013) propose a method for binary treatment variables and binary instruments; to date, that is the only known IV approach to unconditional quantile regressions that is well-behaved. 13 The law was intended to address credit shortages in low-income neighborhoods by allowing the government and the public to observe the the mismatch between lending and needs. 14 See https://www.ffiec.gov/hmda/history2.htm for more details on the evolution toward these thresholds. 15 Again, I estimate this equation with state GDP instead of national GDP in Appendix B.1, and the conclusions do not change. I also estimate it with xed eects at the Census tract level in case the county xed eects are masking signicant heterogeneity in credit markets at the local level, and the results become even stronger. 62 where i indexes each county and j indexes each bank. Then, they predict the \lending supply shock" in each county by multiplying each bank's estimated xed eects, ^ b j , by their market share at the beginning of the period, ms i;j , Z i = X j ms i;j ^ b j : (2.25) The resulting instrument, Z i , captures the predicted credit supply in a given county based on how each bank is lending overall, not based on any endogenous economic conditions in that county that might be motivating lending. We can then use this Z i in place ofL t1 in equation 2.23 to see how the credit supply pressure on each county aects the overall distribution of housing prices. 2.5 Main Empirical Results 2.5.1 Basic Hedonic Model Before we estimate the unconditional quantile partial eects, it would be useful to understand the control variables a little better|and in the process, see how to interpret the output from an unconditional quantile regression. The hedonic pricing model, the workhorse of urban economics, serves this purpose perfectly. It explains the cross-sectional variation in prices across homes using each building's structural characteristics, revealing how much buyers value dierent features of the house. Rather than explaining the cross-section on average, however, I will use an unconditional quantile regression to reveal how much dierent buyers value each feature at dierent points in the distribution, E RIF q (lnp i;t )jX i;t = 0; Beds i;t + 1; Baths i;t + 2; BldgSize i;t + 3; LotSize i;t ; (2.26) where, for example, 0; indicates the eect of adding another bedroom, controlling for baths, building size, and lot size, on the price of homes at the th quantile. An intuitive way to visualize this eect is by graphing the coecient across the quantiles, as in Figure 2.13. On the x-axis are quantiles ranging from the 10th percentile to the 90th in increments of 5. 16 On the y-axis are the estimated coecients, i.e. the unconditional quantile partial eects, in equation 2.26. The graph shows that the coecient for bedrooms is smaller at higher quantiles|that is, as home prices increase. In fact, it switches from positive to negative, meaning low-priced homes become more valuable from adding an additional bedroom, while high-priced homes lose value from the marginal bedroom. It is important to remember that we are controlling for building size. As a result, this eect does not capture an additional bedroom expanding the home, but rather subdividing a home of a given size to create one more bedroom. This graph is consistent with the housing literature, which indicates that poorer households need to subdivide to accommodate more 16 I drop everything below the 10th percentile and above the 90th because Bento, Gillingham, and Roth (2017) show that RIF-OLS regressions are not well-behaved at the tails of the distribution. 63 people living in one house, while richer households prefer more space (Myers, Baer, and Choi 1996). The graph for bathrooms, in contrast, suggests that an additional bathroom is more valuable for high-priced homes. These positive and negative slopes are key to understanding their eect on the dispersion of the distribution. A positive slope suggests that the higher-priced homes are going up in value relative to the lower-priced homes, increasing dispersion across homes, while a negative slope suggests the opposite, compressing the distribution. The graph for building size is the best example of this interpretation. It is nearly exponentially positive. For more expensive homes, it seems, an additional square foot is increasingly more valuable. This eect is consistent with hedonic theory, which suggests that more valuable materials should result in more expensive homes, and the additional square foot is typically built out of better materials for more expensive homes (Gyourko and Linneman 1993, Gyourko and Tracy 1999). We do not see the same eect in the graph for lot size, which is very close to zero throughout the distribution. 2.5.2 Monetary Policy Figure 2.14 gives the punchline upfront. It shows the unconditional quantile partial eect of mon- etary policy, as estimated by equation 2.22. Three things are striking about this graph. First, the eect is positive for most of the distribution. Most homes increase in price following an unexpected increase in the federal funds rate. This eect is very signicant, so much so that it would be nearly impossible to see error bands on this graph, so we leave them out. Second, the slope of the graph is positive, indicating that the eect is greater for higher-priced homes. In other words, tight monetary policy increases dispersion in the housing price distribution, adding more value to homes that are already more expensive|and by extension, loose monetary policy decreases dispersion, benetting the cheaper homes more. Finally, the left tail of the graph is the only negative portion. For the bottom tenth of the distribution, an unexpected increase in the federal funds rate lowers home values. This is consistent with much of the housing nance literature, which shows that the poorest households are the most nancially constrained and therefore the most likely to be hurt by tight credit conditions (Di and Liu 2007, Acolin, Bricker, Calem, and Wachter 2016, Bostic and Orlando 2017). When constraints are binding, it appears that a marginal change in the cost of nancing is more important than any positive signal it may give to the market as a whole. As a robustness check, I run the same equation with xed eects at the county level, and it conrms all of these results. The one caveat is that the standard errors are larger, making the eect statistically indistinguishable from zero for about half of the distribution. Table 2.1 shows these coecients and standard errors for the 10th, 25th, 50th, 75th, and 90th percentiles. I will use this conservative estimate as my preferred specication in later calculations. I also run the regressions without dierent control variables, and I run the regressions at a quarterly level. For all specications, the results are qualitatively similar. 17 There is no indication 17 These results are available from the author upon request. 64 of a negative eect until the sixth quarter, again consistent with \price puzzle" ndings in the VAR literature. These ndings suggest that Taylor's (2009) concerns are unfounded. It is not the case that \articially" low interest rates lead to a bubble in housing prices. On the contrary, they have tended to depress housing prices over the past 47 years. However, that is a long time for one set of coecients to remain stable. Time-varying coecients have been shown to matter in a wide variety of economic contexts (Guirguis, Giannikos, and Anderson 2005, Wu and Zhou 2017, Chen, Gao, Li, and Silvapulle 2018). It is especially important to control for regime changes in monetary policy, which only started targeting the federal funds rate as its primary lever in the 1980s after the Volcker disin ation. Even Taylor himself does not assert that the Fed followed the Taylor rule in the 1970s. It is therefore important to determine whether the eect of monetary policy shocks might dier by decade, thereby opening the possibility that they did in fact boost housing prices in the 2000s. We can control for these time-varying dierences by interacting the monetary policy shocks with dummy variables for each decade, E RIF q (lnp i;t )jM t1 ;X i;t = ;7 M t1 + ;8 D 1980s M t1 + ;9 D 1990s M t1 (2.27) + ;0 D 2000s M t1 +X 0 i;t ; such that ;d captures the unconditional quantile partial eect of monetary policy in a given decade. These betas vary widely. In gure Figure 2.15, for example, we see that the positive eect still holds for the 1970s, but the negative eect disappears for the bottom 5% and the slope is not positive. In fact, the eect seems pretty equal across 80% of the distribution. These results suggest that the institutional environment matters. Monetary policy did not seem to aect house price dispersion in this more egalitarian time period. Figure 2.15 tells a similar story for the 1980s. If anything, it appears that much of the slope is negative. For over half of the distribution, unexpected increases in the federal funds rates are leading to a compression in the housing price distribution. This evidence supports Paul Volcker's decision to engage in tight monetary policy, perhaps suggesting that in ation was so high that it was benecial to everyone to get it under control. The story changes signicantly in the 1990s. Tight monetary policy had the expected negative eect on most housing prices. Then in the 2000s, the original story comes back into play. We see a positive eect for most of the distribution, a negative eect for the cheapest homes, and a positive slope increasing dispersion. The only signicant dierence appears to be the negative eect on a larger portion, approximately one-third, of the population. If Taylor is arguing that low interest rates caused the bubble by pushing up prices on the low end, then he may have a case. But if he is saying that low interest rates pushed up most housing prices|which is what he seems to be saying|then the evidence in this chapter's ndings contradict that hypothesis. The eect of monetary policy diers depending on the institutional environment, but on the whole and especially during the \bubble" period, it 65 does not appear that low interest rates have led to high housing prices. 2.5.3 Credit Supply At rst glance, the unconditional quantile partial eect for credit supply is very dierent. Fig- ure 2.16 shows the results from equation 2.23, with HMDA loan volume as the treatment variable and no xed eects. When more mortgage debt is supplied to California, it appears that the middle-priced homes are the ones that appreciate the most. This is a comforting graph for poli- cymakers who are trying to \build the middle class" by making aordable nancing available for homeownership. When I add county-level xed eects, the same conclusion holds. 18 In the debate between Mian and Su (2009) and Adelino, Schoar, and Severino (2016), these results seem to come down on the latter side. They suggest that mortgage debt was aecting the middle of the distribution more than the low end. They are not specically addressing the \bubble" period, however, as the treatment eect ranges from 1990 to 2015. To better address this debate, we need to break up the treatment into subperiods as we did for monetary policy, E RIF q (lnp i;t )j lnL t1 ;X i;t = ;0 lnL t1 + ;1 D 200006 lnL t1 + ;2 D 200710 lnL t1 (2.28) + ;3 D 201115 lnL t1 +X 0 i;t ; where the subperiods more closely align with \pre-bubble," \bubble," \bust," and \recovery" stages. According to Figure 2.17, the only subperiod that aligns with our overall results is the \pre-bubble" period. In the \bubble," the graph tilts. Now, it appears that Mian and Su are correct: The low-priced homes experienced much higher price appreciation in response to increases in loan volume, and the slope is negative, suggesting that the subprime boom compressed the distribution as it was intended to do. The \bust" and \recovery" stages are completely dierent. First, they are mostly negative. More mortgage debt has led to depressed home values since the Great Recession, and the eect has not dissipated since the housing market has begun to recover. In fact, it only seems to have gotten worse. Second, both graphs are U-shaped, suggesting that the middle-priced homes have been most negatively aected by the debt. These results are both puzzles for future research to unravel. It is reasonable to wonder whether these results have casual implications, given the endoge- nous nature of county-level lending. To test this endogeneity, I calculate the Greenstone, Mas, and Nguyen (2018) instrumental variable that removes county-level changes from year-to-year and replaces them with bank xed eects multiplied by the bank's market share in the previous period. Figure 2.18 shows the results when this IV replaces the HMDA variable from my rst specication. This instrument tells the same story as the original HMDA regression: The middle of the distribu- tion appreciates more than the bottom or the top. While it is dicult to interpret the magnitude 18 In Appendix B.2, I estimate the same regression with xed eects at the Census tract level in case the county xed eects are masking signicant heterogeneity in credit markets at the local level, and the results become even stronger. 66 of the eect because of the transformation of the variable, all the coecients are statistically sig- nicant at the 0.1% level. We can say with condence that credit supply shocks have the strongest positive eect on the middle-priced homes. 2.6 Simulations How much do these eects matter? Are they economically meaningful? How do they relate to recent trends in inequality more generally? In this section, I use the coecients from my preferred specications to simulate the impacts of these credit market shocks on housing prices and wealth across the distribution. 2.6.1 Price Eects For monetary policy, I take the estimation for the full time period with county xed eects as our preferred specication. To use a typical monetary policy shock, I turn to the distribution of annual monetary policy shocks in Figure 2.19. A 50-basis-point increase in interest rates appears to be common and near the median. Table 2.3 shows the eect of an unexpected increase in the federal funds rate by one-half percentage point between 2016 and 2017. At the 10th percentile, home prices were $170,000 in 2016. A monetary policy shock of 50 basis points would decrease home prices at the 10th percentile by 0.3%, or $544, to $169,456 in 2017. At the 90th percentile, in contrast, home prices were $1,050,000 in 2016. The same monetary policy shock would increase their home prices by 6.2%, or $64,681, to $1,114,681. The change in the housing price distribution is sizable, with an increase in 90-10 interquantile dispersion by $65,225. For credit supply, Table 2.2 shows my preferred specication with HMDA loan volume and county xed eects, as graphed in Figure 2.16. Turning to the distribution in Figure 2.20, it appears that 30% is a reasonable delta to use for our simulation. Using these state-level eects, Table 2.4 shows the eect of an increase in loan volume by 30% between 2016 and 2017. At the 10th percentile, home prices increase by 0.73%, or $1,244, to $171,244 in 2017. At the 90th percentile, home prices similarly increase by 0.52%, or $5,457, to $1,055,457. The change in the housing price distribution is much smaller than it was for a monetary policy shock. The 90-10 interquantile dispersion still increases because equal percentages result in more money at the top of the distribution, but the increase is only $4,213. This may seem to suggest that credit supply is a small contributor to increasing price dispersion, but recall from Figure 2.12 that loan volume was increasing much faster than the simulated 30% during the \bubble" years. In some years, it increased as much as 100%. 2.6.2 Wealth Eects Not all of these value changes are of equal importance to the homeowners across the distribution, however. Most households only own a fraction of their home's value as equity. An increase in value therefore lowers their loan-to-value ratio and increases their net worth. The loan-to-value ratios in 67 Tables 2.3 and 2.4 correspond with the estimates in the Survey of Consumer Finances. 19 As is well known, leverage magnies losses and gains. For a one-half percentage point monetary policy shock, for example, the homeowner at the 75th percentile experiences a 10.3% increase in equity, while the homeowner at the 90th percentile only experiences a 9.2% increase, despite a larger dollar gain. Similarly, a 30% increase in credit supply increases wealth at the 10th percentile by 2.9% and at the 90th percentile by 0.8%. It is important to remember that the absolute size of the wealth gap still increases, but the incremental gains are more valuable to the lower quantiles, which have both lower baselines and higher marginal utilities. 2.6.3 A Simulation of the Housing \Bubble" How well can these models explain the \bubble" in housing prices that occurred from 2000 to 2006? As an example, I will use the monetary policy model, for which the inputs (i.e. the monetary policy variable) are more stable over time than the credit supply model. Specically, I will use the \bubble" coecients from equation 2.27, the results of which appear in Figure 2.17. These coecients were positive for most of the distribution, with the highest values for the bottom of the distribution, becoming negative only above the 80th quantile. Figure 2.21 compares the simulated housing prices using the coecients from this model with the actual historical prices that occurred during this time period. Clearly, monetary policy cannot account for the majority of the appreciation, though it does appear that it was pushing in that direction for the top quarter of the distribution in 2004-2006. For the bottom half of the distribution, it may have even been a moderating force. These homes must have appreciated for other reasons. 2.7 Conclusion The housing price distribution has changed signicantly over time, and credit markets have played a starring role. This chapter has shown that tight monetary policy tends to increase dispersion in the distribution|and to increase housing prices overall. Credit supply, on the other hand, increases the middle of the distribution relative to the top and the bottom. The 2000-2006 period was an outlier, however, with credit supply increasing the bottom of the distribution the most, consistent with the ndings of Mian and Su (2009). These ndings suggest that credit supply played an important role in the \bubble" in housing prices at that time, while there is no evidence that monetary policy was an important factor. On the contrary, monetary policy may have been a moderating factor. These ndings have important policy implications. Low interest rates have been blamed for in ating asset markets, but this evidence does not support that characterization. More work should investigate this relationship, and more caution should be used when criticizing this tilt in monetary policy. For decades, aordable housing advocates have supported increased credit availability as a way to build the middle class. This chapter suggests that increased credit supply has indeed had 19 These calculations use the SCF from the 1990s to correspond with the \bubble" simulation below, as the 1990s were a stable precursor before the treatment eects potentially confounded the LTV ratios. 68 this eect. The type of credit matters, however, as we learned from the subprime boom, which has had negative eects that continue to this day. From a methodological standpoint, the unconditional quantile regression has proven itself useful in ways that can be applied across the housing literature and program evaluation more generally. Other housing policies, such as land-use regulations or mortgage modication programs, likely have dierent eects across the distribution as well. Average eects often do not describe the lived experiences of much, if not most, of the population. This chapter demonstrates that public policies can be more carefully, richly, and accurately evaluated using quantile methodologies such as RIF regressions. These methodologies reveal that the entire distribution matters in the housing context. Researchers can use this approach to determine the extent to which heterogeneous eects matter in other policy contexts. 69 Table 2.1: Eect of Monetary Policy Shocks on Housing Price Distribution (1) (2) (3) (4) (5) Q10 Q25 Q50 Q75 Q90 Monetary t1 0:002 0:007 0:054 0:121 0:118 (0:20) (0:65) (1:96) (6:58) (8:16) ln(GDP ) t1 3:963 1:045 0:422 0:814 0:617 (17:62) (5:44) (2:44) (7:10) (3:68) Bedrooms 0:139 0:074 0:014 0:046 0:110 (3:65) (4:28) (1:08) (4:65) (8:14) Bathrooms 0:134 0:041 0:136 0:080 0:152 (3:64) (2:88) (5:24) (5:52) (7:89) BuildingSize 0:000 0:000 0:000 0:000 0:000 (4:07) (5:73) (12:77) (14:77) (9:89) LotSize 0:000 0:000 0:000 0:000 0:000 (1:88) (1:13) (0:14) (0:20) (0:24) N 6,449,731 6,449,731 6,449,731 6,449,731 6,449,731 R 2 0:177 0:216 0:313 0:276 0:188 Notes: All regressions include a quadratic trend and county xed eects. t statistics in parentheses: p< 0:05, p< 0:01, p< 0:001 Bootstrapped standard errors are calculated with 50 repetitions. 70 Table 2.2: Eect of State-Level Credit Supply on Housing Price Distribution (1) (2) (3) (4) (5) Q10 Q25 Q50 Q75 Q90 ln(LoanVolume) t1 0:023 0:035 0:042 0:030 0:017 (5:25) (6:04) (10:01) (10:03) (5:75) ln(GDP ) t1 1:792 2:046 2:585 1:645 0:472 (7:40) (9:29) (19:86) (7:50) (3:31) Bedrooms 0:139 0:073 0:006 0:062 0:153 (4:06) (4:98) (0:50) (5:88) (8:44) Bathrooms 0:098 0:031 0:048 0:102 0:197 (2:67) (2:12) (3:95) (6:53) (6:88) BuildingSize 0:000 0:000 0:000 0:000 0:000 (3:98) (5:04) (8:84) (12:89) (9:05) LotSize 0:000 0:000 0:000 0:000 0:000 (1:50) (1:40) (0:50) (0:22) (0:36) N 8,178,669 8,178,669 8,178,669 8,178,669 8,178,669 R 2 0:068 0:152 0:228 0:202 0:172 Notes: All regressions include a quadratic trend and county xed eects. t statistics in parentheses: p< 0:05, p< 0:01, p< 0:001 Bootstrapped standard errors are calculated with 50 repetitions. Table 2.3: Simulation of Monetary Policy Shock on Housing Price Distribution (1) (2) (3) (4) (5) Q10 Q25 Q50 Q75 Q90 P 2016 170,000 265,000 412,000 650,000 1,050,000 ^ P 2017 169,456 265,038 423,053 691,605 1,114,681 201617 -544 38 11,053 41,605 64,681 LTV 1.25 0.80 0.59 0.38 0.33 %(Equity) -1.3% 0.1% 6.5% 10.3% 9.2% Notes: Simulated eect of one-half percentage point unexpected increase in federal funds rate. Based on coecients from Table 2.1. Loan-to-value (LTV) ratios correspond with the estimates in the Survey of Consumer Finances from the 1990s. 71 Table 2.4: Simulation of Credit Supply Shock on Housing Price Distribution (1) (2) (3) (4) (5) Q10 Q25 Q50 Q75 Q90 P 2016 170,000 265,000 412,000 650,000 1,050,000 ^ P 2017 171,244 267,899 417,402 655,746 1,055,457 201617 1,244 2,899 5,402 5,746 5,457 LTV 1.25 0.80 0.59 0.38 0.33 %(Equity) 2.9% 5.5% 3.2% 1.4% 0.8% Notes: Simulated eect of 30% increase in state-level loan volume. Based on coecients from Table 2.2. Loan-to-value (LTV) ratios correspond with the estimates in the Survey of Consumer Finances from the 1990s. Figure 2.1: Total U.S. Housing Starts, 1959-2016 0 500 1000 1500 2000 2500 3000 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 Total New Privately Owned Housing Units Started Notes: Total new privately owned housing units started each month in the United States. Measured in thousands of units, seasonally adjusted by U.S. Bureau of the Census. Retrieved from FRED, Federal Reserve Bank of St. Louis, https://fred.stlous.org/series/HOUST. 72 Figure 2.2: Average 30-Year Mortgage Rate and Federal Funds Rate 0 5 10 15 20 25 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 Percentage Points 30-Year Mortgage Rate Federal Funds Rate (a) Comparison: Mortgage vs. Fed Funds Rate -6 -4 -2 0 2 4 6 8 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 Percentage Points (b) Spread: Mortgage Minus Fed Funds Rate Notes: Weekly 30-year xed rate mortgage average (ending Thursday) from April 1971 to December 2016, measured in percentage points, not seasonally adjusted, as reported by Freddie Mac. Retrieved from FRED, Federal Reserve Bank of St. Louis, https://fred.stlous.org/series/MORTGAGE30US. Weekly federal funds rate (ending Wednesday) from April 1971 to December 2016, measured in percentage points, not seasonally adjusted. Retrieved from FRED, Federal Reserve Bank of St. Louis, https://fred.stlous.org/series/FF. 73 Figure 2.3: Nominal Single-Family Home Transaction Prices in California, 1970-2016 0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Transaction Price ($) p10 p25 p50 p75 p90 mean Notes: Quantiles of the unconditional distribution of single-family home transaction prices in California in each year from 1970 to 2016. p10 = 10th percentile, p25 = 25th percentile, p50 = 50th percentile, p75 = 75th percentile, p90 = 90th percentile, mean = arithmetic average. Data obtained through private restricted-use agreement with Zillow. 74 Figure 2.4: Real Single-Family Home Transaction Prices in California, 1970-2016 0 50,000 100,000 150,000 200,000 250,000 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Inflation-Adjusted Transaction Price ($) p10 p25 p50 p75 p90 mean Notes: Quantiles of the unconditional distribution of single-family home transaction prices in California in each year from 1970 to 2016. p10 = 10th percentile, p25 = 25th percentile, p50 = 50th percentile, p75 = 75th percentile, p90 = 90th percentile, mean = arithmetic average. Data obtained through private restricted-use agreement with Zillow. Prices measured in constant 1970 dollars. De ated using the core \Personal Consumption Expenditures" (PCE) index, which excludes food and energy. Retrieved from FRED, Federal Reserve Bank of St. Louis, https://fred.stlouis.org/series/DPCCRG3A086NBEA. 75 Figure 2.5: Logged Single-Family Home Transaction Prices in California, 1970-2016 8 9 10 11 12 13 14 15 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Natural Log of Nominal Housing Transaction Price ($) p10 p25 p50 p75 p90 mean Notes: Quantiles of the unconditional distribution of the natural logarithm of nominal single-family home transaction prices in California in each year from 1970 to 2016. p10 = 10th percentile, p25 = 25th percentile, p50 = 50th percentile, p75 = 75th percentile, p90 = 90th percentile, mean = arithmetic average. Data obtained through private restricted-use agreement with Zillow. 76 Figure 2.6: Single-Family Home Sizes in California, 1970-2016 0 500 1,000 1,500 2,000 2,500 3,000 3,500 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Building Size (square feet) p10 p25 p50 p75 p90 mean Notes: Quantiles of the unconditional distribution of building sizes from single-family home transactions in California in each year from 1970 to 2016. p10 = 10th percentile, p25 = 25th percentile, p50 = 50th percentile, p75 = 75th percentile, p90 = 90th percentile, mean = arithmetic average. Data obtained through private restricted-use agreement with Zillow. 77 Figure 2.7: Single-Family Lot Sizes in California, 1970-2016 0 50,000 100,000 150,000 200,000 250,000 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Lot Size (square feet) p10 p25 p50 p75 p90 mean Notes: Quantiles of the unconditional distribution of lot sizes from single-family home transactions in California in each year from 1970 to 2016. p10 = 10th percentile, p25 = 25th percentile, p50 = 50th percentile, p75 = 75th percentile, p90 = 90th percentile, mean = arithmetic average. Data obtained through private restricted-use agreement with Zillow. 78 Figure 2.8: Single-Family Lot Sizes in California, 1970-2016 0 5,000 10,000 15,000 20,000 25,000 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Lot Size (square feet) p10 p25 p50 p75 p90 Notes: Quantiles of the unconditional distribution of building sizes from single-family home transactions in California in each year from 1970 to 2016. p10 = 10th percentile, p25 = 25th percentile, p50 = 50th percentile, p75 = 75th percentile, p90 = 90th percentile, excluding mean from previous graph for better scaling and visual interpretation. Data obtained through private restricted-use agreement with Zillow. 79 Figure 2.9: Eective Federal Funds Rate 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Percentage Points Notes: Monthly federal funds rate from January 1969 to December 2007, measured in percentage points, not seasonally adjusted. Retrieved from FRED, Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/series/FEDFUNDS. Recessions are denoted in gray shaded areas, as dened by NBER Business Cycle Dating Committee. Methodology described at http://www.nber.org/cycles/recessions.html. Business cycle peak and trough months listed at http://www.nber.org/cycles.html. 80 Figure 2.10: Unexpected Monetary Policy Shocks -4 -3 -2 -1 0 1 2 3 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Percentage Points Notes: Residual from regression of change in federal funds rate on intended rate and forecasts of in ation, output, and unemployment: ff m = +ffb m + P 2 i=1 i ~ y m;i + P 2 i=1 i (~ y m;i ~ y m1;i ) + P 2 i=1 ' i ~ m;i + P 2 i=1 i (~ m;i ~ m1;i ) +~ u m;0 +" m . Based on Romer and Romer (2004) methodology. 81 Figure 2.11: Change in Actual Federal Funds Rate -8 -6 -4 -2 0 2 4 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Percentage Points Notes: Monthly change in the federal funds rate, computed from the monthly federal funds rate from January 1969 to December 2007, measured in percentage points, not seasonally adjusted. Retrieved from FRED, Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/series/FEDFUNDS. 82 Figure 2.12: Mortgage Originations in California, 1990-2015 0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 0 100,000,000,000 200,000,000,000 300,000,000,000 400,000,000,000 500,000,000,000 600,000,000,000 700,000,000,000 800,000,000,000 900,000,000,000 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 # Loans Originated Loan Volume ($) Loan Volume ($) # Loans Originated Notes: Mortgage originations reported by lenders in California under the Home Mortgage Disclosure Act from 1990 to 2015. Measured in total dollar volume, represented by line corresponding to primary y-axis on the left. Measured in number of loans originated, represented by columns corresponding to secondary y-axis on the right. 83 Figure 2.13: Eect of Hedonic Characteristics on Housing Price Distribution -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0 10 20 30 40 50 60 70 80 90 100 Unconditional Quantile Partial Effect Quantile of the Housing Price Distribution (a) Bedrooms 0 0.05 0.1 0.15 0.2 0.25 0.3 0 10 20 30 40 50 60 70 80 90 100 Unconditional Quantile Partial Effect Quantile of the Housing Price Distribution (b) Bathrooms 0 0.00005 0.0001 0.00015 0.0002 0.00025 0 10 20 30 40 50 60 70 80 90 100 Unconditional Quantile Partial Effect Quantile of the Housing Price Distribution (c) Building Size 0 5E-11 1E-10 1.5E-10 2E-10 2.5E-10 3E-10 3.5E-10 4E-10 0 10 20 30 40 50 60 70 80 90 100 Unconditional Quantile Partial Effect Quantile of the Housing Price Distribution (d) Lot Size Notes: Coecients for RIF-OLS regressions at each quantile of the housing price distribution at 5% increments from the 10th percentile to the 90th percentile. Hedonic model with year xed eects: E RIF q (lnp i;t )jX i;t = 0; Beds i;t + 1; Baths i;t + 2; BldgSize i;t + 3; LotSize i;t + t +" i;t Data covers single-family home transaction prices in California from 1970 to 2016. Obtained through private restricted-use agreement with Zillow. Bootstrapped standard errors are calculated with 50 repetitions. 84 Figure 2.14: Eect of Monetary Policy Shocks on Housing Price Distribution -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution (a) No Fixed Eects -0.05 0.00 0.05 0.10 0.15 0.20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution (b) County Fixed Eects Notes: Coecients for RIF-OLS regressions at each quantile of the housing price distribution at 5% increments from the 10th percentile to the 90th percentile. Estimated with annual Romer and Romer (2004) monetary policy shocks and controls for omitted variable bias: E RIF q (lnp i;t )jM t1 ;X i;t = M t1 +X 0 i;t . Data covers single-family home transaction prices in California from 1970 to 2007. Obtained through private restricted-use agreement with Zillow. Bootstrapped standard errors are calculated with 50 repetitions. 85 Figure 2.15: Eect of Monetary Policy Shocks on Housing Price Distribution by Decade -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution 1970s 1980s 1990s 2000s Notes: Coecients for RIF-OLS regressions at each quantile of the housing price distribution at 5% increments from the 10th percentile to the 90th percentile. Estimated with annual Romer and Romer (2004) monetary policy shocks, interactions with dummy variables by decade, and controls for omitted variable bias: E RIF q (lnp i;t )jM t1 ;X i;t = ;7 M t1 + ;8 D 1980s M t1 + ;9 D 1990s M t1 + ;0 D 2000s M t1 +X 0 i;t . Data covers single-family home transaction prices in California from 1970 to 2007. Obtained through private restricted-use agreement with Zillow. Bootstrapped standard errors are calculated with 50 repetitions. 86 Figure 2.16: Eect of Loan Volume on Housing Price Distribution 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution (a) No Fixed Eects 0 0.01 0.02 0.03 0.04 0.05 0.06 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution (b) County Fixed Eects Notes: Coecients for RIF-OLS regressions at each quantile of the housing price distribution at 5% increments from the 10th percentile to the 90th percentile. Estimated with annual HMDA loan value and controls for omitted variable bias: E RIF q (lnp i;t )j lnL t1 ;X i;t = lnL t1 +X 0 i;t . Data covers single-family home transaction prices in California from 1990 to 2015. Obtained through private restricted-use agreement with Zillow. Bootstrapped standard errors are calculated with 50 repetitions. 87 Figure 2.17: Eect of Loan Volume on Housing Price Distribution by Subperiod -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution Pre-Bubble Bubble Bust Recovery Notes: Coecients for RIF-OLS regressions at each quantile of the housing price distribution at 5% increments from the 10th percentile to the 90th percentile. Estimated with annual HMDA loan value, interactions with dummy variables by subperiod, and controls for omitted variable bias: E RIF q (lnp i;t )j lnL t1 ;X i;t = ;0 lnL t1 + ;1 D 200006 lnL t1 + ;2 D 200710 lnL t1 + ;3 D 201115 lnL t1 +X 0 i;t . Data covers single-family home transaction prices in California from 1990 to 2015. Obtained through private restricted-use agreement with Zillow. Bootstrapped standard errors are calculated with 50 repetitions. 88 Figure 2.18: Eect of County-Level IV for Lending on Housing Price Distribution 0.00E+00 1.00E-07 2.00E-07 3.00E-07 4.00E-07 5.00E-07 6.00E-07 7.00E-07 8.00E-07 9.00E-07 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Unconditional Quantile Partial Effect Quantile of the Housing Price Distribution Notes: Coecients for RIF-OLS regressions at each quantile of the housing price distribution at 5% increments from the 10th percentile to the 90th percentile. Estimated with Greenstone, Mas, and Nguyen (2018) shift-share strategy applied to mortgage lending and controls for omitted variable bias, as reduced form, not 2SLS: E RIF q (lnp i;t )jZ t1 ;X i;t = Z t1 +X 0 i;t . Data covers single-family home transaction prices in California from 1990 to 2015. Obtained through private restricted-use agreement with Zillow. Bootstrapped standard errors are calculated with 50 repetitions. 89 Figure 2.19: Distribution of Annual Monetary Policy Shocks Notes: On the x-axis, residual from regression of annual change in federal funds rate on intended rate and forecasts of in ation, output, and unemployment: ff m = +ffb m + P 2 i=1 i ~ y m;i + P 2 i=1 i (~ y m;i ~ y m1;i ) + P 2 i=1 ' i ~ m;i + P 2 i=1 i (~ m;i ~ m1;i ) +~ u m;0 +" m . Based on Romer and Romer (2004) methodology. 90 Figure 2.20: Distribution of State-Level Changes in Loan Volume Notes: Annual mortgage originations reported by lenders in California under the Home Mortgage Disclosure Act from 1990 to 2015. x-axis corresponds with ratio of current year's total dollar volume to previous year's. (Multiply by 100 to read in percentages.) 91 Figure 2.21: Simulated Housing Prices, 2000-2006 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 2000 2001 2002 2003 2004 2005 2006 Simulated Price ($) Q10 Q25 Q50 Q75 Q90 (a) Monetary Policy Simulation 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 2000 2001 2002 2003 2004 2005 2006 Transaction Price ($) Q10 Q25 Q50 Q75 Q90 (b) Actual Historical Values Notes: The monetary policy simulation uses the coecients from the state-level loan volume model with subperiods in Figure 2.16. The actual historical values correspond with the 2000-2006 prices in Figure 2.3. 92 Chapter 3 What's Lost in the Aggregate: Lessons from a Local Index of Housing Supply Elasticities 3.1 Introduction Across the United States, urban land prices have been growing signicantly faster than incomes in recent decades, leading many economists and planners to declare a \housing aordability crisis". 1 At the root of this crisis is a growing shortage of housing units (Morrow 2013, Taylor 2015). Economic theory predicts that prices will rise as long as supply fails to keep up with demand, and the empirical literature has overwhelmingly found evidence of this eect. To date, however, this literature has focused on averages across metropolitan areas, whereas supply restrictions are actually enacted at the municipality level. This analysis is the rst to identify where supply is being restricted the most within the metro|and therefore, which cities are driving this aordability crisis. 2 Consider the growth of housing units from 2000 to 2012 in Los Angeles County, shown in Figure 3.1. It is clearly not a homogeneous story. At the municipality level, housing unit growth ranges from 0% to 27.7%. From this graph, however, it is impossible to identify how much of this variation is due to dierences in the supply curve|and not simply from dierences in housing demand. It may be the case, for example, that Calabasas and Pasadena, with their high growth rates, are simply more desirable locations than low-growth cities like Downey and Inglewood. The empirical economist faces the challenge of determining how much supply responds to these dierent demand curves in each city|in other words, how elastic is the supply curve. In this chapter, we construct housing price and quantity indices to calculate these elasticities. For prices, we use a rich new municipality-level dataset from Zillow from 1996 to 2015. For quanti- 1 See, for example, Sinai (2014), Albouy, Ehrlich, and Liu (2016), Watson, Steen, Martin, and Vandenbroucke (2017), Wetzstein (2017). 2 This chapter is co-authored with Christian L. Redfearn. 93 ties, we use annual building permit data to supplement total housing unit counts from the decadal Census. With these two indices, we calculate housing supply elasticities for the cities in Los Angeles County using a sign-restricted vector autoregression (VAR) model that identies positive demand shocks as simultaneous increases in demand and supply. These structural shocks allow us to draw causal inference from the impulse responses of both quantities and prices, which we then use to calculate elasticities. This methodology improves on previous estimates that suered from endo- geneity bias, and it reveals that those estimates were likely overestimating the price elasticity of housing supply by orders of magnitude. We nd that \short-run" supply elasticities range from 0 to 0.2 at the municipality level, and \long-run" elasticities are only slightly higher. These estimates are consistent with recent econo- metric advances in similar markets where investment is costly to reverse and production is therefore hesitant to respond to year-to-year signals (Kilian 2009, Kilian and Murphy 2012). While the major- ity of these estimates are clustered in the 0 to 0.05 range, there is a long right tail in the distribution, suggesting that many cities' supply curves are signicantly more elastic than the average. We exploit this heterogeneity to understand the driving forces behind the housing shortage. We nd evidence that the old adage \location, location, location" still matters: Figure 3.7 shows that elasticities are lowest in the core of the metropolitan area and increase as one travels northeast and northwest, away from the city center and the valuable coastal land. This map provides striking context for Figure 3.1. It suggests that the central cities are restricting housing supply the most and pushing it out to the periphery, contributing to urban sprawl, longer commute times, less agglomeration, and suboptimal allocation of housing. In cross-sectional analysis, we nd that many of the typical explanations for housing supply elasticity (or lack thereof) are not statistically signicant: housing price, population, and even regulations as measured by the commonly used Wharton Residential Land Use Regulatory Index (WRLURI). Only two factors are signicant: The housing supply curve is more elastic in cities with less density and higher income, consistent with the urban sprawl story illustrated in Figure 3.7. These ndings contribute, rst and foremost, to the literature on supply elasticities in housing and land markets. Few papers have attempted to directly estimate these elasticities, likely due to data constraints as well as endogeneity challenges. These early estimates used a simple ordinary least-squares approach, often with lagged independent variables (Smith 1976, Pryce 1999, Mayer and Somerville 2000b, Malpezzi and Maclennan 2001, Green, Malpezzi, and Mayo 2005). Harter- Dreiman (2004) and Wheaton, Chervachidze, and Nechayev (2014) took a step closer to our ap- proach with a vector error correction series of equations, but even that model cannot identify structural shocks. The second approach in the literature has been to measure housing supply restrictions with survey-based measures of land-use regulation and satellite measures of topographic constraints. The most widely-used indices on regulation and geography are Gyourko, Saiz, and Summers (2008) and Saiz (2010), respectively. These types of measures have overwhelmingly shown that inelastic housing supply leads to higher prices (Quigley and Raphael 2005, Glaeser, Gyourko, and Saks 2005, 94 Schuetz 2009, Saiz 2010, Gyourko, Mayer, and Sinai 2013, Ganong and Shoag 2015). More recent structural approaches have concluded that these restrictions have signicant negative eects on economic growth and productivity, particularly for less-skilled workers (Nieuwerburgh and Weill 2010, Moretti 2013, Hsieh and Moretti 2017, Parkhomenko 2017). These eorts all employ indirect proxies for elasticity, however, and they are only interested in averages for each metropolitan statistical area (MSA) as a whole. This chapter, in contrast, directly measures elasticities at the municipality level within the MSA. As such, it also speaks to the broad literature on neighborhood sorting, giving new evidence of how supply restrictions factor into a household's decision about where to live in a given metro. This question draws its original inspiration from the famous Tiebout (1956) model showing how households sort into the municipality with their preferred balance of taxes and public goods and services. Equally important is the literature developed around the Roback (1982) model showing how households trade o amenities, house prices, and wages. Recent work has extended these neighborhood dynamics to include crime rates (Bayer, McMillan, Murphy, and Timmins 2016), path dependence (Malone and Redfearn 2018), pollution (Heblich, Trew, and Zylberberg 2016), public transit (Baum-Snow 2007, Waxman 2017), racial preferences (Bayer, Fang, and McMillan 2014), and school quality (Bayer, Ferreira, and McMillan 2007). Housing supply restrictions are a key tool that neighborhoods use to achieve sorting along all these dimensions, making this chapter an important step toward a more comprehensive theory of these inter-city (intra-metro) equilibria. The remainder of the chapter is organized as follows. Section 3.2 derives theoretical predictions from the canonical urban economics model to motivate our empirical work. Section 3.3 presents our data and methodology for constructing local indices of housing prices and quantities. In Section 3.4, we use these indices to calculate supply elasticities. Section 3.5 analyzes the spatial variation in these elasticities, including their correlation with the traditional explanations in the literature. Section 3.6 concludes. 3.2 Motivating Theory We begin by modeling the supply side of the housing market according to standard urban theory. LetS =N=l represent the capital-land ratio, or the structural density, at a given location. Following Brueckner's (1987) classic unied model, developers maximize the prot function l ph(S)iSr ; (3.1) where p is the rent per square foot paid by consumers, h(S) is the oor space, i is the rental price of capital, and r is the land rent. In equilibrium, each developer earns zero total prot: ph(S)iS =r ; (3.2) 95 and developers maximize their prots by choosing S: ph 0 (S) =i : (3.3) We can conduct comparative statics by dierentiating these equations with respect to variables we care about, such as commuting cost, distance from the central business district, consumer income, and utility, all represented by : @r @ =h @p @ ; (3.4) @S @ = h 0 ph 00 @p @ : (3.5) If h 0 (S) > 0 and h 00 (S) < 0 according to the law of diminishing returns, then @p @ , @r @ , and @S @ all have the same sign. Anything that increases prices, therefore, should increase structural density. The canonical model of urban economics thus predicts that higher prices per square foot should be associated with more structural density, both across space and over time. This is consistent with our conversations with developers, who seek higher density on more expensive land, where less density would not earn a high enough return per square foot to cover the cost basis. Importantly, there are no frictions in this model. It hinges on the assumption that developers can chooseS with certainty. In the real world, however, a number of obstacles prevent this freedom of choice: land-use regulations, topographical constraints, lack of capital, construction delays, and economic uncertainty. When the supply process is sti ed by these factors, price growth often will not be met with a sucient increase in density to meet the demand. Formally, %P i;t > %Q S i;t ; (3.6) whereQ S i;t is the quantity supplied in locality i in yeart andP i;t is the price at which it is supplied. The more imbalanced this equation becomes, the lower will be the price elasticity of supply, " S = %Q S i;t %P i;t = Q S i;t =Q S i;t1 P i;t =P i;t1 = P i;t1 Q S i;t1 Q S i;t P i;t : (3.7) By measuring this elasticity in each city, we can therefore impute the degree to which the supply process is being restricted because density cannot keep up with prices. 3.3 Local Housing Prices and Quantities: Data and Trends 3.3.1 Local Housing Price Index Before calculating housing supply elasticities, the researcher must make two decisions: how to calculate price and quantity indices over time and how to calculate elasticities from those indices. 96 Until recently, these decisions have seemed nearly insurmountable in the housing market. The rst calculation requires a reliable measure of all housing values in a given geography. The classic Case and Shiller (1989) approach forms a repeated-sale index based on multiple transactions of the same property. While this approach makes the return a true measure of price growth in a given asset over time, it does not control for changes in the asset itself, such as modications to or depreciation of the house. Even more concerning, it limits the sample size to the unrepresentative subset of properties that transact multiple times. Other researchers create hedonic indices that expand the sample to all properties that transact at least once, controlling for observable building characteristics. The sample still is not representative of all the properties that an investor could purchase; it only gives the value of those that did transact, a decision that clearly involves selection bias (Englund, Quigley, and Redfearn 1999). Moreover, controlling for the observable characteristics alone is probably inferior to actually comparing the same house over time. This calculation also requires a long enough time period to draw statistically signicant con- clusions at a given geographic level. While the literature has been able to make statements about metropolitan areas, they rarely drill down to the municipality level where they have lacked sucient observations. It is only now that we have at least a decade worth of high-quality transaction data to calculate indices for most cities within a large urban county such as Los Angeles. Zillow owns the most comprehensive dataset of housing values in the United States. Not only do they have all publicly recorded transactions over time, but they can combine these transactions with listing values and other non-transaction data that they collect on their website, which is now the predominant site for buyers and sellers in today's housing market. 3 Zillow uses these data to calculate a median home value index (ZHVI) in ve steps: First, they calculate raw median sale prices for all properties, whether they transacted or not, with r i;j (t) representing the raw median price for market segment i in geographic region j at time t. 4 Second, they adjust for any residual systematic error in region j at time t, b j (t) = Median z j (t 1)s j (t) s j (t) ; (3.8) wheres j (t) is a vector of the actual sales prices transacted andz j (t1) is Zillow's estimate of those properties' value in the period before they transacted. The adjusted median u i;j (t) will correct for this error in Zillow's estimates by incorporating the new sales data about those properties into the raw median price: u i;j (t) = r i;j (t) 1 +b j (t) : (3.9) Third, they apply a ve-term Henderson (1916) moving average lter to reduce noise. Fourth, they adjust for seasonality with a decomposition proposed by Cleveland, Cleveland, McRae, and Terpenning (1990), where the time series is broken down into seasonal, trend, and remainder 3 This predominance has become particularly strong since Zillow's merger with its largest competitor, Trulia, in 2015 (Kusisto and Light 2015). 4 The market segment is the type of building|single family, condo, etc. 97 components, U(t) =S(t) +T (t) +RE(t) ; (3.10) and then the seasonal component S(t) is subtracted. Finally, Zillow deletes all time series that have too few observations, too much volatility, or too many outliers, gaps, or jumps to meet their standard of quality control. 5 The resulting data are available in a variety of forms, from time series of particular building types to dierent quantiles. We employ the median home value per square foot index, which captures all residential buildings and standardizes prices as a function of size for the best comparability. We download these indices at the municipality level, which indicates the median price across all homes in the city. 6 Since we are interested in local policy and planning decisions, we narrow our focus to one major urban county, the lowest level of government within which municipalities operate. At this level, any variation in the cross-section of housing supply elasticities must represent dierences in the municipalities themselves, not in counties or metropolitan areas or other larger geographies. 7 We focus on Los Angeles County for its size and its variety of dierent geographies, topographies, and neighborhood characters. It is one of the most ideal laboratories within which to study cross- sectional variation in municipalities. Within Los Angeles County, Zillow publishes median home value per square foot for over 80 municipalities from 1996 to 2016. These data are available at a monthly frequency. We aggregate up to the annual frequency by averaging over the twelve monthly observations for each city in a given year. 3.3.2 Local Housing Quantity Index To our knowledge, building permits are the only annual data on housing quantity available at a local level. Municipalities, counties, townships, and other towns issue and record building permits on an ongoing basis, and the Census Bureau surveys 9,000 of these \permit-issuing places" every month. They collect information on the amount of new privately-owned single-family homes, as well as the number of new units in two- to ve-unit residential buildings and the overall dollar value of construction. They ask local ocials to describe permits valued at least $1 million and to list the owner or builder. Once a year, the Census Bureau also surveys another 11,000 permit oces. 8 The annual estimate is therefore a larger and more accurate sample, which is one of the reasons why we use it in this chapter. 9 Of course, not everyone responds to the sample, so the Census 5 For more details, see https://www.zillow.com/research/zhvi-methodology-6032/. 6 To download these and other data from Zillow, go to https://www.zillow.com/research/data/. 7 Landvoigt, Piazzesi, and Schneider (2015) take a similar approach to the housing market(s) of San Diego. 8 These numbers refer to recent years. When the survey was initiated in 1959, the number of oces was half of what it is today. The Census Bureau selects the 9,000 monthly survey respondents using a stratied sampling methodology where the most populous areas are chosen with certainty and the rest of the localities are chosen with a sampling factor of 1 in 10. 9 We also use annual data because the monthly price data are more volatile and likely to be driven by outliers, especially at the municipality-level, where very few transactions may occur in a given month|and those transactions 98 Bureau has to impute roughly 19% of the monthly units and 7% of the annual units by assuming that the missing localities issued permits at the same rate as the sampled localities. Figure 3.2 compares single-family home permits, as well as all residential permits, to the re- spective housing prices. 10 In both cases, it appears that the real estate booms of the late 1980s and early 2000s were very dierent. The former was an instance of unusually high building activity with mild price appreciation, while the latter exhibited unusually high price appreciation with strong building activity that peaked lower and earlier than prices. This last point is crucial. One of the leading theories in urban economics alleges that prices rose so high because supply was restricted, but this does not appear to be the case in this graph. On the contrary, from 1992 to 2004, housing quantity growth tracked housing price growth almost exactly. It had no trouble keeping up, in spite of these alleged restrictions. It was only in the last couple years of the \bubble" that prices out- paced quantity. This is unsurprising, given the ndings in Chapter 1 that permit activity typically slows a year or two before a recession hits. The starting point is 1990, when the Census of Population and Housing gives the total housing units. 11 Since 1990, the housing stock has grown less than 1% per year, for a total of only 10% in 22 years. This evidence is consistent with the literature, as well as anecdotal accounts from the real estate market, suggesting that it has been dicult to build in Los Angeles, with construction falling far behind the nation's (and the state's) population growth (Quigley and Raphael 2005, Morrow 2013, Dovey 2015). It does not appear, however, that construction has been on a downward trend over these recent decades, contradicting claims that supply has become more restricted over time, particularly during the recent \bubble" period. 12 3.4 Calculating Housing Supply Elasticities We begin by considering the classic supply-and-demand equations, which represent our ideal goal for estimation: Q S i;t =" S i P i;t +u S t ; (3.11) Q D i;t =" D i P i;t +u D t ; (3.12) where quantity and price variables are expressed in natural logs to achieve the percent changes in Equation 3.7. Unfortunately, Q S i;t and Q D i;t are dicult to measure in the real world. If we make some simplifying assumptions, however, we can estimate a similar system of equations with standard housing indices. Specically, we assume that positive demand shocks manifest themselves in increasing price and increasing quantity, following a standard Marshallian model (Marshall 1890). may not be representative of the average housing value across all properties. 10 Prices were calculated by the authors using transaction-level data from DataQuick to estimate further back in time than Zillow will allow. These are not the prices used in the rest of the chapter. 11 See https://www.census.gov/prod/cen1990/cph2/cph-2-6.pdf. The Census does not report the total number of single-family homes at the county or city level. We therefore do not estimate growth rates for single-family homes. 12 These claims have been made most famously by Edward Glaeser and Joseph Gyourko. See, for example, Glaeser and Gyourko (2003), Glaeser (2004), and Glaeser, Gyourko, and Saks (2005). 99 A structural vector autoregression (SVAR) model allows us to simulate such a shock using the past behavior of prices and quantities. The responses of quantity, %Q S i;t , and price, %P i;t , to these impulse shocks will allow us to calculate the price elasticity of supply, " S i;t . 3.4.1 Sign-Restricted Vector Autoregression Model First, consider a two-variable reduced-form vector autoregression (VAR) model: " Q t P t # = " Q Q;1 Q P;1 P Q;1 P P;1 #" Q t1 P t1 # + " Q Q;2 Q P;2 P Q;2 P P;2 #" Q t2 P t2 # + " e Q;t e P;t # ; (3.13) or Y t = A 1 Y t1 + A 2 Y t2 + E t ; (3.14) where Y t = Q t ;P t . 13 This model extracts the relationship between price and quantity over time, but in this form, the relationship is endogenous, making causal identication impossible. The trouble is that the innovations in the model, E t , are not \economically meaningful or fundamen- tal," to quote Uhlig (2005). They are simply prediction errors. We need to transform them into fundamental innovations, or structural shocks, U t , BE t = U t ; (3.15) using a matrix, B, that weights the VAR residuals to identify only the fundamental innovations. In our case, for example, we are looking for the response of the variables to demand shocks, which we identify as a simultaneous increase in both price and quantity. We therefore need a matrix B that excludes any impulse vector that does not result in positive responses in the rst period. 14 This type of model is called a \sign-restricted VAR." This approach solves the structural identication problem, but it creates a new problem: \model identication" (Preston 1978). There is no unique matrix B. A set of possible solutions exists, and so we say that sign-restricted VARs are \set-identied." A growing literature has proposed various methods to select the most appropriate impulse response from the set of admissible models. 15 In this chapter, we employ the simplest approach, Uhlig's (2005) rejection method, which begins by jointly drawing the VAR parameters from a Normal-Wishart posterior and an n 1 vector from a uniform distribution over the unit sphere. It then computes the impulse response. If the signs all satisfy the exclusion restrictions, it keeps the draw. If not, it rejects the draw. It repeats this process for as many draws as the researcher desires. In selecting our nal point estimate, we follow the standard approach in the literature and use the median response of each variable from the distribution of remaining draws. 13 The two-lag structure has been chosen because it minimizes the information criteria more often than alternative specications while remaining small enough to allow sucient degrees of freedom in a short time window. 14 After the rst period, there is no reason to maintain the exclusion restriction. We do not want to impose a strong prior that demand shocks persist past the rst response period. Rather, we remain agnostic and let the model play out. 15 See Fry and Pagan (2011), Kilian and Murphy (2012), and Baumeister and Hamilton (2015) for critical reviews. 100 3.4.2 Sign-Restricted VAR(2) Results Our goal is to calculate supply elasticities for each municipality in Los Angeles County using this sign-restricted VAR(2) model. These elasticity estimates can best be understood as a combination of impulse responses. Figure 3.3, for example, shows the impulse response graphs for the core city of Los Angeles. It indicates that a one-standard-deviation demand shock leads to a 0.07% increase in housing units and a 3.29% increase in prices after one year. We dene this one-year response as the short run. After four years, the quantity response has increased to 0.20%, while the price response has stabilized at 4.20%. Consistent with economic theory, it appears that there is a longer lag in production than prices, leading the elasticity to rise in the long run. 16 As a comparison, consider the impulse response graphs for the suburb city of Calabasas in Figure 3.4. Calabasas sits on the periphery of the metropolitan area, where land is cheaper, terrain is atter, and density is lower. All else being equal, economic theory predicts that elasticities should be higher as a result. Consistent with this expectation, the sign-restricted VAR reveals a higher increase in units (0.31%) and a smaller increase in prices (2.50%) in Calabasas than in Los Angeles in the short run. In the long run, Calabasas price growth catches up to Los Angeles, but its quantity growth is nearly three times as high. Equation 3.7 allows us to combine these impulse responses into supply elasticities for each city. Table 3.1 lists the short-run elasticities ranked from highest to lowest. At the top are the cities where the supply curve is the attest|that is, where the market responds to a demand shock more by building housing units and less by increasing prices. These municipalities tend to be some of the furthest suburbs from the center of the metropolitan area. At the bottom are the cities where construction responds very little, if at all, to demand shocks. These municipalities appear mostly to hail from low-income neighborhoods in South Central, a historically segregated and high-crime region. The most general takeaway from this table as a whole is that the estimates are very low. Even in the most elastic city, a one-standard-deviation demand shock never leads to more than a 0.55% increase in housing units. For most cities, the response is less than 0.10%. This nding is consistent with a long literature suggesting that inelastic supply is to blame for high housing costs in California (Quigley and Raphael 2005, Morrow 2013). Table 3.2 lists the long-run elasticities, which are not much higher. In many cases, it appears that prices continue to rise, but quantity still has a very muted response. While there may be a lag in production, there simply appears to be very little construction relative to the pent-up demand. Figure 3.5 plots each city's long-run elasticity against its short-run elasticity. If the short-run elasticity captured the entire response, we would expect all the points to align on the 45-degree line. This is not exactly the case, but the majority of the points are near to it. More cities have higher elasticities in the long run, suggesting that quantity does catch up a bit to prices, but many cities experience the opposite, suggesting that the demand is simply never met and the housing shortage grows over time. 16 Chapter 1 demonstrates this lag with a time-series analysis of the production process, leading from permits to starts to completions. 101 These estimates are so low, in fact, that they suggest that previous literature has signicantly overestimated the price elasticity of supply at a local level. Though no one has attempted to measure this elasticity at a municipal level, the MSA-level estimates are instructive. Green, Malpezzi, and Mayo (2005), one of the early canonical works, regresses the annual change in the housing stock on the lagged rst dierences of housing prices. As we discussed earlier, this methodology suers from endogeneity and therefore lack of interpretable identication. It suggests that Los Angeles had a supply elasticity of 3.73 from 1979 to 1996. Our estimates begin in 1996, but even so, it is unlikely that they decreased so drastically between these time periods as to be in the 0 to 0.2 range. The 3.73 estimate is particularly suspect because it places Los Angeles in the middle third of the national range of elasticities, which does not square with the MSA's high price growth, stringent regulations, and challenging topography relative to the national average. Saiz (2010), the most widely cited recent work, estimates a much lower elasticity for Los Angeles, 0.63, making it the second-most inelastic MSA in the country. These elasticities are indirect measures, however, combining regulatory and geographic constraints rather than directly estimating the slope of the supply curve in response to exogenous demand shocks, as this chapter attempts to do. These low estimates are more consistent with recent econometric work in oil markets, where sign-restricted VARs have been used to identify the response of oil prices and production to supply and demand shocks. This structural approach has led to a consensus estimate for the short-run price elasticity of oil supply between 0 and 0.2, precisely the range identied in this chapter for the short-run price elasticity of housing supply (Kilian and Murphy 2012). It is unlikely that this similarity is mere coincidence, as it is consistent with economic theory in both markets. Producers need time to respond to demand shocks, and once they make a decision, it is costly to reverse. As a result, they tend to respond only to persistent shocks that change expectations about the future (Kilian 2009). It is unlikely, therefore, that the true price elasticity of housing supply is as high as previous estimates have suggested. 3.5 Cross-Sectional Analysis The heterogeneity within the metropolitan area is signicant. Figure 3.6 gives a sense of how much variation is lost in the aggregate. It shows normal and kernel density estimates of these distributions. 17 While there is a high clustering between 0 and 0.05, there is also a long tail to the right, which is not captured by the average or the median. This tail suggests that some cities are increasing supply much faster in response to price signals. In these cities, we may nd lessons to overcome the barriers that stand in the way of housing production and aordability in many metropolitan areas. Why does this heterogeneity exist? To return to our original questions, which cities are the most restrictive and why? Table 3.3 reveals some potential answers. It shows bivariate regressions in the year 2000 with the natural logs of price (median price per square foot from Zillow in 2000), density 17 The kernel density is estimated using the (Epanechnikov 1969) function, which optimizes the mean squared error. 102 (population density from the 2000 Census), population (from the 2000 Census), median household income (from the 2000 Census), and the Wharton Residential Land Use Regulatory Index (Gyourko, Saiz, and Summers 2008). Surprisingly, only two of these factors|which are typically considered to be important determinants of a city's housing supply function|are statistically signicant. More elastic housing supply exists in cities with less density and more income. It is also important to note that the R 2 never exceeds 12% in any of these ve regressions. On their own, none of these factors explains the vast majority of the variation in housing supply elasticity within the metropolitan area. Together, they may account for more, but we must conclude that we still do not understand most of this heterogeneity. We have much to learn about how supply responds dierently to demand in dierent cities. One important factor appears to be location. Figure 3.7 shows a heat map of the short- run elasticities, with darker colors indicating more elastic cities. 18 From this picture, it is clear that housing supply is the most restricted in the city center|and least restricted in the northern periphery. (The southern periphery is valuable coastal land.) It is simply hardest to build in the most desirable locations, where it is already most dense, consistent with the regressions in Table 3.3. It is no wonder, therefore, that Los Angeles is such a sprawled metropolitan area. The core is restricting supply and pushing it out to the periphery. The \location, location, location" adage, it turns out, has some merit. 3.6 Conclusion In this chapter, we document local housing supply elasticity. Our intuition rests on the idea that when land prices rise, developers want to respond by building more intensively. Their ability to do so varies signicantly across municipalities within the metropolitan area. We show signicant heterogeneity in housing unit growth across city borders in Los Angeles County, and we nd that much of this heterogeneity is related to variation in the price elasticity of supply. We compute the rst municipality-level indices of housing supply elasticities that have been constructed to our knowledge. We apply a structural vector autoregression model with sign re- strictions to identify a positive demand shock. Though this model has been successfully applied in other contexts, particularly oil markets, it is an important advance for urban economics, which has traditionally suered from endogeneity bias in its elasticity estimates. Using this sign-restricted VAR, we nd that previous work has overestimated housing supply elasticities. On average, our elasticities are very low|in the 0 to 0.2 range, similar to ndings in oil markets|but there is a long right tail in the distribution, suggesting that several cities are responding to demand with much more elastic supply than others. We conduct a cross-sectional analysis that reveals these elasticities to be mostly unrelated to price, population, or regulations as measured by the Wharton index. Cities with lower density tend to have more elastic supply, as do cities with higher incomes. The most striking nding, however, 18 The lightest color is land for which we do not have any elasticities. 103 is the clustering of elastic cities in locations on the outskirts of the city, far away from the city center and the valuable coastal land. The supply curve is least elastic in the city center, it appears, pushing demand out to the periphery. We demonstrate the importance of structurally identifying shocks to accurately estimate the slope of the supply curve in response to demand shocks|and by extension, the degree to which construction activity can be attributed to dierential supply elasticities that can be con ated with dierences in housing demand based on cities' desirability. We also demonstrate that the aggregate ndings of the past have masked important heterogeneity at the local level. Future research should strive to disentangle this variation across municipalities and to help identify policies that can increase supply elasticity and reduce the burdens associated with the growing housing shortage. It should also extend this approach to other cities and other time periods to document how elasticities vary depending on terrain, regulatory environment, and other institutional factors. Hopefully, this chapter is only beginning as we unravel the more nuanced story that lies at this deeper level. 104 Table 3.1: Short-Run SVAR(2) Elasticities, 1996-2015 City Quantity Response Price Response Elasticity Agoura Hills 0:0055 0:0272 0:202 Hidden Hills 0:0022 0:0158 0:142 Calabasas 0:0031 0:0250 0:124 Claremont 0:0020 0:0185 0:109 West Hollywood 0:0018 0:0187 0:097 Pasadena 0:0017 0:0176 0:096 La Verne 0:0021 0:0248 0:084 Temple City 0:0022 0:0269 0:082 Glendora 0:0016 0:0192 0:082 Santa Monica 0:0015 0:0189 0:081 Azusa 0:0026 0:0323 0:080 Santa Clarita 0:0023 0:0292 0:077 Santa Fe Springs 0:0028 0:0365 0:076 Glendale 0:0017 0:0237 0:070 San Dimas 0:0018 0:0271 0:067 Walnut 0:0015 0:0238 0:064 Monterey Park 0:0011 0:0172 0:063 South El Monte 0:0015 0:0267 0:055 Monrovia 0:0011 0:0201 0:052 Beverly Hills 0:0010 0:0200 0:048 Malibu 0:0005 0:0116 0:047 San Fernando 0:0020 0:0454 0:045 Hermosa Beach 0:0006 0:0146 0:042 El Monte 0:0012 0:0286 0:041 Diamond Bar 0:0008 0:0189 0:040 Redondo Beach 0:0006 0:0158 0:040 San Gabriel 0:0007 0:0173 0:039 La Mirada 0:0008 0:0220 0:038 Burbank 0:0008 0:0216 0:038 Inglewood 0:0011 0:0299 0:036 El Segundo 0:0010 0:0273 0:035 Alhambra 0:0008 0:0228 0:033 South Pasadena 0:0007 0:0224 0:032 Duarte 0:0008 0:0260 0:031 Montebello 0:0008 0:0260 0:030 Gardena 0:0009 0:0288 0:030 Commerce 0:0012 0:0419 0:029 Rancho Palso Verdes 0:0005 0:0191 0:028 Sierra Madre 0:0005 0:0200 0:027 Rolling Hills Estates 0:0005 0:0168 0:027 Torrance 0:0006 0:0239 0:027 Manhattan Beach 0:0005 0:0180 0:027 Palos Verdes Estates 0:0005 0:0171 0:026 Baldwin Park 0:0008 0:0321 0:026 Pomona 0:0008 0:0305 0:026 Rosemead 0:0006 0:0237 0:025 Bell Gardens 0:0008 0:0374 0:022 Los Angeles 0:0007 0:0329 0:021 Covina 0:0007 0:0331 0:020 South Gate 0:0008 0:0425 0:020 Long Beach 0:0005 0:0271 0:019 Carson 0:0005 0:0267 0:018 San Marino 0:0003 0:0205 0:016 Artesia 0:0005 0:0363 0:015 Hawaiian Gardens 0:0007 0:0448 0:015 La Canada Flintridge 0:0003 0:0226 0:014 Lynwood 0:0006 0:0432 0:013 Lawndale 0:0004 0:0284 0:013 Norwalk 0:0004 0:0338 0:012 Culver City 0:0002 0:0174 0:012 Avalon 0:0004 0:0441 0:009 Bell ower 0:0003 0:0332 0:009 Whittier 0:0002 0:0237 0:008 Paramount 0:0002 0:0247 0:007 Downey 0:0002 0:0371 0:006 Notes: One-year impulse responses to sign-restricted VAR of one-standard-deviation positive demand shocks, divided to calculate price elasticity of supply, for all available municipalities in Los Angeles County. 105 Table 3.2: Long-Run SVAR(2) Elasticities, 1996-2015 City Quantity Response Price Response Elasticity Hermosa Beach 0:0009 0:0038 0:245 Claremont 0:0024 0:0111 0:218 La Mirada 0:0020 0:0129 0:152 Diamond Bar 0:0010 0:0068 0:143 Temple City 0:0066 0:0467 0:140 Calabasas 0:0058 0:0429 0:135 Hidden Hills 0:0032 0:0238 0:133 Redondo Beach 0:0019 0:0160 0:117 Agoura Hills 0:0055 0:0487 0:113 La Verne 0:0029 0:0317 0:090 Santa Fe Springs 0:0056 0:0644 0:087 Pasadena 0:0036 0:0451 0:081 Pomona 0:0012 0:0155 0:080 South El Monte 0:0028 0:0363 0:078 West Hollywood 0:0078 0:1027 0:076 Azusa 0:0048 0:0676 0:071 Burbank 0:0026 0:0381 0:069 Torrance 0:0017 0:0247 0:067 Commerce 0:0024 0:0367 0:066 Glendale 0:0027 0:0525 0:051 San Gabriel 0:0011 0:0216 0:050 Rosemead 0:0013 0:0265 0:049 San Fernando 0:0041 0:0845 0:049 Los Angeles 0:0020 0:0420 0:047 Manhattan Beach 0:0014 0:0305 0:046 Santa Clarita 0:0019 0:0408 0:046 Sierra Madre 0:0012 0:0266 0:045 El Segundo 0:0017 0:0403 0:042 Glendora 0:0021 0:0498 0:042 Monterey Park 0:0011 0:0287 0:039 Walnut 0:0022 0:0591 0:038 Bell Gardens 0:0018 0:0506 0:036 Santa Monica 0:0020 0:0576 0:035 El Monte 0:0027 0:0762 0:035 South Pasadena 0:0015 0:0460 0:033 Beverly Hills 0:0009 0:0287 0:032 Malibu 0:0003 0:0098 0:030 Hawaiian Gardens 0:0019 0:0652 0:030 Rolling Hills Estates 0:0008 0:0279 0:028 Palos Verdes Estates 0:0007 0:0249 0:027 San Dimas 0:0014 0:0548 0:026 Inglewood 0:0013 0:0565 0:024 La Canada Flintridge 0:0009 0:0398 0:023 Artesia 0:0015 0:0692 0:022 Gardena 0:0009 0:0418 0:022 Lawndale 0:0005 0:0255 0:021 Long Beach 0:0010 0:0521 0:020 Rancho Palso Verdes 0:0003 0:0162 0:020 Covina 0:0011 0:0563 0:020 Lynwood 0:0008 0:0437 0:019 South Gate 0:0012 0:0657 0:019 Carson 0:0005 0:0335 0:016 Baldwin Park 0:0011 0:0681 0:016 Monrovia 0:0006 0:0445 0:014 Whittier 0:0010 0:0740 0:013 Bell ower 0:0007 0:0546 0:013 Montebello 0:0004 0:0352 0:013 San Marino 0:0008 0:0633 0:012 Downey 0:0006 0:0549 0:012 Norwalk 0:0003 0:0442 0:007 Avalon 0:0003 0:0461 0:007 Alhambra 0:0005 0:0708 0:006 Duarte 0:0002 0:0422 0:006 Culver City 0:0001 0:0319 0:003 Paramount 0:0000 0:0487 0:001 Notes: Four-year impulse responses to sign-restricted VAR of one-standard-deviation positive demand shocks, divided to calculate price elasticity of supply, for all available municipalities in Los Angeles County. 106 Table 3.3: Cross-Sectional Analysis of Short-Run Supply Elasticities in LA County (1) (2) (3) (4) (5) ln(Price) 0:0135 (1:03) ln(Density) 0:0180 (3:19) ln(Population) 0:0063 (1:54) Income 0:0302 (2:82) WRLURI 0:0154 (1:47) Observations 65 65 65 65 25 R 2 0:0167 0:1389 0:0365 0:1124 0:0864 p-value 0:3050 0:0022 0:1275 0:0063 0:1538 Notes: OLS regressions of housing supply elasticities on city-level variables. t statistics in parentheses. Income, density, population, and income collected by Census Bureau and geocoded by GeoLytics. t-statistics in parentheses: p< 0:05, p< 0:01, p< 0:001 107 Figure 3.1: Municipal Housing Unit Growth in Los Angeles County, 2000-2012 Notes: Percentage growth in number of housing units by municipality in Los Angeles County. Original housing unit data obtained from 2000 Census. Growth rates calculated using annual building permit data from U.S. Census Bureau. 108 Figure 3.2: Los Angeles County Permits vs. Prices, 1988-2012 0 5000 10000 15000 20000 25000 0 100000 200000 300000 400000 500000 600000 700000 800000 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Median SF Home Price Mean SF Home Price Single-Family Permits (a) Single-Family Homes 50 100 150 200 250 300 350 400 450 0 10000 20000 30000 40000 50000 60000 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 All Residential Permits Median Price/SqFt Mean Price/SqFt (b) All Residential Notes: Permits on left axis; prices in US dollars ($) on right axis, calculated using transaction-level data from DataQuick to estimate further back in time than Zillow will allow. These are not the prices used in the rest of the chapter. 109 Figure 3.3: SVAR Impulse Responses: City of Los Angeles 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 Quantity 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.00 0.02 0.04 0.06 0.08 0.10 Price Impulse response to one-standard-deviation positive demand shock using sign-restricted VAR(2) model for city of Los Angeles. Units are rough percentages because all variables are estimated using natural logs. Each period equals one year. Estimated using Uhlig's (2005) rejection method. Original housing unit data obtained from 2000 Census. Annual growth calculated using building permit data from U.S. Census Bureau. Price data obtained from Zillow. 110 Figure 3.4: SVAR Impulse Responses: City of Calabasas 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.002 0.004 0.006 0.008 0.010 0.012 Quantity 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.02 0.04 0.06 0.08 Price Notes: Impulse response to one-standard-deviation positive demand shock using sign-restricted VAR(2) model for city of Calabasas. Units are rough percentages because all variables are estimated using natural logs. Each period equals one year. Estimated using Uhlig's (2005) rejection method. Original housing unit data obtained from 2000 Census. Annual growth calculated using building permit data from U.S. Census Bureau. Price data obtained from Zillow. 111 Figure 3.5: Long-Run vs. Short-Run Elasticity by City, 1996-2015 0 .05 .1 .15 .2 .25 Long-Run Elasticity 0 .05 .1 .15 .2 Short-Run Elasticity Notes: Elasticities calculated using impulse responses from sign-restricted VAR(2) model for each city in Los Angeles County. \Short-run" = 1 year. \Long-run" = 4 years. 45-degree line shows where cities would be if their elasticities did not change over time. Original housing unit data obtained from 2000 Census. Annual growth calculated using building permit data from U.S. Census Bureau. Price data obtained from Zillow. Figure 3.6: Municipal Housing Supply Elasticity Distributions in Los Angeles County, 1996-2015 0 5 10 15 Density 0 .05 .1 .15 .2 Elasticity Kernel density estimate Normal density kernel = epanechnikov, bandwidth = 0.0123 (a) Short Run 0 5 10 15 Density 0 .05 .1 .15 .2 .25 Elasticity Kernel density estimate Normal density kernel = epanechnikov, bandwidth = 0.0141 (b) Long Run Notes: Elasticities calculated using impulse responses from sign-restricted VAR(2) model for each city in Los Angeles County. \Short-run" = 1 year. \Long-run" = 4 years. Original housing unit data obtained from 2000 Census. Annual growth calculated using building permit data from U.S. Census Bureau. Price data obtained from Zillow. 112 Figure 3.7: Municipal Housing Supply Elasticities in Los Angeles County, 1996-2015 Legend Export_Output Elasticity 0.000000 0.000001 - 0.015000 0.015001 - 0.020000 0.020001 - 0.021000 0.021001 - 0.027000 0.027001 - 0.039000 0.039001 - 0.040000 0.040001 - 0.055000 0.055001 - 0.081000 0.081001 - 0.202000 Notes: Short-run (one-year) elasticities calculated using impulse responses from sign-restricted VAR(2) model for each city in Los Angeles County. Original housing unit data obtained from 2000 Census. Annual growth calculated using building permit data from U.S. Census Bureau. Price data obtained from Zillow. Heat map colors divided by decile. 113 Appendix A Robustness Tests for VAR/VEC Lag Structure A.1 Selection-Order Criteria for VAR Models We want to compare these models on equal footing. That will require the same lag structure for each one. Therefore, the goal here is not to nd the best number of lags for a given geography individually, but rather to nd the number of lags that is best on average. The table below reports Akaike's information criterion (AIC), Schwarz's Bayesian information criterion (SBIC), and the Hannan and Quinn information criterion (HQIC). A lag of two minimizes them most often. 114 (1) (2) (3) (4) (5) US Midwest Northeast South West AIC Lag = 0 39:55 30:36 26:90 35:65 30:22 Lag = 1 33:88 25:85 22:88 29:94 26:31 Lag = 2 33:48 25:28 22:44 29:83 26:21 Lag = 3 33:74 25:11 22:41 29:99 26:42 Lag = 4 33:68 25:24 22:62 29:95 26:36 Lag = 5 33:82 25:20 22:67 30:06 26:35 Lag = 6 33:83 24:63 22:58 29:79 26:36 SBIC Lag = 0 39:60 30:41 26:94 35:69 30:26 Lag = 1 34:06 26:04 23:06 30:12 26:49 Lag = 2 33:80 25:59 23:30 30:14 26:53 Lag = 3 34:19 25:57 22:86 30:44 26:87 Lag = 4 34:27 25:83 23:21 30:54 26:96 Lag = 5 34:55 25:93 23:40 30:79 27:08 Lag = 6 34:70 25:49 23:44 30:65 27:23 HQIC Lag = 0 39:68 30:49 27:02 35:77 30:34 Lag = 1 34:38 26:35 23:37 30:44 26:81 Lag = 2 34:35 26:15 23:30 30:69 27:08 Lag = 3 34:98 26:35 23:65 31:23 27:66 Lag = 4 35:29 26:85 24:23 31:56 27:98 Lag = 5 35:81 27:19 24:66 32:05 28:33 Lag = 6 36:19 26:99 24:94 32:15 28:72 minimizes information criterion 115 A.2 Eigenvalue Stability Condition for VAR and VEC Models The gures below graph the eigenvalues for each VAR model. Each eigenvalue is inside the unit circle. Every model satises the stability condition. Annual VAR(2) Models -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix 116 Monthly VAR(4) Models -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real Roots of the companion matrix The gures below graph the eigenvalues for each VEC model. With three endogenous variables and one cointegrating vector, there should be two unit moduli in the companion matrix. The others should be inside the unit circle, as we observe here. Every model satises the stability condition. 117 Annual VEC Models of Rank One with Two Lags -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real The VECM specification imposes 2 unit moduli Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real The VECM specification imposes 2 unit moduli Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real The VECM specification imposes 2 unit moduli Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real The VECM specification imposes 2 unit moduli Roots of the companion matrix -1 -.5 0 .5 1 Imaginary -1 -.5 0 .5 1 Real The VECM specification imposes 2 unit moduli Roots of the companion matrix 118 Appendix B Robustness Tests for Unconditional Quantile Regressions B.1 National GDP vs. State GDP In our preferred specications, we use the lagged natural log of national gross domestic product (GDP) for the United States because we wish to control for macroeconomic shifts that can aect the supply and demand of credit markets overall. However, it is possible that some of these shifts are specic to California, where our data are contained. It is the largest state in the U.S. and therefore has a large economy that does not move in exact parallel with national trends, though there is a very high correlation over time. As a result, it is worth estimating our unconditional quantile regressions using state GDP instead of national GDP as a control variable. This \gross state product" is available from 1963 to 2016 from the State of California Department of Finance. 1 Substituting the lagged natural log of this variable into the matrix of controls X in Equations 2.22 and 2.23 yields the results in Figure B.1. These graphs are very similar to the original estimates in Figures 2.14 and 2.16. The monetary results are slightly positive for the bottom of the distribution, but the rest of the shapes are identical. Controlling for state GDP does not change the story at all. Our ndings are robust to this control variables. B.2 County vs. Tract Fixed Eects Mian and Su (2009) show how metropolitan area averages can mask signicant heterogeneity at the local level. It is possible that our county xed eects are not suciently accounting for this heterogeneity. If supply and demand is being suciently in uenced by more local factors, they can confound our estimates. As a result, it is worth estimating the unconditional quantile regression for credit supply with xed eects at a smaller level of geography. Mian and Su use ZIP codes, 1 Seehttp://www.dof.ca.gov/Forecasting/Economics/Indicators/Gross_State_Product/ for all such datasets. 119 but we can go even more local to Census tracts. Figure B.2 shows the results of Equation 2.23 with Census tract xed eects. Again, the ndings are robust to this change. Not only does the shape of the curve remain the same, but the point estimates are even more accurate, with smaller standard errors than Figure 2.16 shows for the estimates with county xed eects. 120 Figure B.1: Unconditional Quantile Partial Eects, Controlling for State GDP 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution (a) Monetary Policy 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution (b) Credit Supply Notes: Coecients for RIF-OLS regressions at each quantile of the housing price distribution at 5% increments from the 10th percentile to the 90th percentile. Repeating Equations 2.22 and 2.23 with state GDP instead of national GDP as control. Data covers single-family home transaction prices in California from 1970 to 2015. Obtained through private restricted-use agreement with Zillow. Bootstrapped standard errors are calculated with 50 repetitions. 121 Figure B.2: Eect of Loan Volume on Housing Price Distribution with Tract Fixed Eects 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Unconditional Quantile Partial Effect Quantile of Housing Price Distribution Notes: Coecients for RIF-OLS regressions at each quantile of the housing price distribution at 5% increments from the 10th percentile to the 90th percentile. Estimated with annual HMDA loan value and controls for omitted variable bias: E RIF q (lnp i;t )j lnL t1 ;X i;t = lnL t1 +X 0 i;t . Data covers single-family home transaction prices in California from 1990 to 2015. Obtained through private restricted-use agreement with Zillow. Bootstrapped standard errors are calculated with 50 repetitions. 122 Bibliography Acolin, A., J. Bricker, P. Calem, and S. 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Abstract (if available)

Abstract People are moving back into the cities. It's an urban renaissance, and housing is not being built fast enough. This dissertation explores where it is being built, how to predict construction activity with early development indicators, what is holding it back in tight markets, how local regulations drive the choice of where to build, and how different homes across the distribution are affected by economic factors suggested by theory. ❧ Chapter One begins at the macroeconomic level with a dynamic time-series analysis of the housing production process. It breaks this process down to the three stages at which we have national and regional data: building permits, housing starts, and completed units. It shows how cointegrated these three series are and how well they can be used to predict future production. It reveals how this relationship differs across time and space, how it can be used to improve estimates of housing supply for different research purposes, and how it helps to forecast recessions, thus tying risks in real estate markets directly to the macroeconomy as forecasters failed to do in the run-up to the Great Recession. ❧ Chapter Two unpacks these macroeconomic changes across the housing distribution. It identifies the effect of two financial shocks that have been blamed for the recent “housing bubble”—monetary policy and credit supply—on the entire unconditional distribution of housing prices in California using transaction-level data from 1970 to 2016. It finds that unexpected increases in the federal funds rate lead to increases in home prices for most of the distribution, with higher increases for higher-priced homes, widening the dispersion in the home price distribution. This evidence supports new macroeconomic theories arguing that the positive psychological signal of tight monetary policy can outweigh the negative financial effect on the ability to borrow, except for the most constrained households at the bottom of the distribution where there is some evidence of a decrease in home prices. This chapter also finds that increases in mortgage lending volume lead to increases in home prices for the entire distribution, but the percentage increase is greatest for mid-priced homes. Importantly, however, the dynamic changes during the 2000-2006 “bubble” period, when low-priced homes experience the biggest boost from mortgage lending, shedding new light in the debate in the literature about which households were borrowing the most and driving the unsustainable price appreciation. ❧ Chapter Three drills down to the local level, where homebuilding actually occurs and is regulated, to create the first city-level index of housing supply elasticities. It estimates the effect of a positive demand shock—identified as a simultaneous increase in prices and quantities in a vector autoregressive system of equations—on prices and quantities over time to reveal how the supply curve responds. The resulting elasticities are very low—in the 0 to 0.2 range—consistent with similar estimates in other markets where investments are large, lumpy, and costly to reverse. They suggest that previous research significantly overestimated the slope of the housing supply curve, partly due to less accurate data and partly because of endogeneity bias. This research improves on both dimensions. It shows that elasticities vary greatly across the metropolitan area, with less elastic housing supply in higher-density, lower-income municipalities located in the core, pushing construction activity out to the periphery. These findings are striking new evidence of urban sprawl resulting in longer commute times, less agglomeration, and suboptimal allocation of housing. ❧ Taken together, these chapters give a rich new portrait of real economic risks in real estate markets that can be forecast with a high degree of accuracy, investment returns at different quantiles of the housing price distribution that can be driven by credit market shocks, and the spatial pattern of local regulations that can be implied from housing supply elasticities.

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Asset Metadata

Creator Orlando, Anthony W. (author)

Core Title Risks, returns, and regulations in real estate markets

School School of Policy, Planning and Development

Degree Doctor of Philosophy

Degree Program Public Policy and Management

Publication Date 04/10/2018

Defense Date 02/05/2018

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

Tag credit market,credit supply,Forecasting,housing affordability,housing prices,housing production,housing supply,monetary policy,mortgage lending,OAI-PMH Harvest,quantile regression,Real estate,recentered influence function,recessions,supply elasticity,time series,vector autoregression

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Bostic, Raphael W. (committee chair), Bento, Antonio M. (committee member), Redfearn, Christian L. (committee member)

Creator Email anthony.w.orlando@gmail.com,aorlando@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-9945

Unique identifier UC11670528

Identifier etd-OrlandoAnt-6204.pdf (filename),usctheses-c89-9945 (legacy record id)

Legacy Identifier etd-OrlandoAnt-6204.pdf

Dmrecord 9945

Document Type Dissertation

Rights Orlando, Anthony W.

Type texts

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

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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