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Essays on corporate leasing Zhang, Na 2012

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Essays on Corporate Leasing by Na Zhang B.Sc., Fudan University, 2003 MCom(Hons), The University of New South Wales, 2006 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Economics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) December 2012 c
 Na Zhang 2012 Abstract Leasing is one of the most important sources of external nance to corporate rms. Better understanding of the determinants of corporate leasing behav- ior is critical for us to study the capital structure and investment of rms. However, it has been overlooked in the theoretical and empirical literature on investment. This thesis studies the determinants of corporate leasing. Each chapter presents a separate essay. The rst chapter studies the role of uncertainty and nancial constraint in understanding rms' leasing decisions. Although leasing costs more than owning capital in the long run, it provides operational 
exibility for rms. In addition, leases are easier to nance than purchases. The benets of leasing are particularly attractive to rms with high uncertainty and more nancial constraints. This chapter develops a dynamic model and predicts that rms with high uncertainty and rms that are more nancially constrained lease more of their capital than rms with low uncertainty and rms that are less nancially constrained. Using data on publicly-traded rms in the U.S., this chapter provides evidence consistent with the prediction of the model. The second chapter documents that leasing is countercyclical over busi- ness cycles. Firms lease more during economic downturns, and are more willing to buy capital during up cycles. One key benet of leasing is that leases are easier to nance than purchases. This benet is particularly im- portant to rms with nancial constraints. Firms face tighter nancing conditions during recessions. Therefore, leasing is more attractive during recessions. This chapter develops a model to explain the observed counter- cyclical pattern of leasing. The third chapter utilizes data from 81 countries to examine how legal environments aect rms' leasing behavior. The results suggest that leasing ii is less used in countries with weak legal environments. Firms in countries with weak legal environments tend to avoid the use of leasing contracts because the contracts are costly to enforce. I also nd that leasing has a measurable impact on both rm growth and GDP growth. Leasing can help increase capital availability and improve operational eciency, and thus may contribute to growth. The results provide a policy implication that possible adjustments in legal systems can facilitate the availability of leasing and thus may generate real economics gains. iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 1 Leasing, Uncertainty, and Financial Constraint . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 The Environment . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Benchmark Economy: No Frictions and No Financial Constraint . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.3 An Economy with Frictions but No Financial Con- straint . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.4 An Economy with Frictions and Financial Constraint 14 1.3 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3.2 The Measure of Leasing . . . . . . . . . . . . . . . . . 18 1.3.3 The Measure of Uncertainty . . . . . . . . . . . . . . 19 1.3.4 The Measure of Financial Constraint . . . . . . . . . 20 1.3.5 Summary Statistics . . . . . . . . . . . . . . . . . . . 22 iv 1.3.6 Regressions . . . . . . . . . . . . . . . . . . . . . . . . 28 1.3.7 Indirect Evidence . . . . . . . . . . . . . . . . . . . . 35 1.4 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . 35 1.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 37 2 Leasing and Business Cycles . . . . . . . . . . . . . . . . . . . 41 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . 45 2.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.2.2 The Measure of Leasing . . . . . . . . . . . . . . . . . 46 2.2.3 Sample Statistics . . . . . . . . . . . . . . . . . . . . 47 2.2.4 Correlation Results . . . . . . . . . . . . . . . . . . . 48 2.2.5 Panel Regressions . . . . . . . . . . . . . . . . . . . . 51 2.2.6 Distribution . . . . . . . . . . . . . . . . . . . . . . . 54 2.2.7 Why Leasing is Countercyclical . . . . . . . . . . . . 54 2.3 Financial Constraint, Leasing versus Secured Borrowing . . . 56 2.3.1 The Environment . . . . . . . . . . . . . . . . . . . . 56 2.3.2 The Agent's Problem . . . . . . . . . . . . . . . . . . 57 2.3.3 Lessor's Problem . . . . . . . . . . . . . . . . . . . . . 58 2.3.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 59 2.3.5 Characterization . . . . . . . . . . . . . . . . . . . . . 60 2.3.6 A Temporary Increase in Aggregate Productivity . . 61 2.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 63 3 Leasing, Legal Environments, and Growth: Evidence from 81 countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3 Data and Measurements . . . . . . . . . . . . . . . . . . . . 69 3.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.2 The Measure of Leasing . . . . . . . . . . . . . . . . . 70 3.3.3 Measures of Legal Environments . . . . . . . . . . . . 70 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 v 3.4.1 Summary Statistics . . . . . . . . . . . . . . . . . . . 72 3.4.2 Leasing and Legal Environments . . . . . . . . . . . . 75 3.4.3 The Eect of Leasing on Growth . . . . . . . . . . . . 83 3.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 85 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Appendices A Appendix to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . 92 B Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . 99 C Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . 103 vi List of Tables 1.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . 23 1.2 Sample Correlations . . . . . . . . . . . . . . . . . . . . . . . 23 1.3 Summary Statistics of Dierent Groups . . . . . . . . . . . . 24 1.4 Lease Share Distribution Tests . . . . . . . . . . . . . . . . . 27 1.5 Results of the OLS Regressions . . . . . . . . . . . . . . . . . 30 1.6 Results of the Tobit Regressions . . . . . . . . . . . . . . . . 33 1.7 Robustness Check using the KZ Index . . . . . . . . . . . . . 34 1.8 Results of Some Selected Cross Sectional Regressions . . . . . 34 1.9 Calibration and Simulation . . . . . . . . . . . . . . . . . . . 38 2.1 Lease Share of Total Capital Costs . . . . . . . . . . . . . . . 48 2.2 Cyclical Behavior of the Lease Share . . . . . . . . . . . . . . 49 2.3 Panel Regression Results for the Lease Share . . . . . . . . . 53 2.4 Results of a Numerical Example . . . . . . . . . . . . . . . . 63 3.1 Correlations between Measures of Legal Environments . . . . 72 3.2 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . 74 3.3 Leasing and Legal Environments . . . . . . . . . . . . . . . . 80 3.4 Leasing and Country Growth Rates . . . . . . . . . . . . . . . 85 C.1 Summary Statistics by Country . . . . . . . . . . . . . . . . . 104 vii List of Figures 1.1 Percentage of Leased Capital as a Function of the Uncertainty and the Financial Constraint . . . . . . . . . . . . . . . . . . 13 1.2 Average Lease Shares at Dierent Levels of Uncertainty and Financial Constraints over Time . . . . . . . . . . . . . . . . 25 1.3 The Cumulative Distribution of the Lease Share across Dif- ferent Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1 Financial Conditions . . . . . . . . . . . . . . . . . . . . . . . 43 2.2 Cyclical Behavior of Lease Share . . . . . . . . . . . . . . . . 50 2.3 Distributions of Lease Share . . . . . . . . . . . . . . . . . . . 55 3.1 Leasing and GDP per Capita . . . . . . . . . . . . . . . . . . 73 3.2 Leasing and the Rule of Law . . . . . . . . . . . . . . . . . . 76 3.3 Leasing and Legal Rights . . . . . . . . . . . . . . . . . . . . 77 3.4 Leasing and Economic Freedom . . . . . . . . . . . . . . . . . 78 viii Acknowledgements I would like to express my deep and sincere gratitude to my committee members, Dr. Michael B. Devereux who is my supervisor, and who gave me deep insight into the problems and thus improving the quality of this work in all stages; Dr. Viktoria Hnatkovska who provided me invaluable guidance and persistent encouragement; and Dr. Amartya Lahiri who gave me detailed instruction and helpful comments. I would also like to thank all the faculties and stas in the department of Economics at the University of British Columbia for their sound advices, sustained encouragements, and so many good suggestions. Thank you to all my Ph.D. colleagues, who had a signicant impact on my life both profes- sionally and personally. Many thanks to Dr. Xiongwen Lu at Fudan University, Dr. Garry Barret at the University of Sydney and Dr. Bill Schworm at the University of New South Wales. Without their help, I would have never begun the Ph.D. program. I cannot thank them enough for their support and inspiration. Lastly, and most importantly, I wish to thank my family. My parents raised me, supported me, taught me, and loved me. I could not have pulled o this thesis without the help from my parents-in-law, who helped me take care of my daughter. My husband has always been and continued to be a strong foundation for me. The most important thing that happens during my Ph.D. study is the birth of my daughter Vera. She has brought so much love and happiness to my life. To them I dedicate this thesis. ix Dedication To my parents, Yueying Tian and Shixiao Zhang; to my husband Yixiang; and to my lovely daughter Vera x Chapter 1 Leasing, Uncertainty, and Financial Constraint 1.1 Introduction A lease is an agreement between two parties, the lessor and the lessee. Un- der a lease contract, the lessee pays rental fee and acquires the right to use the asset for a specied period of time, but the asset belongs to the lessor. As a source of external nancing, leasing is comparable to long-term debt. Better understanding of the determinants of corporate leasing behavior is therefore critical for us to study the capital structure and investment of rm- s. According to the Compustat data1, 99.8 percent of publicly-traded rms in the U.S. indicate their usage of operating lease2, whereas 82.8 percent of rms have long-term debt. In addition, operating lease accounts for 7.5 percent of rms' total assets, and the value of long-term debt equals 11.7 1The sample consists of 98,557 observations for rms on Compustat over the period of 1975 through 2009. Foreign incorporated companies and a few industries are excluded. Details of the data are in Section 1.3.1 2For nancial accounting purposes, a lease is classied either as an operating lease or a capital lease. A lease is treated as an capital lease if it meets any one of the following four conditions - (1) if the lease life exceeds 75% of the life of the asset; (2) if the lease transfers the ownership of the asset to the lessee at the end of the lease term; (3) if the lease contains a bargain purchase option; (4) if the present discounted value of the required lease payments exceeds 90% of the fair market value of the asset. Otherwise, it is an operating lease. Capital lease is reported as the corresponding debt obligation on balance sheet. In contrast, operating lease represents o-balance-sheet nancing for the lessee, and is re
ected on the income statement as rent expense. Capital lease is more like a secured debt. Hence, this work focuses on operating lease. All advantages and disadvantages of a lease discussed in this work only apply to an operating lease. 1 percent3. An average publicly-traded rm in the U.S. leases more than 37 percent of its capital. For small rms that are not publicly traded, leasing is even more important. Eisfeldt and Rampini (2009) use micro data from the 1992 U.S. Census of Manufactures and show that the smallest decile rms lease 46 percent of their capital. They claim that leasing may be the largest source of external nance for these small rms. Leasing is not only a key component of a corporate rm's external nancing, but also of particular importance in understanding the capital investment decisions of corporate rms. Given its quantitative importance, this chapter studies the role of uncertainty and nancial constraint in understanding the leasing decisions of corporate rms. A lease provides operational 
exibility in terms of adjusting to changes of technology and capacity; this is because the redeployment of leased capital is easier than that of owned capital. Generally, the lessor has a comparative advantage in disposing assets4. Consequently, the adjustment costs on leased capital are lower than those on owned capital. The low adjustment cost is valuable when future prots are uncertain, because rms are more likely to adjust their capital. Moreover, from the perspective of lessors, in the U.S. bankruptcy code, it is much easier for a lessor to repossess an asset than it is for a secured lender. The lessor is less concerned with the lessee's default, and thus is unlikely to require the lessee to provide collateral to be able to start a leasing agreement. The lessee only needs to pay a leasing fee for one period in advance. But on the other hand, if a rm purchases capital, they would need to pay the full price up front. Even if a rm uses debt to nance their purchase, the lender might require collateral for the loans. Therefore, these factors indicate that leases are easier to nance than 3Measures are from Graham et al. (1998). They report similar results that 99.9 percent of the rm-years report nonzero levels of operating leases, and 88 percent have nonzero levels of long-term debt in 1981-1992 Compustat data. They nd that operating leases and long term debt are 8 percent and 14.2 percent of rm value respectively. 4Lewellen et al. (1976) state: \The lessor may be more active or skillful in dealing the associated second-hand asset market; his specialized knowledge may give him an edge." The potential advantage is from the reduction in search, information, and trans- action costs associated with the lessor's provision of a centralized marketplace for the asset(Benston and Smith (1976)). 2 purchases. Besides operational 
exibility and easiness in nancing, leasing usually costs more in the long run. This is because that leasing involves a separation of ownership and control, which induces an agency cost. The lessee loses the residual value of the asset at the end of the lease term, because he doesn't own the asset. That is, the lessee has less incentive to care for the asset since the lessor bears the full cost. The abusive use of the asset by the lessee is anticipated by the lessor. The lessor therefore usually charges high fees to make the total cost greater than the purchase cost of the asset5. The benets of leasing in terms of its lower adjustment costs and easiness to nance has to be weighed against the higher cost due to the agency prob- lem. This is the basic tradeo that determines whether it is advantageous to lease or buy6. Firms facing high uncertainty about their future prots might adjust their capital more frequently, and hence, value the benet of lower adjustment cost. These rms are therefore more willing to lease capital. Moreover, the benet of easiness to nance makes leasing more attractive to those nancially constrained rms who have diculties in nancing their purchase on capital. This chapter develops a dynamic model which implies that the decision to lease versus buy depends on rms' uncertainty and nancial constraints. The model has four key factors: (1) Firms have heterogeneous stochastic protability; (2) Capital can be bought or leased; (3) Firms face nancing friction; (4) Firms incur transaction costs when selling owned capital. The model predicts that rms facing high uncertainty and rms with greater nancial constraints prefer to lease more of their capital than those with low uncertainty and those with less nancial constraints. This chapter also provides empirical evidence using a rm level panel data set of publicly-traded companies in the U.S.. I measure the fraction of capital from leasing (the lease share) as a ratio of the rental expense to 5Gavazza (2010) estimates the lease rates are on average 20 percent higher than implicit rental rates on owned assets in the aircraft industry 6Tax benets may be another reason for leasing. Leases allow for the transfer of tax shields from lessees to lessors. 3 the total cash expenditures on rent and investment; also, I measure uncer- tainty as the volatility of the rms' equity returns. Financial constraint is measured by an index which combines the information of cash 
ow, debt, rm size and rm age. I nd that rms with high uncertainty and rms with more nancial constraints have a larger lease share than rms with low uncertainty and rms with less nancial constraints on average. The distributions of the lease shares of rms with high uncertainty and rms with more nancial constraints rst order stochastic dominate the distribu- tions of rms with low uncertainty and rms with less nancial constraints. Results from panel regressions indicate that uncertainty and nancial con- straint are signicantly positively related to leasing. Approximately, a one standard deviation increase in uncertainty and the nancial constraint index increases a rm's lease share by 3.5 percent and 9 percent respectively; these eects are economically signicant. Moreover, the countercyclical pattern of leasing over business cycle also provides an indirect evidence. When rms face high uncertainty and tight nancing conditions during recessions, they lease more. There is an extensive literature in nance examining the corporate deci- sions to lease, but the main focus of the literature is tax considerations. The corporate lease-versus-buy decision is typically analyzed under the Miller- Modigliani framework with no transaction costs or information asymmetries. Firms are indierent about choosing between leasing and purchasing except in situations in which they face dierent tax rates (e.g., Miller and Upton (1976), Myers et al. (1976)). Low tax rate rms lease more than high tax rate rms. However, the economics of leasing are recognized beyond tax minimization. Smith and Wakeman (1985) provide an informal list of non tax characteristics of users and lessors that in
uence the leasing decision. Following Smith and Wakeman (1985), several papers have focused on the non tax aspects of leasing. Krishnan and Moyer (1994) examine the use of capital leases and nd that rms with lower retained earnings, higher growth rates, lower coverage ratios, higher debt ratios, higher operating risks and higher bankruptcy potential are more likely to lease. Sharpe and Nguyen (1995) empirically show that the lease share is higher at lower-rated, non- 4 dividend-paying, cash poor rms, which are more likely to face relatively high premiums for external funds. Gavazza (2010) uses data from the com- mercial aircraft industry and nds that more liquid assets make leasing more likely, have shorter operating leases, longer capital leases, and lower markups of operating lease rates. Particularly related to this work are Eisfeldt and Rampini (2009) and Gavazza (2011). This work is not the rst attempt at addressing the re- lationship between leasing and nancial constraints. Eisfeldt and Rampini (2009) incorporate nancial constraints into a model of the choice between leasing and secured lending. Their model also implies that more nancial- ly constrained rms lease more of their capital than less constrained rms. However, my work further considers uncertainty, which is a critical factor in rms' leasing decisions. Gavazza (2011) studies the role of leasing when trading is subject to frictions, and nds evidence from the commercial air- craft industry that leased assets trade more frequently and produce more output than owned assets. The main focus of his paper is on the eects of leasing on trading and allocation of assets while my research's focus is on rms' incentive to lease. This chapter is also related to many theoretical and empirical papers that studies rms' investment under uncertainty through the role of irreversibil- ity and adjustment costs (e.g., Dixit and Pindyck (1994), Abel and Eberly (1996), Leahy and Whited (1996), Bulan (2005) and Bloom et al. (2007)). High uncertainty raises the value of the option to wait and see and decreas- es investment. However, none of these papers consider the role of leased capital. This work is the rst, to the best of my knowledge, to provide a model and empirical evidence that captures how uncertainty aects rms' leasing decisions. This chapter establishes a link between uncertainty, nancing frictions and leasing decisions, and provides an unique complement to the literature in both nance and macroeconomics. The chapter is organized as follows. The next section lays out the model. Then, Section 3 presents the empirical analysis. Section 4 provides quanti- tative analysis. Concluding remarks are oered in Section 5. 5 1.2 Model 1.2.1 The Environment I consider an economy with discrete time and innite horizon. There is a xed amount of homogeneous capital goods X. For simplicity, capital does not depreciate. Capital can be bought or leased. Owned capital and leased capital are perfect substitutes in the production. There are two types of agents in the economy, producing rms and a nancial intermediary. In this economy, producing rms use owned or leased capital to produce nal goods, and the nancial intermediary supplies loans and leased capital to rms. All agents are risk neutral and discount the future at the interest rate of r > 07. Producing Firms There is a unit mass of producing rms. Firms' output function is specied as y = zk, where z is the productivity, and k is the unit of capital used in the production. We can also interpret the production function as a prot function, and z is the protability. In order to be consistent with the liter- ature, I use the term \productivity" instead of \protability" in the model. Following Gavazza (2011), each rm can only operate at most one unit of capital. Thus, k is either one or zero. The productivity z is distributed in the population according to a distribution function F (z). The productivity follows an independent stochastic process. Each rm receives a new pro- ductivity draw from F (z) at rate   0. The parameter  measures the volatility of a rm's productivity. Hence, I call  an uncertainty measure. All rms are facing the same uncertainty. When  is high, the productivity of rms change very frequently, and the uncertainty is high. At the beginning of each period, each rm observes its productivity in this period and its capital holding position which is inherited from the last period, and then makes the decision on production. Firms can choose among 7Interest rate aects both the cost of purchasing capital and the rental rate of leasing capital. In the model, I assume interest rate is constant and it is given exogenously. But in real world, changes in interest rate may aect rms' leasing versus buying decisions. 6 three options: use owned capital to produce, use leased capital to produce, or not produce. If the rm chooses the option to use owned capital to produce and doesn't own any capital at the beginning of the period, it pays price p to purchase new capital. If the rm doesn't have enough internal fund to nance its purchase, it needs to borrow from the nancial intermediary. If the rm decides to lease capital, it pays the per-period lease rate of u to the lessor. If the rm owns capital at the beginning of the period and chooses to not produce, it sells its owned capital. Owned capital is partially irreversible. There is a trade friction when selling capital. The seller receives a fraction of the price p(1  ), where  2 [0; 1]. At the end of the period, the production is done. The rm gets the output y. Leased capital should return to the lessor. Firms who borrowed from the nancial intermediary pay their debt at interest rate of r and own the capital to the next period. The letter S denotes the state of capital holding position. If a rm owns one unit of capital at the beginning of the period, then S = 1. Otherwise, S = 0. There are two state variables in the model: productivity z and capital holding position S. Let VO(z; S) be the value of a rm with productivity z and capital position S choose to own capital and produce; VL(z; S) be the value of a rm that leases capital to produce, and VN (z; S) be the value of a rm that does not produce. All these values are discounted to the beginning of the period. Firms choose the maximum value among VO(z; S), VL(z; S) and VN (z; S). VO(z; S = 0) = p+ z 1 + r + 1 1 + r VO(z; S = 1) +  1 + r Ex[max(VO(x; S = 1); VL(x; S = 1); VN (x; S = 1))] (1.1) A rm in state (z; S = 0) pays p to buy the capital, and has z unit of output at the end of the period and discounts it to the beginning of the period. Then, the rm holds the capital to the next period (S = 1 for next period). At the beginning of the next period, at the rate of 1  , 7 the rm has the same productivity as the previous period. At rate , the rm receives a new draw of productivity from the distribution, so the rm takes expectation over its optimal future actions. Here x is any possible productivity in the distribution. VO(z; S = 1) = z 1 + r + 1 1 + r VO(z; S = 1) +  1 + r Ex[max(VO(x; S = 1); VL(x; S = 1); VN (x; S = 1)] (1.2) It has similar interpretation as VO(z; S = 0) except that the rm doesn't pay price p to buy new capital, because it already has capital at hand. VL(z; S = 0) = u+ z 1 + r + 1 1 + r VL(z; S = 0) +  1 + r Ex[max(VO(x; S = 0); VL(x; S = 0); VN (x; S = 0))] (1.3) A rm pays the per-period lease rate u to lease capital. The leased capital is returned to the lessor at the end of each period, so the rm doesn't have any capital at the beginning of the next period (S = 0 for the next period). If the productivity doesn't change in the next period, the rm would continue to lease. If the rm receives a new draw of productivity in the next period, the rm takes expectation over its optimal future actions. VL(z; S = 1) =(1 )p u+ z 1 + r + 1 1 + r VL(z; S = 0) +  1 + r Ex[max(VO(x; S = 0); VL(x; S = 0); VN (x; S = 0))] (1.4) A rm sells its owned capital rst and then leases. It earns (1  )p from selling. Actually, it is always not protable to sell capital and then 8 lease to produce (VO(z; S = 1)  VL(z; S = 1) 8z), which is proved in the Appendix. By selling owned capital and then leasing, rms would suer two losses. One is the resale loss, and the other is the high lease rate. Hence, rms that own capital at the beginning of the period would never choose to lease capital; rather, they would only make a decision between using owned capital to produce or selling owned capital to not produce. Only those non- owners at the beginning of the period would make decision between owning and leasing capital. VN (z; S = 0) = 1 1 + r VN (z; S = 0) +  1 + r Ex[max(VO(x; S = 0); VL(x; S = 0); VN (x; S = 0))] (1.5) VN (z; S = 1) =(1 )p+ 1 1 + r VN (z; S = 0) +  1 + r Ex[max(VO(x; S = 0); VL(x; S = 0); VN (x; S = 0))] (1.6) The value functions of not producing are similar to the value functions of leasing. But rms don't pay lease rates and don't produce any output. These value functions of not producing are independent of the current productivity z. All rms have the same value of not producing. The Financial Intermediary In this chapter, I mainly focus on the demand side of leased capital and as- sume the nancial intermediary is the lessor. A competitive lessor maximizes its prot with the equilibrium leasing rate u as given. The lessor provides XL unit of capital to the lessee. I assume that there is no deadweight cost when the lessor repossesses the capital8. And there are no transaction costs 8In the U.S. Bankruptcy law, a lessor has specic advantages over a secured lender in terms of the ability to regain control of an asset. 9 when trading leased capital9. The nancial intermediary is able to sell the capital at the price of p. However, leased capital is subject to an agency problem due to the separation of ownership and control. The lessor has to spend mp on each unit of capital on maintenance after repossessing the cap- ital (Eisfeldt and Rampini (2007); Rampini and Viswanathan (2011)). The lessor's problem is: max XL uXL  pXL + pXL 1 + r  mpXL 1 + r Here XL is the amount of leased capital. The rst-order-condition implies that u = (r +m)p 1 + r (1.7) As long as the maintenance cost is greater than zero, the lease rate u is higher than the implicit rental rate on owned capital which is rp=(1 + r). The lessor makes zero prot in the equilibrium. The nancial intermediary is also a lender. It lends money to rms that wants to buy capital but don't have enough internal funds at the interest rate of r. In the equilibrium, the nancial intermediary is indierent between lending capital or lending money, and it earns zero prots. 1.2.2 Benchmark Economy: No Frictions and No Financial Constraint Before considering the eects of frictions and nancial constraint, this chap- ter analyzes the simple case of no frictions and no nancial constraint. There is no trade friction ( = 0) and no agency cost (m = 0). The economy is a Miller-Modigliani world. Proposition 1 When there are no frictions ( = 0 and m = 0) and no nancial constraint in the economy, rms are indierent between leasing or owning capital. There exists a threshold value z such that rms whose 9The lessor has a comparative advantage in disposing of the asset. As long as transac- tion costs on leased capital are lower than owned capital, we can normalize the transaction cost on leased capital to zero. 10 z  z own or lease capital to produce, and those rms whose z < z don't produce. The threshold value z satises X = 1  F (z). The equilibrium price p satises p = z  r . The proofs of all these propositions are found in the Appendix. In this economy, rms can adjust their owned capital freely without any resale loss. The lessor doesn't charge a higher rental rate because of the lack of an agency cost. Without nancial constraints, rms can always borrow enough to buy capital when they need to do so. Thus, all rms are indierent between leasing or owning. When rms have low productivity, they would choose to not produce. The capital is reallocated to rms with high productivity. In addition, the equilibrium threshold value of z and the price of p are independent of the uncertainty parameter . In a perfect market, uncer- tainty does not aect rms' leasing decision. 1.2.3 An Economy with Frictions but No Financial Constraint In this subsection, I introduce frictions into the model. There is a transaction costs when rms sell their owned capital ( > 0) but no transaction costs on leased capital. The lack of transaction costs on leased capital makes leasing attractive. However, the maintenance cost on leased capital (m > 0) causes the lease rate to be higher than the implicit rental rate on owned capital. Firms trade o the low transaction costs on leased capital and the low implicit rental rates on owned capital. Uncertainty matters in this setup. Firms with high uncertainty are more likely to change their productivity in the future. If the rm receives a high draw of productivity in the future, there is no extra gain or loss from owning capital today. But if the rm receives a low draw of productivity in the future, it will have to sell its owned capital and suer from the resale loss. High uncertainty rms adjust their capital more frequently than low uncertainty rms, thus suer more resale loss if they own capital. Therefore, leasing is particularly attractive to rms facing high uncertainty. 11 Proposition 2 1. The choice between owning and leasing does not de- pend on the productivity z. 2. VO(z; S = 0) VL(z; S = 0) is a decreasing function in . 3. When  is not small, there always exists a threshold uncertainty value  such that rms are indierent between owning and leasing. If  > , all rms prefer to lease if they want to produce. If  < , all rms prefer to own capital. Leased capital and owned capital are perfect substitutes in the production process. They produce the same amount of output. The dierence between owning capital and leasing capital is only related to the expected value of the future. Thus, the choice between owning and leasing does not depend on the current level of productivity. Since rms are the same except their current productivity, all rms would have the same preference on leasing or owning. Figure 1.1 illustrates the choice between leasing and buying as a function of uncertainty in a numerical example. If  is low, rms adjust their capital less frequently, which means that the expected transaction costs from adjusting owned capital is lower than the costs of leasing capital from a high lease rate; hence, owning capital dominates leasing for all rms. When  increases to above the threshold, the expected transaction costs from adjusting owned capital is higher than the costs of leasing capital from high lease rates, as a result, leasing dominates purchasing. Firms facing higher uncertainty have higher incentives to lease. Proposition 3 If the uncertainty  is above the threshold  such that all rms prefer to lease than own, then the equilibrium lease rate u satises X = 1  F ((1 + r)u). Firms whose productivity z is above (1 + r)u would lease capital and produce, and those whose productivity z is below (1 + r)u would not produce. When uncertainty is high, rms would always prefer leasing to owning. If their productivity is higher than the lease rate, they would lease capital to 12 0 . 2 . 4 . 6 . 8 1 Th e P er ce nt ag e of  L ea se d C ap ita l 0 .2 .4 .6 .8 1 Uncertainty (alpha) No financial constraint or theta>=1 theta=3/4 theta=1/2 theta=1/4 theta=0 Figure 1.1: Percentage of Leased Capital as a Function of the Uncertainty  and the Financial Constraint Parameter . Notes: In this numerical example, baseline parameters are X = 0:5; r = 0:03;  = 0:05;m = 0:015;  = 0:5, and z is normally distributed with mean equals to 100 and standard deviation equals to 50. The larger the , the higher level of uncertainty. The smaller the , the higher the degree of nancial constraint. 13 produce. Otherwise, they would choose to not produce. In the equilibrium, all capital are leased, and the fraction of leased capital is one. Proposition 4 If the uncertainty  is below the threshold , all rms would prefer to own capital rather than lease. A non-owner that purchases capital has productivity z  z. A owner that sells capital and does not produce has productivity z < z. And z > z. When uncertainty is low, rms always prefer to own capital than lease. Firms only invest when the condition is suciently good, and only disinvest when it is suciently bad. Transaction costs on owned capital generate an option value of waiting. In the region of inaction, the real-option value of waiting is worth more than the returns from investing and disinvesting. This inaction region is wider if uncertainty  is higher but still below the threshold . This is consistent with the result in Bloom (2009). The Appendix reports all equilibrium conditions of this case. In the equilibrium, all capital are owned, and the fraction of leased capital is zero. 1.2.4 An Economy with Frictions and Financial Constraint Without nancial constraints, the fraction of leased capital in the equilib- rium is either zero or one. In this subsection, I introduce the nancial constraint into the model. The nancial constraint is built in a similar way to that of Jermann and Quadrini (2012). Suppose all producing rms have the same amount of internal fund p. If   1, rms have enough internal fund to buy capital and are not nancially constrained. If  < 1, rms need to borrow (1 )p from the nancial intermediary when they make new purchases. Firms with smaller  are more nancially constrained since they have less internal funds and need to borrow more to nance their purchases. I call  the nancial constraint parameter. Now, the ability to borrow is bounded by the limited enforceability of debt contract as rms can default on their obligations. If rms default, the nancial intermediary acquires the right to liquidate the rm. At the moment of contracting the loan, the liquidation value of the 14 rm is uncertain. With probability 1  , the nancial intermediary can recover the full value of the rm. But with probability , the recovery value is zero. If the nancial intermediary can fully recover the rm, the ex-post value of defaulting for the rm is zero. If the nancial intermediary cannot liquidate the rm, the ex-post value of defaulting for the rm at the end of the period is (1 + r)(VO(z; S = 0) + (1  )p). Hence, the ex-ante value of defaulting is (1 + r)(VO(z; S = 0) + (1 )p). The value of not defaulting is (1 + r)VO(z; S = 0). Financial constraint requires that the value of not defaulting is not smaller than the expected value of defaulting, that is: (1 + r)VO(z; S = 0)  (1 + r)(VO(z; S = 0) + (1 )p) Rearrange the constraint to: 1  VO(z; S = 0)  (1 )p (1.8) Firm would not default if the nancial constraint is satised. The nancial constraint indicates that in order to borrow from the nancial intermediary, the expected liquidation value of the rm should be greater than the loan. Firms with smaller  face tighter nancial constraints. The nancial constraint only works on those rms who don't have capital at the beginning of the period and want to make new purchases. Now, only those rms who satisfy the nancial constraints are able to nance enough funds to buy capital. When the uncertainty is fairly high such that all rms prefer to lease, all capital are leased in the economy; nancial constraints cannot aect the equilibrium. Financial constraints aect the outcome only when the uncertainty is not high such that rms would prefer to own if they can borrow freely. Intuitively, if rms are not constrained at all, they can always buy capital using their internal funds. Firms would never lease and all capital are owned in the economy. On the other hand, if rms are constrained, they need to borrow some money to nance their purchases. Because of the nancial constraints, only rms with very good project are able to borrow while others 15 are not. Then, only those rms with particularly high productivity can nance enough funds to purchase new capital. Those rms who can't borrow but still want to produce have to lease capital. In the equilibrium, both leasing and purchasing coexist. Particularly, when rms are more nancially constrained, they need to borrow more. This causes the nancial constraint to be tighter. The nancial intermediary would lend more carefully and less rms are able to borrow. Thus, more rms have to lease capital to produce. The fraction of leased capital in the equilibrium should be higher when rms are more constrained. The below proposition illustrates the equilibrium outcome when leasing and owning coexist in the economy. Non-owners with high productivity satisfy the nancial constraint and are able to buy capital. Non-owners whose productivity is above the lease rate but does not satisfy the nancial constraint use leased capital to produce. Owners with low productivity would sell their owned capital and not to produce. Proposition 5 Assume uncertainty  is low and nancial constraint pa- rameter  is low such that leased and owned capital can coexist. Then, a rm that purchases a capital has productivity z  z. A rm that leases a capital has productivity z  (1+ r)u and z < z. A rm that sells an owned capital has productivity z < z. And z > (1 + r)u > z. Since only those rms with highest productivity are able to satisfy the constraint, the threshold of buying capital with nancial constraints is higher than the threshold of buying capital without nancial constraints. In ad- dition, the threshold of selling owned capital with nancial constraints is lower than the threshold of selling without nancial constraints. When the productivity is very low, owners want to sell their capital and choose not to produce. However, since there are nancial constraints, they might not able to borrow money to buy new capital in the future if they sell their own capital. So, rms are more hesitant to sell even if they have low productivity. An analytic characterization of how the nancial constraint parameter  aects rms' leasing choices cannot be provided. Their choices depend on the equilibrium price of the capital, which cannot be solved in closed 16 form. Thus, this chapter computes numerical solutions to illustrate rms' choices. The Appendix reports all equilibrium conditions. Figure 1.1 shows the percentage of leased capital in the equilibrium for dierent . Given constant uncertainty, when  decreases, the percentage of leased capital increases. More nancially constrained rms lease more. In this numerical example, even for those rms who don't face any uncertainty ( = 0), if rms need to nance their purchase fully by borrowing ( = 0), some rms have to lease capital because they are very constrained and are not able to get loans from the nancial intermediary. Uncertainty aects the equilibrium outcome the same way as it does in the case without nancial constraints. If nancial conditions are constant, when uncertainty increases, leasing is more attractive because of the trade friction. Figure 1.1 shows that the percentage of leased capital increases monotonically as uncertainty increases. The trade friction on owned capital  and the maintenance cost m also aect the equilibrium outcome. An increase in the trade friction  would shift the graph in Figure 1.1 to the left. When rms nd that it is much more dicult to sell assets in the secondary market, they are more interested in leasing. An increase in the maintenance cost m would shift the graph to the right. High maintenance costs will cause the lease rates to be higher, and make leasing less attractive. Nonetheless, they don't aect the monotonic relationships of uncertainty and nancial conditions on the fraction of leased capital in the economy. The model predicts that uncertainty and nancial constraints are impor- tant factors that aect the lease-or-buy decision. The lease ratio increases monotonically as uncertainty increases, and it also increases monotonically as rms are more nancially constrained. 1.3 Empirical Evidence This section uses data from publicly-traded rms in the U.S. to test the main qualitative implications of the model. 17 1.3.1 Data The data set is a rm level panel from the Compustat and CRSP les. Included in the panel are annual observations from 1975 to 2009 10. Several industries are excluded from the panel in this work. I exclude rms from the nancial (two-digit SIC codes: 60-67) and utilities (49) industries. I also exclude petroleum rening (29), mining (10-14), agriculture and shery (1- 9) industries, where real property or natural resources are a large fraction of the rm's capital. In this work, I focus on the leasing behavior of the lessee. Although commercial banks, insurance companies, and nance companies do most of the leasing, it is necessary to exclude those industries where the main business involves leasing such as auto repair (75) and computer rental and leasing (73). Thus, I examine rms in construction, manufacturing, transportation, wholesale, retail, service and public administration. This chapter uses daily rm-level equity returns from the CRSP to construct the estimate of uncertainty. I restrict the sample to rms that have traded for at least 50 percent of the trading days (125 days) in a year and have traded at least 1250 trading days (ve years). These selection criterions yield an unbalanced panel of 8,734 U.S. rms with 98,557 rm-year observations. Outlier rules are imposed on the rms' variables by setting the values at the upper and lower tails equal to the 99th and 1st percentiles respectively. 1.3.2 The Measure of Leasing The main data item from the Compustat that this chapter uses is the report- ed rental expenses (operating lease expenses) from the income statements. The fraction of capital from leasing (the lease share) is measured by the ratio of rental expense to the total cash expenditures on rent and investment11. The total cash expenditures on rent and investment is the sum of rental 10Only few observations have non missing data on leasing before 1975. 11Eisfeldt and Rampini (2009) use the same measure except that their information of rental expenses is from Census data. 18 expenses and capital expenditures. lease share = rental expenses rental expenses+ capital expenditures (1.9) Lease shares below 0 are set equal to 0, and lease shares above 1 are set equal to 1. A second measure of lease shares would be the ratio of rental expens- es to the total capital cost which is the sum of rental expenses, deprecia- tion expenses, and the opportunity cost of xed assets (Sharpe and Nguyen (1995)). I use the rm's reported short-term average borrowing rate to rep- resent the rms' opportunity costs. However, only about a quarter of my observations in the sample report the short-term average borrowing rate12. Although I did a robustness check for all empirical analysis by using the second measure of lease shares and found that all ndings are robust, I will focus on the rst measure of lease shares in this work. 1.3.3 The Measure of Uncertainty The measure of uncertainty employed in this chapter is the volatility of a rm's stock returns taken from CRSP les. It is commonly used in many nance and macroeconomics literature (Leahy and Whited (1996), Bulan (2005), and Gilchrist et al. (2010)). The advantage of this measure is that stock returns capture the changing aspects of a rm's environment that investors view as important (Leahy and Whited (1996)). Increased volatility in the product market is translated into increased volatility in the stock market (Pindyck (1991)). Common stocks are claims on the future prots of a rm. Innovations to a rm's stock returns are reactions to news about 12For rms with missing values of short-term average borrowing rate, I use the sam- ple average interest rate reported that year by rms with the same bond rating (as Sharpe and Nguyen (1995)). There are ve rating groups based upon Standard and Poor's senior debt ratings. Five groups are AAA through AA-, A+ through A-, BBB+ through BBB-, BB+ through D, and unrated. The average reported interest of the top rated group was 1 to 2 percent lower than that of the unrated group. There are a few outliers whose reported short-term average borrowing rates are higher than 20 %. I replace such values with the sample average rate reported by rms with the same bond rating in the same year. 19 the rm's future protability. Thus, the volatility of a rm's stock returns should re
ect the variations in prots and provide an adequate measure of rms' uncertainty. Estimating uncertainty for rm i in year t is based on a two-step proce- dure from Gilchrist et al. (2010). First, I remove the systematic component of stock returns using the standard Fama and French (1992) 3-factor model: ritnrftn = i+Mi (rMtn rftn)+SMBi SMBtn+HMLi HMLtn+uitn (1.10) In this equation, i represents rms, while tn are trading days n in years t. The quantity ritn denotes the return of rms, while r f tn denotes the risk free rate. Also, rMtn marks the return for the market, and SMBtn and HMLtn 13 are the Fama-French risk factors. Secondly, I calculate the standard devia- tion of daily idiosyncratic returns for each rm i in year t : it = vuut 1 N NX n=1 (ûitn  ̂uit)2 (1.11) Here ûitn is the OLS residual from equation (1.10) and ̂uit represents the mean of daily idiosyncratic returns of rm i in year t. Thus, from this equation, it is an estimate of uncertainty for rm i in year t. 1.3.4 The Measure of Financial Constraint The standard empirical approach adopts several separate nancial charac- teristics, e.g. cash 
ow, debt, bond rating and etc., to represent the level of the rms' nancial constraints. Eisfeldt and Rampini (2009) perform empir- ical analysis examining the relationship between lease shares and nancial constraints using cash 
ow, rm size, dividend, and Tobin's Q as their nan- cial constraints indicators. However, the use of separate nancial variables cannot allow us to properly identify nancially constrained rms. To study 13SMB (Small Minus Big) is the average return on three small portfolios minus the average return on three big portfolios. HML (High Minus Low) is the average return on two value portfolios minus the average return on two growth portfolios. 20 the role that nancial constraints have on the behaviors of rms, it is better to have one measure of the severity of these constraints. This chapter con- structs an index of the nancial constraint of corporate rms and uses it to sort rms into two separate groups according to their level of constraints. The commonly used index of nancial constraints is the Kaplan and Zingales (1997) index (KZ index thereafter), which is constructed in Lamont et al. (2001). They classify rms into discrete categories of nancial constraint, then use an ordered logit regression to relate their classications to account- ing variables, and nally use the regression coecients to construct the KZ index. The KZ index loads positively on Tobin's Q and leverage, and neg- atively on cash 
ow, cash, and dividends14. However, Hadlock and Pierce (2010) argued that only cash 
ow and leverage are consistently signicant with a sign that agrees with the KZ index. Other three components display insignicant or con
icting signs. An alternative to the KZ index is proposed by Whited and Wu (2006) (WW index thereafter), which is created by a Euler equation approach from a structural model of investment. The WW index has six factors: cash 
ow, leverage, size, dividend dummy, industry sales growth, and rm sales growth. Hadlock and Pierce (2010) nd that only cash 
ow, leverage and rm size have signicant coecients that agree in sign with the WW index. Hadlock and Pierce (2010) also study several commonly used nancial indicators and nd that only rm sizes and ages are closely related to nancial constraints. Therefore, they suggest using an index based on cash 
ow, leverage, size, and age.15. I rely on Hadlock and Pierce (2010) to construct the nancial constrain- t index. The nancial constraint index (FC index thereafter) is based on four factors. (1) Cash 
ow, proxied by operating income plus depreciation/beginning- of-year book assets. (2) Leverage, proxied by book value of long-term 14KZ Index = -1.002*Cash Flows/K + 0.283*Q + 3.139*Debt/Total Capital - 39.368*Dividends/K -1.315*Cash/K. 15They suggest there are two factors to caution. First, the endogenous nature of lever- age may result in a nonmonotonic or sample-specic relationship between leverage and nancial constraints. Secondly, there may be biases in qualitative disclosures on leverage and cash 
ow. Given these concerns, they suggest another similar nancial constraint measure using only rm size and age. 21 debt/current book assets. (3) Firm size, proxied by the log of in
ation de
ated (to 2004) assets. (4) Firm age, proxied by the current year minus the rst year that the rm has a non-missing stock price. The FC index is calculated using the regression coecients from Hadlock and Pierce (2010). FC = 0:592Cash F low+1:747Leverage0:357Firm Size0:025Firm Age (1.12) The bigger the FC, the higher the degree of nancial constraint. 1.3.5 Summary Statistics Descriptive statistics are given in Table 1.1. Leases account for 37.8 percent of the capital costs on average. The mean value of rms' uncertainty is 0.037, and the mean value of the nancial constraint index is -1.969. Table 1.2 reports the correlations. The correlation of lease share and uncertainty is 0.288. The correlation of lease share and the FC index is 0.282. Both are positively signicant. I also calculated the correlation of lease share with one year lagged uncertainty and FC index. The lagged correlations are a little bit larger than the correlations in the same year, and all are positively signicant. These correlations suggest that rms with high uncertainty and rms with a high FC index (more nancially constrained rms) tend to have high lease shares. The correlation between uncertainty and the FC index is 0.474. Firms with high uncertainty are more likely to be nancially constrained. I categorize rms by their level of uncertainty and their FC index. Firm i in year t is in the high uncertainty group if its uncertainty is above the median of all rms' uncertainty in year t. Otherwise, it belongs to the low uncertainty group. Similarly, I split rms to the less nancially constrained group and the more nancial constrained group according to their FC index. Panel A of Table 1.3 reports the average of lease shares across uncertainty groups. Firms in the high uncertainty group rent 43.6 percent of their cap- ital, whereas rms in the low uncertainty group rent about 31.8 percent on average. Panel B of Table 1.3 shows the average lease share across nancial constraint groups. Firms in the more nancially constrained group lease 22 Table 1.1: Descriptive Statistics Variable Obs. Mean Std. Dev. Min. Median Max. Lease Share 98,557 0.378 0.245 0 0.332 1 Uncertainty 111,724 0.037 0.026 0.001 0.031 1.2 FC Index 101,632 -1.969 0.946 -5.356 -1.867 1.517 Notes: The Sample consists of rms in the U.S. on Compustat and CRSP les over the period 1975 through 2009. Firms in construction, manufacturing, transportation, wholesale, retail, service and public administration are included in the sample. Lease share is the fraction of capital from leasing, and is measured as a ratio of the rental expense to the total cash expenditures on rent and investment. Uncertainty is mea- sured as the volatility of a rm's stock returns. Financial constraint is measured by an index (the FC index) which combines the information of cash 
ow, debt, rm size and rm age. Table 1.2: Sample Correlations Correlation Signicant Level Lease Share and Uncertainty 0.288 0.000 Lease Share and FC Index 0.282 0.000 Lease Share and Lagged Uncertainty 0.295 0.000 Lease Share and Lagged FC Index 0.286 0.000 Uncertainty and FC index 0.474 0.000 Notes: The FC index ia a nancial constraint index. Larger number of the FC index indicates that a rm is more nancially constrained. 44.2 percent of their capital, and rms in the less nancially constrained group lease about 31.9 percent. I did a mean comparison test of lease share for dierent groups and report the t statistics and P-values in the last two columns of Table 1.3. Firms with high uncertainty and rms that are more nancially constrained, on average according to the statistics, lease signi- cantly more. Moreover, Figure 1.2 shows the trend of the mean lease shares across dierent groups over time16. Firms with high uncertainty and rms 16The correlation of a rm being in the high uncertainty group and in the more nancial constrained group is 0.5104. It is higher than the correlation between the uncertainty and FC index because the variables are now dummy variables. 23 that are more nancially constrained always lease more over the whole time series. Table 1.3: Summary Statistics of Dierent Groups PANEL A High uncertainty Low uncertainty t-value P-value Lease Share 0.436 0.318 78.106 0 (0.258) (0.214) Uncertainty 0.052 0.022 (0.029) (0.008) FC Index -1.45 -2.465 (0.68) (0.897) PANEL B More FC Less FC t-value P-value Lease Share 0.442 0.319 77.456 0 (0.262) (0.210) Uncertainty 0.047 0.026 (0.03) (0.015) FC Index -1.26 -2.68 (0.495) (0.732) Notes: The FC index ia a nancial constraint index. Larger number of the FC index indicates that a rm is more nancially constrained. Panel A shows the results of the uncertainty groups, and Panel B shows the results of the nancial constraint groups. The t-value and the P-value refer to the t statistics and the P-value of the mean comparison test of two groups. Standard deviations are in parenthesis. Figure 1.3 plots the empirical cumulative distributions of the lease shares of dierent groups. The cumulative distribution of the low uncertainty group is above the cumulative distribution of the high uncertainty group. The cu- mulative distribution of the less nancially constrained group is above the cumulative distribution of the more nancially constrained group. A stan- dard Kolmogorov-Smirnov test rejects the null hypothesis of equal distribu- tions at the one-percent level. The P-values of KS tests for both uncertainty groups and nancial constraint groups are equal to zero, which is shown in the rst column of Table 1.4. 24 . 2 . 3 . 4 . 5 . 6 A ve ra ge  L ea se  S ha re 1975 1980 1985 1990 1995 2000 2005 2010 Year The high uncertainty group The low uncertainty group The more financially constrained group The less financially constrained group Figure 1.2: Average Lease Shares at Dierent Levels of Uncertainty and Financial Constraints over Time Notes: The nancial index starts from 1976 because the cash 
ow factor is divided by the lagged value of the book assets. 25 0.2 .4 .6 .8 1 Cu mu lat ive  Pr ob ab ility 0 .2 .4 .6 .8 1 The Lease Share The high uncertainty group The low uncertainty group 0 .2 .4 .6 .8 1 Cu mu lat ive  Pr ob ab ility 0 .2 .4 .6 .8 1 The Lease Share The more financially constrained group The less financially constrained group Figure 1.3: The Cumulative Distribution of the Lease Share across Dierent Groups 26 Table 1.4: Lease Share Distribution Tests PANEL A (1) (2) Uncertainty Groups KS Test P-value FOSD Test P-value High versus Low 0.000 0.892 Low versus High 0.000 PANEL B Financial Constraint Groups KS test P-value FOSD test P-value More FC versus Less FC 0.000 0.202 Less FC versus More FC 0.000 Notes: The KS test is the Knlmogorov-Smirnov test of equal distribution, and the FOSD test is a test of rst order stochastic dominance. "High versus low" means that the null hypothesis is that the distribution of lease share of the high uncertainty group rst order stochastically dominates the distribution of lease share of the low uncer- tainty group, and "Low versus High" means the opposite hypothesis. Similarly, "More FC versus Less FC" states that the null hypothesis is that the distribution of lease share of the more nancially constrained group rst order stochastically dominates the distribution of lease share of the less nancially constrained group, and "Less FC versus More FC" means the opposite hypothesis. 27 In addition, I applied a non-parametric procedure which is proposed by Barrett and Donald (2003) to test for rst-order stochastic dominance. The second column of Table 1.4 presents P-values for rst order stochastic dominance tests of lease share distribution comparisons across groups. Panel A of Table 1.4 reports the results for uncertainty groups. The rst row of panel A labeled "High versus low" contains P-values for testing whether lease share distribution of the high uncertainty group rst order stochastically dominates lease share distribution of the low uncertainty group, while the second row tests the opposite hypothesis. The P-values are equal to 0.892 and 0, respectively. The rst P-value implies that one cannot reject that the high uncertainty group dominates the low uncertainty group in lease share, and the second P-value implies that the converse can easily be rejected since the P-value is zero. Panel B of Table 1.4 presents the results for the nancial constraint groups. The P-values suggest that the lease share distribution of the more nancially constrained group rst order stochastically dominates that of the less nancially constrained group. These tests conclude that rms with high uncertainty and rms that are more nancially constrained lease more even if we look at the whole distribution. The results from comparing the mean and the distribution across dier- ent groups are consistent with the prediction of the model. 1.3.6 Regressions To study the relationship between leasing, uncertainty and nancial con- straint, I run regressions of the leasing measure on the uncertainty and the FC index. The dependent variable in these regressions is the value of lease shares. Because the model predicts that rms with high uncertainty and rms that are more nancially constrained lease more of their capital than rms with low uncertainty and rms that are less nancially constrained, the coecients on the uncertainty measure and the FC index are expected to be positive. Table 1.5 reports the results of the OLS estimations. I control for rm xed eects and time xed eects in all OLS regressions. The rst column 28 reports the base regression without additional control variables. Both the uncertainty and the FC index are signicantly positively related to leasing. It is consistent with the prediction of the model. Uncertainty and nan- cial constraint are also quantitatively important. Based on the rst column in Table 1.5, a one standard deviation increase in uncertainty increases a rm's lease share by approximately 3.5 percent. A one standard deviation increase in the FC index increases the lease share by approximately 9 per- cent. Compared to that, the mean lease share of all rms is 37.8 percent; thus, it can be seen that the economic eects of uncertainty and the nancial constraints on lease shares are large. Uncertainty and nancial constraints are important determinants of rms' leasing decisions17. Moreover, the data I used is from publicly-traded rms. They are relatively large rms with low uncertainty and are less nancially constrained. I can reasonably expect the eect of uncertainty and nancial constraints to be much stronger for those small rms that are not publicly traded. I control for other nancial indicators like dividend, cash and Tobin's Q besides the FC index in a check for robustness. Column 2 of Table 1.5 reports the result with these additional nancial controls. The dividend dummy variable equal to one for dividend paying rms and equal to zero for non-dividend paying rms. Cash/Asset is dened as the cash plus the marketable securities divided by the book assets. Tobin's Q is dened as the book assets minus the book common equity minus the deferred tax plus the market equity divided by the book assets. The coecients on uncertainty and the FC index are still positive and signicant, and the level of mag- nitude of these coecients is close to those in the base regression. Based on the second column in Table 1.5, a one standard deviation increase in uncertainty and the FC index increases a rm's lease share by 3.5 percent 17The Compustat data does not distinguish between structures renting and equipment renting. But I expect that the eects of uncertainty and nancial constraints are stronger using data on structures renting. Because structures are usually illiquid assets and are capital intensive, rms are more likely to face nancial constraints and suer more from resale loss if they choose to purchase structures. In Eisfeldt and Rampini (2009), they use census data and report the results for structures and equipment separately. They nd that the eect of nancial constraints on equipment leasing are weaker than on structures. This is consistent with my view. 29 Table 1.5: Results of the OLS Regressions Regression (1) (2) (3) (4) Uncertainty 1.345*** 1.340*** 1.228*** 1.226*** (0.031) (0.031) (0.038) (0.038) FC Index 0.095*** 0.099*** 0.110*** 0.110*** (0.002) (0.002) (0.002) (0.002) Dividend Dummy -0.009*** -0.003 -0.003 (0.002) (0.002) (0.002) Cash/Asset 0.064*** 0.049*** 0.048*** (0.005) (0.006) (0.006) Tobin's Q -0.009*** -0.009*** -0.009*** (0.000) (0.001) (0.001) Average Tax Rate -0.003 -0.003 (0.003) (0.003) R&D/Sales -0.003*** -0.003*** (0.001) (0.001) Total Use of Capital -0.000*** (0.000) No. of rms 8,485 8,428 5,794 5,794 No. of Obs. 90,099 86,520 54,448 54,448 R2 (within) 0.128 0.134 0.146 0.148 Notes: The dependent variable is the value of lease shares. I control for rm xed eects and time xed eects in each regression. Standard errors are in parentheses. *, **, *** statistically signicantly dierent from zero at the 10%, 5% and 1% level of signicance. Larger number of the FC index indicates that a rm is more nancially constrained. 30 and 9.4 percent respectively. Moreover, the regression indicates that non- dividend paying rms signicantly lease more. Surprisingly, the coecient on cash to assets is signicantly positive. Firms holding more cash lease more. The reason might be that, as pointed by Hadlock and Pierce (2010), the choice of cash holdings may not have straightforward relation to nan- cial constraints. They nd that cash holdings generally display a positive and signicant coecient in models predicting nancial constraints if rm size and age are controlled. Although an increase in cash may help rm al- leviate the nancial constraints, the fact that a rm chooses to hold a high level of cash may indicate that the rm is constrained and it holds cash for precautionary reasons. Tobin's Q is always used as a measure of nancial constraint. However, the coecient estimate on Tobin's Q is signicantly negative. The reason is that Tobin's Q might be highly correlated with other nancial variables. These estimates are consistent with the ndings in Eisfeldt and Rampini (2009). They nd that the cash to assets ratio is not signicantly related to leasing behaviors, and the eect of Tobin's Q is insignicant or negative when rm age is controlled18. I also include a measure of the average tax rate to control for the tax proposes. The average tax rate is approximated by the tax expense divided by the pre-tax income. Moreover, I control for the unique characteristics of specic rms' capital by using research and development expenditure to sales ratio. Klein et al. (1978) argued that an asset highly specialized to the rm is more likely to be purchased because it is less valued by other users. The results with the tax and R&D controls are presented in column 3 of Table 1.5. The average tax rate is insignicant. Firms with more R&D spending tend to lease less capital. More importantly, controlling for tax and asset specicity does not alter the results regarding the signicance of uncertainty and the FC index. Both the uncertainty and the FC index are signicantly positive. Approximately, a one standard deviation increase in uncertainty and the FC index increases a rm's lease share by 3.4 percent and 10.2 percent respectively. In addition, in order to avoid the issue that rms with high uncertainty lease more simply because they adjust their 18In my regression, rm age is included in the FC index. 31 capital more frequently, I control for the overall use of capital in the last column of Table 1.5. The results in column 4 are very close to the results in column 3. Again, the uncertainty and the FC index have statistically signicant and positive coecients. Since the value of lease share is truncated between zero and one, I also test for robustness of the results with Tobit regressions19. The results of the Tobit regressions are shown in Table 1.6. The results of the Tobit regressions are similar to the results of the OLS regressions. Again, the uncertainty and the FC index have signicant and positive coecients. The estimated coecients of the uncertainty and the FC index of the Tobit regressions are close to the estimates of the OLS regressions. Lastly, I do another check for robustness by using the KZ index as a nancial constraint indicator instead of my FC index. The results are pre- sented in Table 1.7. The results in columns 1 and 2 of Table 1.7 are from the OLS regressions, and the results in columns 3 and 4 of Table 1.7 are from the Tobit regressions. In these regressions, the estimated coecients on uncertainty are signicant, and they are larger than those in Tables 1.5 and 1.6. The estimated coecients on the KZ index are signicant in most regressions but the magnitude is small20. Besides panel regressions, I examine cross section patterns as well. I run regressions for every year separately, and control for industry xed eect in the regressions. The estimated coecients on uncertainty and nancial con- straint index are statistically signicant and positive in all year regressions. Table 1.8 report the results of some selected years. Overall, both the panel regressions and cross sectional regressions sug- gest that the uncertainty and the nancial constraint positively aect rms' leasing decisions, and the economic eects of uncertainty and nancial con- straint on lease shares are large. 19I control for time xed eects and rm random eects in all Tobit regressions. 20The mean of the KZ index of all rms is -4.246, and the standard deviation of the KZ index is 12.379. Based on the results in Table 1.7, a one standard deviation increase in the KZ index increases a rm's lease share by approximately 1 percent. 32 Table 1.6: Results of the Tobit Regressions Regression (1) (2) (3) Uncertainty 1.431*** 1.421*** 1.333*** (0.030) (0.031 (0.038) FC Index 0.080*** 0.082*** 0.092*** (0.002) (0.002) (0.002) Dividend Dummy -0.006*** 0.001 (0.002) (0.002) Cash/Asset 0.060*** 0.041*** (0.005) (0.005) Tobin's Q -0.010*** -0.009*** (0.000) (0.001) Average Tax Rate -0.001 (0.003) R&D/Sales -0.002*** (0.001) No. of rms 8,485 8,428 5,794 No. of Obs. 90,099 86,520 54,448 Notes: The dependent variable is the value of lease shares. I control rm random eects and time xed eects in each regres- sion. Standard errors are in parentheses. *, **, *** statistically signicantly dierent from zero at the 10%, 5% and 1% level of signicance. Larger number of the FC index indicates that a rm is more nancially constrained. 33 Table 1.7: Robustness Check using the KZ Index Regression (1) (2) (3) (4) OLS Tobit Uncertainty 1.728*** 1.654*** 1.908*** 1.889*** (0.031) (0.038) (0.030) (0.037) KZ Index 0.001*** 0.001*** 0.000 0.001*** (0.000) (0.002) (0.000) (0.000) Average Tax Rate -0.003 -0.003 (0.003) (0.003) R&D/Sales 0.000 0.002*** (0.001) (0.001) No. of Firms 8,420 5,791 8,420 5,791 No. of Obs. 86,254 54,365 86,254 54,365 R2 (within) 0.102 0.106 Notes: The dependent variable is the value of lease shares. The KZ index is based on ve factors as described in Lamont et al. (2001): cash 
ow, Tobin's Q, debt, dividend, and cash. Larger number of the KZ index indicates that a rm is more nancially constrained. Each regression includes controls for time xed eects. I control for rm xed eects in the OLS regressions, and control for rm random eects in the Tobit regressions. Standard errors are in parentheses. *, **, *** statistically signicantly dierent from zero at the 10%, 5% and 1% level of signicance. Table 1.8: Results of Some Selected Cross Sectional Regressions Regression Year1976 Year1981 Year1986 Year1991 Year1996 Year2001 Year2006 Uncertainty 3.492*** 3.103*** 2.937*** 1.666*** 2.415*** 2.046*** 3.623** (0.356) (0.436) (0.306) (0.155) (0.18) (0.173) (0.36) FC index 0.015*** 0.045*** 0.042*** 0.064*** 0.029*** 0.055*** 0.06*** (0.006) (0.006) (0.006) (0.005) (0.005) (0.005) (0.006) No. of Obs. 2202 1885 2303 2580 3299 3252 2829 Adj. R2 0.181 0.166 0.173 0.225 0.214 0.231 0.217 Notes: The dependent variable is the value of lease shares. I control for industry xed eects in all regressions. Standard errors are in parentheses. *, **, *** statistically signicantly dierent from zero at the 10%, 5% and 1% level of signicance. 34 1.3.7 Indirect Evidence Zhang (2011) documents that leasing is countercyclical over business cy- cles. Firms lease more during economic downturns, and are more willing to buy capital during up cycles. Many literature indicate that uncertainty is high during recessions (Bloom et al. (2010), Gilchrist et al. (2010)). More- over, rms face severe nancing conditions during recessions than booms (Jermann and Quadrini (2012)). The survey among senior loan ocers of banks nds that banks tighten the credit standards for commercial and in- dustrial loans during recessions. High uncertainty and tight nancial condi- tions might cause rms to lease more during recessions than during booms. We can view this countercyclical pattern as an indirect evidence to support that uncertainty and nancial constraint are important determinants of the leasing decisions of corporate rms. 1.4 Quantitative Analysis In this section, I calibrate the model in Section 2, and show simulation results of the model when the economy faces higher uncertainty and tighter nancial constraint. The model is highly non-linear. All parameters aect the outcome. The calibration faces challenges because the identication of some key parameters is very dicult. The data does not provide any direct evidence on the level of transaction cost and maintenance cost. I can only infer these costs from other literature. Therefore, this calibration is not an estimation of its structural parameters. It is an investigation on whether the model is quantitatively consistent with the data. The time period in the model is one year. I assume the annual in- terest rate to 3 percent. This is a common setting in the literature. In Cooper and Haltiwanger (2006), they estimate that the transaction cost is from 2.5 percent to 20 percent depending on dierent specications. In Bloom et al. (2007), they set the resale loss for capital to 20 percent. Based on the literature, I set the transaction cost to 20 percent. There are few lit- 35 erature estimating the maintenance cost of leased capital. Gavazza (2011) suggests that the maintenance cost of leased aircraft is about 2.7 percent. Following Gavazza (2011), the maintenance cost of leased capital is set to 3 percent. The mass of assets X aects all prices and thresholds in the equi- librium. However, what I focus on is the ratio of leased capital which is not sensitive to the choice of X. X is set to 0.5 which indicates that half of the rms produce in the equilibrium. I further assume that the productivity z is normal distributed with mean E(z) and standard deviation SD(z). Instead of the absolute value of the mean and standard deviation, it is the relative dispersion of the distribution that aects the lease ratio. Thus, I simply assume the mean E(z) to 100, and calibrate the standard deviation SD(z) to match the key moments. The probability of successful enforcement  is set to 0.5. The equilibrium outcome is aected by  and  together, thus I set  and leave  to match the key moments. I choose three key parameters (uncertainty , nancial conditions , and standard deviation SD(z)) so that the moments computed from the model are close to the moments in the data. The rst moment is the average lease share of rms in 35 years. The second moment is the serial correlation in lease share. And the last moment is the standard deviation of the average lease share of rms. Panel A of Table 1.9 reports the implied parameters, and Panel B of Table 1.9 reports the moments computed from the model and the data. The uncertainty parameter  equals to 0:195. The productivity is very sluggish because of the high serial correlation of rms investment decisions. The nancial parameter  equals to 0:28. Firms nance their capital mainly by secured debt (1 ) which is more than 70 percent. The standard deviation SD is set to 70. All these parameters are suggestive and the magnitudes seem reasonable. The model is quantitatively consistent with the data. I then simulate the model when the economy faces higher uncertainty and tighter nancial constraint. The simulation results can help us separate the eects of uncertainty and nancial constraints. Panel C of Table 1.9 reports the simulated average lease share of dierent scenarios. The pa- rameters are from the calibration. First, I increase the uncertainty  by 36 5 percent given other parameters unchanged. When there is a 5 percent increase in uncertainty, the average lease share in the economy changes to 0.405 and increases 7.1 percent. Higher uncertainty induces rms to adjust their capital position more frequently, and makes leasing more attractive. Firms lease more of their capital than in the steady state. In the second scenario, the nancial constraint parameter  decreases 5 percent. Firms have less internal funding to support their purchase, and face tighter nan- cial constraints. Less rms are able to nance their purchase, and more rms have to lease capital. A 5 percent decreases in the nancial conditions increases the average lease share by 2.6 percent. The results suggest that uncertainty may have stronger eect on leasing than nancial constraints have. Lastly, I increase uncertainty by 5 percent and decrease the nancial parameter by 5 percent together. Now, rms face both higher uncertainty and tighter nancial constraints. Both factors increase the average lease share. The average lease share in the third scenario increases 9.6 percent. The magnitude of the change is almost the same as the sum of changes caused by the uncertainty and nancial constraints separately. The interac- tion eect of uncertainty and nancial constraints is negligible. Uncertainty and nancial constraints seem to aect leasing through separate channels. Although the simulation helps us distinguish uncertainty from nancial con- straints, there is a caveat. All simulation results are suggestive. They are sensitive to the values of the parameters. 1.5 Concluding Remarks This chapter investigates how uncertainty and nancial constraints aect corporate leasing decisions. Leasing incurs an agency costs due to the sep- aration of ownership and control; hence, it costs more in the long run than owning capital. However, leasing provides rms with operational 
exibility, since the leased capital can be more easily disposed at low transaction cost- s. The low transaction costs of leasing are particularly attractive to rms whose future prot is highly uncertain and expect to frequently adjust their capital. Another advantage of leasing is that leases are easier to nance than 37 Table 1.9: Calibration and Simulation Panel A: Parameters The mass of asset X 0.5 Interest rate r 0.03 Trade friction  0.2 Maintenance cost m 0.03 Probability of successful enforcement  0.5 Mean of productivity E(z) 100 Standard deviation of productivity SD(z) 70 Uncertainty  0.195 Financial Constraint parameter  0.28 Panel B: Moments Average lease share 0.378 Serial correlation of the lease share 0.8 Standard deviation of the lease share 0.245 Panel C: Simulation Results Average Lease Percentage Share Change A 5% increase in uncertainty  0.405 7.1% A 5% decrease in FC parameter  0.388 2.6% A 5% increase in  and a 5% decrease in  0.414 9.6% 38 purchases. It is unlikely that the lessee would have to provide any collateral to be able to start a lease. Despite the high cost of leasing in the long run, rms that are more nancially constrained would value the ease of nancing leases due to their high level of nancial constraints. This chapter develops a dynamic model including these tradeos. The model predicts that rms with high uncertainty and rms that are more nancially constrained lease more of their capital than rms with low uncertainty and rms that are less nancially constrained. Then, this chapter nds empirical evidence to support the prediction of the model by using the data of publicly-traded rms in the U.S.. I nd that on average, rms with high uncertainty and rms with more nancial constraints have a larger lease share than rms with low uncertainty and rms with less nancial constraints. The distributions of the lease shares of rms with high uncertainty and rms with more nancial constraints rst order stochastic dominate the distributions of rms with low uncertainty and rms with less nancial constraints. Results from panel regressions indicate that uncertainty and nancial constraint are signicantly positively related to leasing. Approximately, a one standard deviation increase in uncertainty and the nancial constraint index increases a rm's lease share by 3.5 percent and 9 percent respectively; these eects are economically signicant. Moreover, the countercyclical pattern of leasing over business cycles also provides an indirect evidence. Firms facing high uncertainty and tight nancial condition during recessions tend to lease more of their capital. The ndings of this chapter have implications for corporate nance and macroeconomics. In studies of the eects of uncertainty and nancial con- straints on rms' investment, we should consider leased capital. From a macroeconomic perspective, credit constraint is recognized as an important transmission mechanism of business cycles. Moreover, uncertainty shock- s are recently proposed as a new shock that drives business cycles in the literature. Better understanding of the eects of uncertainty and nancial constraints on rms' investment behavior is therefore critical for us to study economic growth and business cycles. Lastly, corporate leasing behavior has many features in common to the housing decisions of households. Under- 39 standing corporate leasing behavior can help us understand the rent versus buy decision in the housing market. 40 Chapter 2 Leasing and Business Cycles 2.1 Introduction How rm nancing varies over business cycles is an important research ques- tion. An increase or decline in the amount of external funds that rms can raise is directly related to rm investment, and thus in turn further alleviate or worsen the recession. Research often focuses on debt and equity nance. It is important to include leasing nance, which is one of the most impor- tant external sources of nancing. This chapter explores the role of business cycles in determining rms' leasing decisions. It empirically documents the countercyclical behavior of leasing, and develops a model to provide expla- nations for this countercyclical pattern. Leasing is of rst order importance as a source of nancing. According to the Compustat data21, nearly all listed rms in the U.S. indicate their usage of operating leases22, whereas 86 percent of rms have long-term debt. In addition, operating leases accounts for 7.4 percent of rms' total assets, and the value of long-term debt equals 10.6 percent23. As a source of external nancing, leasing is comparable to long-term debt. An average publicly- traded rm in the U.S. leases more than 30 percent of its capital. For small rms that are not publicly traded, leasing is even more important. Eisfeldt and Rampini (2009) use micro data from the 1992 U.S. Census of Manufactures and show that the smallest decile rms lease 46 percent of 21The sample consists of 122,297 observations for rms on Compustat over the period of 1984 through 2008. Foreign incorporated companies and a few industries are excluded. Details of the data are in Section 2. 22A lease is classied either as an operating lease or a capital lease for nancial account- ing purposes. This work focuses on operating lease. 23Measures are from Graham et al. (1998). 41 their capital. They claim that leasing may be the largest source of external nance for these small rms. Therefore, leasing has a particular importance in understanding the capital structure and investment of rms, which have been argued to play a key role in determining business cycle 
uctuations and economic growth. This chapter uses a rm level panel data set of listed rms in the U.S. from 1984 to 2008. I adopt two approaches from Covas and Den Haan (2011) to investigate the cyclical behavior of leasing. The rst approach forms rm size groups, and constructs the time series data of the average lease share in each group. Cyclicality of leasing is then measured by the correlation between the cyclical components of these average lease share se- ries and the cyclical component of real GDP. The rst approach indicates a signicantly negative correlation between the cyclical component of GDP and average lease share. The second approach is a panel data approach that relates rms' lease share to both rm-specic variables and a business cy- cle indicator. This panel data approach can quantitatively assess the eect of the business cycle on rms' leasing behavior. The estimated coecients of the business cycle indicator are signicantly negative. According to the estimation, the lease share decreases approximately 2 percent when the e- conomy condition changes from the worst (Year 1991 in the sample period) to the best (Year 2000). Both approaches conclude that leasing is coun- tercyclical over business cycles. Firms prefer to lease more of their capital during economic downturns, and are more willing to buy capital during up cycles. Why do rms lease more capital when the economy is in recession? This is because rms face tight nancing conditions during recessions than boom- s. Leases are easier to nance than purchases (Zhang (2012)). Although leasing is a more costly way of nancing than owning capital because of the agency costs originated from the separation of ownership and control, the benet of easiness to nance outweighs the high cost for nancially constrained rms. More nancially constrained rms lease more of their capital than less constrained rms (Eisfeldt and Rampini (2009) and Zhang (2012)). Firms face more severe nancing conditions during recessions than 42 booms (Jermann and Quadrini (2012)). Figure 2.1 shows an index of cred- it tightness constructed from a survey among senior loan ocers of banks. Clearly, banks tighten credit standards for commercial and industrial loan- s in recessions. Firms have diculties in obtaining bank loans to support their purchases in recessions, thus choose to lease capital instead. Therefore, leasing is more prevalent in recessions. − 20 0 20 40 60 80 Ti gh te ni ng  S ta nd ar ds  fo r C om m er ia l a nd  In du st ria l L oa ns 1990 1995 2000 2005 2010 Year Figure 2.1: Financial Conditions Notes: Sources: Federal Reserve Bank. Gray shaded area is quarters in recession dened by NBER. In this chapter, I also develop a model to explain the observed coun- tercyclical pattern of leasing. The model analyzes the decision of leasing versus secured borrowing in an economy with overlapping generations. I use this model to simulate the impact of a temporary technology shock during the business cycle. I nd that a positive technology shock generates a rapid decrease in the average lease share in the economy. The model's simulation is consistent with the observed countercyclical fact. There is an extensive literature on leasing in nance, but the main focus 43 of literature is tax considerations. However, the economics of leasing are recognized beyond tax minimization. Smith and Wakeman (1985) provide an informal list of non tax characteristics of users and lessors that in
uence the leasing decision. Following Smith and Wakeman (1985), a small but growing literature have focused on the non tax aspects of leasing. In par- ticular, Eisfeldt and Rampini (2009) incorporate nancial constraints into a model of the choice between leasing and secured lending. Their model implies that more nancially constrained rms lease more of their capital than less constrained rms. Zhang (2012) investigates the role of uncertainty and nancial constraint in understanding the leasing decisions of corporate rms. She nds that rms with high uncertainty over their future prots and rms that are more nancially constrained prefer to lease more of their capital than rms with low uncertainty and rms that are less nancially constrained. All these papers focus on rms' incentive to lease while this work's focus is on how rms leasing behavior changes over business cycles. This chapter is also related to a series of papers study the cyclical behav- ior of other sources of external nance. Jermann and Quadrini (2012) use aggregate data and nd that debt is procyclical and equity issuance is coun- tercyclical. In contrast, Covas and Den Haan (2011) document that both debt and equity issuance are procyclical for most size-sorted rm categories of listed U.S. rms by using Compustat data. I am the rst, to the best of my knowledge, to document the cyclical behavior of leasing and theoretically explain the countercyclical pattern. The ndings of this chapter have implications for corporate nance and macroeconomics. In studies of rm investment over business cycles, atten- tion should not be limited to capital expenditures. Leased capital should also be considered. From a macroeconomic perspective, current business cycle models typically assume that external nance occurs only through one-period debt contracts (e.g. Kiyotaki and Moore (1997), Bernanke et al. (1999)). In these models, the key mechanism by which the eects of shocks persist and are amplied is the dynamic interaction between credit limits of secured borrowing and asset price returns. The facts that rm lease more that 30 percent of their capital and their leasing behavior is countercyclical 44 over business cycle suggest studying a new transmission mechanism. This chapter is organized as follows. The next section empirically docu- ments the countercyclical behavior of leasing by examining the correlation and running panel regressions to quantify the magnitude. Section 3 lays out the model and presents the simulation analysis. Concluding remarks are oered in Section 4. 2.2 Empirical Results 2.2.1 Data The data source that this work uses is Standard and Poor's Compustat. In- cluded in the panel are annual observations of publicly listed U.S. rms from 1984 to 2008. Foreign incorporated companies are excluded. This chapter focuses on the period after 1984 for three reasons. First, by excluding the seventies, the analysis avoids issues related to possible missing values and the bad coverage of some variables by Compustat during this period. Second, several empirical studies have documented a change in the behavior of sev- eral economic variables, and the so{called Great Moderation of 1984. Third, as documented in Jermann and Quadrini (2012), major changes have been seen in U.S. nancial markets during this period compared to the previous period. These changes can have impacts on rms' external nance. Several industries are excluded from the panel in this work. I exclude - nancial (two-digit SIC codes: 60-67), utilities (49) and public administration (91-97)24. I also exclude industries including those where real property or natural resources are a large portion of rm's capital, like petroleum rening (29), mining (10-14), agriculture and shery (1-9). In this work, I focus on the leasing behavior of the lessee. Although commercial banks, insurance companies, and nance companies do most of the leasing, it is necessary to exclude those industries where the main line of business involves leasing such as auto repair (75) and computer rental and leasing (73). Thus, I examine 24The economy condition could directly aect government spending that is very impor- tant to public administration industry. Thus, I exclude rms in the public administration industry. 45 rms in construction, manufacturing, transportation, wholesale, retail, and service. My full data set is an unbalanced panel of 13,691 rms with 122,297 rm-year observations. Firm entry or exit could distort the dependence of the cyclical properties. For example, new entry rms are typically small rms and prefer to lease capital. Therefore, I consider a survivor subset sample in which rms are only included if they have been in the Compustat data set for all 25 years from 1984 to 2008. There are 891 rms in the subset sample. In the main text, I report results for both the full sample and the subset sample. Firms are categorized by rm size. Firm size categories are based on the mean of the de
ated book value of assets25. Four quartile size categories are used in the analysis. 2.2.2 The Measure of Leasing The main data item from the Compustat that this chapter uses is the report- ed rental expenses (operating lease expenses) from the income statements. The fraction of capital from leasing (the lease share) is measured by the ratio of rental expense to the total cash expenditures on rent and investment26. The total cash expenditures on rent and investment is the sum of rental expenses and capital expenditures. lease share = rental expenses rental expenses+ capital expenditures (2.1) Lease shares below 0 are set equal to 0, and lease shares above 1 are set equal to 1. A second measure of lease shares would be the ratio of rental expens- es to the total capital cost which is the sum of rental expenses, deprecia- tion expenses, and the opportunity cost of xed assets (Sharpe and Nguyen 25I also categorizes rms by their number of employees, and all empirical ndings are robust. 26Eisfeldt and Rampini (2009) use the same measure except that their information of rental expenses is from Census data. 46 (1995)). I use the rm's reported short-term average borrowing rate to represent the rms' opportunity costs. However, only about a quarter of my observations in the full sample report the short-term average borrowing rate27. Although I did a robustness check for all empirical analysis by using the second measure of lease shares and found that all ndings are robust, I will focus on the rst measure of lease shares in this work. My measure for real activity is real gross domestic product per capita. 2.2.3 Sample Statistics Table 2.1 presents the mean values of lease share by rm size group. The Panel A of Table 2.1 reports the summary statistics for the full sample. In the full sample, an average rm leases 33.5 percent of its capital. Firms in the smallest quartile rent more than 40 percent of their capital, whereas rms in the top quartile rent about 25.8 percent of capital on average. The fraction of leased capital is monotonically decreasing across size groups. Small rms lease more of their capital than large rms. It is consistent with the ndings in Sharpe and Nguyen (1995) and Eisfeldt and Rampini (2009). The Panel B of Table 2.1 shows the descriptive statistics of the subset sample. Leases account for 28.8 percent of the capital on average. The lease share ranges from a low of 24.8 percent for the largest quartile rms to a high of 36.2 percent for the smallest quartile rms. In the subset sample, the fraction of leased capital is still monotonically decreasing across size groups. Leased capital is important for all rms, but is of particular importance for small rms. The average lease share in the subset sample is smaller than the average lease share in the full sample. 27For rms with missing values of short-term average borrowing rate, I use the sam- ple average interest rate reported that year by rms with the same bond rating (as Sharpe and Nguyen (1995)). There are ve rating groups based upon Standard and Poor's senior debt ratings. Five groups are AAA through AA-, A+ through A-, BBB+ through BBB-, BB+ through D, and unrated. The average reported interest of the top rated group was 1 to 2 percent lower than that of the unrated group. There are a few outliers whose reported short-term average borrowing rates are higher than 20 %. I replace such values with the sample average rate reported by rms with the same bond rating in the same year. 47 Table 2.1: Lease Share of Total Capital Costs Panel A: Full sample Firm Size Group Mean Std. Dev. Obs. 0%-25% 0.439 0.237 23,353 25%-50% 0.364 0.206 28,950 50%-75% 0.322 0.201 32,078 75%-100% 0.258 0.184 37,916 Total 0.335 0.214 122,297 Panel B: Subset sample Firm Size Group Mean Std. Dev. Obs. 0%-25% 0.362 0.235 4,473 25%-50% 0.268 0.182 4,724 50%-75% 0.279 0.190 4,839 75%-100% 0.248 0.161 4,907 Total 0.288 0.197 18,943 2.2.4 Correlation Results It is well known that debt and equity issuance are procyclical (Covas and Den Haan (2011)). However, less is known about leasing. I adopt two approaches which are used in Covas and Den Haan (2011) to examine the cyclical pattern of leasing behavior. The rst approach measures cyclicality by using the correlation between the cyclical components of lease share series and the cyclical component of real GDP. This approach is commonly used in the macroeconomics literature. The correlation between an individual rm's lease share and the real GDP is likely to be small because of idiosyncratic shocks. Therefore, I rst generate time series of average lease share by size group, and then document the cyclical behavior by looking at the correlation between the HP-ltered group average lease shares and HP-ltered GDP28. The cyclical properties of leasing is documented in Table 2.2. The corre- 28I use a weight of 100 in the lter to extract the cyclical component from annual data. 48 lation of output and the lease share of all rms in the full sample is negative, with a point estimate of -0.462. For the subset sample the correlation is - 0.563, strongly negative and statistically signicant. The countercyclical nature of rms' leasing behavior is more clearly presented when graphed. Figure 2.2 plots the cyclical components of average lease share series of all rms in the full sample and in the subset sample against GDP. All lease share series counter move with GDP29. The boom in 2000 is associated with considerable drop in the level of lease share, and the recession in 1991 is associated with a rise in the lease share. I conclude that leasing is coun- tercyclical over business cycles. These properties also hold, and are even stronger when we use the book value of asset as weights in calculating the aggregate lease share series. Table 2.2: Cyclical Behavior of the Lease Share Full Sample Subset Sample Size Group Correlation Size Groups Correlation 0%-25% -0.322 0%-25% -0.331 (0.354) (0.31) 25%-50% -0.426 25%-50% -0.628*** (0.324) (0.214) 50%-75% -0.54** 50%-75% -0.638*** (0.241) (0.186) 75%-100% -0.649*** 75%-100% -0.575** (0.193) (0.242) All rms -0.462 All rms -0.563** (0.3) (0.24) Notes: Standard errors are computed using a GMM approach adapted from the Hansen, Heaton, and Ogaki GAUSS programs, and are reported in parentheses. *, **, *** statistically signicant- ly dierent from zero at the 10%, 5% and 1% level of signicance. 29The lease share is dened as rental expenses over the sum of rental expenses and capital expenditures. I examine the cyclical patterns of rental expenses and capital expenditures separately. The rental expenses are countercyclical over business cycles, whereas the capital expenditures are procyclical. Firms substitute their purchases by leasing capital during recessions. 49 − 4 − 2 0 2 4 C yc lic al  c om po ne nt 1985 1990 1995 2000 2005 Year GDP Lease Share of the full sample Lease Share of the subset sample Figure 2.2: Cyclical Behavior of Lease Share 50 As documented in Table 2.2, I nd that for both samples, the counter- cyclical pattern is not very strong in the bottom quartile group (0%-25%). The correlation coecients in the bottom quartile group are small and in- signicant. The second quartile group (25%-50%) of the full sample has higher negative value than it has in the bottom quartile group, but the corre- lation coecient is still insignicant. The leasing behaviors in all remaining large size groups for the full sample are signicantly countercyclical. For the subset sample, all quartile groups except the bottom one have signicantly countercyclical pattern. 2.2.5 Panel Regressions Although it is common in the macroeconomics literature to characterize cyclicality by looking at the correlation, it cannot quantitatively assess the cyclical movements. The correlation coecients do not help us evaluate the magnitudes of the changes in the lease share over the business cycle. In this subsection, I use panel regressions to provide such an assessment. The literature has pointed out that cash 
ow and Tobin's Q are likely to be indicators of future rm protability. It is important to establish the em- pirical nding of rms' leasing behavior while controlling for cash 
ows and Tobin's Q. The specication is similar to the well known regression speci- cation used to study the eects of cash 
ows and Tobin's Q on investment. The specication of the regression equation is the following: LSi;t =0 + JX j=1 Ii;j(j)(j;tt+ j;tt 2 + j;Y cY c t + j;CF ( CFi;t Ai;t  CFj;t Aj;t ) + j;Q(Qi;t Qj;t)) + vi + ui;t (2.2) LSi;t is the lease share of rm i at year t. Ii;t(j) is an indicator function that takes on a value equal to 1 if rms i is in group j and equal to 0 if not in group j. I use the same four size groups for both the full sample and the subset sample. For the cyclical component of output Y ct , I use the scaled 51 HP-ltered GDP. The minimum observed value of HP-ltered GDP (Year 1991 in the sample period) is set to 0 and the maximum observed value (Year 2000 in the sample period) is equal to 1. Thus, the scaling ensures that the coecient j;Y c measures the change in the lease share when the economy moves from the worst to the best. The lease share displays trend, therefore, I add a linear and a quadratic trend as explanatory variables. Firm level cash 
ow is scaled by the total assets. In order to measure how the rms' cash 
ow and Tobin's Q change relative to the observed values of the other rms in the same group, I subtract cash 
ow over assets and Tobin's Q from each group mean in the corresponding period. In addition, I control for rm xed eect vi in the regressions. The results for panel regressions are reported in Table 2.3. Panel A reports the results for the full sample. All size groups have highly signicant and negative coecients on the cyclical component of GDP. The lease share is countercyclical in all size groups. The lease share increases approximately 2 percent when the economy moves from the best condition (Year 2000) to the worst condition (Year 1991). Coecients on cash 
ow are insignicant in most size groups except in the second quartile. 30. Tobin's Q is signicantly and positively related to leasing in all size categories. Tobin's Q is used as a measure of nancial constraints since such constraints imply that the value of capital inside the rm exceeds its replacement cost. Low cash 
ow and high Tobin's Q indicate that the rm is nancially constrained. A positive relationship between Tobin's Q and leasing suggests that nancially constrained rms lease more of their capital. Panel B of Table 2.3 reports the panel regression results of the subset sample which only includes rms that are in the Compustat data set in all 25 years. The lease share is also countercyclical in all size groups. When the economy changes from the best condition (year 2000) to the worst condition (year 1991), the fractions of leased capital increases more than 2 percent. 30I also have a robustness check by adding interaction terms of cash 
ow and Y c. The coecients on the interaction terms for all size groups are slightly positive. The results indicate that GDP 
uctuations have smaller eects on the leasing behavior of those rms that have more cash 
ow and are less nancially constrained. 52 Table 2.3: Panel Regression Results for the Lease Share Panel A: Regression of the Full Sample Y c Cash
ow/Asset Q Size 0%-25% -0.018*** 0.000 0.000** (0.003) (0.000) (0.000) Size 25%-50% -0.028*** -0.011*** 0.004*** (0.003) (0.001) (0.000) Size 50%-75% -0.032*** 0.002 0.004*** (0.003) (0.002) (0.000) Size 75%-100% -0.026*** 0.001 0.002*** (0.002) (0.004) (0.000) Within R2 0.032 No. of Obs. 101,908 Panel B: Regression of the Subset Sample Y c Cash
ow/Asset Q Size 0%-25% -0.021*** -0.001 0.002*** (0.006) (0.001) (0.000) Size 25%-50% -0.023*** -0.033** 0.003*** (0.006) (0.013) (0.001) Size 50%-75% -0.022*** -0.053** -0.001 (0.006) (0.020) (0.002) Size 75%-100% -0.024*** -0.059** 0.003* (0.006) (0.025) (0.002) Within R2 0.041 No. of Obs. 17,237 Notes: In the regressions, I control for rm xed eects. Standard errors are in parentheses. *, **, *** statistically signicantly dierent from zero at the 10%, 5% and 1% level of signicance. 53 Cash 
ow to assets is negatively related to leasing, and Tobin's Q is posi- tively related to leasing in most size groups. Overall, the panel regressions suggest that leasing is countercyclical for all size-sorted categories of listed U.S. rms. 2.2.6 Distribution The results of the panel regressions together with the negative correlation between the HP-ltered lease share and GDP suggest that leasing is counter- cyclical over business cycles. It is worth a comparison of the distributions of lease share in booms and recessions. Using the subset sample to draw the distributions avoids the disturbance from rms' enter and exit since the subset sample only includes rms who are in the data set every year. Figure 3.3 plots the distributions of lease share of the subset sample in 1991, 1999, 2000, and 2008. Year 1991 and year 2008 are two recessions over the sample period, and the boom years are 1999 and 2000. We clearly see that the distribution shifts to right in recession years. Firms lease more capital in recessions. 2.2.7 Why Leasing is Countercyclical From the prospective of lessors, in the U.S. bankruptcy code, it is much easier for a lessor to repossess an asset than it is for a secured lender. The lessor is less concerned with the lessee's default, and thus is unlikely to re- quire the lessee to provide collateral for a leasing agreement. The lessee only needs to pay a leasing fee for one period in advance. But on the other hand, if a rm purchases capital, they would need to pay the full price up front. Even if a rm uses debt to nance their purchase, the lender might require collateral for the loans. Therefore, leases are easier to nance than purchases. This is one advantage of leasing. As a result, rms who are more nancially constrained would lease more of their capital, as suggest- ed by Eisfeldt and Rampini (2009) and Zhang (2012). In terms of business cycles, rms are more nancially constrained during recessions than dur- ing booms. During recessions, demand and sales are low; thus rms have 54 0 1 2 3 K er ne l D en si ty 0 .2 .4 .6 .8 1 The lease share 1991 recession 2008 recession 2000 boom 1999 boom Figure 2.3: Distributions of Lease Share 55 less sales revenue and less internal funding. Moreover, debt and equity are both procyclical (Covas and Den Haan (2011)). As suggested by Figure 2.1, banks tighten credit standards for loans in recessions. The amount of funds that rms can raise externally through debt and equity issuance decline dur- ing an economic downturn. Firms don't have enough internal funding and can't raise enough external nance through debt and equity to support their capital purchases. Therefore, they decrease their investment on purchasing capital. Since rms buy less capital in recessions than they should have, the marginal return of capital is higher, and thus leasing is more attractive in recessions. Although leasing costs more in the long run, the benets of leasing outweigh the costs. Firms lease more in recessions. 2.3 Financial Constraint, Leasing versus Secured Borrowing 2.3.1 The Environment I consider an economy with overlapping generations. Time is discrete and indexed by t = 0; 1; 2; :::: At each time t, a generation with measure one is born. Generations live for two periods. In the economy, I have two good- s, a durable asset and a nondurable commodity. Like Kiyotaki and Moore (1997), we can think of the durable asset as land, which does not depreciate and has a xed total supply of K31. The nondurable commodity may be thought of as consumption good. Agents have identical preferences, born with the same endowments of land (e), and access to the same aggregate productive technologies (At). But agents dier in their idiosyncratic produc- tivity (!). The preference of an agent born in generation t are d0t+ d1t+1, where d0t and d1t+1 are the non-negative dividends at time t and at time t+ 1. At time t, each agent in generation t receives the endowment of land e, and observes the aggregate productivity At and his idiosyncratic productiv- 31Fixed supply of capital is not the crucial factor to the mechanism of the model. The key mechanism is the nancial constraint. 56 ity ! 2  which is distributed independently and identically across agents with density (!) on . Each young agent has access to a concave pro- duction technology that produces consumption good of At!e . At the end of period t, each young agent chooses how much to pay dividend, and how much to invest in buying capital and leasing capital to use in the production at the next period time t+1. They can buy capital (ib) or lease capital (il), and both ib and il are non-negative. Owned capital and leased capital are assumed to be perfect substitutes in production, k = ib+il. Furthermore, an agent can borrow or save at a rate of return R = 1=, which is determined exogenously. An agent can only borrow against a fraction 0    1 of the resale value of his owned capital and cannot borrow against future output. Thus, the agent needs to provide collateral for loans. At time t+1, each old agent (generation t) produces consumption good of At+1!t+1k , where k is the capital that the agent chooses at the end of period t. The !t+1 is agent's new idiosyncratic productivity which is distributed independently and identically across agents with density (!) on . After the production, each old agent sells his owned capital to agents from the next generation (generation t+1), returns the leased capital to the lessor, pays his debt and pays the remaining consumption goods as dividend. The government collects a tax 1  from holding the capital for both rms and nancial intermediary. Therefore, the government has (1 ) K unit of capital and give this equally to new born agents. I consider a stationary equilibrium where the price of the capital is de- termined such that the capital market is clear. 2.3.2 The Agent's Problem Consider the problem of an agent in generation t, t 2 0; 1; 2; :::. Since all generations are identical, I only consider the problem of one generation to simplify notation. Agents take the price of owning capital qt, the price of leasing capital UL, and the rate of return R as given. They maximize their utility by making choice of paying dividends, investment in buying capital and leasing capital, and borrowing after observing the rst period aggre- 57 gate productivity and idiosyncratic productivity. Specically, the agent's problem is: max (d0t;d1t+1;ib;il;b) Et(d0t + d1t+1) subject to d0t + qtib + ULil = At!e  + qte+ b (2.3) d1t+1 +Rb = At+1!t+1(ib + il)  + qt+1ib (2.4) Rb  Et(qt+1ib) (2.5) 0  il (2.6) 0  ib (2.7) 0  d0t (2.8) 0  d1t+1 (2.9) Equations (2.3) and (2.4) are the budget constraints of generation t for time t and t + 1. Constraint (2.5) is the borrowing constraint which restricts borrowing to a fraction  of the resale value of capital after tax. Moreover, (2.6), (2.7), (2.8) and (2.9) are the non-negativity constraints on investments and dividends. 2.3.3 Lessor's Problem In this work, I mainly focus on the demand side of leasing capital and assume the nancial intermediary is the lessor. A competitive lessor maximizes its prots with the equilibrium leasing rate UL as given. The lessor provides il unit of capital to the lessee. I assume that there is no deadweight cost when the lessor repossesses the capital32. And there are no transaction costs when trading leased capital. The nancial intermediary is able to sell the amount of capital il at the price qt+1 when the capital is returned at time 32In the U.S. Bankruptcy law, a lessor has specic advantages over a secured lender in terms of the ability to regain control of an asset. 58 t+ 1, and needs to pay a fraction of tax. However, leased capital is subject to an agency problem due to the separation of ownership and control. The lessor has to spend m units of nal good on maintenance after repossessing the capital. The lessor's problem is: max il ULil  qtil + qt+1il R  mil R The rst-order-condition implies that UL = qt + m R  qt+1 R (2.10) As long as the maintenance cost is greater than zero, the lease rate UL is higher than the implicit rental rate on owned capital which is qt  qt+1R . The lessor makes zero prots in equilibrium. The nancial intermediary is also a lender. It lends money to rms who want to borrow to nance their purchases at the exogenously given rate of return R. In the equilibrium, The nancial intermediary is indierent between lending capital or lending money, and it earns zero prots. 2.3.4 Equilibrium A equilibrium for an economy f; ;m; ; ; ; (!)g is a sequence of prices qt and an allocation of dividends fd0t(!); d1t+1(!)g, investments in leased and owned capital fibt(!); ilt(!)g, and borrowing fbt (!)g for all ! 2  such that: 1. The allocation solves the problem of each agent, 8! 2 ; t, 2. Given the price of capital qt, the capital market clear 8t:X !2  (!)(ilt(!) + i  bt(!)) =  K The left hand side is the aggregate amount of capital bought or leased by generation t at the end of period t. The right hand side is the aggregate amount of capital which are available for purchasing or leasing at the end 59 of period t. The government collects a fraction of 1  of K at the end of period t, and distribute them equally to new born generation t + 1 at the beginning of period t+1. In this work, I only consider a partial equilibrium, and I assume that the nancial intermediary is willing to provide debt to agents at a exogenous given rate of return R. Therefore, the debt market is not clear in equilibrium. 2.3.5 Characterization If the purchase price of the capital was not expensive in terms of its leasing rate, then all agents would only buy capital, since the implicit rental rate on owning capital is cheaper than the lease rate as long as the maintenance cost is greater than zero. In this case, all capital is purchased in the economy. On the other hand, if the purchase price of the capital was too expensive in terms of its leasing rate, then all agents would never purchase their capital and instead choose to lease capital. Under the condition, all capital is leased in the economy. In order to guarantee an equilibrium in which leasing and purchasing coexists, the price of capital is assumed to satisfy the following assumption. Assumption 1 The price of capital satises Rm1 > q > Rm 1 in equilibri- um. The proofs of all assumptions and propositions are in the Appendix. I characterize the solution to the agent's problem under the assumption. In such an economy, any agent who leases a positive amount of capital must be nancially constrained and he pays zero dividend in the rst period. The nancially constrained agent always wants to postpone paying dividend because the preference is linear. I obtain the following proposition. Proposition 6 Suppose Rm1 > q > Rm 1 . If il > 0, then the multiplier on the borrowing constraint B > 0 and d0 = 0. I characterize the solution to the agent's problem as a function of his rst period idiosyncratic productivity !. 60 Proposition 7 There exist cuto levels of idiosyncratic productivity !L < !B < ! and levels of capital k < k such that the solution to the agent's problem satises: 1. For !  !L, il > 0, ib = 0, and b = 0. Moreover, @il@! > 0. 2. For !L  !  !B, il > 0, ib > 0, and b = qibR . il+ ib = k. Moreover, @il @! < 0 and @ib @! > 0. 3. For !B  !  !, il = 0, ib > 0, and b = qibR . Moreover, @ib@! > 0. 4. For ! > !, il = 0, ib = k, and b < qibR . The lease versus buy decision depends on agents' rst period idiosyncratic productivity. Agents with low idiosyncratic productivity (! < !L) are most nancially constrained rms. Their marginal cost of leasing capital is small- er than their marginal cost of buying capital. Thus, they only lease capital. Since they don't own capital to be the collateral, they can't borrow from the nancial intermediary. Moreover, their marginal product of producing is larger than their marginal cost of leasing. They lease as much capital as they can. When the idiosyncratic productivity increases to a range (!L; !B), agents invest in both leased capital and owned capital. Now, the marginal cost of leasing is the same as the marginal cost of owning. As idiosyncrat- ic productivity increases, agents substitute leasing by purchasing capital. When agents' idiosyncratic productivity is in the range of (!B; !), they on- ly purchase capital. They are also nancially constrained, and borrow at their full debt capacity. When agents have very high idiosyncratic produc- tivity ( ! > !), they are not constrained. They only purchase capital. They choose a optimized amount of capital to make the marginal product equals to the marginal cost. Their collateral constraints are relaxed as idiosyncratic productivity increases. 2.3.6 A Temporary Increase in Aggregate Productivity As mentioned in the last subsection, there are several cuto levels of idiosyn- cratic productivity which determine lease versus buy decision in the equilib- 61 rium. These cuto levels depend on the rst period aggregate productivity. When we have a temporary positive shock to aggregate productivity, these cuto levels of idiosyncratic productivity decrease. Because it is a temporary shock on aggregate productivity at time t, it doesn't aect generation t + 1's investment decision. The demand side of the capital at period t+ 1 would not change. In addition, generation t has to sell all his owned capital at the end of period t+1, the supply side of the capital in period t+1 is also xed. Therefore, the price of capital qt+1 in the period t+1 would not change. A temporary shock to aggregate productivity at time t only aects agents in the current generation t. Agents are richer when a positive aggregate productivity shock hits, and they are less nancially constrained compared to with no shock. They would like to invest more capital because of larger net worth. Thus, the price of capital would increase since there is a constant supply of capital in the economy. The lease rate of capital also goes up. Meanwhile, their cuto level of idiosyncratic productivity of leasing (!L) goes down. Some agents, who would only lease capital before, both purchase and lease capital now. The cuto level of idiosyncratic productivity of purchasing capital (!B) goes down as well. Some agents who would both lease capital and purchase capital only purchase capital now. Putting it together, there are less agents who lease capital when the shock hits. Moreover, an increase in the lease rate decrease the amount of capital agents can lease although they face a positive aggregate productivity shock. Those agents who lease lease less of their capital compared to with no shock. Therefore, the total amount of leased capital in the economy decreases. A numerical example can give us a good understanding about how things go when there is a positive productivity shock. Table 2.4 shows the origi- nal steady state value of the numerical example and the new values when there is a 1 percent temporary increase in the aggregate productivity. When the shock hits, the price of capital is 0:17 percent higher than the original steady state, and the leasing price increase 1:19 percent. All cuto level- s of idiosyncratic productivity drop. Now, few agents lease capital. The extensive margin decreases leasing by 1:39 percent. In addition, a one per- 62 cent increase in aggregate productivity induces a one percent increase in net worth, but the leasing price increase more than one percent. For those agents who lease, they lease less than they should if no shock hits. This is the intensive margin. The intensive margin decreases leasing activity by 2:7 percent. Together, the leasing activity decreases 4:1 percent in total. This numerical example clearly shows that a positive shock to aggregate produc- tivity causes agents lease less capital. The nancial constraint can explain the countercyclical pattern we observed in section 2. Table 2.4: Results of a Numerical Example Original 1% Temporary Increase in TFP Steady State New Value Percentage Change Price of Capital 16.679 16.708 0.17% Lease Rate 2.428 2.457 1.19% Total Leased Capital 8.466 8.119 -4.10% Cuto Level 1 !L 0.166 0.162 - Cuto Level 2 !B 0.514 0.5 - Cuto level 3 ! 2.418 2.361 - Total Debt 1,053 1,057 0.38% Extensive Margin -0.118 -1.39% Intensive Margin -0.229 -2.70% Notes: In this numerical example, I assume that the production technology pa- rameter  = 0:3, the collateralization rate  = 0:8, the tax rate of selling capital 1   = 0:05, the discount factor  = 0:96, and the interest rate R = 1:04. I also assume that the steady state aggregate productivity At is equal to 1. I assume there are 2000 agents in each generation, and their idiosyncratic productivity is uniformly distributed: ! = [0:001 : 0:001 : 2]. The mean of the idiosyncratic productivity is 1. The maintenance cost for the lessor of one unit of capital is assumed to be one unit of nal good. There are 100 unit of capital in the economy. 2.4 Concluding Remarks This chapter documents the cyclical behavior of leasing of listed U.S. rms. I nd that leasing, as one of the most important external sources of nancing, is countercyclical over the business cycle. Firms lease more during bad times, and are more willing to buy capital in up cycles. The distribution of the lease 63 share shifts to the right in recession years. I provide a plausible explanation about this countercyclical pattern. One key benet of leasing is that leases are easier to nance than purchases. This benet is particularly important to rms with nancial constraints. Firms face tighter nancial constraints during recessions. Therefore, leasing is more attractive during recessions. In this chapter, I also develop a model to explain the observed countercyclical pattern of leasing by including the nancial constraint. The model predicts that a positive technology shock can generate a rapid decrease on the lease share in the economy. It is consistent with the empirical evidence. Zhang (2012) suggests that uncertainty aects corporate leasing deci- sions. We know that over business cycles, uncertainty is strongly counter- cyclical (Bloom et al. (2010), Gilchrist et al. (2010)). Uncertainty could be another explanation of the countercyclical pattern of leasing. Future work might consider developing a model with both the nancial constraint and uncertainty to match the observed pattern. Furthermore, current business cycle models typically assume that ex- ternal nance occurs only through one-period debt contracts. It would be interesting to modify the current business cycle models and examine the eects of shocks on the real economy by introducing the option of leasing. 64 Chapter 3 Leasing, Legal Environments, and Growth: Evidence from 81 countries 3.1 Introduction Previous literature shows that leasing is one of the most important sources of external nance for both publicly traded rms and small and medium-size rms33. However, our knowledge about corporate leasing has been mostly derived from the U.S. rm data. There was little evidence of leasing in other countries. Given the importance of leasing in corporate external nancing, the use of leasing across dierent countries should be a topic of signicant research interest to academics and an issue of great importance to policy makers around the world. This study attempts to ll the gap in the literature by examining panel data about 70,000 listed rm-year observations in 81 developed and developing countries from Compustat Global. In this chapter, I rst examine the leasing choices of listed rms across dierent countries. Evidence suggests that rms in the developed countries lease more of their capital than those in the developing countries. For exam- ple, Japan has the highest ratio of lease share (51 percent) while an average rm in Egypt only leases 5 percent of its capital. Why do some countries have so much larger lease share than others? Then, I investigate what factors can explain this large dierence. Many literature suggests that the dier- 33Zhang (2012) found that an average publicly-traded rm in the U.S. leases more than 37 percent of its capital, and Eisfeldt and Rampini (2009) indicated that the smallest decile rms in the census data lease 46 percent of their capital. 65 ences in the legal maturity might help explain why rms are nanced so dierently in dierent countries (La Porta et al. (1997) and La Porta et al. (1998)). Following their thoughts, I examine the relationship between leas- ing and legal environments. I use three variables { the rule of law, legal rights, and economic freedom to measure the legal environments. Previous literature (Eisfeldt and Rampini (2009), Berger and Udell (2006)) indicates that leasing should be prevalent in low income countries and in environments with weak law enforcement. However, I nd that leasing decisions depends on legal environments but in an opposite way. The use of leasing increases signicantly with increasing in the rule of law, legal rights, and economics freedom. Although leasing might be a good source of external nance in weak legal environments where rms have diculty to obtain loans, rms would tend to avoid the use of leasing contracts because the contracts are costly to enforce. I also investigate the relationship between leasing and growth. My anal- ysis indicates that leasing has a measurable positive eect on rm growth. Leasing can help rms increase their capital availability and improve their operation eciency, and thus may facilitate rm growth. Consequently, I examine the relationship between leasing and growth at the aggregate level. I nd that subsequent growth in GDP per capita is signicantly positively related to the average lease share of the country. Taken together, leasing nance might play a positive rule in growth. The results provide a policy implication that possible adjustments in legal systems could facilitate the availability of leasing and thus might generate real economic gains. The chapter is organized as follows. The next section reviews the related literature. Then, Section 3 describes the data sets, and in section 4 I present the main results of the work. Concluding remarks are oered in section 5. 3.2 Literature Review This chapter is related to several strands of literature. First, a series of paper study the corporate decisions to lease. Main focus of the corporate nance literature is the tax advantages of leasing. However, the economics 66 of leasing are recognized beyond tax minimization. Smith and Wakeman (1985) provide an informal list of non tax characteristics of users and lessors that in
uence the leasing decision. Following Smith and Wakeman (1985), a small but growing literature have focused on the non tax aspects of leasing. In particular, Eisfeldt and Rampini (2009) incorporate nancial constraints into a model of the choice between leasing and secured lending. Their model implies that more nancially constrained rms lease more of their capital than less constrained rms. Zhang (2012) investigates the role of uncertainty and nancial constraint in understanding the leasing decisions of corporate rms. She nds that rms with high uncertainty over their future prots and rms that are more nancially constrained prefer to lease more of their capital than rms with low uncertainty and rms that are less nancially constrained. One key potential benet of leasing, as analyzed in Eisfeldt and Rampini (2009) and Zhang (2012), is to allow rms that are subject to nancial con- straints and don't have enough assets to pledge for loan collateral to access capital. Furthermore, people commonly believe that rms in low income countries or in environments with weak law enforcements are dicult to ob- tain loans. Thus, it is believed that the advantage of leasing on easy access to capital may be particularly important in low income countries and countries with weak legal environments. Moreover, there are more uncertainty about property rights in countries with weak legal environments. Leasing would be a better source of external nance than loans in low income countries and countries with weak legal environments. Although there is not a nite con- clusion, previous literature indicates that leasing should be prevalent in low income countries and in environments with weak legal environments. How- ever, the ndings in this work do not support the hypothesis. I nd that developed economies have higher usage of leasing activities than developing economies, and rms in strong legal environments lease more than those in weak legal environments. A study by Casas-Arce and Saiz (2010) rejects the above hypothesis as well by using evidence from housing markets in the developing countries. They show that renting of housing is underutilized in countries with weak law environments. Market participants will tend to 67 avoid the use of renting contracts in countries with weak legal systems be- cause the contracts are costly to enforce. Leasing is a substitute of bank nancing in presence of weak legal environments, but weak institutions at the same time also hinder the development of leasing. Secondly, a strand of cross-country research in the literature investigates the impact of business environments on nance. La Porta et al. have a series of paper (La Porta et al. (1997) and La Porta et al. (1998)) study law and nance by using country level data from 49 countries. They show that countries with poorer investor protections, measured by the character of legal rules and the quality of law enforcement, have smaller and narrow- er capital markets. And they nd that common-law countries generally have the strongest legal protections of investors, and French-civil-law coun- tries have the weakest. Several papers also explore the relationship between institutions and external nance by using rm level data. For example, Chavis et al. (2011) study small rms in over 100 countries by using World Business Environment Survey data set. They nd that across all countries younger rms rely less on bank nancing and more on informal nancing. Particularly related to this work is Brown et al. (2011). Their research uti- lizes data from the World Bank Investment Climate Survey, and studies the use of all sources of external nancing around the world. They nd coun- tries with weak rule of law use much less formal nancing (bank and lease nancing) but instead rely more on informal sources of capital (friends and family nancing). Their sample is a cross sectional data while my sample is a panel data set. Their sample includes small and medium-sized rms and well represents low income countries. My sample focuses on listed large rm- s which have more precise accounting procedures and nancial statements, and my sample covers more high income countries. In addition, their paper focuses more on the switch out of informal nance toward to formal nance while my work's focus is on how legal environments aect leasing activities. Lastly, this work is related to the literature on growth. Cross-country evidence has shown positive eects of nancial system development on GDP growth (Levine et al. (2000), Levine (2005)). Moreover, several papers ex- plore the eect of capital structure decisions on rm performance, at both 68 the rm and the country level. For instance, Saeed (2009) nd that formal - nancing sources facilitate rm growth in transition economies. Ayyagari et al. (2010) studies a sample of Chinese companies, and conclude that although more rms used informal nancing than bank nancing, only bank nancing was associated with higher growth rates. In particular, several papers point out the special role of lease nancing in growth (Berger and Udell (2006), Brown et al. (2011)). Leasing can be useful in facilitating greater access to nance and helps alleviate rms' growth constraints. My work adds to this literature by examining the eect of leasing on both rm growth and GDP growth. 3.3 Data and Measurements 3.3.1 Data The data source that this work uses is Standard and Poor's Compustat Global. Included in the panel are annual observations of listed rms from 1995 to 201034. I restrict the sample to countries that have at least 5 rm observations in the sample period. Thus, in the sample, I have rms from 81 countries 35. Several industries are also excluded from the panel in this work. I exclude nancial (two-digit SIC codes: 60-67), and utilities (49). I also exclude industries including those where real property or natural resources are a large portion of rm's capital, like petroleum rening (29), mining (10-14), agriculture and shery (1-9). In this work, I focus on the leasing behavior of the lessee. Although commercial banks, insurance companies, and nance companies do most of the leasing, it is necessary to exclude those industries where the main line of business involves leasing such as auto repair (75) and computer rental and leasing (73). Thus, I examine rms in construction, manufacturing, transportation, wholesale, retail, service and public administration. These selection criterions yield an unbalanced panel of 13,563 rms with 75,398 rm-year observations in 81 countries. 34The earliest measure of legal environments starts from 1995 35Detail information about 81 countries is shown in the appendix. 69 3.3.2 The Measure of Leasing The main data item from the Compustat that this work uses is the reported rental expenses from the income statements. The fraction of capital from leasing (the lease share) is measured by the ratio of rental expense to the total cash expenditures on rent and investment36. The total cash expen- ditures on rent and investment is the sum of rental expenses and capital expenditures. lease share = rental expenses rental expenses+ capital expenditures (3.1) Lease shares below 0 are set equal to 0, and lease shares above 1 are set equal to 1. An alternative measure of lease shares would be the ratio of rental ex- penses to the total capital cost which is the sum of rental expenses, deprecia- tion expenses, and the opportunity cost of xed assets (Sharpe and Nguyen (1995)). However, the Compustat Global data set doesn't have any infor- mation, such as reported short-term average borrowing rate, to represent the rms' opportunity costs. I will focus on the measure of lease shares constructed by rental expense over total cash expenditures on rent and in- vestment in this chapter. 3.3.3 Measures of Legal Environments In my analysis, I use three measures of legal environments that have been identied by previous studies as important institutional characteristics for external nance and that are available for a wide range of countries and years that I examine. The rst measure is the rule of law which is from the Worldwide Gov- ernment Indicators (WGI) project over the period 1996 to 2010. The rule of law (Kaufmann et al. (2010)) captures "perceptions of the extent to which agents have condence in and abide by the rules of society, and in partic- 36Eisfeldt and Rampini (2009) use the same measure except that their information of rental expenses is from Census data. 70 ular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence". It is a broad measure of the legal environment, but it also contains specic factors that are particularly related to external nance, such as the quality of contract enforcement and property rights. The rule of law ranges from -2.5 to 2.5. In the sample, Zimbabwe is the country with the weakest rule of law. Four northern European countries, Finland, Norway, Denmark, and Sweden, have the highest scores of the rule of law. In order to supplement the rule of law, I utilize a second indicator of legal environment { legal rights from the World Bank. The legal rights measures the degree to which collateral and bankruptcy laws protect the rights of borrowers and lenders and thus facilitate lending. The index ranges from 0 to 10, with higher scores indicating that these laws are better designed to support access to credit. The information of legal rights is available since 2004. New Zealand, United Kingdom, Singapore, Hong Kong, Latvia, Malaysia, South African, and Kenya have the highest legal rights (10 points), while Venezuela has the lowest score (just 1 point). Lastly, I consider the economic freedom index which is constructed by the Heritage Foundation. It is on a scale of 0 to 100 and collected since 1995. The index of economic freedom measures country performance in 10 separate areas, property rights, freedom from corruption, scal freedom, government spending, business freedom, labor freedom, monetary freedom, trade freedom, investment freedom, and nancial freedom. Hong Kong is the region with the highest economic freedom, and Zimbabwe is the least economic free country. These three measures capture a wide range of important legal factors related to the possible determinants of rms' leasing behavior. The cor- relations of these measures are shown in Table 3.1. Although these three measures are signicantly correlated, they appear to capture dierent fea- tures of legal environments. 71 Table 3.1: Correlations between Measures of Legal Environments Rule of Law Legal Rights Economic Freedom Rule of Law 1 Legal Rights 0.338 1 (0.003) Economic Freedom 0.83 0.42 1 (0) (0) Notes: numbers in parentheses report the signicance level of each correlation coe- cient. 3.4 Results 3.4.1 Summary Statistics Table 3.2 reports country-level (Panel A) and rm-level (Panel B) summary statistics of my sample by country income group37. I use the World Bank denitions to categorize countries into low income, lower-middle income, upper-middle income, and high income groups. I have a limit coverage on low income countries. Only three low income countries are covered in the sample (Kenya, Zimbabwe, and Bangladesh). But other country income groups are well represented. The average lease share ranges from 16 percent in lower- middle income countries to over 30 percent in high income countries. GDP per capita ranges from 434 constant 2000 USD in low-income countries to 22,933 USD in high-income countries. Although the average lease share does not strictly monotonically increase with GDP per capita at country income group level, rms in higher income countries use leases more frequently than those in lower income countries. As a more careful investigation, I plot the relation of the average lease share at the country level and the average GDP per capita in Figure 3.1. The results reveal a positive relation between leasing and GDP. It indicates that leasing is associated with the increase of GDP. 37Descriptive statistics of each country are given in the Appendix. 72 ARE ARG AUS AUT BEL BGD BGR BHR BMU BRA BWA CHE CHL CHN COL CYP CZE DEU DNK EGY ESPEST FINFRA GBR GRC HKG HRV HUNIDN IMN IND IRL ISL ISRITA JAM JOR JPN KAZ KEN KOR KWT LKA LTU LUX LVA MAR MEX MLT MUS MYS NGA NLD NOR NZL OMN PAK PER PHL POL PRT QAT ROU RUS SAU SGP SVK SVN SWE THA TTO TUN TUR WN VENVNM ZAF ZMB ZWE 0 . 1 . 2 . 3 . 4 . 5 A ve ra ge  L ea se  S ha re 0 20000 40000 60000 GDP per capita Figure 3.1: Leasing and GDP per capita Notes: The unit of GDP per capita is constant 2000 USD. Average lease share is the mean of lease share of all rm year observations in the country. 73 Table 3.2: Summary Statistics Panel A: Country-Level Variables Low Lower-Middle Upper-Middle High All Income Income Income Income Countries No. of Country 3 10 23 45 81 No. of Country-Year Obs. 35 110 245 534 924 Average Lease Share 0.223 0.163 0.194 0.313 0.26 (0.142) (0.128) (0.13) (0.158) (0.16) GDP per Capita 434 878 3808 22933 14166 (75) (431) (1675) (12310) (13726) Rule of Law -1.149 -0.428 -0.039 1.204 0.567 (0.391) (0.442) (0.633) (0.57) (0.944) Legal Rights 8 5.507 5.679 6.802 6.339 (1.449) (2.402) (2.462) (2.117) (2.336) Economic Freedom 46.84 55.314 62.269 70.335 65.305 (10.845) (4.129) (7.167) (7.862) (9.899) GDP growth (%) 0.531 3.663 3.325 1.9 2.449 (5.989) (2.828) (4.482) (3.575) (3.965) Panel B: Firm-Level Variables Low Lower-Middle Upper-Middle High All Income Income Income Income Countries No. of Firms 42 2,349 2,064 9,108 13,563 No. of Firm-Year Obs. 172 14,227 10,496 50,503 75,398 Sales growth (%) -36.8 8.6 3.6 6.8 6.6 (164.7) (54.5) (52.6) (58.8) 57.9 Asset growth (%) -53.4 7.7 5.5 9.3 8.2 (152.2) (39.2) (39) (46.6) (44.6) Prot growth (%) -23.2 13.3 5.3 8 8.7 (151.4) (102.5) (91.9) (89.9) (93.4) Notes: The Sample consists of rms on Compustat Global les over the period 1995 through 2010. Firms in construction, manufacturing, transportation, wholesale, retail, service and public administration are included in the sample. Reported values are sample means except numbers in parentheses are standard deviation. Income groups are determined by World Bank Classication. The unit of GDP per capita is constant 2000 USD. GDP growth is the GDP per capita growth. 74 slower growth. The Panel B of Table 3.2 presents rm-level statistics. I have a large number of rms in low-middle, upper-middle, and high income countries in the sample. Each group has more than 2,000 rms and 10,000 rm-year observations. But there are fewer rms and rm year observations in the low income group. The data set contains only listed rms, and low income countries have few listed rms. I also report rm growth in terms of sales, assets, and prots in the panel B of Table 3.2. Firms in lower-middle income countries have the fastest growth in sales and prot, and rms in high income countries have the fastest growth in assets. Firms in low income countries have negative growth rates in both sales, assets, and prots. 3.4.2 Leasing and Legal Environments Previous literature (Eisfeldt and Rampini (2009), Zhang (2012)) compared the relative merits of leasing and purchasing which is usually nanced by debt. The law in the U.S. implies that a lender has less ability than a lessor to regain control of an asset, if rms default or are in bankruptcy. They believe it is probably the case in most legal environments that leasing facilitates regaining control of an asset, and thus leasing is easier to nance and enables rms access more capital. They also suggest that this advantage may be particularly important in a weak legal environment because rms would have diculties to nance their purchase by debt with weak legal enforcements. Thus, the literature (Berger and Udell (2006)) indicates that leasing might be more prevalent in environments with weak legal enforcements. In this subsection, I test this hypothesis. At a rst pass, I plot the relations of leasing and measures of legal environments at country level. Figure 3.2 plots the use of leasing over the rule of law, Figure 3.3 plots the relationship between leasing and legal rights, and Figure 3.4 plots leasing and economic freedom. These plots suggest that leasing has a strong positive relation to all measures of legal environments. The positive relation is against the hypothesis that leasing is more prevalent in weak legal environments. However, these plots do not control for other 75 factors, and do not provide formal tests. ARE ARG AUS AUT BEL BGD BGR BHR BMU BRA BWA CHE CHL CHN COL CYM CYP CZE DEU DNK EGY ESPEST FINFRA GBR GRC HKG HRV HUNIDN IND IRL ISLISR ITA JAM JOR JPN KAZ KEN KOR KWT LKA LTU LUX LVA MARMEX MLT MUS MYS NGA NLD NOR NZL OMN PAK PER PHL POL PRT QAT ROU RUS SAU SGP SVK SVN SWE THA TTO TUN TUR TWN VEN VNM ZAF ZMB ZWE 0 . 1 . 2 . 3 . 4 . 5 A ve ra ge  L ea se  S ha re −2 −1 0 1 2 Rule of Law Figure 3.2: Leasing and the Rule of Law Notes: The value of leasing is the mean of all rm year observations of the country in the sample. The value of the rule of law is the mean of the rule of law of the country over the sample period. 76 ARE ARG AUS AUT BEL BGD BGR BHR BRA BWA CHE CHL CHN COL CYP CZE DEU DNK EGY ESPEST FINFRA GBR GRC HKG HRV HUNIDN IND IRL ISL ISR ITA JAM JOR JPN KAZ KENKOR KWT LKA LTU LUX LVA MAR MEX MUS MYS NGA NLD NOR NZL OMN PAK PER PHL POL PRT QAT ROU RUS SAU SGP SVK SVN SWE THA TTO TUN TUR VEN VNM ZAF ZMB ZWE 0 . 1 . 2 . 3 . 4 . 5 A ve ra ge  L ea se  S ha re 0 2 4 6 8 10 Legal Rights Figure 3.3: Leasing and Legal Rights Notes: The value of leasing is the mean of all rm year observations of the country in the sample. The value of the legal rights is the mean of the legal rights of the country over the sample period. 77 ARE ARG AUS AUT BEL BGD BGR BHR BRA BWA CHE CHL CHN COL CYP CZE DEU DNK EGY ESP EST FINFRA GBR GRC HKG HRV HUNIDN IND IRL ISLISR ITA JAM JOR JPN KAZ KEN KOR KWT LKA LTU LUX LVA MAR MEX MLT MUS MYS NGA NLD NOR NZL OMN PAK PER PHL POL PRT QAT R U RUS SAU SGP SVK SVN SWE THA TTO TU TUR TWN VEN VNM ZAF ZMB ZWE 0 . 1 . 2 . 3 . 4 . 5 A ve ra ge  L ea se  S ha re 20 40 60 80 100 Economics Freedom Figure 3.4: Leasing and Economic Freedom Notes: The value of leasing is the mean of all rm year observations of the country in the sample. The value of the economic freedom is the mean of the economic freedom of the country over the sample period. 78 To more rigorously estimate the relations between leasing behavior and legal environments, I estimate multiple regressions. First, I estimate regres- sions at country level and present the results in the panel A of Table 3.3. The rst three columns in the panel A of Table 3.3 show the results of pooled OLS regressions. The dependent variables are the average lease share of each country in each year. The independent variables are log of GDP per capita and indicators of legal environments. Coecients on the GDP in the rst three columns are signicantly positive. Developed countries use leasing more extensively than developing countries. It is consistent with Figure 3.1. What more important is that all measures of legal environments have positive eects on countries' average lease share. A one standard devia- tion increases in the rule of law, legal rights, and economic freedom increase the average lease share by approximately 3.3 percent, 4.2 percent, and 1 percent. The economic eects are large. The adjusted R square is high when I include legal rights as one independent variable. The legal rights, which measures how collateral and bankruptcy laws protect the rights of borrowers and lenders, contains the most relevant legal factor to explain the leasing activity. Overall, the results of the pooled OLS regressions suggest that weak legal environments constrain leasing activity. It is opposite to the view suggested by some previous research that weak legal environments promote leasing. Legal environments can aect leasing in two aspects. On one hand, from the lessee's prospective, rms in weak legal environments can be dicult to obtain loans. Thus, leasing is valuable in those countries, and leasing could be a better alternative option for rms who want to access capital. According to this logic, leasing should be popular in countries with weak legal environments. However, on the other hand, potential lessors would tend to avoid the use of leasing contracts in countries with weak legal sys- tems. Because the contracts could be very costly to enforce. Lessors may decide to avoid possible contractual disputes by choosing not to lend cap- ital. In addition, the rights of the lessor to regain control of an asset is aected by legal environments. Although it is easier than a loan lender, the lessor might still have diculties to repossess its owned asset in weak legal 79 Table 3.3: Leasing and Legal Environments Panel A: Results of Regressions at the Country Level Pooled OLS Regressions IV Regressions (1) (2) (3) (4) (5) (6) GDP per Capita 0.033*** 0.053*** 0.042*** -0.012 0.007 0.055*** (log) (0.007) (0.004) (0.005) (0.019) (0.012) (0.004) Rule of Law 0.035*** 0.116*** (0.01) (0.032) Legal Rights 0.018** 0.014*** (0.002) (0.003) Economic Freedom 0.001** 0.008*** (0.001) (0.002) No. of Obs. 722 496 877 706 489 859 Adj. R2 0.232 0.358 0.178 0.176 0.37 0.115 Panel B: Results of Regressions at the Firm Level Pooled OLS Regressions IV Regressions (1) (2) (3) (4) (5) (6) GDP per Capita 0.04*** 0.054*** 0.061*** 0.04*** 0.054*** 0.049*** (log) (0.003) (0.002) (0.002) (0.004) (0.002) (0.003) Rule of Law 0.034*** 0.036*** (0.006) (0.01) Legal Rights 0.003** 0.003** (0.001) (0.002) Economic Freedom -0.001** 0.001*** (0.000) (0.000) Firm Specic Controls YES YES YES YES YES YES Time Fixed Eects YES YES YES YES YES YES Industry Fixed Eects YES YES YES YES YES YES No. of Obs. 13,296 10,457 14,093 13,295 10,457 14,092 Adj. R2 0.345 0.371 0.341 0.345 0.371 0.34 Notes: The dependent variables in Panel A are the average value of lease shares of each country- year. The dependent variables in Panel B are the value of lease shares of each rm in each year. Firm specic controls are rm size, cash 
ow, leverage, dividend, R&D and tax. The rst three columns in each panel are the pooled OLS regressions, and the last three columns are the IV regressions. The instruments for the rule of law, legal rights, and economic freedom are legal origin dummies. Standard errors are in parentheses. *, **, *** statistically signicantly dierent from zero at the 10%, 5% and 1% level of signicance. 80 environments with bad property rights and bankruptcy law if lessee rms default or in bankruptcy. With these concerns, potential lessors are hesitant to lend capital, and the supply of leasing in weak legal environments can be very small. Moreover, potential lessees might also worry about the high enforcement cost in case of contractual disputes, and thus have less incen- tive to use leasing contracts. From this aspect, weak legal environments constrain the development of leasing. The results suggest that the second aspect dominates the rst one38. Possible problems with the pooled OLS regressions are the endogenity issue and the reverse causality. To address these issues I use the legal origin dummies as instruments to measures of legal environments. Most countries in the world inherited their legal system from colonial time. Legal systems are aected by their origins. Legal systems based on the laws of England are described common law tradition, compared to French, German, and S- candinavian civil law. In general, common law countries tend to have less regulation, stronger property rights protection, less corruption and more ecient governments, and more political freedom than countries with any other origins (La Porta et al. 1999). Law origins are highly correlated with legal environments. Moreover, except for the role through legal en- vironments, legal origins should be exogenous to rms' nancing decisions. Therefore, I use legal origin dummies as instruments of legal environments. I use four dummies to identify the legal origin of each country: English Common Law; French Commercial Code; German Commercial Code; Scan- dinavian Commercial Code; and Socialist/Communist laws. The results of the IV regressions are presented in the last three columns of the panel A of Table 3.3. Again, legal environments have signicant and positive coe- 38This result that leasing is associated with the increase of legal environments is not apparently contrary to the conclusion of the rst two chapters. In the rst two chapters, I only consider the lessee side and nd that rms who are more constrained lease more capital. However, dierent countries have dierent leasing markets and dierent lessors. Lessors decide how much capital they would provide to the market. In those low income countries and countries with weak legal environments, lessors are hesitant to provide capital. They want to avoid possible contractual disputes, and they are worried about the repossessing process. Thus, leasing is less popular in low income countries and countries with weak legal environments. 81 cients on the average lease share. The estimated coecients of legal rights and economic freedom in the IV regressions are close to the estimates of the pooled OLS regressions, but the estimated coecient of the rule of law in the IV regression is much larger than it is in the pooled OLS regressions. Brown et al. (2011) have a similar analysis of probit regressions by using data of small and medium rms from the World Bank Investment Climate Surveys. Their dependent variable is a binary variable describing the use of leasing. They showed that rms' decision to use leasing or not is posi- tively correlated with the rule of law39. My results are consistent with their conclusion but more robust. I also estimate regressions at rm level. The dependent variables are the lease share of rm i in year t. The independent variables are log of per capita GDP and measures of legal environments. In these rm year level regression- s, I control some rm-specic variables which could aect leasing decisions. Firm-specic control variables are rm size (proxied by number of employ- ees), cash 
ow (proxied by operating income plus depreciation/beginning-of- year book assets), leverage (proxied by book value of long-term debt/current book assets), dividend dummy (equals to 1 if paying dividend, otherwise e- quals to 0 ), R&D (proxied by R&D expenses over sales), and tax (proxied by average tax rate). Moreover, rms in dierent industries could behave very dierently. Manufacturing industry has the lowest ratio of lease share and retail industry has the highest ratio of lease share. Retail stores often rent the place, and rental fee is a large fraction of their total expenses on capital. Therefore, it is necessary to control for industry xed eects40. I control for time xed eects as well. Firm level results of both OLS regressions and IV regressions are pre- sented in the panel B of Table 3.341. The instruments of legal environments 39Their results about legal rights are insignicant. 40I am interested in the eects of legal environments on rms' leasing behavior. Legal environments are the same to every rm in the same country. Firm xed eects include country xed eects. Thus, I don't control for rm xed eects in these regressions but instead control for industry xed eects. 41Many rms have missing data on rm specic variables. Thus, sample size shrinks to over 10000 observations. 82 are still dummies of legal origins. For simplicity, I only report the coef- cients on the log GDP per capita and legal environment measures. The results indicate that both GDP and legal environments are important de- terminants of rms' leasing decisions. The rule of law and legal rights are signicantly and positively related to the use of lease nancing in both OLS and IV regressions. The OLS regression suggests that economic freedom negatively aects rm's leasing behavior, but the IV regression indicates a positive relationship between economic freedom and leasing. The results in the second panel of Table 3.3 also suggest that weak legal environments constrain leasing activities. 3.4.3 The Eect of Leasing on Growth Clearly, leasing pattern varies across rms and countries. Then one question naturally raises. Does leasing play a role in promoting growth? My panel data allow me to provide some insight on this question both at the rm and country level. We know that there is a positive relation between leasing and rm growth. One possible explanation is the reverse causality. Firms with faster growth prefer to use more leasing. Although I cannot rule out reverse causal- ity, there are two possible explanations for the positive eect. First, leasing can help increase capital availability. As previous literature pointed out (Eisfeldt and Rampini (2009), Zhang (2012)), leasing is particularly impor- tant for those rms with nancial constraints. Leasing may enable rms to access capital based on their cash 
ows rather than their credit, or collateral. Moreover, leasing lowers the down payment, and helps rms nance more capital than from bank borrowing. Leasing can also provide a channel for accessing foreign capital outside of the domestic market. For instance, the International Lease Finance Corporation, the founder of the aircraft-leasing business, describe its business as leasing aircrafts to airlines throughout the world. Second, leasing can help rms improve their operational eciency. Because of the specialization and division factors, capital becomes dierenti- ated. Leasing is a result of the dierentiation. Some particular asset is leased 83 from the lessor and the lessor provide expertise in operations and logistic- s to the lessee. The dierentiation improves the operational eciency42. Moreover, Carter et al. (1996) and Zhang (2012) note that leasing provides operational 
exibility. It is usually faster to process a leasing transaction than a loan. Further, leased capital has higher utilization and produces more output. Gavazza (2011) shows that leased aircrafts are less frequent- ly parked inactive than owned aircrafts, and that, conditional on being in use, leased aircrafts have a higher capacity utilization than owned aircrafts. Putting it together, leasing can have an eect on both capital availability and operational eciency. Therefore, leasing may contribute to rm growth. I also analyze the eect of leasing on country level growth. Examining country level growth is meaningful from a policy perspective. For instance, if leasing only allows listed rms to grow more quickly at the expense of s- mall and medium size rms, there might be no gains for the whole economy. I use the growth rate of GDP per capita (percent level) of each country as the dependent variable. The key independent variable that I am interested in is the last period average lease share of the country. I use one year lagged value in order to reduce reverse causality. In the pooled OLS regression, I also include the measures of legal environments and the log level of GDP per capita. All these controls variables are using one year lagged values. Moreover, the growth rate of GDP are usually very persistent. Thus, I con- trol for this persistence by adding the growth rate of the last year as one independent variable. The result is shown in Table 3.4. Leasing has a s- tatistically signicant and positive impact on the rate of GDP per capita growth. The economic signicance of the eects is not small. A one stan- dard deviation increase in the average lease share increases GDP per capita growth by approximately 0.52 percent. Brown et al. (2011) estimate that a one standard deviation in using leasing increases GDP per capita growth by 0.2 percent. My result is consistent with their estimation. The whole economy might benet from enhanced leasing activities. The results con- rms the International Finance Corporation's eorts to promote leasing in 42Thanks to Professor Mick Devereux for pointing out this explanation. Many growth models in the literature are based on dierentiation. 84 emerging markets (Carter et al. (1996)). This nding has important policy implications. It suggests that possible adjustments to legal policy and other policies that promote leasing may generate signicant real economic gains. Table 3.4: Leasing and Country Growth Rates Average Lease Share 3.26* (1.769) Log GDP per Capita -1.274*** (0.288) GDP per Capita Growth 0.415*** (0.045) Rule of Law 0.462 (0.446) Economic Freedom 0.027 (0.035) Legal Rights -0.107 (0.101) No. of Obs. 420 Adj. R2 0.243 Notes: The dependent variable is country growth rate of GDP per capita. The indepen- dent variables are one year lagged values. S- tandard errors are in parentheses. *, **, *** statistically signicantly dierent from zero at the 10%, 5% and 1% level of signicance. 3.5 Concluding Remarks This chapter utilizes detailed rm-level panel data for publicly listed compa- nies in 81 countries to compare the leasing activities across countries. I nd that rms in the developed countries lease more of their capital than rm- s in the developing countries. I then look at how legal environments aect leasing. Previous literature believes that leasing should be more prevalent in countries with weak legal environments because rms might have diculty in obtaining loans in these countries. However, the evidence suggests that 85 leasing is less used in countries with weak legal environments. Although leasing might be a good alternative to loans, rms tend to avoid the use of leasing contracts because the contracts are costly to enforce in weak legal environments. 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Working Paper. 91 Appendix A Appendix to Chapter 1 Equations (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) can be written as VO(z; S = 1) = z r + +  r + Ex[max(VO(x; S = 1); VL(x; S = 1); VN (x; S = 1)] (A.1) VO(z; S = 0) = p+ VO(z; S = 1) (A.2) VL(z; S = 0) = z  (1 + r)u r + +  r + Ex[max(VO(x; S = 0); VL(x; S = 0); VN (x; S = 0)] (A.3) VL(z; S = 1) = (1 )p+ VL(z; S = 0) (A.4) VN (z; S = 0) =  r + Ex[max(VO(x; S = 0); VL(x; S = 0); VN (x; S = 0)] (A.5) VN (z; S = 1) = (1 )p+ VN (z; S = 0) (A.6) I prove that owners would always prefer to own capital rather than sell 92 their owned capital and then lease capital. VO(z; S = 1) = (1 )p+ z 1 + +  r + Ex[max(VO(x; S = 0) + p; VL(x; S = 0); VN (x; S = 0)]  VL(z; S = 1) 8z Proof of Proposition 1 There are no frictions ( = 0 and m = 0). Using equations (A.1) (A.2) and (A.3), I obtain that VO(z; S = 0) = rp r + + z r + +  r + Ex[max(VO(x; S = 0); VL(x; S = 0); VN (x; S = 0)] = VL(z; S = 0) And VL(z; S = 1) = VO(z; S = 1). Firms are totally indierent between leasing or buying capital. Using equations (A.1) and (A.5), I get that VO(z; S = 0) VN (z; S = 0) = VO(z; S = 1) VN (z; S = 1) = z  rp r + There exists a threshold value z = rp, such that rms with z > z choose to own or lease capital to produce. The market clear condition determines the threshold value z. X = 1 F (z) (A.7) Uncertainty parameter  does not aect any equilibrium condition. 93 Proof of Proposition 2 The choice between leasing and owning is based on the value of VO(z; S = 0) VL(z). VO(z; S = 0) VL(z; S = 0) =  r + Exmax[VO(x; S = 1); VL(x; S = 1); VN (x; S = 1)] + (m )p r +  r + Exmax[VO(x; S = 0); VL(x; S = 0); VN (x; S = 0)] (A.8) The value of VO(z; S = 0) VL(z; S = 0) is independent of the productivity z. Hence, the choice between owning and leasing does not depend on the productivity. All rms would have the same preference about leasing or owning regardless their current productivity. @(VO(z; S = 0) VL(z)) @ = (1 )(Exmax[VO(x; S = 1); VL(x; S = 1); VN (x; S = 1)] p) (r + )2  (1 )(Exmax[VO(x; S = 0); VL(x; S = 0); VN (x; S = 0)] +mp) (r + )2 < 0 (A.9) When  increases, owning capital is less attractive. When  = 0, VO(z; S = 0)  VL(z; S = 0) = mpr > 0. If there is no uncertainty, rms would prefer to own capital. If  is not small, I can always nd an  that is large enough to make VO(z; S = 0)  VL(z; S = 0) < 0. Hence, there exists an  such that rms are indierent between purchasing capital and leasing capital. Proof of Proposition 3 Since the uncertainty is high, rms would make their choice between leasing and not producing. We know that VL((1 + r)u) = VN . Hence, when z  (1+ r)u, VL((1+ r)u)  VN , and rms lease capital. Otherwise, they would 94 not produce. The market clear condition X = 1  F ((1 + r)u) determines the lease rate u in equilibrium. Proof of Proposition 4 In this setup, rms only consider to own capital or not produce. There- fore, z satises the indierence between buying the capital or not, and z satises the indierence between keeping the capital or selling it. I obtain that z satises VO(z; S = 0) = VN (z; S = 0). All rms with productivity z  z purchase capital, while rms with z < z do not purchase capital. Similarly, z satises VO(z; S = 1) = VN (z; S = 1). All rms with productivity z  z keep the capital they owned, while rms with productivity z < z sell their owned capital. We know that VO(z ; S = 1)p = VO(z; S = 1)(1)p, and VO(z; S = 1) is increasing in z, thus z > z. Equilibrium: An Economy with Frictions but No Financial Constraint An equilibrium in which uncertainty is high such that rms always prefer to own capital requires that the following conditions hold: 1. Leasing rate u = (r +m)p=(1 + r) 2. All rms prefer to own VO(z; S = 0) > VL(z; S = 0) 8z 3. The marginal rm purchasing capital has z satises VO(z; S = 0) = VN (z ; S = 0) 4. The marginal rm selling capital has z satises VO(z; S = 1) = VN (z ; S = 1) 5. Market clear condition X = X(1 ) +X(1 F (z)) + (1X)(1 F (z)) 95 The rst item on the right hand side is rms whose productivity don't change and still own capital in the next period. The second item is rms whose productivity change but above the threshold of selling capital in the next period. The last item indicates that rms who purchase new capital in the next period. Rearrange the market clear condition, I obtain that: X = 1 F (z) 1 F (z) + F (z) Equilibrium requires all above equations are satised. In this equilibrium, nobody lease and all capitals are owned, and the percentage of leased capital is zero. Proof of Proposition 5 In this setup, z satises the nancial constraint such that 1  VO(z ; S = 0)  (1 )p Since in the equilibrium both leased and owned capital coexist, so 1  VO((1 + r)u; S = 0) < (1 )p Thus, z > (1 + r)u. Moreover, z satises the indierence between keeping the capital or selling it VN (z ; S = 1) = VO(z; S = 1) We know that VL((1 + r)u; S = 0) = VN ((1 + r)u; S = 0). Firms always prefer to own capital if no constraint, so VO((1 + r)u; S = 0) > VL((1 + r)u; S = 0) 96 Thus, I can get VO((1 + r)u; S = 0) > VN ((1 + r)u; S = 0) VO((1 + r)u; S = 0) > VO(z ; S = 1) (1 )p VO((1 + r)u; S = 0) > VO(z ; S = 0) Therefore, (1 + r)u > z. Equilibrium: An Economy with Frictions and Financial Constraint An equilibrium in which leased and owned capital coexist requires the fol- lowing conditions hold: 1. Leasing rate u = (r +m)p=(1 + r) 2. All rms prefer to own if without nancial constraint VO(z; S = 0) > VL(z; S = 0) 8z 3. The marginal rm purchasing capital z is the smallest number that satises the nancial constraint 1 VO(z ; S = 0) > (1 )p 4. The marginal rm leasing capital has (1 + r)u 5. The marginal rm selling capital has z satises VO(z; S = 1) = VN (z ; S = 1) 6. Denote XO as the amount of owned capital XO = 1F (z) 1F (z)+F (z) . It is derived similarly to the one in the equilibrium without nancial constraint 7. Denote XL as the amount of leased capital XL =XL(1 ) +XL(F (z) F ((1 + r)u)) + (1XO XL)(F (z) F ((1 + r)u)) 97 The rst item on the right hand side is rms whose productivity don't change and still lease capital. The second item is rms whose produc- tivity change but above the threshold of leasing capital and below the threshold of buying capital. The last item indicates that rms who didn't produce last period change productivity to lease this period. Rearrange it: XL = (1XO)(F (z) F ((1 + r)u)) 8. Market clear condition: XO +XL = X Equilibrium requires all above equations are satised. 98 Appendix B Appendix to Chapter 2 This appendix provides the analytical characterization of the agent's prob- lem. The multipliers on the budget constraints (2.3) (2.4) and nancial constraint (2.5) are denoted by 0, 1 and B. The multipliers on the non- negativity constraints (2.6) (2.7) and (2.8) are denoted by L, N , and d, respectively. The non-negativity constraint on the dividend at time t + 1 (2.9) is redundant. It is always satised if the nancial constraint is satised. The rst-order conditions of the agent's problem are d = BR (B.1) 1 =  (B.2) 0 = 1 + BR (B.3) 0qt = EtAt+1!t+1(ib + il) 1 + qt+1 + Bqt+1 + N (B.4) 0UL = EtAt+1!t+1(ib + il) 1 + L (B.5) Proof of Assumption 1 Substituting (2.10) into (B.5) and subtracting (B.5) from (B.4) gives: B[(1 )qt+1 Rm] = [m (1 )qt+1] + N  L (B.6) 99 If (1  )qt+1  Rm < 0, then L is always greater than zero, which means rms never lease capital. If m (1 )qt+1 < 0, then N is always greater than zero, which means rms never purchase capital. Thus, we need (1)qt+1Rm > 0 and m(1)qt+1 > 0 to guarantee that leasing and buying coexist in the equilibrium. Proof of Proposition 6 Suppose assumption 1 holds, we know that (1  )qt+1  Rm > 0 and m (1 )qt+1 > 0. If il > 0, then the multiplier L = 0. From equation (B.6), we can get that B must be greater than zero. It indicates that d > 0 and d0 = 0. Proof of Proposition 7 By the theorem of the maximum, the maximizing choices are continuous in the idiosyncratic productivity !. First, suppose il > 0. Then we know that the multiplier L = 0. By Proposition 6, we know that B > 0 and b = ib=R. In the case where ib = 0, the rst order condition (B.5) can be written as 0UL = EtAt+1!t+1i 1 l using (B.3) to substitute for 0, and totally dierentiating we can get @il @! = R  1 @B @! > 0 Next, consider the case where both il > 0 and ib > 0, such that the rst order conditions (B.4) and (B.5) become to: 0qt = EtAt+1!t+1k 1 + qt+1 + 0  1 R qt+1 (B.7) 0qt + 0m=R 0qt+1=R = EtAt+1!t+1k1 (B.8) 100 Rearrange the above two equations (B.7) and (B.8), and make all items with 0 on the left hand side of equations. Then, I can divide the two equations by each other and get qt  qt+1=R qt +m=R qt+1=R = EtAt+1!t+1k 1 + qt+1  qt+1=R EtAt+1!t+1k1 (B.9) The equation (B.9) suggests that the capital is constant, and the value of k is determined by (B.9). Then, the rst cuto level of idiosyncratic productivity !L is determined by the following equation !L = kUL  qte Ate (B.10) The second cuto level of idiosyncratic productivity !B is pinned down by !B = k(qt  qt+1=R) qte Ate (B.11) Totally dierentiating the second period budget constraint (2.4) gives @d1t+1 @! = (1 )qt+1@ib @! (B.12) From Proposition 6, we know that d0t = 0. When the idiosyncratic produc- tivity increases, rms enjoy more dividend in the second period @d1t+1@! > 0. Thus, @ib@! > 0. Since the capital k is constant, @il@! = @ib@! < 0. Finally, suppose ib > 0 and il = 0. In the case that where agents' idiosyncratic productivity is not very high and B > 0, agents are nancially constrained. We dierentiate the rst period budget constraint (2.3). We can get @ib@! > 0. In the case where agents' idiosyncratic productivity is very high and B = 0, agents are unconstrained. Then 0 = 1. The rst order condition (B.4) simplies to qt = EtAt+1!t+1k 1 + qt+1 (B.13) 101 The above equation denes k. From the budget constraint, we can derive the third cuto level of idiosyncratic productivity ! = k(qt  qt+1=R) qte Ate (B.14) Since the maximizing choices are continuous functions, I conclude that agents whose idiosyncratic productivity is below !L lease capital only, agents whose idiosyncratic productivity is between !L and !B lease capital and purchase capital, and agents whose idiosyncratic productivity is above !B purchase capital. Moreover, the agent is nancially constrained below ! and unconstrained above that value. 102 Appendix C Appendix to Chapter 3 103 Table C.1: Summary Statistics by Country Country Code Lease GDP Growth Rate of Rule Legal Economic No. of Share per Capita GDP per Capita of Law Rights Freedom Firm-Year Obs. United Arab Emirates ARE 0.20 27,490.97 -6.87 0.44 4.00 65.35 105 Argentina ARG 0.17 9,591.11 5.63 -0.63 4.00 53.43 89 Australia AUS 0.42 24,452.90 1.29 1.76 9.00 80.82 5,129 Austria AUT 0.25 26,563.48 1.00 1.88 7.00 71.10 237 Belgium BEL 0.32 24,499.49 0.54 1.32 7.00 71.14 269 Bangladesh BGD 0.17 505.26 4.78 -0.80 7.00 48.41 69 Bulgaria BGR 0.15 2,404.94 3.84 -0.14 8.00 62.90 37 Bahrain BHR 0.30 13,432.39 -5.00 0.53 4.00 73.04 20 Bermuda BMU 0.38 62,590.48 1.28 1.01 3,362 Brazil BRA 0.21 4,425.37 2.99 -0.22 3.00 56.59 489 Botswana BWA 0.26 4,099.00 -0.03 0.65 7.00 69.05 13 Switzerland CHE 0.38 37,061.79 1.03 1.82 8.00 79.28 714 Chile CHL 0.14 6,031.94 2.14 1.27 4.00 77.52 94 China CHN 0.16 1,824.71 10.19 -0.40 5.20 52.64 787 Colombia COL 0.14 2,973.79 2.45 -0.53 5.00 62.62 69 Cayman Islands CYM 0.35 1.09 2,383 Cyprus CYP 0.37 14,859.64 1.19 1.08 9.00 71.67 105 Czech Republic CZE 0.24 7,167.62 2.89 0.88 6.52 67.69 28 Germany DEU 0.40 24,919.99 1.31 1.68 7.39 70.56 1,820 Denmark DNK 0.33 31,443.97 -0.51 1.93 8.91 77.35 351 Egypt EGY 0.05 1,848.80 3.48 -0.07 3.00 57.59 20 Continued on next page 104 Table C.1 { continued from previous page Country Code Lease GDP Growth Rate of Rule Legal Economic No. of Share per Capita GDP per Capita of Law Rights Freedom Firm-Year Obs. Spain ESP 0.36 15,809.96 -0.43 1.14 6.00 69.14 291 Estonia EST 0.35 6,725.51 2.31 1.10 6.14 76.34 65 Finland FIN 0.43 27,435.59 0.64 1.94 8.00 73.64 427 France FRA 0.42 23,006.47 0.13 1.45 6.59 62.78 885 United Kingdom GBR 0.44 26,766.62 1.81 1.68 10.00 78.15 11,299 Greece GRC 0.32 14,141.76 0.02 0.74 4.00 60.46 378 Hong Kong HKG 0.31 32,184.71 3.49 1.52 10.00 89.63 1,803 Croatia HRV 0.18 6,354.17 1.18 0.09 5.73 54.88 84 Hungary HUN 0.22 5,543.11 1.78 0.86 7.00 65.20 41 Indonesia IDN 0.22 964.71 3.36 -0.69 3.00 54.76 1,143 Isle of Man IMN 0.32 27,635.55 6.24 12 India IND 0.16 611.15 6.17 0.07 7.50 52.60 11,940 Ireland IRL 0.34 27,513.62 2.44 1.65 9.00 79.74 432 Iceland ISL 0.43 35,962.78 -0.55 1.81 7.00 75.33 23 Israel ISR 0.44 20,621.47 1.77 0.88 9.00 65.44 666 Italy ITA 0.44 19,582.48 -1.01 0.36 3.00 62.46 718 Jamaica JAM 0.39 3,731.98 -0.50 -0.48 8.00 65.60 28 Jordan JOR 0.16 2,276.39 4.03 0.39 4.00 65.20 63 Japan JPN 0.51 38,309.28 0.82 1.28 6.86 70.13 11,497 Kazakhstan KAZ 0.10 2,347.73 4.27 -0.79 4.00 60.52 6 Kenya KEN 0.14 448.92 1.84 -0.96 10.00 58.84 64 Korea, Rep. KOR 0.13 13,044.17 4.00 0.88 8.00 68.04 29 Kuwait KWT 0.32 24,357.53 2.79 0.58 4.00 66.52 79 Continued on next page 105 Table C.1 { continued from previous page Country Code Lease GDP Growth Rate of Rule Legal Economic No. of Share per Capita GDP per Capita of Law Rights Freedom Firm-Year Obs. Sri Lanka LKA 0.17 1,213.92 5.25 -0.03 3.83 56.56 157 Lithuania LTU 0.16 5,405.70 2.97 0.64 5.00 70.61 71 Luxembourg LUX 0.39 51,808.80 1.18 1.80 6.81 75.67 88 Latvia LVA 0.28 5,398.95 0.45 0.73 10.00 66.94 52 Morocco MAR 0.25 1,676.98 3.45 -0.16 3.00 56.60 56 Mexico MEX 0.24 6,097.29 0.12 -0.56 5.00 66.16 179 Malta MLT 0.19 10,728.40 1.65 1.53 66.38 40 Mauritius MUS 0.13 4,631.81 3.51 0.92 6.00 70.19 59 Malaysia MYS 0.24 4,658.48 2.93 0.51 10.00 62.82 5,935 Nigeria NGA 0.13 479.25 4.68 -1.23 9.00 53.65 25 Netherlands NLD 0.41 26,222.16 1.10 1.77 6.00 75.52 462 Norway NOR 0.39 40,702.76 0.01 1.94 7.00 68.43 436 New Zealand NZL 0.43 14,768.38 0.43 1.85 10.00 81.51 529 Oman OMN 0.17 10,130.69 3.15 0.58 4.00 66.18 200 Pakistan PAK 0.12 562.80 1.90 -0.83 6.00 55.68 222 Peru PER 0.14 2,897.25 5.80 -0.70 6.90 64.48 40 Philippines PHL 0.33 1,253.30 2.99 -0.52 4.00 57.10 573 Poland POL 0.27 6,046.13 4.40 0.52 8.41 60.36 264 Portugal PRT 0.34 11,780.25 -0.05 1.03 3.00 64.20 103 Qatar QAT 0.16 33,633.73 0.99 0.75 4.00 64.53 73 Romania ROU 0.27 2,607.96 3.47 -0.04 8.81 60.62 26 Russian Federation RUS 0.17 2,716.96 4.38 -0.90 3.00 51.25 242 Saudi Arabia SAU 0.08 9,359.20 0.27 0.14 3.22 62.84 112 Continued on next page 106 Table C.1 { continued from previous page Country Code Lease GDP Growth Rate of Rule Legal Economic No. of Share per Capita GDP per Capita of Law Rights Freedom Firm-Year Obs. Singapore SGP 0.35 29,160.54 3.37 1.65 10.00 87.41 3,462 Slovak Republic SVK 0.50 7,590.02 4.27 0.53 9.00 68.25 11 Slovenia SVN 0.09 12,673.81 1.48 0.97 4.41 61.56 35 Sweden SWE 0.47 31,623.80 0.97 1.90 6.84 70.40 1,396 Thailand THA 0.29 2,588.66 2.50 -0.15 5.00 63.30 476 Trinidad and Tobago TTO 0.18 10,521.63 2.82 -0.24 8.00 68.78 20 Tunisia TUN 0.14 2,939.10 3.31 0.14 3.00 58.48 38 Turkey TUR 0.22 5,103.35 1.76 0.07 4.00 59.02 374 Taiwan TWN 0.18 11,340.00 3.69 0.89 70.49 20 Venezuela VEN 0.10 5,678.49 2.16 -1.54 1.00 42.84 10 Vietnam VNM 0.10 664.37 5.76 -0.44 7.74 49.98 85 South Africa ZAF 0.34 3,523.94 1.94 0.11 10.00 63.69 1,319 Zambia ZMB 0.08 390.78 3.72 -0.52 9.00 56.47 6 Zimbabwe ZWE 0.33 391.05 -4.81 -1.66 7.00 34.29 39 Notes: Reported numbers are sample means except for the last column number of rm-year observations. The unit of GDP per capita is constant 2000 USD . 107

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