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Essays on structural models in corporate finance Valdivieso, Ercos 2017

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Essays on Structural Models in Corporate FinancebyErcos ValdiviesoB.Eng. Industrial Engineering, University of Chile, 2006M.Sc. Economics, University of Chile, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Business Administration)The University of British Columbia(Vancouver)August 2017c© Ercos Valdivieso, 2017AbstractThis thesis contains two essays in Structural Corporate Finance. The first essay studies the effect ofasset redeployability on the cross-section of firms’ financial leverage and credit spreads. Particularly,I show that in the data firms’ ability to sell assets —captured by a novel measure of asset redeploya-bility —correlates positively with financial leverage, and negatively with credit spreads. At odds withtraditional notions of asset redeployability, I show that these predictions remain even after controllingfor proxies of creditors’ recovery rates. To understand these empirical findings, I build a quantita-tive model where firms’ asset redeployability decreases the degree of investment irreversibility anddeadweight cost of bankruptcy. According to the model, while higher overall asset redeployabilitypredicts larger financial leverage and lower credit spread; these relations are mainly driven by differ-ences in the degree of investment irreversibility across firms. Also, within the model, differences inrecovery rates are mainly explained by differences in deadweight costs of bankruptcy. Based on theseresults, I conclude that the link between firms’ asset redeployability and disinvestment flexibilities iskey to understand the empirical ability of asset redeployability to predict financial leverage and creditspreads.The second essay provides new evidence about the cross-sectional distribution of debt issuance:its dispersion is highly procyclical. Furthermore, I show that this dynamic feature is mainly drivenby large adjustments of the stock of debt and capital observed in good times. Previous research hashighlighted the role of non-convex rigidities on inducing large adjustments on firms decisions. Then,to quantify the contribution of real and financial non-convex frictions on shaping the dynamic of thedebt issuance cross-sectional distribution, I build a quantitative model where firms take investmentand financing decisions. According to the model, both real and financial non-convex frictions arerequired to reproduce the dynamic of the cross-sectional dispersion of debt issuance. Indeed, thepresence of these frictions makes firms’ decisions less responsive during recessions. Yet, in booms,both non-convex costs induce large adjustment on the capital and debt stock of high-growth firms.iiLay SummaryThis thesis contains two essays in Structural Corporate Finance. The first essay shows that an assetredeployability measure —capturing firms’ ability to sell assets —predicts higher leverage and lowercredit spreads. At odds with traditional notions of asset redeployability, these predictions remain aftercontrolling for proxies of recovery rates. A model where asset redeployability reduces disinvestmentand bankruptcy costs shows that while disinvestment costs affect significantly leverage and creditspreads, they exhibit offsetting effects on recovery rates. These results are used to explain motivatingempirical findings.The second essay provides new evidence about the cross-sectional debt issuance distribution: itsdispersion is highly procyclical. I show empirically that major investment and debt issuance ad-justments observed during booms can explain this procyclical behavior. I rationalize these findingsthrough a quantitative model that highlights real and financial non-convex rigidities as necessary in-gredients for rendering the cross-sectional debt issuance dispersion procyclical.iiiPrefaceThe research project in chapter 2 was identified and performed solely by the author. The essayin chapter 3 is based on unpublished research with Howard Kung (London Business School) andHyunseob Kim (Cornell University). In this co-authored project, all authors worked on all aspects ofthe paper. While hard to quantify exactly, my personal share of contribution to chapter 3 amounts toabout one third.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Asset Redeployability, Capital Structure and Credit Spreads . . . . . . . . . . . . . . 32.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 A simple model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Benchmark model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Model parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.1 Functional forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5 Quantitative results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5.1 Aggregate moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5.2 Asset redeployability moments . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.3 Assessing asset redeployability channels . . . . . . . . . . . . . . . . . . . . 212.6 Panel regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22v2.6.1 Bond sample construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.6.2 Asset redeployability measure . . . . . . . . . . . . . . . . . . . . . . . . . 242.6.3 Asset redeployability and the cross section of credit spreads . . . . . . . . . 242.6.4 Asset redeployability and the cross section of leverage . . . . . . . . . . . . 262.6.5 Asset redeployability decomposition . . . . . . . . . . . . . . . . . . . . . . 262.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Cyclical Distribution of Debt Financing . . . . . . . . . . . . . . . . . . . . . . . . . . 443.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.1.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2 Empirical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.1 Data and variable description . . . . . . . . . . . . . . . . . . . . . . . . . . 513.2.2 Debt issuance lumpiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.2.3 Implication of debt issuance lumpiness . . . . . . . . . . . . . . . . . . . . 533.3 Benchmark model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.3.1 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3.2 Aggregate state of the economy . . . . . . . . . . . . . . . . . . . . . . . . 593.3.3 Household problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.4 Model parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.4.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.5 Quantitative results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.5.1 Aggregate moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.5.2 Assessing contribution of real and financial non-convexities . . . . . . . . . 633.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80A Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87A.1 Data appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87A.1.1 Bond-level data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87A.1.2 Variables description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88A.1.3 Variables descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . 89A.1.4 KMV model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89A.2 Numerical procedure appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90A.2.1 Shareholders’ stationary problem . . . . . . . . . . . . . . . . . . . . . . . 90A.2.2 Numerical solution details . . . . . . . . . . . . . . . . . . . . . . . . . . . 91viA.2.3 Derivation of first-order conditions . . . . . . . . . . . . . . . . . . . . . . . 92A.2.4 Derivation of debt credit spreads as a function of pd and rr . . . . . . . . . . 93B Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100B.1 Data appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100B.1.1 Variables description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100B.1.2 Robustness test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101B.2 Numerical procedure appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101B.2.1 Shareholders’ stationary problem . . . . . . . . . . . . . . . . . . . . . . . 101B.2.2 Derivation of first-order conditions . . . . . . . . . . . . . . . . . . . . . . . 102B.2.3 Recursive equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103B.2.4 Numerical solution details . . . . . . . . . . . . . . . . . . . . . . . . . . . 104viiList of TablesTable 2.1 Benchmark monthly calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Table 2.2 Aggregate business cycle, asset pricing and financing moments . . . . . . . . . . 31Table 2.3 Asset redeployability moments . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Table 2.4 Portfolios sorted by investment irreversibility and deadweight cost . . . . . . . . 33Table 2.5 Credit spreads by investment irreversibility and recovery rates (short-term debt) . 36Table 2.6 Univariate analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Table 2.7 Asset redeployability and the cross-section of capital structure outcomes . . . . . 38Table 2.8 Asset redeployability channels and the cross-section of capital structure outcomes 39Table 3.1 Statistics of the cross-sectional distribution of debt issuance and investment rates . 67Table 3.2 Benchmark quarterly calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 69Table 3.3 Aggregate business cycle, and financing moments . . . . . . . . . . . . . . . . . 70Table 3.4 Effect of non-convex costs on the moments of the cross-sectional distribution ofdebt issuance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 3.5 Effect of non-convex costs on the moments of the cross-sectional distribution ofinvestment rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table A.1 Yield data per rating category . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Table A.2 Yield data per duration category . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Table A.3 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Table A.4 Asset redeployability by two-digit sic . . . . . . . . . . . . . . . . . . . . . . . . 99Table B.1 Moments and statistics of the cross-sectional distribution of debt issuance and in-vestment rate (excluding small firms) . . . . . . . . . . . . . . . . . . . . . . . . 106Table B.2 Moments and statistics of the cross-sectional distribution of debt issuance and in-vestment ratio (ipo firms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Table B.3 Moments and statistics of the cross-sectional distribution of debt issuance and in-vestment ratio (total assets redefined) . . . . . . . . . . . . . . . . . . . . . . . . 108viiiList of FiguresFigure 2.1 Aggregate impulse-response functions . . . . . . . . . . . . . . . . . . . . . . . 40Figure 2.2 Asset redeployability impulse-response functions . . . . . . . . . . . . . . . . . 41Figure 2.3 Simple model’s solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 2.4 Time-series of baa spreads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 3.1 Average debt issuance cross-sectional distribution . . . . . . . . . . . . . . . . . 73Figure 3.2 First moment of firm-level debt issuance and investment rate distribution . . . . 74Figure 3.3 Dispersion of firm-level debt issuance and investment rate distribution . . . . . . 75Figure 3.4 Fraction of firms exhibiting positive and negative debt issuance spikes . . . . . . 76Figure 3.5 Fraction of firms exhibiting positive investment and debt issuance spikes . . . . . 77ixAcknowledgmentsI would like to express my special gratitude to my thesis advisors, Jack Favilukis and Howard Kung.Certainly, your guidance and advice were crucial throughout my graduate studies; allowing me tocontinuously grow as a researcher.I am also grateful to Ron Giammarino and Kai Li for accepting to join my committee and pro-viding many constructive suggestions as well as insightful conversations that allow me to sharp myeconomic intuition. More broadly, I would like to thank the rest of the UBC Finance faculty.More importantly, I would like to express my deepest and heartfelt thanks to my beloved wife,Macarena. This thesis would not have been possible without your unconditional love, support, andpositivity.Lastly, I would like to acknowledge the financial support provided by University of BritishColumbia over my graduate studies.xChapter 1IntroductionUnderstanding the dynamic of firms’ investment and financing decisions is relevant for investors andpolicymakers. While firms’ investment is a key component of aggregate activity; the firms’ financingbehavior conveys information regarding the economy’s exposure to aggregate cyclical fluctuations.Accounting for their importance, the finance literature has devoted increasing attention to studyingthe economic mechanisms that affect these decisions at the micro-level. The general consensus is thatfrictions associated to capital adjustment and external financing costs are necessary to explain mostof the time-series properties of the cross-sectional distribution of investment and financing decisions.Indeed, frictionless models fail dramatically even in the restricted analysis of aggregate moments.The implications of capital adjustment costs have been extensively studied by the literature oninvestment. Although there has not been clear agreement about the degree of the cost associatedto additions to an individual firm’s capital stock, the common view is that disinvestment carries asignificant cost. Indeed, in reality, firms face installation costs of new capital and/or costs of removingused capital that will be not possible to recover entirely. More broadly, firms use specialized capitalthat may be difficult to redeploy and therefore difficult to sell given its low liquidation value.In this regards, in the first essay of this thesis, I examine the effects of asset redeployability on thecross-section of financial leverage (debt-to-asset ratio) and credit spreads. In the data, a measure ofasset redeployability correlates positively with financial leverage and negatively with credit spreads.Furthermore, the asset redeployability measure used contains information about financial leverage andcredit spreads that goes over and above expected recovery rates. Then, using a quantitative model,I assess the effect on financial leverage and credit spreads of two components of asset redeployabil-ity affecting the riskiness of a firm simultaneously. That is, a component related to disinvestmentcosts and a second component associated to bankruptcy costs incurred upon corporate default. Toaccomplish this goal, I add varying degrees of investment irreversibility and deadweight costs to astandard production-based asset-pricing model featuring firms that make optimal production, financ-ing and default decisions. As a main result of this chapter, I highlight the link between a firm’s assetredeployability and the degree of investment irreversibility that the firm faces as a key mechanism toexplain the ability of asset redeployability to predict financial leverage and credit spreads in the data.1Nevertheless, in reality, firms maneuver adverse economic conditions not only by reducing un-productive capital. Indeed, firms also use external financing to keep the operating company solvent.Experience from past financial crisis suggests the presence of important frictions on raising externalfinancing; given the severity and persistence of the economic contractions suffered on those periods.Effectively, influential works have not only confirmed the existence of financing frictions but alsoquantified their aggregate effects. As a consequence, operating firms have to balance capital adjust-ment and financial costs in order to maximize their value over time. Recently, this interaction hasbeen proven to be key to explain the wide heterogeneity observed in debt issuances at the firm-level.In the data, on average, few firms experience large and infrequent adjustments of their stock of debt;whereas the majority of firms show small adjustments on their debt stock from quarter to quarter.Although the literature on corporate finance has studied the importance of financing friction on thetime-series properties of the aggregate debt issuance; little is known about their role on inducing busi-ness cycle dynamics on the entire firm-level distribution. Studying the dynamics of entire firm-leveldistribution of debt issuance is crucial as it can guide our understanding about the wide range of re-sponses exhibited by firms in terms of their use of debt over the business cycle. As a response to thisconcern, in the second essay of this thesis I contribute to this research area.In the second essay, I start documenting that the cross-sectional dispersion of debt issuance issignificantly procyclical. Next, I show evidence that suggests that periods of both positive debt-issuance and investment lumpiness are responsible of this procyclical pattern exhibited by the debtissuance cross-sectional dispersion. Then, to further investigate the economic determinants of thisbehavior, I construct a structural general equilibrium model of heterogeneous firms featuring bothlumpy investment and debt financing decisions. The model shows that neither non-convex cost ofinvestment nor non-convex cost of issuing debt alone can reproduce the empirical behavior of thedebt issuance distribution. In fact, I show that the model needs a careful calibration of both types offrictions to account for the motivating empirical results.Finally, because each essay intends to answer a different research question, chapters are designedto be self-contained. Indeed, I provide a detailed discussion of the research question and contributionof each essay in the introductory section specific to each chapter.2Chapter 2Asset Redeployability, Capital Structureand Credit Spreads2.1 IntroductionA seminal idea in economics is that assets which are redeployable - that is, have alternative uses -also have high liquidation values.1 While assets with high liquidation values can be sold at pricesthat are close to their value in best use, firms selling assets with low liquidation values can experiencesignificant discounts. Early literature on corporate finance has claimed that costly liquidation of assetsis an important determinant of the partial irreversibility of investment faced by an operating firm (Abeland Eberly (1995)). This link arises since costly liquidation of assets drives a wedge between thepurchase and selling price of a firm’s capital stock.2 Furthermore, costly liquidation of assets has alsobeen identified as a source of the indirect deadweight costs incurred upon corporate defaults (Acharyaet al. (2007)). Indeed, indirect deadweight costs can be substantial in the case the shocks that cause afirm’s default also have the potential to force it to liquidate assets at abnormal discounts.3 Recently,a growing literature on corporate finance has used different proxies of firms’ asset redeployabilityto examine its positive effect on the terms for debt. Yet, to the extent that low asset redeployabilityincreases real frictions faced by a firm at several stages of its life, existing studies are silent about therelative effect of these frictions on the firms’ capital structure decisions. The goal of this chapter isto examine whether firms’ capital structure and credit spreads are affected by asset redeployabilitypurely through the investment-irreversibility channel and/or through the deadweight-cost channel. I1Riordan and Williamson (1985), and Williamson (1988) represent early papers articulating this relation.2Bertola (1988) and Abel and Eberly (1995, 1996) study firms’ investment in the presence of asymmetric capital adjust-ment costs. Barnett and Sakellaris (1998) presents empirical evidence that supports these theories.3Shleifer and Vishny (1992) proposes a theory of fire sales where assets’ selling prices of a distressed firm depend onits peers financial condition. Pfunder (2008) argues that even if a firm’s peers could raise funds, antitrust regulations canprevent them from purchasing the liquidated assets. In the data, Schuermann (2004) show that recovery rates are 19% and15% points lower in recessions and in periods of industrial distress, respectively.3do so by studying comprehensively the determinants of firms’ leverage and credit spreads in the dataand through the lens of a quantitative model.This chapter makes three contributions. First, I complement existing studies linking firms’ as-set liquidity to capital structure outcomes, by showing that a novel measure of asset redeployabilityproposed by Kim and Kung (2016) is able to predict not only leverage ratios but also credit spreads.Second, I show that the information captured by the asset redeployability measure that is not explainedby expected recovery rates also predicts leverage ratios and credit spreads. Specifically, in the data,I show that both expected recovery rates as well as the component of the asset redeployability mea-sure that is not explained by expected recovery rates contribute to predict leverage ratios and creditspreads.4 Motivated by this result and previous literature linking creditors’ recovery rates to indirectdeadweight costs caused by costly liquidation of assets (Acharya et al. (2007)), the last contributionof this chapter is to quantify the relative importance of both the investment-irreversibility and thedeadweight-cost channels to determine leverage ratios decisions and credit spreads. I do so by addingvarying degrees of deadweight costs and investment irreversibility to a standard production-basedasset-pricing model in order to assess the contribution on leverage ratios and credit spreads of thesetwo dimensions.In line with the notion that indirect deadweight costs affect negatively creditors’ recovery valuesat default (Acharya et al. (2007)), I find that a high level of deadweight costs implies higher creditspreads in the data and in the model. Intuitively, since shareholders declare bankruptcy when thelevered equity value becomes negative, which is more likely to happen in recessions when the priceof risk is high, assets associated to high deadweight costs will be less desirable to firms’ investors.Bondholders will anticipate higher costs upon default translating them to lower debt prices. Conse-quently, asset redeployability will decrease equilibrium credit spreads through the deadweight-costchannel. Importantly, I find in the data and in the model that the increase in credit spreads caused bythe deadweight-cost channel does not lead to lower firms’ leverage ratios. Within the model, firms’investment decisions do not change significantly when deadweight costs increase. Then, in the pres-ence of more expensive debt, firms facing higher deadweight costs increase debt issuances to continuecovering their financial needs. Lastly, despite the direction of the effect of the deadweight-cost chan-nel on credit spreads being clear, its magnitude is less obvious. Within the model, I show that theimportance of this channel on credit spreads depend on the degree of the investment irreversibility. Inparticular, the deadweight-cost channel becomes relevant for firms facing significant real frictions.Within the model, the low levels of investment irreversibility will have two reinforcing effects oncredit spreads. First, since increasing investment irreversibility increases the value of the option ofdelaying investment, the firms’ unlevered value upon default will tend to be lower. Second, in thepresence of fixed operating costs in the production function of the firm, larger disinvestment adjust-ment costs will make it harder for firms to deploy their excess capital when the economy experiences4Expected recovery rates are built by implementing a KMV-like model in the data (Bohn and Crosbie (2003)). Section2.6 provides more descriptions of the KMV model implemented. Appendix A shows technical details.4bad shocks, which will end up increasing the aggregate probability of default. Within the model,bondholders anticipate the reduction of the expected value of their claims by decreasing debt pricesand therefore increasing credit spreads. Regarding the effect of the investment-irreversible channelon leverage ratio, note that the lower value of investment options will impact negatively firms’ finan-cial needs which will allow them to decrease their debt issuance and therefore their leverage ratios.Overall, the effect of low asset redeployability throughout the investment irreversibility channel willhave a positive effect on credit spreads and a negative effect on leverage. I expect these effects to benon-linear.To assess the quantitative importance of these two channels affected by asset redeployability, Icalibrate the quantitative model to match a broad set of aggregate moments and moments associatedto portfolios formed based on the asset redeployability dimensions. In the model, differences alongindirect deadweight costs, partial irreversibility of investment and idiosyncratic technology shocks arethe only differences across firms. The degree of cross sectional heterogeneity in indirect deadweightcost is set to match the cross sectional dispersions of recovery rates reported by Altman et al. (2004).Similarly, the degree of cross sectional heterogeneity in partial irreversibility of investment is chosento match the cross sectional difference in excess return exhibited in the data by firms in the lowestand highest asset redeployability quintile.In line with recent empirical studies, I find that both the deadweight - cost and investment - irre-versibility channels increase credit spreads. The benchmark calibration produces a large differencein credit spreads between the low- and high-asset redeployability portfolios, about 46bps. This pre-diction of the model is validated in the data using a panel of publicly corporate bond transactions. Inthe data, firms with low levels of asset redeployability pay about 20bps more on their debt. Theseresults are statistically significant and are robust to various controls. Notably, in economic terms,this difference in credit spreads represents $0.8 millions of additional annual interest payments forfirms with less redeployable assets.5 In the model, as in the data, the higher cost of debt leads firmswith low redeployable assets to use less financial (book) leverage. The difference in book leveragebetween the high- and low-asset redeployability quintile is 5.6%. This last result accords with Kimand Kung (2016) who reports that average book leverage increases in firms’ ability to redeploy theirassets. In short, the model’s prediction that the degree of asset redeployability leads firms to use moreand less expensive debt is supported in the data, both qualitatively and quantitatively.The dynamic model also allows us to quantitatively assess to what extent asset redeployability af-fects credit spreads and leverage purely through the investment-irreversibility channel and/or throughthe deadweight-cost channel. By performing multiple simulations and averaging firms within differ-ent combinations of deadweight cost and degree of investment irreversibility, I compute the averageelasticity of credit spreads with respect to changes in the degree of investment irreversibility anddeadweight cost. On average, the elasticity of credit spreads with respect to changes in investment5These values are obtained assuming a debt face value of $392 millions (the average face value in the sample).5irreversibility is about twice as large as the elasticity of credit spreads with respect to changes indeadweight cost. Particularly, a 1% decrease in deadweight cost implies a 0.17% increases in averagecredit spreads. The larger effect of investment irreversibility is explained by two reinforcing effects.First, for a given deadweight cost, a firm facing a higher degree of investment irreversibility will op-timally reduce its investment which leads to a lower capital stock in equilibrium. The lower capitalstock occurs at the same time the firm faces low flexibility to restructure its assets, which will affectthe claim of firm’s creditors upon a likely default. Indeed, in the presence of operating costs, higherdegree of investment irreversibility will impact firms’ ability to adapt operations in response to pooreconomic conditions.It is worth mentioning that although the investment-irreversibility channel seems to play a moreimportant role than the deadweight-cost channel in determining credit spreads, the effects of thesetwo dimensions are not enough quantitatively to explain the empirical average credit spreads in amodel that only considers one-period debt. The average credit spreads in the data is about 90bpswhereas the one-period debt version of the model can only generate an average credit spreads of53bps. This drawback of short-term debt has been pointed out in the recent literature (e.g. Michauxand Gourio (2012)). Intuitively, when only short-term debt is considered, firms can easily changetheir total leverage which lowers default probabilities and leads to low credit spreads in equilibrium.Furthermore, long-term debt plays a role generating the difference in credit spreads exhibited bylow- and high-asset redeployability firms. A version of the model that only considers one-period debtonly generates a difference of 12bps between credit spreads exhibited by firms with low and highredeployable assets; which is significantly lower to the same difference generated by the benchmarkmodel (46bps). To understand the intuition of the results, it is useful to compare the choice of debtmaturity structure of firms with high redeployable assets versus the one chosen by firms with lowasset redeployability. Relative to the one-period debt model, in the benchmark model both high- andlow-asset redeployability firms increase their debt maturity structure on average. Yet, firms with lessredeployable assets tend to keep a longer debt maturity structure than firms with high redeployableassets. This occurs because these firms face large financial needs in bad times due to the presence ofoperating cost and the impossibility of scaling down their unproductive capital. Within the model, theterm structure of credit spreads is upward sloping in bad times; making long-term debt more expensivethan short-term debt. Ultimately, firms with less redeployable assets end up combining costly equityissuances and debt issuance at high credit spreads in order to fund their financial needs. In contrast,firms with highly redeployable assets pay their financial needs in bad times mainly using short-termdebt which is cheaper than long-term debt in recessions. These optimal debt maturity strategies leadto a more procyclical debt maturity structure of firms with high redeployable assets relative to the oneexhibited by firms with low redeployable assets. Particularly, in the data, the correlation between theoutput growth and the average maturity exhibited by firms in the highest asset redeployability quintileis 0.25 higher than the correlation between the output growth and the average maturity exhibited byfirms in the lowest asset redeployability quintile. The model is able to generate similar results.62.1.1 Literature reviewThis chapter contributes to the literature which studies the effect of a firm’s ability to redeploy andsell its assets on determining its risk and capital structure outcomes.Early works by Riordan and Williamson (1985) and Williamson (1988) argue that a firm’s assetredeployability is an important determinant of liquidation value of the firm’s assets. Theoreticalworks by Hart and Moore (1991), Shleifer and Vishny (1992), and Holmstrom and Tirole (1997),have suggested that high liquidation value of assets allows managers to alleviate firms’ financialconstraints. Intuitively, these works claim that high liquidation values allow firms to reduce indirectdeadweight costs of corporate bankruptcy which increases the amount recovered by firm’s creditorsupon default. In contrast, Myers and Rajan (1995), Weiss and Wruck (1998) and Morellec (2001)reach opposite conclusions by arguing that lower asset liquidity makes it more costly for distressedmanagers to expropriate value from bondholders and thus, under this notion high asset redeployabilitydoes not alleviate firms’ financial constraints. Kim and Kung (2016) show empirically that low assetredeployability, by decreasing liquidation values of assets, is also an important source of investmentirreversibility that can impair firms’ operating flexibility over their entire life and particularly duringeconomic downturn. In fact, Mauer and Triantis (1994) and Aivazian and Berkowitz (1998) use atheoretical framework to show that real flexibilities create value by lowering firms’ default risk andincreasing their debt capacity. My work intends to fill a gap in this literature by analyzing to whatextent corporate decisions as well as credit spreads can be explained by asset redeployability throughtwo distinct channels, namely the investment-irreversibility and the deadweight-cost channels.Based on measures that capture creditors’ recovery upon default, recent empirical work finds apositive link between assets’ liquidation values and a wide set of capital structure outcomes. Ben-melech (2008), using a novel data set of nineteenth-century American railroads, shows that highliquidation values of assets allow firms to increase the debt maturity as well as the amount of debtissued.6 Benmelech and Bergman (2009) finds that debt tranches of airlines secured with more rede-ployable collateral exhibit lower credit spreads. Using a broader sample of industries, Ortiz-Molinaand Phillips (2010) also find that firms in industries with more liquid assets, and during periods ofhigh asset liquidity, face a lower cost of capital.7 Campello and Hackbarth (2012) uses a theoret-ical model to show a positive effect of liquidation value at default on corporate financing, amongfinancially constrained firms. Recent literature studies to what extent a firm’s ability to adjust assetsenhances its operating and financial flexibility. Schlingemann et al. (2002), using Compustat Full-Coverage Industry Segment File (CISF) database, examines how asset liquidity can explain firms’internal restructuring process; which, as showed by Almeida et al. (2011), is especially valuable tofirms facing economic hardship.6In a related paper, Liu and Liu (2011) use real estate firms, i.e. the real estate investment trusts (REITs), to examinehow asset liquidation values influences a firm’s debt capacity.7Campello and Giambona (2013) validates these results using Compustat-based measure that entails breaking downtangible assets into their identifiable parts, which include land and buildings, machinery and equipment.7In the asset pricing literature, Kogan (2004), Gomes et al. (2003a), Carlson et al. (2004), Zhang(2005) and Cooper (2006) argue that since firms facing difficulties in scaling down their unproduc-tive capital due to adjustment costs will be unable to cut fixed costs in economic downturn, theywill offer less protection against aggregate negative shocks and therefore their investors will requirehigher returns in exchange of capital.8 Gala (2010) provides a general equilibrium argument to ex-plain why investors require a higher return for investing in firms facing important real frictions to(dis)investment. More broadly, this chapter relates to the growing production-based asset-pricingliterature that studies firms’ optimal real and financial decisions in the context of multiple marketfrictions to explain the relationship between corporate decisions and asset prices. In economic terms,firms become safer as they are able to respond to negative shocks by using efficiently both their oper-ational and financial flexibilities. Bloom (2009) and Belo et al. (2014) are recent papers that belongto the investment and labor demand literature that investigates the importance of capital and laboradjustment costs in explaining corporate decisions’ dynamics. Gomes (2001), Hennessy and Whited(2005, 2007), Carlson et al. (2006), and Belo et al. (2016) are a subsample of papers that examine theimpact of financial frictions on corporate investment and asset prices. Among these papers, firms’ in-ability to adapt operations and/or substitute between different marginal sources of financing (internalor external) during bad economic times plays an important role in determining firms’ risk premiumsat the equilibrium. I contribute to this literature by studying capital structure’s implications of dis-investment and bankruptcy deadweight costs affecting firms’ ability to liquidate their assets over thebusiness cycle. Interestingly, I find that the degree of the disinvestment rigidity amplifies the effect ofdeadweight costs on firms’ credit spreads.By studying the effect of debt maturity decisions on credit spreads, this chapter also relates toa growing strand of literature studying debt maturity decisions. In terms of theoretical research, awidely used framework for debt maturity structure is based on Leland (1994, 1998) and Leland andToft (1996) who, for the sake of tractability, take the frequency of debt refinancing as a fixed param-eter. Chen et al. (2012), and Brunnermeier (2009) develop a calibrated model to match procyclicalityof aggregate debt maturity structure. Unlike recent papers studying debt maturity structure and creditspreads (e.g. Brunnermeier and Oehmke (2013) and He and Milbradt (2015)), my work incorporatesdynamic investment decisions. As mentioned by Michaux and Gourio (2012), adding this layer to themodel is key to match credit spreads.Credit spreads and debt maturity decisions has also been studied in the context of models withasymmetric information (e.g. Flannery (1986), and Diamond (1991)). These models price debt con-tracts assuming the existence of a pooling equilibrium. In contrast to this class of models, the modelproposed in this chapter features complete information and produces equilibrium where firms withhighly redeployable assets use their operating flexibility and low (indirect) deadweight costs to issuethe cheapest type of debt leading to low credit spreads and high leverage. In contrast, in models with8In constrast, Ozdagli (2012) proposes a model without operating leverage where partial irreversibility of investmentmakes firms less risky since the value of the disinvestment option provides insurance in bad times.8asymmetric information, good type firms will prefer to issue short-term debt to differentiate them-selves from the bad type firms that prefer long-term debt to minimize their probability of default.The rest of the chapter is organized as follows. Section 2.2 develops a simple two-period modelwhere I describe how the two channels proposed in this chapter, that relate to asset redeployability,affect a firm’s leverage and credit spreads. Section 2.3 extends the simple model into a quantitativemodel. Section 2.4 discusses the baseline calibration. Section 2.5 investigates some of the model’squantitative implications for the cross-section of capital structure and credit spreads. Section 2.6presents several empirical tests and it is followed by a few concluding remarks in section 2.7.2.2 A simple modelThis section develops a two-period model to highlight how the two economic channels studied in thischapter that relate to asset redeployability can affect firms’ leverage and credit spreads.Economic environment I assume agents are risk neutral and the gross interest rate is set to 1. Thesimple model incorporates a capital adjustment cost function that is general enough to consider bothsymmetric-convexity and irreversibility as special cases. The firm’s indirect deadweight cost at de-fault is modeled as a proportional cost. Thus, at default, creditors take over the firm and incur abankruptcy cost when liquidating the capital stock.Technology A firm is in place for two periods t ∈ {1,2} and faces a technology shock representedby the stochastic term Xt which is described by a lognormal random-walk process, Xt = Xt−1eεt withεt ∼ i.i.d N(µ,σ2). Technology is described by a decreasing return to scale Cobb-Douglas productionfunction Y (Xt ,Kt) = XtKαt with α ∈ (0,1).Capital adjustment cost Φ(Kt , It) denotes the cost of changing the stock of capital by It units whenthe capital stock is Kt . As in Zhang (2005), the functions Φ(Kt , It) writes,9Φ(Kt , It) = Kt(ItKt−δ)2 [I{It≥0}θ1+ I{It<0}θ2]= φ(Kt , It)[I{It≥0}θ1+ I{It<0}θ2](2.1)where θ1,θ2 > 0 and I{x} represents an indicator function that takes value 1 if x is true and zerootherwise. The partial-irreversible-investment case corresponds to θ1 < θ2.Deadweight cost of bankruptcy It is denoted by χ ∈ [0,1], where χ is a proportional bankruptcy cost—proportional to creditors’ recovery at default, i.e. the unlevered firm value —that creditors incurwhen the firm’s capital stock is liquidated upon default.Timeline In period 1 the firm starts with a capital stock K1 and decides its investment I after ob-serving the technology shock X1. Investment allows the firm to change its capital stock to K2 =9 This expression is similar to the one used in the benchmark model. This functional form guarantees that it becomeszero at the steady state of the dynamic problem. As discussed by Cooper and Haltiwanger (2006) this functional form alsoguarantees that, in the firm’s problem, the (expected) marginal productivity of capital depends on investment rate values.9K1(1− δ )+ I at period 2. Due to the presence of equity issuance costs, Ψ(·), the firm also financesI by issuing one-period debt which is priced by competitive creditors. To decide the amount of debtissued, i.e. face value B, the firm balances equity issuance and bankruptcy costs. In period 2, afterobserving the shock X2, shareholders decide whether or not to declare bankruptcy. If default doesnot occur, the firm pays the promised debt B, liquidates its assets and distributes all residual claim asdividend. Importantly, if the firm declares bankruptcy, creditors take over the unlevered firm incurringthe additional bankruptcy cost χ .Firm’s value At period 2, the firm’s value conditional on the initial capital stock K2 and technologyshock X2 writes as a call option granted by creditors to shareholders on the company’s operating assetswith a strike price that is equal to the debt face value. Shareholders will continue operating the firmas long as its operating assets are enough to honor debt payments,V2(X2,B) = max{0 , Π(X2,K2)+L(K2)−B}subject to: Π(X2,K2)≡ Y (X2,K2)− f0L(K2) ≡ K2−φ(K2,−K2)θ2 = K2(1−θ2)(2.2)where V2 represents the firm’s value at period 2, and f0 denotes a fixed cost that is necessary to pay inorder to operate the firm’s assets. The value of the option of equity considers the benefit shareholderscan obtain from selling the firm’s assets at the end of period 2, i.e. L(K2). When liquidating its assets,the firm incurs the cost φ(K2,−K2)θ2 = K2θ2. Default occurs if the shock at period 2 is below thethreshold X?2 (K2,B) that makes V2 equal to zero. Formally,Π(X?2 (K2,B),K2)+L(K2)−B = 0 (2.3)From equation (2.3), an increase of the investment irreversibility (high θ2) does not only affect theliquidation value of the capital stock K2 but it also reduces the firm’s value. This, since the firm willoptimally decrease investment at period 1 due to a lower expected marginal productivity of capital.Note that because of the lower financial needs at period 1, the firm will also reduce the amount of debtissued at this period. The final effect of an increase of θ2 on the probability of default will depend onthe relative change of K2 and B, that is the firm’s leverage ratio. The effect of θ2 on credit spreads willbe a function of the change in the expected default probability and expected recovery rates (definedbelow). If the firm decides to default, i.e. X2 < X?2 (K2,B), bondholders will take over the unleveredfirm and keep operating it for values of the technology shock X2 larger than the threshold X?2 (K2,0),which satisfies Π(X?2 (K2,0),K2)+L(K2) = χK2. An increase of χ will decrease liquidation value ofthe firm’s assets as an increase of θ2 will do. Yet, an increase in θ2 will have stronger effects due toits large negative link with investment. In period 1, after observing X1 and the capital stock K1, thefirm’s problem reduces to,10V1(X1,K1) = max{0,maxI,B{D(X1,K1, I,B)+E(V2(X2,K2,B)I{X2>X?2 (K2,B)})}}subject to: K2 ≡ K1+ ID(X1,K1, I,B)≡ E(X1,K1, I,B)−Ψ(E(X1,K1, I,B))E(X1,K1, I,B)≡Π(X1,K1)− I−Φ(K1, I)+P(B,K2)(2.4)where δ has been set to zero in the first constraint. The second constraint shows that distributions toshareholders, D(·), are given as equity payout E(·) net of equity issuance costs Ψ(E(·)). As in thebenchmark model, equity issuance costs are modeled as the sum of a fixed ψ0, and a proportional ψ1component. Lastly, P(B,K2) denotes the debt price associated to the face value B and conditional onthe firm’s optimal decisions.Price of debt In a competitive market, P(B,K2) equals the discounted future bond payoffs obtainedwhen the firm is operating and in the case shareholders decide to default,P(K2,B) = E(B · I{X2>X?2 (K2,B)})+E((Π(X2,K2)+L(K2)−χK2)I{X?2 (K2,0)<X2<X?2 (K2,B)}) (2.5)In words, the first term in equation (2.5) represents the debt payment in the case shareholders con-tinue operating the firm, whereas the second term denotes payments at default. Finally, given theassumptions of the model, the firm’s credit spreads CS(B,K2) can be written as,CS(B,K2) =BP(B,K2)−1 = 1−RR(B,K2)1−PD(B,K2) −1 (2.6)The first equality in equation (2.6) implies that adding the credit spreads to the (gross) risk freerate allows agents to recover the risky debt price by discounting the debt face value as if default neveroccurs. The second equality in equation (2.6) shows that the credit spreads can be written in term ofthe expected default probability PD(B,K2) and recovery rate RR(B,K2).10Results The remainder of this section discusses the role of the degree of partial irreversibility ofinvestment θ2 and deadweight cost χ in determining the firm’s credit spreads and leverage. At period1, the firm balances equity issuance and bankruptcy costs to determine the optimal debt level B.Indeed, a low level of debt forces the firm to use a combination of internal earnings and costly equityissuance to finance capital expenditures. Yet, by decreasing the probability of default at period 2, a10Where the expected default probability PD≡ PD(B,K2) and recovery rate RR≡ RR(B,K2) are defined as,PD = E(I{X?2 (K2,0)<X2<X?2 (K2,B)})and, RR =1P(B,K2)E((Π(X2,K2)+K2(1−χ−θ2))I{X?2 (K2,0)<X2<X?2 (K2,B)})for more details refer to Appendix B that shows how to compute PD(·) and RR(·) for the more general case.11low level of debt reduces the exposure to bankruptcy costs. To determine the relative importance ofpartial irreversibility of investment and deadweight cost on the firm’s decisions, the model is solvedfor multiple values of θ2 and χ . Next, I compute marginal effects of θ2 and χ on different firm’sdecisions. In Figure 2.3, red (black) lines show the average marginal effect of increasing the degreeof partial irreversibility of investment, θ2, (deadweight cost, χ) on multiple firm’s variables; keepingthe deadweight cost, χ , (partial irreversibility of investment, θ2) unchanged.The top-left graph shows that investment, I, decreases more after an increase of investment ir-reversibility (high θ2) than after increasing of deadweight cost (high χ). A decline in investmentreduces the firm’s financial needs which translates to a reduction of the amount of debt issued (top-center graph). Note that the reduction of debt issuance is more pronounced after an increase ofinvestment irreversibility than after a decline in deadweight cost. Ultimately, the top-left graph showsthe effect on leverage of changes in the two parameters studied.When investment becomes more irreversible, the optimal capital stock of the firm decreases due toa lower value of the option to invest; this, at the same time, decreases significantly the firm’s financialneeds which leads to a lower leverage ratio. In contrast, even when the deadweight cost increases,the firm does not adjust its investment significantly and thus its financial needs continue being high.However, due to higher deadweight costs, the firm’s creditors provide less funds per unit of face value.Consequently, the firm needs to increase its leverage ratio in order to be able to fund its investment.Note that in this numerical example, changes in credit spreads only come from change in theexpected recovery rate of the debt issued. Due to the discrete nature of Xt in the numerical exercise,the range of values for θ2 and χ guarantees that the probability of default remains unaltered (bottom-left graph). It is worth mentioning that for reasonable values of the level of investment irreversibilityand deadweight cost, both channels studied in this chapter that relate to asset redeployability exhibitsimilar effects on credit spreads but their effects on leverage ratios differ. To summarize, the simplemodel shows that there is a positive relationship between investment irreversibility and credit spread,and a negative one with financial leverage. On the other hand, there is a positive link between higherdeadweight costs, and both credit spread, and financial leverage.The distinct effects of the channels of asset redeployability studied highlight the importance ofconsidering different aspects of a firm affected by its ability to redeploy its assets. Furthermore, de-spite that the simple model allows us to understand the main mechanisms, a rigorous quantificationof the contribution of each channel must consider that in practice partial irreversibility of investmentwill not necessary be an important constraint for all firms; which may end up weakening the marginaleffects found in this section. Indeed, the importance of partial irreversibility of investment will de-pend on —among other factors —the firm’s current stock of capital and the degree of its financialconstrains. Additionally, and as it is shown in the dynamic model, the importance of the deadweightchannel will depend on how close the firm is to distress. Intuitively, when a firm is far from defaultingits creditors will not be concerned with factors affecting their recovery upon default. The next sectionintends to address these issues that at first are difficult to be captured by a simple two-period model.122.3 Benchmark modelThis section extends the simple model into a dynamic stochastic partial equilibrium model. It consid-ers infinitely lived firms in discrete time. Firms issue debt and equity and are owned by risk-averseinvestors. I study whether the channels highlighted previously are quantitatively sufficient to explainthe cross-sectional differences in the data showed by firms sorted on asset redeployability. The rela-tive importance of each channel is assessed based on its contribution to leverage and credit spreads.2.3.1 FirmsThe core of the model consists of a stochastic discount factor and a cross-section of heterogenousfirms that make optimal investment and financing decisions by balancing real and financing costs. Thestochastic discount factor is derived from a representative household who has recursive preferencesand an exogenous consumption process as in Kuehn and Schmid (2014).At period t, the firm’s chooses its new factor demand, kt+1 and how to finance these purchasesin order to maximize the present value of shareholders’ after-tax cashflows. To finance its capitaldemand and distributions, the firm can use either internal earnings available at the beginning of theperiod or new debt issues. If the funding raised through these two sources is not enough, the firm canalso choose to issue new costly equity. Regarding debt contracts, firms issue a combination of short-and long-term debt.11 Specifically, at each period t the firm can control the total face value of debtoutstanding bt+1 and the speed at which its debt matures over time by adjusting its average maturity.The firm’s average maturity of its bonds is determined by the variable λt+1 ∈ [0,1] which implies thatat time t + 1 only a fraction λt+1 of the total face-value of the debt outstanding bt+1 is paid back tobondholders.12 In addition to the fraction of principal repaid, borrowers pay a coupon per period thatcorresponds to a proportion of the total debt face value determined by a fixed coupon rate c ∈ (0,1).Production TechnologyAt period t, output is given by the production function yt = y(kt ,xt ,zt); where xt denotes a persistentaggregate productivity shock which follows a random walk with time-varying drift and volatility; andzt denotes an idiosyncratic shock affecting the firm’s cash flows through its operating leverage whichfollows a mean-reverting process. Particularly, xt and zt follow,ln(xt+1/xt) = g+µx(st)+σx(st)εxt (2.7)ln(zt) = (1−ρz)z¯+ρz ln(zt−1)+σzεzt (2.8)where εxt and εzt ∼ i.i.d N(0,1). The low-frequency component in the aggregate productivity equation,µx(st) is used to generate sizeable risk premia as in Bansal and Yaron (2004) whereas the time-varying11Following a similar framework as in Brunnermeier (2009), Michaux and Gourio (2012), Chen et al. (2012), Brunner-meier and Oehmke (2013) and He and Milbradt (2015).12Ignoring the coupon, the average debt maturity is computed as, λt+1∑∞j=1 j× (1−λt+1) j−1 = 1/λt+1.13volatility is useful to generate realistic credit spreads. Each firm produces according to the decreasingreturn to scale Cobb-Douglas production function,y(kt ,xt ,zt) = x1−αt kαt − f zt −φkt (2.9)where f and φ represent a fixed and a proportional cost, respectively. In the calibration, φ is set tomatch the average book-to-market ratio and f is used to calibrate default rates.13InvestmentFirms are allowed to scale operations by choosing the level of capital kt+1 which is accomplishedthrough investment, it . Firms’ capital accumulation is such that, it ≡ kt+1− (1− δ )kt , where thedepreciation rate of capital is denoted by δ ∈ (0,1). I model real options by assuming that firms facea cost of adjusting capital Φ(kt , it ,ωt) where the stochastic variable ωt controls one of the dimensionsof asset redeployability studied, i.e. the investment-irreversibility channel, described in Section 2.4.Equity valueShareholders have the right to firms’ dividends as long as they are operating. Distributions to share-holders, dt are given by equity payout et net of issuance costsΨ(·). Equity payouts are equal to firms’free cash-flow; that is, the operating profit, net of cash flows from financing and investment activities,e(kt ,bt ,λt ,Γt) = (1− τ)y(kt ,xt ,zt)− it −Φ(kt , it ,ωt)− (λt + c(1− τ))bt + τδkt+P(kt+1,bt+1,λt+1,Γt)(bt+1− (1−λt)bt)(2.10)where τ denotes the effective tax rate and Γt summarizes the vector of aggregate and idiosyncraticstochastic variables (xt ,zt ,ωt ,χt), where χt is the stochastic variable related to the deadweight-costchannel (described in Section 2.3.1). The first term captures the firm’s operating profit, from which therequired investment expenses, it +Φ(kt , it ,ωt), and debt repayments, (λt + c(1− τ))bt are deducted.Note that capital depreciation and debt interest payment generate tax shields. The debt price functionP(kt+1,bt+1,λt+1,Γt) will be a function of stochastic variables Γt and optimal decisions at time t. Itfollows that the value of the firm to its shareholders, denoted J(·), is the present value of distributionsdt ≡ et−Ψ(et) plus the expected firm’s continuation value. Following Gomes et al. (2014), it writes,J(kt ,bt ,λt ,Γt) = max{0, maxkt+1,bt+1,λt+1{dt +Et(Mt,t+1J(kt+1,bt+1,λt+1,Γt+1))}}(2.11)where Mt,t+1 is the equilibrium stochastic discount factor derived from the representative household’spreferences (described in Section 2.3.2). The first max operator captures the limited liability of share-holders. The second max operator relates to the determination of optimal decisions of firms’ manager.13Since the economy is persistently growing, g> 0, in the solution of the model the fixed cost f is multiplied by aggregatetechnology shock xt to keep it economically sizable along the balance growth path of the firm.14DefaultSeveral observations about the value of equity will be useful later. First, limited liability impliesthat equity value, J(·), is bounded and will never fall below zero. This implies that equity holderswill default on their credit obligations whenever their idiosyncratic shock zt is above a cutoff levelz?(kt ,bt ,λt ,xt ,ωt ,χt) determined by the threshold default condition,J(kt ,bt ,λt ,Γ?t ) = 0 with, Γ?t ≡ (xt ,z?(kt ,bt ,λt ,xt ,ωt ,χt),ωt ,χt) (2.12)To simplify notation, I define z?t ≡ z?(kt ,bt ,λt ,xt ,ωt ,χt) and z0t = z?(kt ,0,0,xt ,ωt ,χt). The last defi-nition, z0t , represents the idiosyncratic shock realization that makes the unlevered firm’s value equalto zero, i.e. the highest value of zt at which the unlevered firm keeps operating.Deadweight CostUpon default, bondholders can seize a fraction (1−χt)∈ [0,1] of a firm’s value. That is, the higher thestochastic variable χt , the lower the bondholders’ recovery. At this point χt and ωt are independentalthough in the data, they may be correlated. As it is described in Section 2.4.2, the points of the gridfor χt are equally spaced and belong to the interval [χ,1]; where χ and the number of points in thegrid are set to match the mean and volatility of recovery rates upon default as in Chen (2010).To explain the differences in credit spreads and leverage observed empirically between the highestand lowest asset redeployability quintiles (see Table 2.6) as well as the relative importance of ωt andχt , I will look at portfolios that vary by ωt and χt .14Debt ContractsThe firm’s creditors buy corporate debt at price P(kt+1,bt+1,λt+1,Γt) and collect coupon and principalpayments until the firm defaults. If default occurs at period t, shareholders walk away from the firm,while creditors take over and restructure the unlevered firm incurring proportional deadweight lossesχt . With these assumptions, period-t per unit market price of debt P(kt+1,bt+1,λt+1,Γt), is pinneddown by an arbitrage condition such that the amount of money creditors are willing to pay for thecontract must equal the expected value of future payments. Formally, this condition implies thefollowing identity,bt+1×P(kt+1,bt+1,λt+1,Γt) = a︸︷︷︸aEt(Mt,t+1bt+1(λt+1+ c+(1−λt+1) ·P(kt+2,bt+2,λt+2,Γt+1))I{zt+1<z?t+1}︸ ︷︷ ︸solvent states)+Et(Mt,t+1(1−χt+1)J(kt+1,0,0,Γt+1)I{z?t+1<zt+1<z0t+1}︸ ︷︷ ︸default states) (2.13)14I provide more details about the portfolio construction from the model simulation in Section 2.5.15Importantly, corporate bonds are held by the representative household and are thus valued using thehousehold equilibrium pricing kernel Mt,t+1. The first term on the right-hand-side of equation (3.6)contains the cash flows received by bondholders if no default takes place at period t+1; whereas thesecond term reflects the payments upon default net of deadweight costs.2.3.2 HouseholdsThe model is completed by specifying the household stochastic discount factor of a representativehousehold who features recursive preferences and consumes according to an exogenous consumptionprocess, Ct . Following Epstein and Zin (1991), the household utility is given by,Ut =(1−β )C1− 1ψt +βEt (U1−γt+1 ) 1−1ψ1−γ 11− 1ψ (2.14)where the preference parameters are the rate of time preference, β ∈ (0,1), the elasticity of intertem-poral substitution, ψ , and the coefficient of relative risk aversion, γ . Further, as in Bhamra et al.(2010) and Kuehn and Schmid (2014), aggregate consumption growth is assumed to follow a randomwalk process with time-varying drift and volatility,ln (Ct+1/Ct) = g+µc(st)+σc(st) ηt+1 (2.15)where µc(st) and σc(st) depend on the aggregate state of the economy denoted by st . The standardnormal innovations ηt+1 are independent of the other stochastic variables of the model. In the nu-merical solution, the aggregate state st is modeled as a persistent Markov chain. The representativehousehold’s stochastic discount factor will be computed as,Mt,t+1 = β θ(Ct+1Ct)−γ(Wt+1+1Wt)−(1−κ)(2.16)where Wt denotes the wealth-to-consumption ratio and κ ≡ (1− γ)/(1− 1/ψ). Importantly, thewealth-to-consumption ratio will be a function of the state of the economy, st . In fact, it is notdifficult to show that W (st) solves the system,W (st) = Et(β κ(Ct+1Ct)1−γ(W (st+1)+1)κ∣∣∣st)1/κ (2.17)which is solved through a value-function-iteration procedure conditional on the Markov chain for theaggregate of the economy st and the stochastic processes of the remaining model’s variables.162.4 Model parametrizationThis section describes the benchmark model calibration and provides details on the functional formsfor the adjustment costs Φ(·) and equity issuances costs Ψ(·). The model is solved using a globalmethod after normalizing all non stationary variables by the aggregate technology shock. Detailsabout the numerical solution and the normalized problem are shown in the Appendix.2.4.1 Functional formsCapital adjustment costThe capital adjustment cost function Φ(·) is modeled as in Zhang (2005), but adding a degree ofrisk in the level of partial irreversibility of investment given by ωt > 1. The capital adjustment costfunction is quadratic in the firm’s investment rate, and its convexity is determined by θ > 0 and θωtwhen the firm chooses to invest and disinvest, respectively. Formally, Φ(·) writes,Φ(kt , it ,ωt) = kt(itkt−δ)2 [I{it≥0}θ + I{it<0}θωt](2.18)In the numerical solution of the model, the stochastic variable ωt is modeled as a Markov chain withpersistence denoted by ρω . Then, a low (high) ωt implies that the firm’s capital investment is highlyreversible (irreversible). As is described in Section 2.4.2, the points of the ωt grid are equally spaced(in logs) and belong to the interval [1, ω¯]; where ω¯ is set to match differences in excess returns showedby the highest and lowest asset redeployability quintiles in the data.Equity issuance costLastly, I consider a fixed and a proportional equity issuance costs, which are denoted by e0 and e1,respectively. Then, the total equity issuance cost is given by the function, Ψ(et) = (e0+e1|et |)I{et<0},where the indicator function I{et<0} implies that these costs apply only when the firm is raising newequity finance, that is, when the net payout, et , is negative.2.4.2 CalibrationStandard real business cycles parameters and preference parameters of the benchmark model are setto values taken from the existing literature. The remaining set of parameters are chosen to match ag-gregate moments and moments derived from sorting firms based on the asset redeployability measurein the data. All parameters values of the monthly calibration implemented are reported in Table 2.1.Preference parameters are standard in the long-run risk literature (Bansal and Yaron (2004)). Theelasticity of intertemporal substitution ψ is set to 2 and the coefficient of relative risk aversion γ is setto 10, as in Kung (2015); and the subjective discount factor β is set to 0.994.17In term of the technology parameters, the productivity process is calibrated following Kuehn andSchmid (2014). Indeed, I model the aggregate Markov chain, st , to jointly affect the drift and volatilityof the aggregate productivity shock xt and consumption growth ln(Ct/Ct−1). Specifically st consistsof five states. To calibrate the Markov chain, I set the persistence of the Markov chain (ρ) to 0.95, themean and volatility of the consumption drift states are set to zero and 8.69e−4/√2, respectively; andthe mean and volatility of the consumption variance states are set to 1.51e−4/√2 and 1.05e−5/√2,respectively. Following Kuehn and Schmid (2014), the drift and volatility of aggregate productivity xtscale with the respective moments of consumption growth by a factor of 1.7. This calibration allowsme to match annualized consumption growth moments and obtain a sizable aggregate stock returnsvolatility. I set g to yield an annual average growth of 1.8%.At the firm level, the capital share α is set to 0.35, and the depreciation rate of capital δ is setto 1.0%. These values are close to those used in Kung (2015). Firms face proportional costs ofproduction, φ , of 0.07 and a fixed cost, f , of 0.05, similar to Kuehn and Schmid (2014) and Gomeset al. (2003a) respectively. As in Zhang (2005) we set the capital adjustment parameter θ to 15. Icalibrate the volatility and persistence of the idiosyncratic productivity process to match the annualdefault rate.The effective corporate tax rate τ is set to 14%, consistent with the evidence (Binsbergen et al.(2010)). The annual coupon payment, c, is set to 3.0%. Equity issuance cost parameters are set tomatch the frequency of equity and debt issuance. Lastly, the persistences of the underlying investmentirreversibility and deadweight cost processes are set to be high, that is, ρω and ρχ are set to 0.9. Theremaining parameters controlling the grids of the deadweight cost χt and the degree of investmentirreversibility ωt are set as follows. The points of the grid for χt are equally spaced in the interval[χ,1]; where χ and the number of points in the grid are set to match the mean recovery rate of 45%,and the volatility of recovery rates of 10% (Chen (2010)). Finally, the points of the grid for ωt areequally spaced (in logs) and belong to the interval [1, ω¯]; where ω¯ is set to match the difference inexcess returns exhibited by the highest and lowest asset redeployability quintiles (see Table 2.6).2.5 Quantitative resultsIn this section, I quantitatively assess the importance of both the investment-irreversibility and thedeadweight-cost channel as determinants of the cross-sectional credit spreads and leverage. Giventhat most of the parameters of the model are set to match empirical aggregate moments, I start thissection by assessing how the benchmark model performs by comparing the aggregate moments ob-tained from simulating the model to their empirical counterparts.To complement the analysis, I report moments of portfolios formed based on asset redeployabilityfrom simulated data. The objective of this exercise is to assess whether differences in firms’ assetredeployability can generate substantial cross-sectional differences observed in the data.Next, I decompose credit spreads and leverage of portfolios formed based on asset redeployability18from simulated data. Specifically, the goal is to quantify the contribution of each asset redeployabilitydimension considered in this chapter, i.e. the investment-irreversibility and deadweight-cost channels.2.5.1 Aggregate momentsTable 2.2 reports the business cycle moments generated from the simulation of the benchmark cali-bration of the model and compares them with their empirical counterparts. The benchmark calibrationgenerates an average investment-output ratio of 26% which is in line with its 20% obtained from thedata. Furthermore, the output volatility σ∆y and relative macro volatilities are close to the data. Thebenchmark calibration of the model also replicates correlations across some business cycle variablessuch as the procyclicality of consumption, and stock returns. The implied persistence of output andinvestment are also quite close to the ones in the data.Impulse response functions in Figure 2.1 describe the model dynamics in response to a positiveproductivity shock. An increase in aggregate productivity ∆x leads to positive growth of firms’ invest-ment. As showed by Croce (2014), in the context of a model with elasticity of substitution greaterthan one, a positive shock of the long-run component generates an increases in investment growthwhich leads to an increase in firm valuation proxies such as the market-to-book ratio as showed byFigure 2.1. The increase in firms’ valuation translates to an important increase of the aggregate excessreturn (re− r f ). An increase of the long-run component of the aggregate productivity ∆x also raisesfirms’ continuation values so that the number of firms declaring bankruptcy decreases leading to alower aggregate probability of default. Consistently, credit spreads (cs) also suffer a contraction. Asdiscussed by Chen et al. (2012), after this positive aggregate shock, firms will choose longer debtmaturity in order to mitigate costs associated with deadweight losses of default that are more likelyto occur in economic downturns when firms are not able to honor their maturing debt.Table 2.2 also shows key asset pricing moments from the benchmark model’s simulations. In par-ticular, the model is able to generate a sizable annual equity risk premium (4.25%), and an importantexcess returns volatility (7.58%). The strong demand for precautionary savings drives the risk-freerate down to 1.4%, which is below the data, as well as the risk free rate volatility (1.4%). The modelgenerates a sizable credit spreads of 106bps with a volatility of 57bps, both values slightly above theirempirical counterparts.As showed by Table 2.2, and as in the data, credit spreads are counter-cyclical showing a correla-tion with the output growth of -0.19 which is somewhat below the empirical correlation (-0.36). Table2.2 also reports several key aggregate corporate financing moments. Specifically, the model gener-ates an annual book leverage of 0.30 and a frequency of equity issuance of 0.15. The unconditionalprobability of default derived from the model is 1.66%. Overall, the model performs well matchingunconditional moments and key dynamics of both macro aggregates and asset prices.192.5.2 Asset redeployability momentsIn this section, I assess the ability of firms’ asset redeployability to explain some significant dif-ferences in capital structure outcomes. The analysis is conducted by disaggregating moments andimpulse response functions by distinct levels of asset redeployability. To understand the strategy fol-lowed in this section, let us recall that ωt and χt are modeled independently. Then, in order to assessthe importance of the asset redeployability measure through the lens of the quantitative model de-scribed in this chapter, I construct three portfolios that are intended to represent a portfolio formed byfirms with high, moderate and low degree of asset redeployability. Specifically, from the simulatedpanel of firms resulted from the model, each period, the high- (low-) asset redeployability portfolio iscomprised of firms featuring an investment irreversibility level ωt and deadweight cost χt belongingto the three lowest (highest) set of points of the variable’s grids. All the remaining firms are allocatedto the portfolio representing firms with a moderate level of asset redeployability.Table 2.3 reports various moments of the high- and low- asset redeployability portfolios con-structed in the model and compared to their empirical counterpart. Both in the model and the data,high asset redeployability firms have higher book leverage, a lower default rate, a lower credit spread,a more procyclical debt maturity structure, and a lower equity return. I will now explain each of thesein turn.Table 2.3 shows that firms with more redeployable assets have larger book leverage ratios thanthose exhibited by firms with less redeployable assets. Intuitively, firms’ enjoying more redeployableassets have higher operating flexibilities which translates to lower probabilities of defaults. Fur-thermore, in case of default, firms with highly redeployable assets provide more protection to theirbondholders since they experience higher recovery rates. Overall, these effects increase firms’ debtcapacity leading to larger debt-to-asset ratios. The last two columns compare the difference betweenthe high- and low- asset redeployability portfolios in the model and in the data. The cross-sectionaldifference in the book leverage ratio is 0.056, similar to its empirical counterpart of 0.023. This resultis consistent with previous studies (e.g. Benmelech (2008)).As in the data, the low-asset redeployability portfolio exhibits a more stable debt maturity struc-ture than the high-asset redeployability portfolio does. Low asset redeployability exposes firms tosystematic shocks which makes them more concerned with rollover risk associated to short-term debtand thus, these firms prefer to issue long-term debt even when implementing this strategy could becostly. Indeed, firms with less redeployable assets face higher credit spreads. The equilibrium creditspreads of the high-asset redeployability portfolio is lower (85bps) than the credit spreads faced bythe low-asset redeployability portfolio (130bps). Note that the magnitude of the difference in themodel, -46bps, is larger than its empirical counterpart, i.e. -19bps. This difference can be explainedby noticing that the data used is biased towards larger firms.15 As pointed out by Corhay (2015) credit15As is described in Section 2.6, I compute corporate bond credit spreads from the National Association of InsuranceCommissioners (NAIC) bond transaction file which records all public corporate bond transactions by life insurance com-panies, property and casualty indurance companies, and Health Maintenance Organizations.20spreads on bank loans for small firms is twice as high as the credit spreads of large firms. Moreover,besides the bias of the sample data toward large firms, firms in the sample varies across many moredimensions than those captured in the model and it is likely that these dimensions are not capturedby a univariate analysis. To address this concern, in Section 2.6, I run a set of panel regressions thatinclude various controls.The model also generates substantial differences in equity risk across asset redeployability port-folios. The average excess return is about 3.5% withing high-asset redeployability firms comparedto 5.02% within low-asset redeployability firms; which leads to a difference of -1.55%. Notably, inthe data, this premium is -0.85%. To understand why the risk premium on equity is lower in firmswith more redeployable assets, note that low asset redeployability implies less flexibilities for firmsto deploy their excess capital over their lives and in particular when the economy faces bad shocks.In contrast, firms with more redeployable assets do not face the same problem, since they do not havetoo much excess capital. This lower flexibility is exacerbated in the model since firms also face fixedoperating costs in the profit function (as in Carlson et al. (2004)).In short, the model predicts that firms with highly redeployable assets exhibit higher leverage ra-tios, and lower credit spreads. These predictions are in line with earlier studies and more importantly,match the data quantitatively.2.5.3 Assessing asset redeployability channelsIn what follows, I use the simulated panels from the model to assess the relative importance of thetwo aspects of asset redeployability studied in this chapter.To measure the importance of ωt and χt in shaping debt credit spreads, Table 2.4 Panel A showsthe average credit spreads exhibited by firms for each combination of partial irreversibility of invest-ment (ωt) and deadweight cost (χt). As described in the previous section, bold numbers representthe portfolios used to construct the high- and low-asset redeployability portfolios. The last row andcolumn of the table reports the elasticity of credit spreads with respect to changes of ωt and χt , re-spectively. Elasticities of credit spreads with respect to each variable are intended to capture the per-centage change of the portfolio’s average credit spreads after a one percentage change of the variableexamined, keeping everything else constant. Overall, the larger the degree of investment irreversibil-ity or deadweight costs, the higher the credit spreads of the firm. Furthermore, the sensitivity of creditspreads to changes in ωt and χt increases with the magnitude of each variable. These results capturethe notion discussed by Kuehn and Schmid (2014) regarding the convexity of the value of the invest-ment and default option which are convex functions of the state variables. Panel A reveals that bothchannels reinforce each other by increasing the sensitivity of credit spreads with respect to the otherchannel. These results show that changes in asset redeployability can be substantial if we consider allpossible aspects of firms that can be affected by changes of the assets’ liquidity value.Panel B shows that an increase in investment irreversibility reduces a firm’s leverage ratio. As21showed in the simple model, this relation is mainly explained by the fact that firms’ optimal capitalstock decreases substantially when future disinvestment is costly (see Panel C). Unlike the simplemodel, lower capital stock and higher levels of investment irreversibility also lead to a higher proba-bility of default (Panel D) since the likelihood of reaching the idiosyncratic-shock default thresholdincreases. Then, an increase of ωt will not only lower financial needs but also will tend to increasedebt credit spreads since default is more likely to occur; this will motivate the firm to decrease theamount of debt issued leading to lower leverage ratios. In contrast, the effect of larger deadweightcosts on leverage varies depending on the level of the investment irreversibility faced by the firm. Forlow levels of ωt , higher deadweight costs upon default do not have a sizable negative impact on creditspreads and thus, the firm continue to issue debt in order to finance its investment plans. In this case,the low impact of deadweight costs on credit spreads is explained by the small probability of defaultfaced by firms. However, when defaults become more likely after an increase in the investment ir-reversibility, credit spreads increase importantly in the level of the deadweight cost. Overall, in thiscase, firms’ desire to increase their debt issuances reduces significantly.Note that unlike the simple model, Panel E shows that the value of recovery rates is not impor-tantly affected by changes in investment irreversibility. However, deadweight costs relate negativelywith the value of recovery rates. Two opposite effects explain the apparent independency of the valueof recovery rates to investment irreversibility. In fact, despite that the probability of default increasesin ωt , in the model, the unlevered value of the firm upon default decreases in ωt since the optimalcapital stock decreases.Lastly, Panel H shows that the effect of both channels on excess returns is mixed; however, as isdiscussed in the previous section, on average the low-asset redeployability portfolio exhibits largerexcess returns than the high-asset redeployability portfolio does.2.6 Panel regressionsIn this section, I test in the data the implications of the asset redeployability measure (Kim and Kung(2016)) on credit spreads and leverage ratios predicted by the quantitative model. Also, motivated bythe results of the quantitative model that link changes in the value of recovery rates to changes in thedeadweight cost, I test the importance of the two channels of asset redeployability documented in theprevious section. The strategy is to use a data set of publicly traded bonds to compute firms’ creditspreads; while firms’ leverage ratios are computed from standard accounting data. To compute theasset redeployability measure, I follow closely Kim and Kung (2016); whereas, expected recoveryrates are computed using the KMV model.2.6.1 Bond sample constructionI obtain corporate bond prices from the National Association of Insurance Commissioners (NAIC)bond transaction file. The NAIC file records all public corporate bond transactions by life insur-22ance companies, property and casualty insurance companies, and Health Maintenance Organizations(HMOs).16 The database covers from 1994 to 2012.The first step is to link the NAIC bond transactions table to the Mergent Fixed Income SecuritiesDatabase (FISD) to obtain bond specific information. The criteria defined to form the final sampleis such that it only includes bonds issued by U.S. firms and paying a fixed coupon. As in Campbelland Taksler (2003), bonds with special features such as put, call, exchangeable, asset backed, andconvertible are eliminated from the sample. Furthermore, I only keep bonds with an investment graderating.17 Following a common practice, I also remove from the sample firms that belongs to theregulated utilities industry and financial institutions. Furthermore, as in Bessembinder et al. (2009),I eliminate transactions smaller than $100,000, sell transactions that involved the bond issuer, andthose with the terms called, cancelled, conversion, direct, exchanged, issuer, matured, put, redeemed,sinking fund, tax-free exchange, and tendered in the transaction name field. To eliminate potentialdata-entry errors contained by the database, I decide to remove observations that show return rever-sals.18 Finally, I exclude observations with obvious data errors such as negative price or transactiondates occurring after maturity. Importantly, in cases where there are several bond transactions in aday, the daily bond price is obtained by weighting each transaction price by its volume.In terms of constructing the credit spreads associated with each transaction, note that the reportedprices in the NAIC file are clean bond prices, then accrued interests are added in order to obtain thefull settlement price (i.e. the bond dirty price). Transactions’ yields are computed by equating thedirty price to the present value of cash-flows.19 Then, credit spreads are defined in excess of thebenchmark treasury at the date of transaction. To obtain the benchmark treasury for each transaction,I match the bond duration to the zero-coupon Treasury yields curve provided by Gu¨rkaynak et al.(2007) - linearly interpolating if necessary. I complement Gu¨rkaynak et al. (2007) database withTreasury yields with maturity shorter than one year by appending the CRSP risk-free series for oneand three months. Following Gilchrist and Zakrajsˇek (2011), I truncate the credit spreads in thesample to be between 5bps and 3,500bps.Issuers’ accounting information are from Compustat and are matched using the six-digit issuerCUSIP. Stock price information is obtained in a similar way from the CRSP file. To ensure that16The NAIC database represents a substantial portion of the corporate bond market. Insurance companies hold betweenone-third and 40% of issued corporate bonds (Campbell and Taksler (2003)). Bessembinder et al. (2006) estimates thatInsurance companies represent a substantial proportion (12.5%) of total bond trading volume. While if the database used isrepresentative can be debatable, I would like to point out that there are other (complementary) sources of bond data; suchas Trace US corporate bond database.17Unlike some papers working with the NAIC data base, my results do not depend on whether AAA bonds are excludedor not from the analysis (Campbell and Taksler (2003))18I define return reversal as a return of more than 15% in magnitude immediately followed by a more than 15% return inthe opposite direction.19To reconstruct the stream of a bond’s cashflows I use either the information about the date of the last coupon paymentor the date at which the principal is repaid. To decide which date determines the bond cashflow’s timing more precisely Icompute accrued interests under both assumptions and compare them to the accrued interest reported by NAIC. The datethat reproduces more closely the accrued interests reported by NAIC is used.23all information is included in asset prices, stock returns and bond credit spreads from July of year tto June of year t + 1 are matched with accounting information for fiscal year ending in year t − 1.Monthly credit spreads observations are constructed using the last transaction of the month. Thesample consists of an unbalanced panel of 16,587 bond-month transactions. Appendix A.1 presentsdescriptive statistics of the bond sample data used.2.6.2 Asset redeployability measureTo construct the asset redeployability measure of a firm in a year, I employ the value-weighted aver-age of industry-level redeployability indices obtained from Kim and Kung (2016)20 across businesssegments in which the firm operates over the year. To generate this measure every year, I use annualsales information obtained from the Compustat Segment files as weights. Then, the redeployabilityof assets of firm i at year t, (Redeployabilityi,t) is computed as,Redeployabilityi,t =ni,t∑j=1wi, j,t ×Redeployability j,t (2.19)where ni,t is the number of industry segments, and wi, j,t is industry segment j’s sales divided by thetotal sales for firm i in year t.21 Following Kim and Kung (2016), when information is missing inCompustat Segment files for a firm-year, I use Redeployabilityi,t from previous year, and when thisinformation is also missing I impute the asset redeployability measure corresponding to the firm i’sindustry classification in year t.2.6.3 Asset redeployability and the cross section of credit spreadsIn this section I investigate empirically the effect of the firm’s asset redeployability on credit spreadsand leverage ratios. The objective is to test the results from the model that relate the degree of assetredeployability negatively to credit spreads and positively to leverage ratios.To accomplish this objective, I define the variable Redepi,t−1 as a dummy equal to one if the assetredeployability measure of firm i is in the highest quintile of the sample distribution of the variable atthe previous year to which the observation (i, t) belongs to; and zero otherwise. This specification willfacilitate the economic interpretation of the coefficient associated to this variable and also mitigatepotential measurement errors on the construction of the asset redeployability measure. Using themonthly panel data, I investigate whether the asset redeployability measure has any predictive poweron corporate credit spreads csi,t for public debt. To implement this plan, I test the following regressionmodel,20To construct the data on industry-level asset redeployability, Kim and Kung (2016) use the 1997 Bureau of EconomicAnalysis (BEA) capital flow table. I thank Hyunseob Kim and Howard Kung for making the data available.21This measure of asset redeployability is similar to asset liquidity measures used in Ortiz-Molina and Phillips (2010).Furthermore, Benmelech and Bergman (2009), and Gavazza (2011) implement similar measures for the airline industry.24csi,t = α+δ ×Redepi,t−1+βXi,t−1+ εi,t (2.20)where (i, t) denotes a specific firm-month observation, Redepi,t−1 is the asset redeployability measuredescribed above, and Xi,t−1 is a vector of controls that will include time, and/or industry fixed effects.The parameter of interest is δ and it will capture the difference in credit spreads, csi,t , for firmsexhibiting high levels of asset redeployability. Additionally, I test a similar regression where bookleverage ratio is set as the dependent variable.In the regressions, controls variables Xi,t−1 are grouped into three categories: (i) equity charac-teristics; (ii) bond characteristics; and (iii) macroeconomic variables.22 Particularly, in the equitycontrols category I include the mean of the firm excess returns (net of the risk-free rate) computedusing the past 12 months of equity returns prior to the month when the transaction occurs. Also, inthis category, I include the equity beta; which is computed using the past 36 months of equity returnsand value-weighted market returns prior to the month when the transaction occurs. Note that previ-ous literature has shown a positive effect of exposure to systematic risk on credit spreads (Chen et al.(2012)). I also control for well-known determinants of the cross-section of credit spreads includingleverage (total debt to capitalization), asset tangibility, book-to-market ratio, the firm size (log-asset),return on assets (ROA), and Tobin’s Q. I complement this set of controls with the fitted SIC-basedIndustry concentration index (Hoberg and Phillips (2010)). Corhay (2015) shows that measures ofindustry competition affect positively credit spreads.Bond specific variables include the Altman Z-Score and bond ratings to take into account theoverall risk of the firm.23 Maturity and coupon are also included. Leland and Toft (1996) shows thatlonger maturity bonds are likely to be risker; whereas Elton et al. (2001) claims that bonds with highcoupon payments suffers from higher taxation which should be translated as higher credit spreads.To control for bond-specific illiquidity which can generate an illiquidity premium in my data (Dick-Nielsen et al. (2012)), I include a measure of trading turnover defined as the average of trading volumeover the past 12 months as a proportion of total amount outstanding. The log amount outstanding ofthe bond is also added since a small issue will likely be less liquid.Finally, I include a series of macroeconomic variables such as three-month Treasury Bill yield.I also include the 36-month moving average and standard deviation of the aggregate market return.Lastly, I also control for the aggregate labor share obtained from Bureau of Labor Statistics (Fav-ilukis et al. (2015)). Further, equity and macroeconomic data are lagged one month to ensure thatinformation is included in credit spreads at the time the bond transaction takes place. All t-statisticsare calculated using standard errors clustered at the firm level.Table 2.7 Columns (4) presents coefficients from estimating the specification of equation (2.20)22It is important to control for all these characteristics because, in contrast to the model, the bond data set exhibits vastheterogeneity in both bond and firm characteristics.23Moody’s ratings are converted to numerical values by creating an index starting at 12 (Baa3) and linearly increasingby one for each credit rating notch.25when credit spreads are the dependent variable. The coefficient of interest, δ , reveals that a firm withassets exhibiting a degree of redeployability in the highest asset redeployability quintile is expectedto have credit spreads about 30bps lower than others firms, compared to 46bps in the model.Note that the estimates presented in this section are in line with findings in previous empiricalliterature that finds that firms with more liquid assets face a lower cost of debt (Ortiz-Molina andPhillips (2010)).2.6.4 Asset redeployability and the cross section of leverageSimilarly to the previous section, I run the following regression model using annual balance sheetdata from Compustat,book leveragei,t = α+δ ×Redepi,t−1+βXi,t−1+ εi,t (2.21)as before, the parameter of interest is δ and it will capture the difference in book leverage, for firmsexhibiting high levels of asset redeployability. The independent variables used in this specificationare similar to the one already described in the previous section.Table 2.7 reports the main regression results of this section estimated from the NAIC bond trans-action panel. The first column presents coefficients from estimating the specification of equation(2.21). The coefficient of interest, δ , is estimated to be around 2.2% and is statistically significant.That is, a firm with assets exhibiting a degree of redeployability in the highest asset redeployabilityquintile is expected to have a leverage ratio, on average, 2.2 percentage points higher than other firms.Table 2.3 shows that the calibrated model reflects a similar effect of asset redeployability on leverage.Indeed, the difference between the leverage ratio of the high- and low-asset redeployability portfolioin the simulated data is, on average, 5.6 percentage points.Importantly, the estimates presented are in line with findings in previous empirical literature thatfinds that firms with more liquid assets exhibit larger leverage ratios.2.6.5 Asset redeployability decompositionIn the model, the value of recovery rate relates importantly to deadweight costs, χt . In this section,I use this result to motivate a decomposition of the asset redeployability measure, Redeployabilityi,t ,in two components: (i) a component that contains information about expected recovery rates and (ii)a component that is not able to predict expected recovery rates, Redeployability(residual)i,t .Specifically, I start running a specification similar to the those described by equations (2.20)and (2.21), but now the coefficient δ is separated in two based on the estimation of an intermediateregression. This intermediate regression allows me to find the component of asset redeployability that26does not explain expected recovery rates; and thus to test the following specification,Yi,t = α+δ0×Redep(residual)i,t−1+δ1×E(recovery rate)i,t−1+βXi,t−1+ εi,tRedeployabilityi,t−1 = γ×E(recovery rate)i,t−1+Redeployability(residual)i,t−1(2.22)where the independent variable Yi,t is either the credit spreads or the book leverage ratio; furthermore,Redep(residual)i,t−1 is defined as a dummy equal to one if the component of asset redeployability thatis not explained by recovery rates is in the highest quintile of the sample distribution of the variableat the previous year to which the observation (i, t) belongs to; and zero otherwise. The final goalis to test empirically whether or not credit spreads and book leverage are explained by other firms’characteristics linked to asset redeployability apart from deadweight cost at default; such as, operatingflexibilities related to the firms’ ability to adapt their operations. To accomplish this goal, first I startdescribing how expected recovery rates were computed.Expected recovery ratesFollowing Altman et al. (2004) and Bohn and Crosbie (2003), a measure of expected recovery ratesis derived from adjusting a Merton-like default model to firms’ observations in the data. Specifically,the method applied estimates the parameters of the KMV model by solving a system of equationsfor each observation of the database used. Appendix A.1 provides technical details of the modelimplemented.Intuitively, the system of equations corresponds to two identities derived from a set of assump-tions regarding the dynamic of a firm’s assets, debt structure, and market perfection. The system ofequations uses a set of observable variables, i.e. the value and volatility of equity in conjunction withtotal debt, to estimate the value and volatility of the firm’s assets (unobservable). The general ideais based on the notion that firm’s equity is a call option on the the firm’s assets. Once the value andvolatility of the firm’s assets are estimated, expected recovery rates are computed as the expected ratioof the asset value to the total debt conditional on default.Asset redeployability decomposition and credit spreadsTable 2.8, column (4), presents coefficients from estimating the specification in equation (2.22) whenthe dependent variable Yi,t represents credit spreads. The coefficient δ1 reveals that a higher expectedrecovery rate allows firms to reduce their credit spreads. Moreover, the coefficient δ0 shows thatthe asset redeployability measure contains information that is not related to recovery rates but stillcorrelates negatively with credit spreads. Specifically, the coefficients δ0 shows that firms in thehighest quintile of the asset redeployability component that does not relate to recovery rates exhibitslower credit spreads.Despite that both coefficients δ0 and δ1 are statistically significant, the expected recovery ratesvariable seems to affect less credit spreads. Indeed, reducing credit spreads in δ0 basis points requires27a two-SD increase in expected recovery rates; whereas to have a similar effect, the asset redeployabil-ity component of a firm that does not relate to recovery rates must show less than a one-SD increaseso that the dummy Redep(residual)i,t−1 becomes equal to one. Importantly, in the data, these re-sults stays economically and statistically significant, even after controlling for many variables used topredict credit spreads and leverage.In the model, Table 2.4 Panel A shows a similar effect. The elasticities of credit spreads to changesin investment irreversibility are larger than elasticities of credit spreads to the deadweight costs.Asset redeployability decomposition and book leverageThe first column of Table 2.8 reports the main regression results from estimating the specification(2.22) when the dependent variable Yi,t represents the book leverage ratio. The coefficients of interest,δ0 and δ1, are estimated to be around 2.2% and -0.2%, and are statistically significant. That is, a firmwith assets exhibiting a degree of redeployability in the highest quintile is not only expected to havea book leverage ratio on average 2.2 percentage points larger than other firms (see Table 2.7); Table2.8 also shows that this positive effect comes mainly from aspects of the firm that relate to its assetredeployability but are different from expected recovery rates.To the extent that within the model expected recovery rates are primarily related to the deadweightcost χt , Table 2.4 shows that the calibrated model generates implications for leverage ratios that are inline with the one presented in this section. Table 2.4 Panel B shows that in the model firms’ leverageratios vary mainly due to changes in investment irreversibility. In contrast, in the model, deadweightcosts shows mixed effects on explaining firms’ leverage ratios.2.7 ConclusionBy affecting the liquidation value of a firm’s assets, low asset redeployability increases both the costof disinvesting of an operating firm, as well as the cost of corporate default by decreasing the valueat which a distressed firm can liquidate its assets. Motivated by these two aspects of a firm affectedby the redeployability of its assets, this chapter studies the importance of asset redeployability ondetermining leverage ratios and credit spreads through two main channels; that is, the investment-irreversibility and the deadweight-cost channel.Using a production-based asset-pricing model that incorporates varying degrees of investmentirreversibility and deadweight costs, this chapter shows that even though both channels affect creditspreads positively, the importance of the deadweight-cost channel depends on the degree of invest-ment irreversibility. Credit spreads are affected by deadweight costs as long as the level of investmentirreversibility imposes significant real frictions to the firm over its life, increasing its probability ofdefault. Further, the model reveals that the positive link between leverage ratios and asset redeploya-bility is mainly driven by the investment-irreversibility channel. In most of the cases, an increase indeadweight costs is not enough to affect significantly a firm’s investment decisions and thus, the firm28continues issuing debt to fund its financial needs.Despite that the model is calibrated to match a set of aggregate moments and to replicate cross-sectional differences in excess returns exhibited by the highest and lowest asset redeployability quin-tiles,24 the resulted magnitudes across portfolios formed based on the degree of asset redeployabil-ity for leverage ratios and credit spreads accord with the existing empirical literature. I verify themodel’s predictions using a panel of publicly corporate bond transactions in conjunction with stan-dard accounting data. In the data, I find that asset redeployability decreases credit spreads by 30bpsand increases leverage ratios by 2.2 percentage points. Also, credit spreads and leverage ratios showto be more sensitive to the asset redeployability’s component that is not related to expected recoveryrates. These results are robust to various controls.24As is described in Section 2.4.2, the deadweight-cost channel is modeled as a Markov chain where the number of pointsin the grid is set to match the mean and volatility of recovery rates as in Chen (2010).29Table 2.1: Benchmark monthly calibrationParameter Description ValueA. Preferencesβ discount factor 0.994γ relative risk aversion 10.0ψ elasticity of intertemporal substitution 2.0B. Productionα capital share 0.35δ capital depreciation rate 0.01f operational (fixed) cost 0.05φ operational (linear) cost 0.07θ capital adjustment cost parameter 15ρω persistence of the asset redeployability state ωt 0.90ρχ persistence of the recovery rate state χt 0.90C. Productivityg growth rate of consumption 0.018/12ρ persistence of aggregate state st 0.95σz conditional volatility of the idiosyncratic shock 0.13ρz persistence of idiosyncratic shock 0.90D. Financeτ tax rate 0.14c coupon rate 3.0%/12e0 equity issuance cost: fixed component 0.06e1 equity issuance cost: linear component 0.03Benchmark monthly calibration. This table reports the parameter values used in thebenchmark monthly calibration of the model. Section 2.4 describes the moments targetedto set each parameter.30Table 2.2: Aggregate business cycle, asset pricing and financing momentsMoment Data Model Moment Data ModelA. Business cycleE(∆y)(%) 1.80 1.55 corr(∆c,∆y) 0.39 0.49σ∆y(%) 3.56 3.69 corr(∆c,re− r f ) 0.25 0.43E(I/Y ) 0.20 0.26σ∆c/σ∆y 0.71 0.79 ACF1(∆y) 0.35 0.33σ∆i/σ∆y 4.50 4.30 ACF1(∆i) 0.85 0.80E(maturity)(yrs) 7.6 4.7 σ(maturity)(yrs) 11.3 9.4B. Asset pricesE(re− r f )(%) 7.22 4.25 σ(re− r f )(%) 16.5 7.58E(r f )(%) 1.51 1.40 σ(r f )(%) 2.2 1.4E(cs)(bps) 90 106 σ(cs)(bps) 44 57C. FinancingBook leverage 0.26 0.30 corr(equity payout,∆y) 0.45 0.35Freq. of equity issuance 0.09 0.15 corr(debt repurchase,∆y) -0.70 -0.37Default rate (%) 0.84† 0.85 corr(cs,∆y) -0.36 -0.19Aggregate business cycle, asset pricing and financing moments. I/Y denotes the investment-output ratio. ∆y, ∆c, ∆i denote output, consumption, and investment growth respectively. Aver-age and standard deviation of debt maturity exhibited by the data is computed directly from theMergent’s Fixed Income Security Database (FISD). re− r f is the aggregate stock market excessreturn, r f is the one-period real risk-free rate, and cs is the aggregate credit spreads. Debt repay-ment and equity payout are normalized by total assets. Data moments are obtained from Jermannand Quadrini (2009) and Chen (2010). Model moments are calculated by simulating the modelfor 3,000 firms and 6,000 months, with a 1,000 months burning period. Aggregate returns andcredit spreads are equally-weighted. Growth rates, and returns moments are annualized percent-age, credit spreads are in annualized basis point units.† The average default rate reported correspond to average expected default rates resulted from im-plementing the KMV model in the panel data described in Section 3.2.1. Appendix A elaborateson the technical details of the KMV model used.31Table 2.3: Asset redeployability momentsSimulated Moments High minus LowHigh AR Low AR Data ModelBook Leverage 0.308 0.252 0.023 0.056Market Leverage 0.240 0.234 -0.008 0.006Default rate (%) 0.788 0.978 -0.310† - 0.190Recovery rates (%) 0.534 0.407 -0.182† -0.127corr(maturity,∆y) 0.710 0.350 0.250 0.360E(cs)(bps) 85 130 -19 -46E(ri− r f )(%) 3.465 5.015 -0.850 -1.550Asset redeployability moments. This table reports key moments of ex-treme asset redeployability portfolios. Model moments are calculated bysimulating the model for 3,000 firms and 6,000 months, with a 1,000months burning period. From the simulated data, each period the high-(low-) asset redeployability portfolio is comprised of firms with an invest-ment irreversibility level ωt and deadweight cost χt belonging to the threelowest (highest) values of ωt and χt , respectively. Market leverage is ob-tained as the ratio of the debt market value and the sum of the equity anddebt market values. The market value of debt is defined as total debt timesthe market value of 1$ of debt obtained from my data sample. The remain-ing variables are described in Table 2.2.† The default and recovery rates used to compute the difference reportedcorrespond to expected default and recovery rates resulted from implement-ing the KMV model in the panel data described in Section 3.2.1. AppendixA elaborates on the technical details of the KMV model.32Table 2.4: Portfolios sorted by investment irreversibility and deadweight costPanel A: CREDIT SPREADS (cs)ω χ1 = χ = 0.18 χ2 χ3 χ4 χ5 χ6 χ7 = 1 %∆cs/%∆χω1 = 1 77.0 79.5 80.5 81.6 83.3 86.0 90.7 0.11ω2 82.5 84.8 85.6 86.7 88.3 90.4 95.3 0.10ω3 88.0 90.3 92.4 94.9 98.4 104.3 116.1 0.19ω4 93.5 95.8 98.2 101.1 105.2 112.0 125.7 0.20ω5 99.5 101.8 104.1 107.0 111.8 119 133.2 0.20ω6 105.5 107.5 110.5 113.9 119.5 127.7 144.1 0.22ω7 = ω¯ =3.8 111.5 113.5 116.7 120.4 126.3 136.3 153.8 0.22%∆cs/%∆ω 0.25 0.24 0.26 0.27 0.29 0.32 0.37Panel B: BOOK LEVERAGE RATIO (b/k)ω χ1 = χ = 0.18 χ2 χ3 χ4 χ5 χ6 χ7 = 1 %∆(b/k)/%∆χω1 = 1 0.32 0.32 0.32 0.33 0.34 0.34 0.35 0.06ω2 0.31 0.31 0.31 0.31 0.32 0.32 0.32 0.01ω3 0.29 0.29 0.29 0.29 0.29 0.29 0.28 -0.03ω4 0.27 0.27 0.27 0.27 0.26 0.26 0.26 -0.05ω5 0.26 0.26 0.26 0.26 0.26 0.25 0.25 -0.03ω6 0.26 0.25 0.25 0.25 0.25 0.25 0.25 -0.02ω7 = ω¯ =3.8 0.25 0.25 0.25 0.25 0.25 0.25 0.25 -0.01%∆(b/k)/%∆ω -0.16 -0.17 -0.17 -0.18 -0.2 -0.21 -0.22Panel C: INVESTMENT RATE (i/k)ω χ1 = χ χ2 χ3 χ4 χ5 χ6 χ7 =1 %∆(i/k)/%∆χω1 = 1 0.055 0.058 0.054 0.055 0.048 0.052 0.045 -0.12ω2 0.038 0.039 0.038 0.038 0.035 0.029 0.027 -0.23ω3 0.030 0.025 0.026 0.028 0.021 0.026 0.023 -0.13ω4 0.019 0.021 0.021 0.014 0.018 0.018 0.010 -0.27ω5 0.009 0.010 0.011 0.006 0.007 0.008 0.011 0.33ω6 0.004 0.008 0.008 0.004 0.005 -0.001 0.000 -0.80ω7 = ω¯ =3.8 0.003 -0.001 0.002 0.001 0.002 0.001 0.002 -2.89%∆(i/k)/%∆ω -1.46 -1.81 -1.52 -1.82 -1.55 -3.41 -6.93(continues)33Panel D: DEFAULT PROBABILITY (CONDITIONAL ON DEFAULT) IN BPS (PD)ω χ1 = χ = 0.18 χ2 χ3 χ4 χ5 χ6 χ7 = 1 %∆PD/%∆χω1 = 1 77.1 73 73.9 76.7 77.6 65.3 61.4 -0.12ω2 79.2 77.7 76.7 70.6 75.0 71.5 64.9 -0.08ω3 82.1 85.6 84.0 78.6 84.8 81.8 69.9 00ω4 87.6 84.6 87.1 82.9 90.4 89.8 76.5 0.02ω5 92.8 92.2 91.1 85.9 98.2 88.7 77.6 -0.02ω6 95.9 93.7 93.1 88.5 98.2 98.1 80.9 0.02ω7 = ω¯ =3.8 97.4 95.2 92.1 97.7 101.5 101.9 80.9 0.04%∆PD/%∆ω 0.16 0.19 0.15 0.17 0.19 0.31 0.19Panel E: VALUE OF THE RECOVERY RATE (CONDITIONAL ON DEFAULT) IN BPS (RR)ω χ1 = χ = 0.18 χ2 χ3 χ4 χ5 χ6 χ7 = 1 %∆RR/%∆χω1 = 1 55.4 54.6 50.7 46.2 45.6 36.0 0.0 -0.32ω2 55.1 53.4 51.3 47.6 45.6 36.0 0.0 -0.32ω3 55.2 53.7 51.3 47.3 45.6 36.0 0.0 -0.32ω4 55.1 53.3 51.0 47.1 45.6 36.0 0.0 -0.32ω5 55.1 53.5 51.4 47.5 45.6 36.0 0.0 -0.32ω6 55.1 53.3 51.3 47.2 45.6 36.0 0.0 -0.32ω7 = ω¯ =3.8 54.0 51.8 51.0 48.0 45.0 36.0 0.0 -0.30%∆RR/%∆ω -0.02 -0.03 0.0 0.03 -0.01 0.0 -Panel F: CREDIT RISK IN BPS (CR)ω χ1 = χ = 0.18 χ2 χ3 χ4 χ5 χ6 χ7 =1 %∆CR/%∆χω1 = 1 55.3 61.1 57.3 51.1 51.3 56.7 29.3 0.03ω2 58.4 60.4 60.2 63.7 58.9 55 30.4 -0.04ω3 61.1 58.3 59.7 63.6 59.2 58.5 46.2 -0.03ω4 60.9 64.4 62.2 65.3 60.3 58.2 49.2 -0.03ω5 61.8 63.0 64.3 68.6 59.2 66.3 55.7 0.07ω6 64.7 67.1 68.7 72.7 66.9 65.6 63.2 0.02ω7 = ω¯ =3.8 68.1 70.1 75.6 70.7 69.7 70.4 72.9 0.03%∆CR/%∆ω 0.14 0.1 0.19 0.24 0.22 0.15 0.7(continues)34Panel G: DEBT AVERAGE MATURITY (m) IN YEARSω χ1 = χ = 0.18 χ2 χ3 χ4 χ5 χ6 χ7 =1 %∆m/%∆χω1 = 1 2.40 3.05 3.51 3.43 3.32 3.75 5.54 0.65ω2 2.89 3.31 3.54 3.42 3.25 3.89 7.57 0.85ω3 3.56 3.78 3.85 3.82 3.79 4.02 4.74 0.20ω4 4.64 4.40 4.36 4.40 4.46 4.42 4.32 -0.05ω5 4.52 4.70 4.72 4.76 4.83 4.79 4.70 0.03ω6 4.47 4.87 4.88 4.89 4.92 4.90 4.87 0.06ω7 = ω¯ =3.8 4.42 5.05 5.05 5.06 5.06 5.06 5.05 0.1%∆m/%∆ω 0.46 0.36 0.25 0.27 0.3 0.21 0.04Panel H: EXPECTED EXCESS RETURNS (E(ri− r f ))ω χ1 = χ = 0.18 χ2 χ3 χ4 χ5 χ6 χ7 =1 %∆E(ri− r f )/%∆χω1 = 1 3.10 3.57 3.60 2.93 3.81 3.63 3.74 0.17ω2 3.33 3.79 3.34 3.93 3.38 3.46 4.09 0.17ω3 3.69 3.99 4.01 3.54 4.43 3.85 4.31 0.14ω4 4.01 3.91 4.10 4.68 4.11 4.93 5.49 0.24ω5 4.61 4.72 4.20 4.16 4.46 4.82 4.85 0.04ω6 4.57 4.37 4.76 4.82 4.91 4.73 5.90 0.19ω7 = ω¯ =3.8 5.23 4.59 4.85 5.01 4.86 5.71 5.56 0.06%∆E(ri−r f )%∆ω 0.37 0.19 0.22 0.43 0.2 0.34 0.31Portfolios sorted by investment irreversibility and deadweight cost. This table reports average creditspreads, book leverage, investment rate, default probability, value of recovery rate, credit risk, averagematurity and excess returns for portfolios formed by grouping simulated firms based on their partialirreversibility of investment, ωt , and deadweight cost, χ . The model is simulated for 3000 firms and6,000 months, with a 1,000 months burning period. The Markov chain of χt includes seven equally-spaced points. The Markov chains of ωt includes seven equally-spaced points in logs. Bold numbersrepresent the portfolios used to construct the high- and low-asset redeployability portfolios in Table 2.3.The last row (column) in each table shows the elasticity of the moment reported respect to changes on ωt(χt ).35Table 2.5: Credit spreads by investment irreversibility and recovery rates (short-term debt)χω χ1 = χ = 0.18 χ2 χ3 χ4 χ5 χ6 χ7 =1 %∆cs/%∆χω1 = 1 41.0 43.5 44.5 48.0 48.3 48.4 48.4 -0.11ω2 43.5 45.8 46.7 50.1 50.4 50.5 50.5 -0.10ω3 44.8 47.1 47.6 45 45.1 45.2 45.2 -0.01ω4 47.0 49.3 49.9 50.3 47.6 45.1 42.8 0.06ω5 56.3 58.5 59.2 59.6 56.1 52.7 49.7 0.08ω6 62.4 64.4 65.2 65.6 61.5 57.6 54.1 0.09ω7 = ω¯ =3.8 70.6 72.6 73.4 73.9 70.5 67.2 64.1 0.06%∆cs/%∆ω 0.38 0.36 0.35 0.31 0.28 0.24 0.21Credit spreads by investment irreversibility and recovery rates (short-term debt). This tablereports information described in Table 2.4 for the case where the parameter controlling firms’ debtmaturity is set to λ = 1. That is, firms are forced to issue short-term debt. Model moments arecalculated by simulating the model for 3000 firms and 6,000 months, with a 1,000 months burningperiod.36Table 2.6: Univariate analysisHigh Redeployability Low Redeployability Test of differencesMean Median Mean Median t-test Wilcoxon testRedeployability 0.42 0.39 0.21 0.23Yield Spread 118 bps 108 bps 137 bps 126 bps 5.41*** 9.48***Book Leverage 0.265 0.247 0.242 0.269 -7.06*** -3.96***E(ri− r f ) 8.49 % 6.86 % 9.34 % 11.27 % 1.16 3.65***Univariate analysis. Panel A reports the means and medians of asset redeployability measure, yield spreadsand excess returns aggregated across all firms/months of the NAIC data is from 1994 and 2012. High Re-deployability corresponds to the highest asset redeployability quintile and Low Redeployability to the lowestasset redeployability quintile. The yield spreads is defined as the bond yield in excess of a government bondwith equal duration and ri− r f is the annualized realized stock return over the following year in excess of themonthly bill. The last two columns of the table present test statistics of the t-test and the Wilcoxon test ofthe differences in mean and median across the two samples. Panel B documents the correlations between theannual (seasonally adjusted) percentage change of gross value added of nonfinancial corporate business andfive variable of the highest and lowest redeployability quintiles: cash-to-asset, investment-to-asset, total debt-to-asset, equity-to-asset and long-term debt share. ***, **, and * denote statistical significance at the 1%, 5%,and 10% levels, respectively.37Table 2.7: Asset redeployability and the cross-section of capital structure outcomesLeverage Yield spreads (bps)(1) (2) (3) (4)Asset Redeployability 0.022*** -10.18** -28.74** -29.3*** -28.84***(3.65) (-2.28) (-2.29) (-2.65) (-2.64)Mean excess return (%) 0.001** -5.47*** -4.4*** -5.46*** -5.53***(-2.13) (-13.64) (-5.35) (-6.86) (-6.92)Market Beta -0.005*** -8.6*** 20.49*** 13.06** 12.61*(-3.36) (-4.14) (2.75) (2.01) (1.95)Leverage 140.01*** 82.68* 38.76 37.71(9.11) (1.85) (1.23) (1.2)Tangibility 0.234*** -36.15*** -21.86 -4.32 -4.05(22.14) (-3.11) (-0.93) (-0.2) (-0.19)Book-to-Market (log) -0.053*** 4.67 8.29 10.65 10.43(-15.18) (1.4) (0.8) (1.06) (1.03)Asset Size (log) 0.023*** -0.34 -10.45*** 8.29** 8.13**(19.98) (-0.21) (-2.73) (2.29) (2.25)ROA (%) 0 -2.14*** -1.26 -0.39 -0.38(-0.35) (-6.34) (-1.42) (-0.48) (-0.47)Tobin’s Q -0.039*** -4.33*** -5.13 -1.49 -1.45(-27.33) (-2.6) (-1.02) (-0.3) (-0.29)Concentration 0.001*** 0.03 0.16 0.18 0.17(9.15) (0.47) (0.78) (1.15) (1.1)Bond characteristicsZ-Score -0.009*** 17.79*** 12.45 15.31** 15.12**(-8.58) (5.66) (1.38) (2.07) (2.04)Credit rating -17.12*** -17.19***(-8.96) (-8.97)Years to maturity 1.03*** 1.02***(6.67) (6.71)Coupon rate (%) 10.95*** 10.81***(8.97) (8.83)Issue size (log) -4.92* -4.86*(-1.9) (-1.9)Trading turnover (log) 1.06* 1.02*(1.79) (1.71)Macroeconomic variablesThree-month T-Bill yield (%) 0.004* -0.99 1.08 1.17(1.75) (-0.46) (0.69) (0.75)Vol. of daily index ret (%) 0.064** 15.59*** 17.11*** 17.24***(2.29) (6.92) (7.41) (7.4)Mean of daily index ret (%) 0.045 -15.18*** -13.33*** -13.01***(1.19) (-5.22) (-4.76) (-4.73)Labor Share (%) -0.168*** 8.53*** 8.06*** 7.53***(-2.7) (9.78) (9.67) (9.33)Constant -0.249* 278.7*** 298.45*** 343.44*** 341.75***(-1.91) (9.68) (6.05) (4.83) (4.8)Observations 40534 14418 14418 14418 14418R2 0.26 0.27 0.35 0.41 0.42Time FE Yes No No No YesIndustry FE No Yes Yes Yes YesAsset redeployability and cross-section of capital structure outcomes. The controls variables aregrouped into three categories: (i) equity characteristics; (ii) bond characteristics; and (iii) macroeco-nomic variables. Variable descriptions are given in Section 3.2.1 and Appendix A.38Table 2.8: Asset redeployability channels and the cross-section of capital structure outcomesLeverage Yield spreads (bps)(1) (2) (3) (4)Asset Redeployability (residual) 0.022*** -21.17*** -21.75* -21.49** -22.6**(3.6) (-4.14) (-1.88) (-2) (-2.14)Expected recovery rate -0.002*** -4.86*** -3.61** -3.29** -3.36**(-9.01) (-14.17) (-2.32) (-2.26) (-2.29)Mean excess return (%) -0.003*** -4.84*** -4.21*** -5.2*** -5.28***(-9.76) (-12.49) (-5.7) (-6.95) (-7.01)Market Beta 0.001 -11.69*** 15.83** 8.43 7.8(-1.12) (-6.03) (2.17) (1.29) (1.2)Leverage 87.19*** 81.14 42.53 40.56(5.35) (1.54) (1.13) (1.07)Tangibility 0.079*** -46.41*** -31.58 -16.77 -16.73(7.28) (-4.2) (-1.19) (-0.88) (-0.88)Book-to-Market (log) -0.06*** 6.43* 8.59 11.51 11.29(-14.85) (1.91) (0.84) (1.11) (1.09)Asset Size (log) 0.008*** 0.68 -9.22*** 7.49** 7.34**(6.47) (0.44) (-2.61) (2.41) (2.37)ROA (%) 0.001*** -1.68*** -0.93 -0.15 -0.14(3.75) (-5.23) (-1.08) (-0.18) (-0.16)Tobin’s Q -0.05*** -5.76*** -3.91 1.98 1.96(-16.86) (-3.25) (-0.67) (0.33) (0.33)Concentration 0 0.05 0.17 0.16 0.14(1.53) (0.68) (0.74) (0.85) (0.78)Bond characteristicsZ-Score -0.022*** 16.4*** 13.1 15.95** 15.72**(-10.53) (5.1) (1.41) (2.02) (1.98)Credit rating -17.17*** -17.26***(-7.61) (-7.61)Years to maturity 1.06*** 1.05***(6.45) (6.51)Coupon rate (%) 10.58*** 10.44***(8.48) (8.36)Issue size (log) -3.77 -3.71(-1.55) (-1.53)Trading turnover (log) 1.25** 1.2*(2.06) (1.97)Macroeconomic variablesThree-month T-Bill yield (%) -0.007*** -2.02 0.16 0.2(-3.31) (-0.81) (0.08) (0.11)Vol. of daily index ret (%) 0.048** 11.27*** 13.37*** 13.4***(2.31) (4.58) (6) (5.94)Mean of daily index ret (%) 0.058* -15.31*** -13.3*** -12.85***(1.68) (-4.54) (-4.33) (-4.29)Labor Share (%) -0.129*** 7.84*** 7.62*** 6.82***(-2.81) (9.05) (9.38) (8.42)Constant 0.247** 734.38*** 646.06*** 657.39*** 663.39***(2.34) (17.8) (4.03) (3.69) (3.69)Observations 21996 13436 13436 13436 13436R2 0.16 0.29 0.36 0.42 0.43Time FE Yes No No No YesIndustry FE No Yes Yes Yes YesAR channels and the cross-section of capital structure outcomes. First two control variables aredescribed in Section 2.6. Refer to Table 2.7 for remaining variables.39Figure 2.1: Aggregate impulse-response functions0 20 40 600246∆ x [%]period  LRSR0 20 40 6001234∆ i [%]period0 20 40 60−4−3−2−10Debt payout [%]period0 20 40 6000.511.522.5Equity payout [%]period0 20 40 6000.050.10.150.2Market to Bookperiod0 20 40 60−101234re − rf [%]period0 20 40 60−0.04−0.03−0.02−0.0100.01Default [%]period0 20 40 60−8−6−4−20cs [bps]period0 20 40 60−0.08−0.06−0.04−0.0201/maturityperiodAggregate impulse-response functions. This figure plots the impulse-response function to a positive long-run (black solid) and short-run (red dashed) productivity shock for productivity growth (∆x), investmentgrowth (∆i), the aggregate debt and equity payout, the aggregate Market to Book ratio, the aggregate stockmarket excess return (re− r f ), the aggregate default probability (Default), the aggregate credit spreads (cs),and the inverse of aggregate maturity. The plots are calculated as deviation from the steady state. Units, whenapplicable, are specified next to the plot title.40Figure 2.2: Asset redeployability impulse-response functions0 20 40 6000.20.40.60.8∆ x [%]period  High ARLow AR0 20 40 6000.20.40.60.8∆ i [%]period0 20 40 60−2−1.5−1−0.50Debt payout [%]period0 20 40 6000.020.040.06Market to Bookperiod0 20 40 60−0.500.511.52re − rf [%]period0 20 40 60−0.04−0.03−0.02−0.010Default [%]period0 20 40 60−6−5−4−3−2−1cs [bps]period0 20 40 60−0.08−0.06−0.04−0.0201/maturityperiodAsset redeployability impulse-response functions. This figure plots the impulse-response functions to apositive long-run productivity shock for industries that differ in their degree of asset redeployability. Theresponses in the low asset redeployability are plotted in red solid while those in the high asset redeployabilityare plotted in black solid. Each variable is described in Figure 2.1. The plots are calculated as deviation fromthe steady state. Units, when applicable, are specified next to the plot title.41Figure 2.3: Simple model’s solutions0.1 0.15 0.2 0.25 0.3−0.6−0.4−0.200.20.4γ2 , ξ  Avg[∆I∆γ2∣∣∣ξ fixed]Avg[∆I∆ξ∣∣∣γ2 fixed]0.1 0.15 0.2 0.25 0.3−0.6−0.4−0.200.20.4γ2 , ξ  Avg[∆B∆γ2∣∣∣ξ fixed]Avg[∆B∆ξ∣∣∣γ2 fixed]0.1 0.15 0.2 0.25 0.3−0.6−0.4−0.200.20.4γ2 , ξ  Avg[∆(B/K2)∆γ2∣∣∣ξ fixed]Avg[∆(B/K2)∆ξ∣∣∣γ2 fixed]0.1 0.15 0.2 0.25 0.3−0.6−0.4−0.200.20.4γ2 , ξ  Avg[∆PD∆γ2∣∣∣ξ fixed]Avg[∆PD∆ξ∣∣∣γ2 fixed]0.1 0.15 0.2 0.25 0.3−0.6−0.4−0.200.20.4γ2 , ξ  Avg[∆RR∆γ2∣∣∣ξ fixed]Avg[∆RR∆ξ∣∣∣γ2 fixed]0.1 0.15 0.2 0.25 0.3−0.6−0.4−0.200.20.4γ2 , ξ  Avg[∆CS∆γ2∣∣∣ξ fixed]Avg[∆CS∆ξ∣∣∣γ2 fixed]Simple model’s solutions. The graph shows investment (I1), leverage ratio (B/K1), expected recovery rates (χ), and credit spreads (cs = B/P(K1,B)−1)resulted from solving the simple model for different values of investment irreversibility γ2 and bankruptcy losses ξ . The grid of γ2 and ξ are identical. Theblack line represents the difference between the variable obtained with the highest value of ξ and the lowest ξ keeping γ2 constant. The red line representsthe difference between the variable obtained with the highest value of γ2 and the lowest γ2 keeping ξ constant. To construct the graphs we set, X1 = 0.5,µ = 0, σ = 0.6, α = 0.4, φ = 0.1, ψ f = 0.1, f = 0.25, K0 = 1e−3, γ1 = 0.02, and ε is modeled as a discrete-state space with three states. In most of thesolutions, the firm chooses to invest at the highest value of ε2; whereas the firm prefers to disinvest at the mid and lowest value of ε2.42Figure 2.4: Time-series of baa spreads100200300400500600yield spread (bps)1994q3 1999q1 2003q3 2008q1 2012q3yearsNAIC Baa spread Moody’s Baa spreadTime-series of Baa spreads from NAIC sample and Moody’s. This figure compares the quarterlytime series of average Baa bond spreads reported by Moody’s and the same series constructed fromthe NAIC bond transaction file between 1994 and 2012. Yield spreads are in basis points. Bonds fromNAIC are in U.S. dollars and have no special features (call, put, convertibility, etc.).43Chapter 3Cyclical Distribution of Debt Financing3.1 IntroductionRecent research has documented that the cross-sectional dispersion of investment rate comoves withthe business cycle (Bachmann and Bayer (2014)). The authors argue that this procyclical behavior isa result of lumpy investment at the micro level.1 Intuitively, a non-convex real cost that induces largeand infrequent adjustments of the capital stock on a significant fraction of firms in good times canhave a stronger effect on shaping the cross-sectional investment rate distribution than a countercyclicaluncertainty shock.2 In this chapter, I extend the result of Bachmann and Bayer (2014) to the cross-sectional debt issuance distribution. Specifically, I show that —as the cross-sectional dispersion ofinvestment rate —the cross-sectional dispersion of debt issuance is also significantly procyclical.3Moreover, I build a DSGE model featuring heterogenous firms that show investment and debt issuancelumpiness to investigate the economic contribution of non-convex real and financing frictions.To understand the sources of the procyclicality exhibited by the cross-sectional dispersion of thedebt issuance distribution, I start documenting its significant positive correlation with measures of theextensive margin of firms’ debt issuance and investment; namely, the fraction of firms undertakinglarge positive adjustments to either their stock of debt, capital or both.4 To the extent that these groupsof firms are potentially affected by different non-convex rigidities, I claim that the sources inducinglumpiness on firms’ debt issuance and investment decisions have also the ability to shape the time-series dynamic of the cross-sectional dispersion of the debt issuance distribution. Then, to furtherinvestigate the economic determinants of the firm-level procyclical dispersion of debt issuance, I1Gourio and Kashyap (2007) show that part of the aggregate investment can also be explained by investment lumpiness.2The role of non-convex costs on shaping the distribution of investment rates has also been studied by Doms and Dunne(1998), Caballero et al. (1995), Cooper and Haltiwanger (2006), Bachmann et al. (2013) and Bachmann and Bayer (2014).3As described in details in Section 3.2, debt issuance is defined as the change of total debt (sum of short- and long-term)scaled by total assets as in Salomao et al. (2014) and Covas and Den Haan (2011, 2012).4As Bachmann and Bayer (2014), large positive (negative) adjustment of the capital stock —i.e. investment spikes —aredefined as investment rates higher (lower) than 5% (-5%) of total assets. Large positive (negative) adjustments of the debtstock —i.e. debt issuance spikes —are defined as debt issuance higher (lower) than 5% (-5%) of total assets.44build a structural model of heterogeneous firms facing non-convex real and financing costs.The model shows that a non-convex real rigidity is not sufficient to cause a procyclical dispersionof the cross-sectional distribution of debt issuance. In short, within the model, investment lumpinessdoes not produce enough debt issuance lumpiness. Consequently, investment lumpiness by itself can-not reproduce the time-series dynamic showed by the firm-level debt issuance distribution in the data.Intuitively, even if capital adjustments are large and infrequent, in the absence of a non-convex debtadjustment cost firms will tend to adjust their debt stock too smoothly; only responding to changesof the tax-benefit of debt and/or the risk of bankruptcy cost. In the model, the tax-benefit of debt andthe risk of bankruptcy cost are mainly driven by a firm’s profitability which in the simulations doesnot exhibit extreme adjustments. Thus, after calibrating the model to a series of aggregate and cross-sectional moments, I discuss and quantify the contribution of both non-convex cost of capital anddebt adjustment on shaping the business cycle properties of firm-level investment and debt issuancedecisions.This chapter makes three contributions. First, I complement existing works studying the time-series properties of aggregate debt financing (Jermann and Quadrini (2009)) by showing that in thecross-section, the dispersion of the firm-level distribution of debt issuance also shows a significantpositive correlation with the business cycle. This finding highlights the fact that looking at aggregatevariables can mislead our comprehension of firms decisions. Second, I add to the analysis undertakenby Bachmann and Bayer (2014) of the cross-sectional distribution of investment rate by investigatingthe economic mechanism leading to a procyclical dispersion of the cross-sectional distribution of debtissuance. The analysis conducted in this chapter provides evidence regarding an important implicationof micro-decisions that a model featuring heterogenous firms undertaking investment and financialdecision should consider to account for. Lastly, I complement the study conducted by Bazdresch(2005) regarding the role played by large and infrequent changes of firms’ debt stock on shapingthe cross-sectional distribution of debt issuance. Bazdresch (2005) focus on studying the averageasymmetry of the firm-level debt issuance distribution. In this chapter, I use Bazdresch (2005)’spremise to show that non-convex rigidities affecting both capital and debt adjustments in addition toa countercyclical price of risk induce a cyclical dynamic not only on the cross-sectional average ofthe debt issuance distribution but also on its second moment.In the empirical motivating section of this chapter, I start showing that the cross-sectional distribu-tion of debt issuance is indeed positive skewed on average; i.e. reproducing Bazdresch (2005) results.The average coefficient of the asymmetry of the distribution—quantified by a skewness coefficientof about 3.4 —, appears to be shaped by large and positive adjustments of the debt stock.5 Indeed,the average fraction of firms exhibiting positive large debt issuance spikes from 1984 and 2016 isabout 8.1%; whereas the average fraction of firms exhibiting negative large debt issuance spikes in5Refer to footnote 4 in this chapter for a detailed definition of —positive and negative —investment and debt issuancespikes used throughout tables.45the period studied is lower in magnitude, i.e. 5.9%.6Next, I proceed to explore further these periods of large adjustments of the debt stock in the databy studying their relation to aggregate variables. In particular, I continue showing that both positiveand negative large adjustment of debt stock correlates positively (0.61) and negatively (-0.42) with thebusiness cycle,7 respectively. That is, despite that there are some firms adjusting strongly their debtstock in response to various shocks, these large responses seem to be stronger in good times of theeconomy. Furthermore, I show that the strong link with the business cycle exhibited by the fraction offirms showing positive debt issuance spikes induces a cyclical time-series dynamic on the dispersionof the cross-sectional distribution of debt issuance; which is quantified by a correlation with thebusiness cycle of about 0.43. Indeed, the cross-sectional dispersion of debt issuance appears to beclosely related to positive debt issuance spikes. The time-series correlation between both variables inthe sample is positive and significant (0.85).8Interestingly, the data also suggests that the procyclicality of the dispersion of the debt issuancedistribution does depend on both real and financial frictions. From the first quarter of 1984 to thelast quarter of 2016, the correlations of the cross-sectional dispersion of the debt issuance distributionwith the fraction of firms showing either positive debt issuance spikes, positive investment spikes orboth simultaneously, result significant and positive. Then, to the extent that these different groups offirms undertaking large adjustments of capital and/or debt are affected differently on the margin byreal and financial rigidities, these findings reveal that the features of the cross-sectional dispersion ofdebt issuance distribution do depend on a combination of real and financial frictions.9I use this result to further explore the economic mechanisms behind the procyclicality of the firm-level debt issuance in terms of its cross-sectional dispersion. The second building block of this chapteris based on a quantitative model of heterogenous firms that allows me to study the importance of non-convex costs of capital and debt adjustment on shaping the firm-level distributions. To accomplishthis goal, I conduct several comparative statics in terms of the real and financial non-convex costs.The main objective is to quantify the contribution of both rigidities on determining the distribution ofdebt issuance and investment rate in terms of their (i) coefficient of asymmetry (skewness), (ii) time-series correlation with the business cycle exhibited by the fraction of firms showing large positiveadjustments (spikes), and; (iii) time-series correlation with the business cycle exhibited by the bothcross-sectional dispersion. Broadly, the model predicts that a combination of both real and debtissuance rigidities are required to reproduce the empirical behavior of the firm-level distribution ofdebt issuance described before.6Refer to Table 3.1, Panel A for more details regarding these results.7Real output is measured by real GDP (in local currency at constant prices) and its cyclical component is obtained bydetrending the time-series using the band-pass (BP) filter due to Baxter and King (1999).8In contrast, the correlation of the cross-sectional dispersion of debt issuance with the fraction of firms exhibitingnegative debt issuance spikes in the sample is slightly significant (-0.22). Note that, as discussed by Bachmann and Bayer(2014) for the investment rate distribution, the correlation of the cross-sectional dispersion of investment rate with thefraction of firms exhibiting positive investment spikes in the sample is highly significant (0.94).9Table 3.1 provides more details about these results. Footnote 4 gives definitions of investment and debt issuance spikes.46Indeed, in the model, low values of the non-convex cost of capital adjustment reduces not onlythe asymmetry on the cross-sectional investment rate but also makes the cross-sectional debt issuancedistribution more symmetric. Intuitively, in the context of countercyclical aggregate uncertainty andmore flexible (dis)investment, positive adjustments of capital stock in good times are as frequentas negative adjustments of capital stock in bad times; that is, the overall asymmetry of the cross-sectional distribution of investment rates decreases in this context. Within the model, aspects ofthe firms investment decisions are also reflected on firms’ financial needs. Then, in the presence ofdifficulties for obtaining equity financing,10 debt issuance distribution becomes more symmetric sincepatterns of investment decisions will also affect debt issuance decisions. Effectively, when firms donot show large financial needs, adjustment of the stock of debt will tend to be frequent and smallbalancing both the tax-benefit of debt and the risk of bankruptcy cost. As discussed by Bazdresch(2005), in this case debt adjustments are mainly determined by changes in firms’ profitability; which,under careful modeling of the idiosyncratic productivity shocks,11 will not show extreme variationsfrom period to period. Consequently, when real non-convex cost are small, the drivers of the time-series dynamic of the cross-sectional dispersion of investment rate and debt issuance will not bestrong enough to induce procyclicality on both dispersions. In fact, in this case, the cross-sectionaldispersion of both firms’ variables will end up reflecting more the business cycle properties of theunderlying idiosyncratic productivity shock which in the model follows an heteroskedastic processwith countercyclical volatility (as in Bloom (2009), and Bachmann and Bayer (2014); among others).In contrast, a high non-convex real cost renders large adjustment of the capital and debt stock notonly more likely but concentrated in booms. This behavior of positive investment and debt issuancespikes induces a more procyclical behavior on the cross-sectional dispersion of both distributionsinvestment rate and debt issuance. Within the model, a high non-convex real friction reduces thefirms’ incentive to scale down capital in response to a higher dispersion of the idiosyncratic shocksat recessions when the price of risk is sizable. Intuitively, in the presence of high non-convex realfriction, in recession the value of the option to disinvest is not high enough to offset the fixed costassociated to this decision. On the other hand, in the model, large adjustment of the capital stockbecomes relatively more frequent in good times due to a real option effect. Indeed, in good times,firms decide to adjust their capital stock by paying the fixed adjustment cost since their risk becomelower due to both lower dispersion of the idiosyncratic technology shock in conjunction with a lowerprice of risk. Then, in this case, due to large financial needs faced in booms and in the presenceof rigidities on issuing equity, firms will also tend to exhibit large debt adjustments in good times.As a consequence, an increase on the non-convex real cost in the model leads to an increase of theprocyclicality of the cross-sectional dispersion of both debt issuance and investment rates.10In the model, firms also face difficulties for obtaining equity financing which are calibrated to match the aggregatefrequency of equity issuance, as described in Section 3.4.11As described in Section 3.3, idiosyncratic productivity shocks are modeled as a persistent process implemented usinga grid containing enough points to avoid dramatic changes in firms’ profitability.47Simulations from the quantitative model reveals that some degree of the non-convex debt is-suance cost is required to reproduce the business cycle dynamics of the cross-sectional dispersion ofdebt issuance. When the fixed cost of issuing debt is low, firms tend to adjust their debt position toofrequently. Indeed, as mentioned above even in the presence of non-convex costs of capital adjust-ment, firms adjust optimally their debt stock every period in order to balance the tax benefit of debtand the costs associated to bankruptcy risks. In the context of countercyclical aggregate uncertainty,a low value of the non-convex real cost will not only reduce large adjustment of the stock of debt;but also negative adjustments will be as frequent as positive adjustments. This behavior will lead to aless procyclical cross-sectional dispersion of the debt issuance distribution. Furthermore, when debtfinancing does not involve important additional costs, changes in capital will become more frequentand thus large investment lumps will be less likely to observe and will also resemble the evolution ofthe aggregate uncertainty. Overall, low fixed cost of issuing debt will lead to a more symmetric distri-bution of investment rate and debt issuance. And, it will also imply a less procyclical cross-sectionaldispersion of the debt issuance distribution.In contrast, increasing the fixed cost of issuing debt makes debt adjustment less frequent, largeand significantly linked to firms’ financial needs. Consequently, in the presence of countercyclicalprice of risk and countercyclical dispersion of idiosyncratic shocks, high levels of non-convex debtissuance and investment cost render debt adjustment spikes more likely to be observed in good timesand therefore; the cross-sectional dispersion of debt issuance distribution in this case becomes morecorrelated with the business cycle.Specifically, to quantitatively assess the importance of non-convex costs of capital and debt ad-justments on shaping the firm-level distributions of debt issuance and investment, I start calibratingthe quantitative model to match a broad set of aggregate and cross-sectional moments. Importantly, inthe model, differences along idiosyncratic technology shocks are the only difference across firms.12Using the model, I find that both non-convex rigidities linked to debt issuance and investment lumpi-ness are key to match procyclical behavior of the cross-sectional dispersion of debt issuance andinvestment rate. The benchmark calibration produces a large significant correlation of these cross-sectional moments with the aggregate output (0.49 and 0.45, respectively). Note that these valuesare in line with their empirical counterparts I obtained from the CRSP/Compustat Merged (CCM)Fundamentals Quarterly file (0.56 and 0.43, respectively).13In the next section, I provide a discussion about how this chapter fits and contributes to the existingliterature on corporate finance that studies the link of firms’ decisions to aggregate economic shocks.12As in Bloom (2009), Bachmann and Bayer (2014), idiosyncratic technology shocks are modeled as a heteroskedasticprocess with time-varying transition matrices between idiosyncratic productivity states, where the matrices correspond todifferent values of the technology shock dispersion.13Refer to Table 3.1, Panel A for more details regarding these results.483.1.1 Literature reviewI contribute to the literature on corporate finance that studies the response of firms’ investment andfinancing decisions to changing economic conditions by studying higher-order moments of the firm-level debt issuance distribution.Influential works by Kiyotaki and Moore (1997), Bernanke et al. (1999), Caballero (1999), Gourioand Kashyap (2007), Jermann and Quadrini (2009), Khan and Thomas (2011), and Khan et al. (2014)use structural models of default with financial frictions to study cyclical fluctuations of aggregatefinancing in response to aggregate shocks. The general consensus is that financial frictions exacerbatethe negative effect of economic recessions. I add to this discussion by pointing out that, despite thaton average debt issuance increases in good times, firms respond differently to good aggregate shocks.Specifically, I claim that these distinct behaviors ultimately affect other (higher-order) moments ofthe cross-sectional distribution of debt issuance.At the firm-level, the corporate finance literature has showed that firms’ response to aggregateshocks in terms of their financing decisions depend on other firms’ characteristics. For instance,Covas and Den Haan (2011, 2012), and Salomao et al. (2014) show that, unlike large firms, small firmsdo not substitute equity by debt financing over the business cycle. They argue that since the cost ofdebt of small firms increases importantly in bad times, small firms’ ability to fund their financial needsby issuing debt is importantly reduced in recessions. Similarly, Korajczyk and Levy (2003) discussto what extent negative macroeconomic conditions affect the capital structure decision of financiallyunconstrained firms, but have little impact on financially constrained firms. In this chapter, I build onthis literature by showing empirically that the distinct response of firms to aggregate shocks —in termsof their debt issuance decision —induces business cycle dynamics not only on the aggregate debtissuances, but also on the dispersion of its cross-sectional distribution. Indeed, using a quantitativemodel, I claim that this dynamic of the cross-sectional dispersion of debt issuance depends mainly onthe underlying firms’ ability to costlessly adjust their debt stock over time.Previous research has also studied the effect of firms’ financial rigidities on their investment de-cisions. In a model where firms face fixed debt issuance costs, Cummins and Nyman (2004) arguethat financial non-convexities help to understand why firms in the data hold external finance and idlecash simultaneously. Gomes (2001) construct a general equilibrium model of investment and financ-ing and show that even in the presence of financial constraints, Tobin’s Q is a sufficient statistic toexplain firms’ investment. Cooper and Ejarque (2001) show that firms’ financial constraints are notnecessary to obtain a strong relationship between investment and profits. In contrast to some of theseworks, in this chapter I show that non-convex financial cost are key to match the empirical businesscycle dynamic of the firm-level debt issuance and investment rate distribution. Particularly, in thischapter, I propose large infrequent change in debt and investment stock as an important source ofthese time-series properties.The investment literature has extensively highlighted the role played by non-convex costs of cap-49ital adjustment on shaping the firm-level investment rate distribution (Abel and Eberly (1996), Ca-ballero and Engel (1999), Bachmann and Bayer (2014), among others). As in Bazdresch (2005), inthis chapter I also emphasize the importance of non-convex costs of debt adjustment to shape thebusiness cycle dynamic exhibited by the entire cross-sectional distribution of debt issuance. Further-more, I discuss the interaction between real and financial non-convexities which I use to rationalizethe empirical motivating results presented in the introductory section and discussed in details in Sec-tion 3.2. Recent empirical work points out that firms’ capital adjustment decisions are importantlyaffected by the corporate bond market. In addition to the tight link between credit spreads and ag-gregate investment growth suggested by Lettau and Ludvigson (2002), Philippon (2009) shows thata bond-market-based Q can explain an important part of the variation of aggregate investments.14The aim of this chapter is to contribute to this discussion by showing that both investment as well asdebt issuance lumpiness are required to reproduce empirical correlations of different moments of thefirm-level distribution of debt issuance with the business cycle.More broadly, in this chapter I exploit the high degree of heterogeneity that firms’ debt issuancedecisions exhibit in the cross-section (Bazdresch (2005)) in conjunction with their link to the businesscycle to assess the importance of commonly financial frictions used in the literature to understandfirms’ financing decisions. Specifically, I target the asymmetry exhibited by firms’ debt issuanceand investment decisions in the cross-section to discipline an otherwise standard DSGE model withheterogenous firms facing investment and financing decisions in order to reproduce the business cycledynamic exhibited by the cross-sectional dispersion of debt issuance and investment rate distribution.The rest of the chapter is organized as follows. Section 3.2 presents several empirical resultsthat motivate this work. Section 3.3 develops a DSGE model featuring heterogenous firms that I useto study the importance of non-convex costs of capital and debt adjustment on shaping the cross-sectional distributions of debt issuance and investment. Section 3.4 discusses the baseline calibration.Section 3.5 investigates some of the model’s quantitative implications for the cross-section of invest-ment rate and debt issuance that is followed by a few concluding remarks in Section 3.6.3.2 Empirical analysisIn this section, I start describing the database used to compute the results that motivate this chapter.Next, I provide empirical evidence showing that large positive adjustments of firms’ debt stock notonly explain the average asymmetry exhibited by the cross-sectional distribution debt issuance, butalso induce its dispersion to comove with the business cycle. Business cycle is defined as the cyclicalcomponent of real GDP growth obtained by detrending real GDP growth time-series using a band-pass (BP) filter (Baxter and King (1999)). Lastly, I complement the previous finding by documentingthat large positive adjustments of capital stock also contribute to the cyclical pattern of the cross-14Recently, Yamarthy et al. (2015) examine the role of financial frictions in determining firms’ investment decisions.Yamarthy et al. (2015) argue that the effect of contracting friction on firms’ real decisions is much weaker relative to astandard convex adjustment cost.50sectional dispersion of the debt issuance distribution. Using these findings, I conclude motivating thestudy of the effect of debt issuance and investment lumpiness on the cross-sectional debt issuancedistribution conducted in Section 3.3.3.2.1 Data and variable descriptionThe empirical part of this chapter is based on the CRSP/Compustat Merged (CCM) FundamentalsQuarterly file. In order to be consistent with the quantitative business cycle literature, I work withdata from the first quarter of 1984 to the last quarter of 2016. In the empirical analysis, I also use dataon real quarterly GDP and the price level from NIPA tables.Next, I describe the data treatment applied to the original CCM Fundamentals Quarterly database.As standard in the corporate finance literature, I start dropping financing firms (SIC codes 6000-6999),regulated utilities (SIC codes 4800-4999), and non-profit firms (SIC code 9000-9999). For the resultsof this section, I do not consider the information of the first year a firm appears in the database toeliminate any IPO effect. Following Salomao et al. (2014), I also drop firms where total assets arezero or missing. Firms where the accounting identity is violated by more than 10% of total assetsare discarded. Observations where leverage ratio is larger than the unity are eliminated as well asobservations of those firms that where recorded in the database less than one year.15 These filtersleave a sample of 363,512 firm-quarter observations from 11,236 different firms. On average, a firmis observed in the sample for 32 quarters. The average number of firms in the cross-section of anygiven year is 3,195. The resulting sample covers roughly 43 percent of the original sample.16In what follows, I describe the definitions of the variables used in the empirical analysis; whichfollow closely Salomao et al. (2014). In the analysis, debt issuance are defined as the change oftotal debt stock; where total debt stock is defined as the sum of long- and short-term debt. Fromthe definitions of the CCM database, long-term debt comprises debt obligations that are due morethan one year from the company’s balance sheet date; where debt obligations include long-term leaseobligations, industrial revenue bonds, advances to finance construction, loans on insurance policies,and all obligations that require interest payments. Short-term debt is defined as the sum of long-termdebt due in one year and short-term borrowings. In the analysis conducted, I work with debt issuancescaled by total assets. I compute total assets as the average of last three years assets adjusted by theprice level. I choose this definition of total assets to obtain most of the variation of the ratio from debtissuances.17 In terms of the investment rate, I follow the literature on investment and define a firm’sinvestment rates as the firm’s capital expenditures scale by total assets.In the next section, I start studying the average properties of the cross-sectional distribution of15Filters applied to the CCM Fundamentals Quarterly database are very similar to those applied in Colla et al. (2013).16In the Appendix B.1, I show that the empirical results presented in this section also remain robust to the exclusion ofsmall firms. To assess the importance of small firms in the results, I conduct the same analysis by excluding firms with totalasset lower than $10,000. Table B.1 shows that business cycle dynamics of the cross-sectional distribution of debt issuanceand investment reported in Table 3.1 remain quantitatively unchanged.17Similarly, Salomao et al. (2014) scale debt issuance by the firm’s total asset trend.51debt issuance following the analysis conducted for the firm-level investment rate by Caballero et al.(1995), Bazdresch (2005), and Bachmann and Bayer (2014). The main goal is to show that the debtissuance cross-sectional distribution is affected importantly by large positive adjustments determiningits average asymmetry. After this analysis, in the following section, I proceed to link the cyclicalfeatures of large positive adjustments of the debt stock to the cyclical pattern showed by the dispersionof the debt issuance firm-level distribution.3.2.2 Debt issuance lumpinessThe purpose of this section is to study some features of the debt issuance cross-sectional distribution.While I show that the debt issuance cross-sectional distribution is importantly affected by large ad-justments of the debt stock (as in Bazdresch (2005));18 I add to these findings by showing that thepositive large adjustments of the debt stock have a stronger effect on the cross-sectional debt issuancedistribution which is reflected not only on its average asymmetry but also its business cycle properties.As a starting point, I proceed to compare the observed firm-level debt issuance distribution toits normally simulated counterpart. As in Bazdresch (2005), for each firm that exhibits continuousquarterly observations over the sample period 1984Q1-2016Q4, I proceed following the next steps.First, I rank the firm’s quarterly debt issuance from the highest to the lowest debt issuance into bins.19Next, I compute the simulated debt-issuance counterparts of the firm for each bin. Specifically, Iassume the simulated variable comes from a normal distribution with mean and standard deviationgiven by the sample mean and standard deviation of the firm’s quarterly debt issuance ratios. Then, thesimulated debt issuance ratio (x j,i) of firm j-th associated to bin i ∈ [1,Nb] corresponds to the solutionof the equation Φ j(x j,i) = i/Nb ; where Φ j represents the cumulative density function of a normaldistribution with mean and standard deviation equal to the sample mean and standard deviation offirm j-th quarterly debt issuance. After repeating the exercise for each firm, I construct the averagesover all firms by bin.Figure 3.1 shows, in red bars, the sample average debt issuance over all firms by bins. Note thatby construction bars are decreasing (on average). Figure 3.1 also presents, in blue line, the averageby bin that resulted from the simulated debt issuance ratios (x j,i). As can be observed in Figure 3.1,a small number of periods account for most of the debt issuance action across firms. Unlike to thesimulated debt issuance (blue line), extreme values of the observed debt issuance (red bars) are muchlarger compared to the values in the middle of the distribution. In fact, on average, while 85% ofthe firm-quarter observations shows a debt issuance lower than 3% of the firm’s total assets; only 5%of the firm-quarter observations accounts for 52% of the firm’s total (positive) debt issuance in the18The importance of large adjustments on shaping the distribution of firm-level decisions has also been documented forinvestment rates (Doms and Dunne (1998), Caballero et al. (1995), Cooper and Haltiwanger (2006), Bachmann et al. (2013)and Bachmann and Bayer (2014)).19Since this exercise uses firms that exhibit continuous quarterly observations from the first quarter of 1984 to the lastquarter of 2016, the total number of bins used is 4× (2016−1984+1).52data. The corresponding numbers for the simulated debt issuances (blue line) are 66% of the firm-quarter observations being below 3% of the firm’s total assets; and 5% of the firm-quarter observationsaccounting for only 24% of the firm’s total (positive).Following Bazdresch (2005) definition of a debt-issuance inaction period, I proceed to define alarge positive (negative) debt issuance spike as a change in debt issuance higher (lower) than 5%(-5%) of the firm’s total assets.20 Table 3.1 Panel A first columns reports the average fraction offirms with positive (+) and negative (−) debt issuance spikes per period. While the average fractionof firms with positive debt issuance spike is 8.1%, the average fraction of firms with negative debtissuance spike is only 5.9%. This difference between positive and negative large adjustments ofdebt issuance induces asymmetry on the debt issuance distribution as can be observed in its averagepositive skewness (3.4) exhibited on Figure 3.1. Note that the simulated debt issuance distribution inFigure 3.1 —which does not present important differences between positive and negative spikes byconstruction —shows a coefficient of asymmetry of only 0.14.Furthermore, as evidenced by Figure 3.4,21 the difference between the fraction of firms with pos-itive debt issuance spike and the fraction of firms with negative debt issuance spike seems to increasein good time and decrease in recessions. Indeed, as reported in Table 3.1 Panel A second column,while the fraction of firms with positive debt issuance spike correlates positively with the businesscycle (0.61); the fraction of firms with negative debt issuance spike shows a negative correlation withthe business cycle (-0.42). As illustrated by Figure 3.4, during recessions large positive debt issuancespikes decreases dramatically. For instance, during the last two financial crisis the fraction of firmsexhibiting positive debt issuance spikes falls by almost half. It is noteworthy to mention that the rela-tive importance and procyclicality of large positive spikes can also be observed in the cross-sectionaldistribution of investment rates as reported by Table 3.1 Panel A last two columns.22In the next section, I describe the implications of the behavior of positive debt issuance spikesas well as investment spikes on the time-series dynamic of the cross-sectional distribution of debtissuance.3.2.3 Implication of debt issuance lumpinessIn this section I start showing that the relative importance and procyclicality exhibited by the posi-tive debt issuance spikes induce a procyclical behavior on the cross-sectional dispersion of the debt20For annual investment rates, Cooper and Haltiwanger (2006), Gourio and Kashyap (2007) and Bachmann and Bayer(2014) define spikes as cases where investment relative to the beginning of period capital is greater than 20 percent. SinceI base my results on quarterly data I choose 5%. Moreover, in the CCM quarterly database, firms with debt issuance largerthan 5% (lower than -5%) correspond to firms in the top (bottom) decile of the average debt issuance distribution.21In this section, while seasonally smoothed variables are used to construct time-series pictures; correlation statistics arecomputed using variables resulted from applying a band-pass filter to the deflated original variable. In this aspect of theanalysis, I followed closely Salomao et al. (2014).22The correlation of the fraction of firms exhibiting positive investment spikes with the business cycle is positive andsignificant (0.59). Whereas, the correlation of the fraction of firms exhibiting negative investment spikes with the businesscycle is not statistically significantly different from zero.53issuance distribution. Next, I document a similar result for the cross-sectional dispersion of the invest-ment rates distribution; i.e. highlighting the role of high and procyclical positive investment spikes onshaping the dynamic of the investment rate cross-sectional distribution.23 Finally, I show suggestiveevidence regarding the importance of the interaction between positive debt issuance and investmentspikes on the business cycle dynamics of the cross-sectional distribution of debt issuance.I start describing the positive correlation of the cross-sectional dispersion of the debt issuancedistribution with the business cycle.24 Table 3.1 Panel A reports that this correlation is significant andequal to 0.43. Figure 3.3, blue line, illustrate the procyclicality of the cross-sectional dispersion ofthe debt issuance distribution. To my knowledge, this property has not been previously documentedand explored in the literature. Table 3.1 Panel B shows suggestive evidence about the importanceof positive debt issuance spikes on shaping the cross-sectional dispersion of the debt issuance distri-bution. In fact, the correlation between the fraction of firms with positive debt issuance spikes andthe cross-sectional dispersion of the debt issuance distribution is significant and equal to 0.85. Notethat the importance of positive large adjustments on shaping the cross-sectional distribution is alsopresent in the investment rate distribution. Table 3.1 shows that the cross-sectional dispersion of theinvestment rate distribution is highly procyclical; and furthermore, its correlation with the fraction offirms with positive investment spikes is significant and equal to 0.94.Intuitively, these findings suggest that the procyclicality showed by the cross-sectional dispersionof debt issuance as well as investment rates is driven by an important increase of the right tail of thedistribution in good times. Knowing this feature of the cross-sectional distribution of firms’ decisionscan be important for understanding the procyclical behavior of aggregate variables. In fact, as pointedout by Gourio and Kashyap (2007) for aggregate investment, the results in Table 3.1 Panel B suggestthat the variation in aggregate debt issuance depends mainly on a small fraction of firms undergoingdebt issuance spikes in good times. It is noteworthy that although recent works in corporate financehave focused on analyzing the implicit information in other moments of the debt issuance distributions(e.g. Bazdresch (2005)), still we know little about its time-series properties. This chapter intends toadd to this area.Table 3.1 Panel B shows that a potential driver of the procyclical dispersion of debt issuancedistribution is a set of firms showing a dramatic increase of their debt stock —i.e. debt issuancelumpiness. In reality, debt issuance lumpiness can occur in response of either in response to finan-cial non-convex frictions that hamper the adjustment of the debt stock or/and investment lumpiness.Recent literature on corporate finance highlights the role played by real and financial non-convexitieson shaping the average asymmetry of the debt issuance cross-sectional distribution. More broadly,frictions of different types will be affecting simultaneously multiple firms’ decisions. Table 3.1 Panel23Bachmann and Bayer (2014) present a similar results using a panel of German firms with annual observation from1973 to 1998. The authors’ primary data source is the Deutsche Bundesbank balance-sheet database, USTAN.24Business cycle corresponds to a band-pass (BP) filter of real GDP (in local currency at constant prices) using themethodology proposed by Baxter and King (1999).54C intends to provide evidence about this interaction.To understand the economic mechanism behind the procyclicality of the cross-sectional disper-sion of the debt issuance distribution, Table 3.1 Panel C (second column) reports its correlation withvarious types of firms potentially affected by non-convex rigidities; that is, firms likely experiencingdebt issuance and/or investment lumpiness. For instance, since firms showing positive debt issuancespikes (Panel C, first row) can be facing both real and financial non-convex costs simultaneously, Ialso present correlations with the group firms experiencing debt issuance lumpiness but not invest-ment lumpiness (Panel C, third row). In fact, within this last group, while firms are increasing thedebt stock importantly; they adjust their capital stock marginally. Similarly, I study the correlationsof the cross-sectional dispersion with those firms showing investment lumpiness (Panel C, secondrow) as well as with those firms experiencing investment lumpiness but not important changes in thestock of debt (Panel C, fourth row). Results reported in Table 3.1 Panel C show that the evolution ofthe number of firms in each group exhibits a positive significant correlation with the cross-sectionaldispersion of both debt issuance and investment distribution. Furthermore, as evidenced in Figure 3.5,the fraction of firms within these groups experiencing either debt issuance lumpiness or investmentlumpiness varies importantly over time.In the next section, I use these findings to argue that both real and financial non-convex rigiditiescan affect the cross-sectional dynamics of the debt issuance as well as investment rate distributionand therefore, the cross-sectional dispersion of debt issuance is not just a reflection of the propertiesshowed by the cross-sectional dispersion of investment rate (Bachmann and Bayer (2014)). Thus,the objective of pursuing a quantitative model in this chapter is to quantify the contribution of thesetwo type of non-convex rigidities on driving the dynamic of the cross-sectional dispersion of the debtissuance distribution. Specifically, to accomplish this quantitative analysis in Section 3.3, I developa structural general equilibrium model of heterogeneous firms featuring both lumpy investment anddebt financing decisions.3.3 Benchmark modelIn this section, I describe the dynamic stochastic general equilibrium model used in this chapter toexplain the empirical motivating facts regarding the cross-sectional distribution of debt issuance. Inthe model, time is discrete and firms’ horizon is infinite. The economy consists of a distribution ofvalue-maximizing, each able to produce a homogeneous good and owned by risk-averse investors.Firms make investment, hiring and financing decisions given the stochastic discount factor derivedfrom the representative household’s problem in a general equilibrium setting. Firms’ external financ-ing sources consist of equity and non-contingent long-term debt. As, in Khan et al. (2014), Firmsissue non-contingent long-term debt to a perfectly competitive representative financial intermediary55at loan rates determined by their individual characteristics.25 Importantly, firms adjust capital anddebt stock facing non-convex costs of capital and debt stock adjustment.3.3.1 FirmsA cross-section of heterogenous firms make optimal investment and financing decisions by takingas given real and financing costs as well as the representative household stochastic discount factorthat is derived from a representative household who has recursive preferences. Each period, a firmchooses its new capital stock (kt+1) and how to finance these purchases with the goal of maximizingthe present value of after-tax cash flows to shareholders. To finance its investment and shareholders’distributions at period t, a firm uses internal earnings, new debt issues and/or new equity issuance. Inthe model debt is long-term. As in Kuehn and Schmid (2014), at each period t, a firm can controlsthe book face value of debt outstanding bt+1; and corporate bonds have a fixed coupon rate c ∈ (0,1)and repay a constant fraction λ ∈ (0,1) of the bond’s face-value each period.Production TechnologyThere is one homogenous commodity in the economy which can be consumed or invested. The j-th firm produces the homogenous commodity using capital k j,t and labor l j,t and subject to both anaggregate shock xt and an idiosyncratic shock z j,t ; according to a Cobb-Douglas production function,y j,t = ext(1−α) ez j,t (k j,t)α (l j,t)1−α̂ , with α, α̂ > 0 and α+ α̂ < 1 (3.1)where xt and z j,t are log aggregate and log idiosyncratic productivity shocks, respectively. The growthrate of the aggregate shock is modeled as a random walk with time-varying drift and volatility,∆xt+1 = g+µx(st)+σx(st)εxt (3.2)where the low-frequency component in the aggregate productivity equation, µx(st) is used to gen-erate sizeable risk premia whereas the time-varying volatility is useful to generate realistic creditspreads. The variable st is an aggregate variable taken as given by all firms each period to solve theirmaximization problem. The exogenous aggregate state (st) will be modeled as a persistent processthrough a Markov chain described in Section 3.2. The idiosyncratic log productivity process is mod-eled as a Markov process with autocorrelation ρz and time-varying conditional standard deviation,σ(st) ≡ st + σ¯ > 0. That is, firms can observe their idiosyncratic technology shock once the aggre-gate state of the economy st is revealed. In the solution used, I assume that shocks to the exogenousaggregate states, and idiosyncratic productivity shocks are independent. Further, idiosyncratic pro-25Having the assumption of the existence of a financial intermediary participating in a competitive market facilitatesthe market clearing conditions in the definition of the recursive equilibrium. A complete characterization of the recursiveequilibrium is provided in the Appendix B.2.3.56ductivity shocks are independent across productive firms. Using these definitions and assumptions,the flow of operating profits Π j,t of firm j at period t is given by,Π j,t = y j,t −wt × l j,t − f × k j,t (3.3)where the aggregate wage is denoted by wt , and f > 0 represents a proportional cost of production. Iuse f to match the book leverage. In the economy, capital stock depreciates at the rate δ ∈ (0,1); butfirms possess the option to adjust their capital stock by pursuing investment decisions.InvestmentThe investment of firm j at period t, (i j,t), required to change the capital stock to k j,t+1 is definedby, i j,t ≡ k j,t+1− (1− δ )k j,t . Yet, each period, the firm j-th faces a non-convex cost Ωk(i j,t) if itsinvestment differs from zero. I model this cost as a deduction from firms’ profits. Specifically,Ωk(i j,t) = 0 if i j,t = 0ωk > 0 if i j,t 6= 0The parameter ωk > 0 will be one of the key parameters of the model which I use along the compar-ative static exercises to measure the contribution of the investment lumpiness induced by non-convexreal rigidities on shaping the properties of the cross-sectional distribution of debt issuance.Debt FinancingCorporate investment, as well as any distribution, can be financed with internal funds generated byoperating profits, new issues of equity or new issues of long-term debt. Firm j-th incurs a costΩb(a j,t) each time it decides to change the amount of debt outstanding from b j,t to b j,t+1; wherea j,t ≡ b j,t+1− (1−λ )b j,t represents the firm’s new bond issuance. Note that in the context of long-term debt, each period only a fraction λ ∈ (0,1) of the face-value is paid back to bondholders. Then,similar to the non-convex real cost function, Ωb(a j,t) corresponds to a fixed cost incurred when newdebt is issued, i.e.,Ωb(a j,t) = 0 if a j,t = 0ωb > 0 if a j,t 6= 0where ωb represents the second key parameters of the model used in the comparative static exercisesperformed in Section 3.5. Note that this type of debt issuance cost function has also been implementedby other works (e.g. Kuehn and Schmid (2014)).57Equity valueThe firm j-th’s shareholders receive dividends as long as the firm is operating. Distributions to share-holders, d j,t are given by equity payout e j,t net of issuance costs. In the model, equity payouts of afirm j-th are equal to the firm’s operating profit net of cash flows from its financing and investmentactivities,e j,t ≡ e(k j,t ,b j,t ,z j,t ,Γt) = (1− τ)Π j,t + τδk j,t −(i j,t +Ωk(i j,t))− (c(1− τ)+λ )b j,t+(P(k j,t+1,b j,t+1,z j,t ,Γt)(b j,t+1− (1−λ )b j,t) − Ωb(a j,t)) (3.4)with τ ∈ (0,1) as the firm’s effective tax rate and Γt the vector of aggregate states of the economy(∆xt ,st ,µt).26 The first term of equity payouts captures the firm’s operating profit, from which therequired investment expenses, i j,t +Ω(i j,t), and debt repayments, (λ + c(1− τ))b j,t are deducted.Note that capital depreciation and debt interest payment generate tax shields. The debt price functionP(k j,t+1,b j,t+1,z j,t ,Γt) is such that it will be a function of the current vector of stochastic variables(z j,t ,Γt) and optimal decisions at time t. The value of the firm to its shareholders denoted by J j,tconsiders the present value of distributions d j,t plus the expected firm’s continuation value.J j,t ≡ J(k j,t ,b j,t ,z j,t ,Γt) = max{0, maxk j,t+1,b j,t+1{d(k j,t ,b j,t ,z j,t ,Γt)+Et(Mt,t+1× J j,t+1)}}(3.5)where Mt,t+1 is the equilibrium stochastic discount factor derived from the representative household’spreferences.27 Furthermore, in the model, the equity issuance cost is modeled as a fixed cost ψe > 0that is paid if equity payouts turn out to be negative. Then, the firm’s distributions are computed asd j,t ≡ e j,t −ψe× I{e j,t<0}, where I{e j,t<0} denotes an indicator function that takes value of one whene j,t is negative and zero otherwise. Lastly, note that the first max operator in equation (3.5) capturesthe limited liability of shareholders, whereas the second max operator relates to the determination ofthe optimal decisions of the firm’s manager regarding next-period capital and debt outstanding.DefaultShareholders’ limited liability implies that equity value, J j,t , is bounded and will never fall below zero.This implies that equity holders will default on their credit obligations whenever their idiosyncraticshock z j,t is below a cutoff level z?j,t ≡ z?(k j,t ,b j,t ,Γt) determined by the threshold default condition,J(k j,t ,b j,t ,z?j,t ,Γt) = 0. To simplify the notation below, I define z0j,t = z?(k j,t ,0,Γt) which representsthe idiosyncratic shock realization that makes the unlevered firm’s value equal to zero; i.e. the lowest26The normalized version of the model, which is described in the Appendix B.2.1, depends on the growth rate of theaggregate technology shock ∆xt instead of the level of the aggregate technology shock xt . The aggregate state µt denotesa measure over the distribution of capital stocks (k j,t ), debt outstanding (b j,t ), and idiosyncratic shocks (z j,t ); which ischaracterized in the definition of the recursive equilibrium in the Appendix B.2.3.27The stochastic discount factor derived from the household’s maximization problem is described in Appendix B.2.3.58value of z j,t at which the unlevered firm keeps operating.Debt ContractsAt period t, the representative financial intermediary allows a firm j-th to change its debt outstandingto b j,t+1 by buying corporate debt at price Pj,t ≡ P(k j,t+1,b j,t+1,z j,t ,Γt) and collect coupon and prin-cipal payments until the firm’s manager decides to default. If default occurs at period t, shareholderswalk away from the firm, while the financial intermediary recovers a fraction (1− χ) ∈ (0,1) of theunlevered firm’s value. As in Khan et al. (2014), I assume the remainder of any defaulting firm’s valueis lump-sum rebated to households so that default implies no direct loss of resources. Under theseassumptions, period-t per unit market price of debt Pj,t , is pinned down by an arbitrage condition suchthat the amount of money creditors are willing to pay for the contract must equal the expected valueof future payments. Formally, this condition implies,b j,t+1×Pj,t = Et(Mt,t+1b j,t+1(λ + c+(1−λ ) ·Pj,t+1)I{z?j,t+1<z j,t+1}︸ ︷︷ ︸solvent states)+Et(Mt,t+1(1−χ)J(k j,t+1,0,z j,t+1,Γt+1)I{z0j,t+1<z j,t+1<z?j,t+1}︸ ︷︷ ︸default states) (3.6)The first term on the right-hand-side of equation (3.6) contains the cash flows received by bondholdersif no default takes place at period t +1; whereas the second term reflects the payments upon defaultnet of deadweight costs.3.3.2 Aggregate state of the economyAs standard in DGSE models with heterogeneous agents (Krusell and Smith (1998)), the aggregatestate of the economy will be described by the vector Γt ≡ (∆xt ,st ,µt), where (∆xt ,st) represents thevector of aggregate shocks and µt denotes a measure over the distribution of capital stocks (k j,t), debtoutstanding (b j,t), and idiosyncratic shocks (z j,t). To close the economy, I specify the law of motionof µt as the mapping Γt that satisfies µt+1 = Γ(∆xt+1,st+1,µt). Γt is characterized in the definition ofthe recursive equilibrium that I describe in the Appendix B.2.3.Following Krusell and Smith (1998), I do not model the measure µt completely. Instead, I proxyit by using only some moments of the aggregate distribution that I include as aggregate variables.Then, for each element of the aggregate state space, I allow firms to form expectation about otheraggregate variables (such as consumption, and wages) that allow them to solve their maximizationproblem each period.2828As described in Appendix B.2.4, the belief formation process adds an extra layer of iteration in the numerical solution.593.3.3 Household problemI close the model with a unit measure of identical households. Representative household’s has Epsteinand Zin preferences and holds her wealth invested in (i) one-period noncontingent bonds issued bythe perfectly-competitive financial intermediary; and, (ii) firms’ shares. The investment in one-periodbonds and shares are represented by mbt and the measure {msj,t}, respectively.Then, given prices (dividend-inclusive) the representative household receives for their currentshares(p0(k j,t ,b j,t ,z j,t ,Γt)), the risk-free bond price (Pf (Γt)), and the real wage (w(Γt)); she choosespaths of consumption Ct , hours worked Nt , new bond holdings mbt+1, and the numbers of news shares{msj,t+1} to purchase at ex-dividend prices(p1(k j,t+1,b j,t+1,z j,t+1,Γt))in order to maximize her life-time utility flows.29,30 The representative household receives as a lump-sum rebate, (T (Γt)), both thenet proceeds of corporate income taxes as well as the remainder of any defaulting firms’ value notrecovered by the financial intermediary.31 The lifetime household’s utility maximization problem is,Ht ≡ H({msj,t},mbt ,Γt) = Max{Ct ,Nt ,{msj,t+1},mbt+1}(1−β )Ĉ(Ct ,Nt)1− 1ψ +β Et (H1−γt+1 | Γt)1− 1ψ1−γ11− 1ψsubject to : Ct +Pf (Γt)×mbt+1+∫Sp1(k j,t+1,b j,t+1,z j,t+1,Γt)ms(d(k j,t+1×b j,t+1× z j,t+1))≤ w(Γt)×Nt +mbt +∫S∗p0(k j,t ,b j,t ,z j,t ,Γt)ms(d(k j,t ×b j,t × z j,t))+T (Γt)where γ is the coefficient of relative risk aversion, ψ is the elasticity of intertemporal substitution,and β is the household’s subjective discount factor. The contemporaneous component of the utilityfunction is represented by Ĉ(C,N)≡C1−νt (1−Nt)ν , where ν ∈ (0,1) controls the relative preferencefor labor. The space S represents the product space R+×R+×Z ; whereZ denotes the space of theidiosyncratic technology shock zi, j. Whereas, the space S∗ denotes the product space that includessolvent firms. The recursive equilibrium of this economy is characterized in the Appendix B.2.3.3.4 Model parametrizationIn this section, I describe the benchmark calibration of the model. I cite related works that I use asreferences to guide part of this calibration. I also provide details on the moments targeted to set someof the parameters. As described in Appendix B.2.4, the model is solved using a global method.29Households have access to state-contingent claims. But, since there is no heterogeneity across households, thesesecurities are in zero net-supply at the equilibrium. So, I do not explicitly model them.30Although, z j,t+1, is drawn by individual firms at the start of the next period, the household can choose its ownershipof type (k j,t+1,b j,t+1,z j,t+1) firms as well as its long-term bonds in the current period, since she knows the transitionprobabilities of z j,t and the law of large numbers applies.31As in Khan et al. (2014), I assume that corporate default implies no direct loss of resources. This assumption, inconjunction with the presence of a perfectly competitive representative financial intermediary, allows to define the model’srecursive equilibrium described in the Appendix B.2.3.603.4.1 CalibrationPreference and standard real business cycles parameters of the model are set to values taken from theexisting literature. The remaining set of parameters are chosen in order to match aggregate momentsand moments derived from the cross-sectional distribution of debt issuance as well as investment ratein the data. All parameters values of the quarterly calibration implemented are reported in Table 3.2.Preference parameters are standard in the long-run risk literature (Bansal and Yaron (2004)). Theelasticity of intertemporal substitution ψ is set to 2 and the coefficient of relative risk aversion γ isset to 10, as in Kung (2015). The subjective discount factor β is set to 0.994 in order to match theaverage risk-free rate. The relative preference for labor, ν , is set such that the household works 1/3of her time endowment in the steady state.On the technology side, I follow Bachmann and Bayer (2014) to set production function. Firms’capital share α is set to 0.20 and the parameter controlling the labor share α̂ is set to 0.50. Thedepreciation rate of capital δ is set to 9.4%/4 to match the average aggregate investment rate inthe data. The productivity process is calibrated following Kuehn and Schmid (2014). Within themodel, the aggregate Markov chain (st) jointly affects the drift and volatility of the growth rate of theaggregate productivity shock xt and the dispersion of the idiosyncratic technology shock. Specificallyst consists of five states. To calibrate the Markov chain, I set the persistence of the Markov chain (ρ) to0.95. Following Kuehn and Schmid (2014), the mean and volatility of the drift states of the aggregategrowth rate (µx(st)) are set to zero and 1.48e−3, respectively. Whereas, the mean and volatility ofthe variance of the aggregate growth rate (σx(st)) are set to 2.6e−4 and 1.8e−5, respectively. Thiscalibration allows to match the annualized output and consumption growth moments and also obtaina sizable aggregate stock returns volatility. I set g to yield an annual average growth of about 1.8%.Following Bachmann and Bayer (2014), I set the volatility σ¯ and persistence of the idiosyncraticproductivity process ρz to 0.091/2 and 0.90 respectively; which allows me to match the aggregatedefault rate. Firms face proportional costs of production, f , of 0.05, similar to Gomes et al. (2003b)which I use to match the average book leverage ratio and the aggregate investment-to-output ratio.The effective corporate tax rate τ is set to 14%, consistent with Binsbergen et al. (2010). The annualcoupon payment, c, is set to 3.0%. The bankruptcy deadweight cost χ is set as in Bazdresch (2005),whereas the parameter controlling the average debt maturity, λ , is set to match observed averagematurity in corporate bonds traded in the NAIC database. Lastly, the equity issuance fixed costparameter ψe is set to match the frequency of equity issuance. The remaining parameters controllingthe non-convex costs hampering capital and debt stocks adjustment, (ωk,ωb), are set to match averagemoments of the cross-sectional investment and debt issuance distribution. Specifically, I choose totarget average skewness of the cross-section distributions; that is, 3.4 and 1.9 respectively.613.5 Quantitative resultsIn this section, I assess quantitatively the contribution of the non-convex costs affecting the adjustmentof the stock of debt and capital, (ωk,ωb), on determining the time-series dynamics of the cross-sectional dispersions of debt issuance and investment rates. Since most of the parameters of themodel are set to match empirical aggregate moments, I start in Section 3.5.1 evaluating the abilityof the benchmark model to produce simulated data supporting aggregate moments similar to theirempirical counterparts (Table 3.3).Furthermore, to completely assess the performance of the benchmark calibration, in Section 3.5.2I report multiple moments of the cross-sectional debt issuance and investment rate distribution ob-tained from the model’s simulated data. Specifically, I conduct several comparative statics in terms ofthe investment (ωk) and debt issuance (ωb) non-convex costs. The main objective is to quantify thecontribution of both rigidities on determining the distribution of debt issuance and investment rate interms of their: (i) coefficient of asymmetry (skewness), (ii) time-series correlation with the aggregateoutput of the fraction of firms showing positive debt issuance as well as investment spikes, and; (iii)time-series correlation with the business cycle of the cross-sectional dispersion of the distributions.3.5.1 Aggregate momentsTable 3.3 shows the aggregate moments produced by simulating the model under the benchmarkcalibration and compares them with their empirical counterparts.Panel A shows that the benchmark calibration generates an average investment-to-output ratio of18% in line with the 20% obtained from the data. Furthermore, the output volatility σ∆y and relativemacro volatilities of consumption and investment are close to the data. Particularly, the annual outputvolatility σ∆y in the model is about 3.4%. The consumption annual volatility is about 0.64 of the out-put volatility; whereas the aggregate investment volatility resulted from the simulations is about 5.4times the output volatility. The benchmark calibration of the model also replicates correlations acrosssome business cycle variables such as the procyclicality of consumption. The implied persistence ofoutput and investment are also quite close to the ones in the data.In terms of the aggregate capital structure, Panel B shows that the model produces a book lever-age which seems to be in line with its empirical counterpart (0.28). The frequency of equity issuanceproduced by the model (7%) shows that the equity issuance friction (ψe) in the model is reason-able. Default rates, which are importantly affected by the calibration of the idiosyncratic technologydispersion in the model, resulted in line with their empirical counterpart. Also, Panel B shows theimportance of having in the model both, a countercyclical price of risk in conjunction and coun-tercyclical uncertainty. Indeed, since these two ingredients together render corporate bonds’ creditspread countercyclical (Chen (2010), Kuehn and Schmid (2014)), firms’ financing decisions becomesimportantly influenced by aggregate economy shocks. In particular, within the model, firms tend tosubstitute equity for debt financing during recessions. Panel B shows that on average debt issuance62correlates positively with the business cycle whereas aggregate equity issuance shows a slightly coun-tercyclical pattern.Table 3.3 Panel C reports some asset pricing moments from the model’s simulations. The modelgenerates a large equity risk premium of about 6.8% per year, and produces substantial variations inexcess returns. The annualized standard deviation of excess stock returns is about 8.0%. The strongdemand for precautionary savings to alleviate aggregate uncertainty shocks drives the risk-free ratedown to 1.64%. The volatility of the risk free rate is also low (1.71%). The model generates a sizablecredit spreads of 83bps which exhibits substantial time-series variation. The standard deviation in themodel is 69bps and about 44bps in the data.In the following section of the chapter, I focus on assessing the performance of the model in termsof its cross-sectional implications. In particular, I report multiple moments of the cross-sectional debtissuance and investment rate distribution obtained from the model’s simulations and compare them tothe main findings exhibited in Table 3.1.3.5.2 Assessing contribution of real and financial non-convexitiesIn this section, I assess the cross-sectional implications of the model. In particular, I use the model’ssimulations to quantify the contribution of the real and financing non-convex rigidities on determiningthe cross-sectional distribution of both debt issuance and investment rates. To conduct this analysis,I report in Table 3.4 and 3.5 the result of multiple comparative statics in terms of the variables of themodel represented by ωk and ωb.Effect on average cross-sectional asymmetry: Panels A in Table 3.4 and 3.5 show the model’spredictions about the asymmetry (skewness) of the cross-sectional distribution of debt issuance andinvestment rate respectively, for different values of (i) the non-convex capital adjustment cost (in-creasing along rows) and; (ii) the non-convex debt issuance cost of (increasing along columns). Asshowed in Panels A, the model’s simulations indicate that a combination of both non-convex costsare required to reproduce the sample skewness of the firm-level distribution of debt issuance andinvestment rate.Within the model, a low non-convex cost of capital adjustment(ωk)reduces not only the asym-metry on the cross-sectional investment rate (Table 3.5 Panel A); but also makes the cross-sectionaldebt issuance distribution less asymmetric (Table 3.4 Panel A). In the context of more flexible invest-ment, firms react more frequently adjusting their capital in good and bad times. Within the model,aggregate uncertainty is countercyclical. And at the equilibrium of the model with low adjustmentreal costs, positive adjustments of capital stock in good times are as frequent as negative adjustmentsof capital stock in bad times.32 This ends up reducing the overall asymmetry of the cross-sectionaldistribution of investment rates (Table 3.5 Panel A, along the rows). Within the model, aspects of the32In the model, a modest level of the non-convex real friction (the lowest level used in the comparative static exercises is0.5×ωk) supports a slightly positive skewed distribution of investment even in the presence of countercyclical uncertainty.63firms investment decisions are also reflected on firms’ financial needs. Furthermore, in the presenceof equity financing rigidities (ψe > 0), patterns of investment decisions will also affect debt issuancedecisions. Then, in this context of a low value of the real non-convex cost, adjustments of the debtand capital stock will be on average more symmetric and thus show a low average skewness coeffi-cient (Table 3.4 Panel A, along the rows). In contrast, a high non-convex real cost makes not onlylarge adjustment of the capital stock more likely; but also in this context, negative large adjustmentsin bad times will become less likely. In response to high uncertainty in bad times most firms facingimportant non-convex real rigidities will choose to postpone their decisions and wait, holding theircapital stock unchanged. On the other hand, in good times, low uncertainty and a positive economicenvironment will motivate firms to readjust their capital stock. This will ends up increasing the av-erage uncertainty of the investment rate distribution reflected on a high skewness coefficient. In thecontext of equity financing rigidities, large positive debt issuance will also increase importantly ingood times. In general, despite that firms will tend to maintain a stable level of debt stock in orderto balance tax-benefits of debt and the risk of bankruptcy cost by adjusting it frequently, firms fac-ing large financial needs in good times due to high capital expenses will increase importantly debtissuance at these periods. Thus, when non-convex real costs are high, the debt issuance distributionwill also become on average positive skewed.Table 3.4 and 3.5 in Panel A show that the non-convex financial cost(ωb)also increases boththe asymmetry of the cross-sectional debt issuance and investment rate distributions. A larger non-convex financial cost will hamper the frequent adjustment of the debt stock intended to balance thetax-benefit of debt and costs associated to bankruptcy risk. In fact, in the model, when the non-convex of issuing debt increases firms tend to adjust their debt stock more importantly in periodswhere investors value corporate bonds the most (periods of low credit spreads); i.e. in good times.Furthermore, in the presence of non-convex real rigidities, periods where credit spread are low willalso coincide with periods of large financial needs to fund large positive investment decisions; whichwill render the debt issuance distribution more positive skewed. The effect of a larger non-convexdebt issuance cost on the asymmetry of the investment rate distribution is twofold. First, while alarger debt issuance cost will make more difficult the funding of large positive investment in goodtimes which will lowers its asymmetry; a larger debt issuance cost will also reduce the possibility offinancing small positive changes of the capital stock which will contribute to the positive skewnessof the distribution. Note that the contribution of a higher debt issuance cost(ωb)to an increase ofthe average skewness of investment rate distribution is lower, the higher is the real rigidity faced byfirms. Intuitively, when the non-convex real cost is high enough, an increase on the debt issuance costwill mainly affect the investment decisions of those firms planning to adjust importantly its capitalstock in good times. Overall, a higher non-convex debt issuance cost(ωb)increases the asymmetryof both the cross-sectional debt issuance and investment rate distributions.64Effect on time-series dynamics of spikes: As showed in Panels B, the model’s simulations indicatethat a combination of both non-convex costs are required to reproduce the strong business cycledynamic exhibit by the fraction of firms exhibiting both positive debt issuance and investment spikes.A high non-convex real cost makes large adjustment of the capital and debt stock not only morelikely but concentrated in booms. In fact, a high non-convex real friction reduces the firms’ incentiveto scale down capital in response to a higher dispersion of the idiosyncratic shocks in bad times. Thatis, the value of the option to disinvest in bad times will not be high enough to offset the real fixed costassociated to this decision. On the other hand, even in context of non-convex real costs, in good timessome firms will be willing to increase their capital stock in response to good aggregate productivityshocks and low uncertainty. As pointed out by Bachmann and Bayer (2014), this real option effectinduced on firms’ investment decisions by non-convex real cost makes positive investment spikesmore procyclical. In terms of the firms’ debt issuance decisions, in the absence of strong financialneeds as well as high credit spreads in bad times, firms will not have enough incentives to moveaway from their desired level of debt in bad times which in general can be accomplished by smalladjustment of their debt stock. In contrast, in good times, some of the firms facing large non-convexreal costs will also show high financial needs; which in the presence of equity issuance rigidities willalso create high debt issuance needs. This will render debt issuance positive spikes more procyclical.Simulations from the quantitative model reveal that the presence of a non-convex debt issuancecost is also required to reproduce the business cycle dynamics reported in Panel B. When the debtissuance non-convex cost is low, firms will tend to adjust their debt position too frequently and insmall changes in order to balance the tax-benefit of debt and the cost of bankruptcy risk. Then, alow non-convex debt issuance cost will lower the importance of large adjustment since many firmsare performing marginal adjustments of their debt stock and thus, the procyclicality of positive debtissuance spikes decreases. Furthermore, low non-convex debt issuance costs will also allow firms tofinance capital adjustment costs so that they can adjust their capital stock more often; specially ingood times when credit spreads are low. Overall, a low non-convex debt issuance cost will reduce therelative importance of large adjustments of capital in good time and thus will reduce their comovementwith the business cycle.Effect on time-series dynamics of the cross-sectional distribution: As it is showed in Table 3.4and 3.5 Panels C, the ability of non-convex real and financing costs to increase positive spikes of debtissuance and investment in good times makes the cross-sectional dispersion of debt issuance and in-vestment rates also larger in those periods; inducing procyclicality on the cross-sectional dispersions.As I mentioned before, on average, low levels of non-convex rigidities make large infrequentadjustment of the capital as well as debt stock less likely to occur. This effect should lower the overalldispersion of the distributions. However, in the presence of countercyclical aggregate uncertaintyrisk, large adjustment will become more infrequent in good times than in bad times. In fact, thecountercyclical feature of the dispersion of the idiosyncratic productivity shock will dominate the65effect that large positive adjustments of debt and capital stock have in good times on increasing thecross-sectional dispersion of debt issuance and investment rates distributions. Effectively, when non-convex rigidities are low, some firms facing extreme negative shocks in bad times (i.e. in periods whenuncertainty is high) will find optimal to apply large adjustments on their capital stock which will bereflected in part on their debt stock which will also experience a negative adjustment in response tothe negative prospect of those firms. Consequently, in this case, the cross-sectional dispersion of bothdebt issuance and investment rate will tend to reflect the business cycle properties of the dispersion ofthe idiosyncratic productivity shock; which in the benchmark calibration follows an heteroskedasticprocess with countercyclical volatility (as in Bloom (2009), Bachmann and Bayer (2014)).More broadly, as indicated in Tables 3.4 and 3.5, the model’s simulations predict that a com-bination of both investment and debt issuance non-convex rigidities —once calibrated to averagecross-sectional asymmetry of the debt issuance and investment rate distributions —are required to re-produce the time-series dynamics of the entire cross-sectional distribution of both debt issuance andinvestment rates.3.6 ConclusionIn this chapter, I add to the study of the cross-sectional implications of firms decisions by investigatingthe properties of the firm-level distribution of debt issuance. Interestingly, previous results reportedfor the firm-level distribution of investment rate also manifest in the distribution of debt issuance. Inparticular, the cross-sectional dispersion of the firm-level debt issuance is robustly and significantlyprocyclical. The empirical analysis conducted suggests that this result is driven by large adjustmentsof the debt stock at the firm level (debt issuance lumpiness).In order to explore to what extent these findings are not just a reflection of the behavior of thecross-sectional distribution of investment rate, I build a general equilibrium model featuring heteroge-nous firms that face investment and financing decisions in the context of non-convex real and financialfrictions. The literature on investment has succeeded explaining the role that non-convex real frictions(fixed physical cost) played on shaping the investment distribution. The calibrated model indicatesthat although frictions affecting investment decisions directly contribute to the time-series propertiesof the cross-sectional debt issuance distribution, they are not sufficient to explain moments computedin the data. Particularly, the model’s simulations show that non-convex costs of issuing debt arenecessary to explain the procyclicality of the dispersion of the firm-level debt issuance distributionand link this behavior to time-series dynamic of extreme adjustment of the debt stock. In contrast,non-convexities affecting investment decision alone are not enough to reproduce these links.66Table 3.1: Statistics of the cross-sectional distribution of debt issuance and investment ratesPanel A debt issuance investment ratemoments of firm-level distr.: average corr(·,BP-Y) average corr(·,BP-Y)mean 0.005 0.54 ∗∗∗ 0.017 0.63 ∗∗∗(0.005) (0.004)standard deviation 0.062 0.43 ∗∗∗ 0.022 0.56 ∗∗∗(0.011) (0.004)fraction of firms with (−) spikes 0.059 −0.42 ∗∗∗ 0.015 −0.13(0.021) (0.018)fraction of firms with (+) spikes 0.081 0.61 ∗∗∗ 0.051 0.59 ∗∗∗(0.021) (0.017)test of differences between the average fraction of firms with:t-test W-test t-test W-test(+) debt issuance spike (+) inv. spikeand (−) debt issuance spike −8.64∗∗∗ −7.97∗∗∗ and (−) inv. spike −16.62∗∗∗ −12.15∗∗∗Panel B corr(·,C-S st.dev.) corr(·,C-S st.dev.)fraction of firms with (−) spikes −0.20∗ −0.04fraction of firms with (+) spikes 0.85∗∗∗ 0.94∗∗∗(continues)67Panel C average corr(·,C-S st.dev.) corr(·,C-S st.dev.)fraction of firms with:(+) debt issuance spikes, 0.015 0.75 ∗∗∗ 0.91 ∗∗∗and (+) investment spikes (0.007)(+) debt issuance spikes, 0.066 0.81 ∗∗∗ 0.62 ∗∗∗and no-(+) investment spikes (0.015)no-(+) debt issuance spikes, 0.036 0.51 ∗∗∗ 0.87 ∗∗∗and (+) investment spikes (0.011)(−) debt issuance spikes, 0.003 0.21 ∗ 0.32 ∗∗and (−) investment spikes (0.003)(−) debt issuance spikes, 0.055 −0.22 ∗ −0.21 ∗and no-(−) investment spikes (0.017)no-(−) debt issuance spikes, 0.012 0.03 0.03and (−) investment spikes (0.015)Statistics of the cross-sectional distribution of debt issuance and investment ratio. This table shows someempirical facts of the cross-sectional distribution of debt issuance and investment rates. The table is built usingthe CRSP/Compustat Merged Fundamentals Quarterly from 1984Q1 to 2016Q4. Financing firms (SIC 6000-6999), regulated utilities (SIC 4800-4999), and non-profit firms (SIC 9000-9999) are excluded. Data treatment isexplained in Appendix B.1. Data treatment leaves a sample of 363,512 firm-quarterly observations from 11,236different firms which represents roughly 43 percent of the original database. Balance-sheet data is adjustedby the price level from NIPA. Y denotes the cyclical component of real GDP growth obtained by detrendingthe time-series using a band-pass (BP) filter. Debt issuance is defined as the change of total debt where totaldebt is defined as the sum of long- and short-term debt; scaled by total assets. Investment rates are defined ascapital expenditures; scaled by total assets. Total assets are computed as the average of last three years assets.Correlation statistics, ρ(·, ·) are constructed by applying a band-pass filter to the deflated variable. Positive(negative) investment spikes are defined as investment rate higher (lower) than 5% (-5%) of total assets; asin Doms and Dunne (1998), Gourio and Kashyap (2007) and Bachmann and Bayer (2014) for quarterly data.Positive (negative) debt issuance spikes are defined as debt issuance higher (lower) than 5% (-5%) of total assets.Panel A shows on the second (fourth) column the sample average of the mean, standard deviation, fraction of firmswith negative debt issuance (investment) spikes, and fraction of firms with positive debt issuance (investment)spikes. Standard errors are reported in parenthesis. Panel A shows in the third (fifth) column the correlationwith the band-passed GDP growth exhibited by the mean, standard deviation, fraction of firms with negative debtissuance (investment) spikes, and fraction of firms with positive debt issuance (investment) spikes. ***, **, and* denote statistical significance at the 1%, 5%, and 10% levels, respectively. Panel A also shows the results oftwo tests of differences applied to the average fraction of firms exhibiting positive spikes and the average fractionof firms exhibiting negative spikes. “W-test” denotes the statistic obtained from Wilcoxon test. These test areapplied to both the debt issuance and investment rate cross-sectional distribution. Panel B shows in the second(third) column the correlation between the fraction of firms exhibiting debt issuance (investment) spikes and thecross-sectional dispersion of the firm-level debt issuance (investment rate) distribution. Panel C shows in thethird (fourth) the correlation between the sample average of the fraction of firms exhibiting debt issuance and/orinvestment spikes and the cross-sectional dispersion of the firm-level debt issuance (investment rate) distribution.68Table 3.2: Benchmark quarterly calibrationParameter Description ValueA. Preferencesβ discount factor 0.994γ relative risk aversion 10.0ψ elasticity of intertemporal substitution 2.0B. Productionα capital share parameter 0.20α̂ labor share parameter 0.50δ capital depreciation rate 0.094/4f operational (proportional) cost 0.05ωk non-convex real capital adjustment cost 0.22C. Productivityg growth rate of consumption 0.018/4ρ persistence of aggregate state st 0.95σ¯ conditional volatility of the idiosyncratic shock 0.091/2ρz persistence of idiosyncratic shock 0.90D. Financeτ tax rate 0.14λ parameter controlling average debt maturity 0.10c coupon rate 3.0%/4ωb non-convex debt issuance cost 0.04ψe equity issuance cost: fixed component 0.06χ bankruptcy deadweight cost 0.70Benchmark quarterly calibration. This table reports the parameter values used inthe benchmark quarterly calibration of the model. Section 3.4 describes the momentstargeted to set each parameter.69Table 3.3: Aggregate business cycle, and financing momentsMoment Data ModelA. Business cycleE(∆y)(%) 1.80 1.97E(I/Y ) 0.20 0.18σ∆y(%) 3.56 3.37σ∆c/σ∆y 0.71 0.64σ∆i/σ∆y 4.50 5.38ACF1(∆y) 0.35 0.29ACF1(∆i) 0.85 0.71corr(∆c,∆y) 0.39 0.43B. FinancingBook leverage 0.26 0.28Freq. of equity issuance 0.09 0.07Default rate (%) 0.84 1.79corr(debt issuance,∆y) 0.54 0.62corr(equity issuance,∆y) -0.45 -0.19C. Asset pricesE(re− r f )(%) 7.22 6.79σ(re− r f )(%) 16.5 8.07E(r f )(%) 1.51 1.64σ(r f )(%) 2.2 1.71E(cs)(bps) 90 83σ(cs)(bps) 44 69Aggregate business cycle and financing moments. I/Y de-notes the investment-output ratio. ∆y, ∆c, ∆i denote output, con-sumption, and investment growth respectively. re− r f is the ag-gregate stock market excess return, r f is the one-period real risk-free rate, and cs is the aggregate credit spreads. The model;smoments are calculated by simulating the model for 5,000 firmsand 10,000 quarters, with a 1,000-quarters burning period. Ag-gregate returns and credit spreads are equally-weighted. Growthrates, and returns moments are annualized percentage. creditspreads are in annualized basis point units. Average defaultrates for the data corresponds to average expected default ratesresulted from implementing the KMV model in the panel datadescribed in previous chapter. Refer to Table 2.2 in previouschapter for the definition of most variables of the data.70Table 3.4: Effect of non-convex costs on the moments of the cross-sectional distribution of debtissuancePanel ASkewness of debt issuance distribution0.50×ωb 0.75×ωb 1.00×ωb 1.25×ωb 1.50×ωb0.50×ωk 0.29 1.21 2.09 2.72 3.310.75×ωk 0.56 1.81 2.81 3.86 4.461.00×ωk 0.83 2.17 3.53 4.53 5.041.25×ωk 0.95 2.53 3.78 4.57 5.341.50×ωk 1.07 2.57 3.95 4.86 5.62Panel BCorr(Fraction of (+) debt spike adjusters, BP-Y )0.50×ωb 0.75×ωb 1.00×ωb 1.25×ωb 1.50×ωb0.50×ωk 0.21 0.35 0.49 0.63 0.760.75×ωk 0.25 0.42 0.57 0.71 0.81.00×ωk 0.28 0.48 0.65 0.76 0.831.25×ωk 0.33 0.52 0.71 0.79 0.841.50×ωk 0.36 0.56 0.72 0.8 0.8Panel CCorr(Standard deviation of debt issuance, BP-Y )0.50×ωb 0.75×ωb 1.00×ωb 1.25×ωb 1.50×ωb0.50×ωk -0.18 0.08 0.33 0.55 0.710.75×ωk -0.08 0.08 0.23 0.39 0.531.00×ωk -0.05 0.21 0.45 0.62 0.771.25×ωk -0.05 0.11 0.25 0.41 0.541.50×ωk 0.04 0.29 0.49 0.65 0.76Effect of non-convex costs on the moments of the cross-sectional dis-tribution of debt issuance. This table shows the effect that both debt andcapital adjustment non-convex costs (ωk,ωb) exhibit in the model on thecross-sectional and time-series properties of the firm-level debt issuancedistribution. Model variables and statistics are calculated by simulatingthe model for 5,000 firms and 10,000 quarters, with a 1,000-quartersburning period. Panel A shows the effect of both non-convex rigiditieson the skewness of the debt issuance distribution. Panel B shows the im-pact of both non-convex costs on the correlation with the business cycleof the fraction of firms exhibiting large infrequent positive adjustment inthe debt stock. Panel C shows the impact of both non-convex costs on thecorrelation with the business cycle of the dispersion of the firm-level debtissuance ratio distribution. Refer to Table 3.1 for details about variables’definitions.71Table 3.5: Effect of non-convex costs on the moments of the cross-sectional distribution of in-vestment ratePanel ASkewness Investment rate0.50×ωb 0.75×ωb 1.00×ωb 1.25×ωb 1.50×ωb0.50×ωk 0.13 0.43 0.71 0.85 0.970.75×ωk 1.18 1.43 1.51 1.81 1.921.00×ωk 2.17 2.25 2.27 2.43 2.491.25×ωk 2.61 2.67 2.74 2.85 2.891.50×ωk 2.96 3.08 3.09 3.21 3.20Panel BCorr(Fraction of investment spike adjusters, BP-Y )0.50×ωb 0.75×ωb 1.00×ωb 1.25×ωb 1.50×ωb0.50×ωk 0.05 0.1 0.13 0.14 0.140.75×ωk 0.24 0.29 0.34 0.35 0.341.00×ωk 0.42 0.47 0.51 0.52 0.531.25×ωk 0.52 0.52 0.61 0.64 0.651.50×ωk 0.49 0.56 0.63 0.66 0.68Panel CCorr(Standard deviation of investment rate, BP-Y )0.50×ωb 0.75×ωb 1.00×ωb 1.25×ωb 1.50×ωb0.50×ωk -0.31 -0.19 -0.05 0.02 0.080.75×ωk -0.15 0.04 0.23 0.31 0.391.00×ωk 0.03 0.26 0.49 0.58 0.671.25×ωk 0.25 0.44 0.59 0.65 0.691.50×ωk 0.45 0.58 0.66 0.67 0.68Effect of non-convex costs on the moments of the cross-sectional dis-tribution of investment rate. This table shows the effect that both debtand capital adjustment non-convex costs (ωk,ωb) exhibit in the model onthe cross-sectional and time-series properties of the firm-level investmentrate distribution. Model variables and statistics are calculated by simulat-ing the model for 5,000 firms and 10,000 quarters, with a 1,000-quartersburning period. Panel A shows the effect of both non-convex rigidities onthe skewness of the investment rate distribution. Panel B shows the im-pact of both non-convex costs on the correlation with the business cycleof the fraction of firms exhibiting large infrequent positive adjustment inthe capital stock. Panel C shows the impact of both non-convex costs onthe correlation with the business cycle of the dispersion of the firm-levelinvestment rate distribution. Refer to Table 3.1 for details about variables’definitions.72Figure 3.1: Average debt issuance cross-sectional distributionmean            =   0.005                       mean            =   0.004median         =  -0.002                       median         =   0.006sd                 =   0.056                       sd                 =   0.060skewness     =   3.359                       skewness     =    0.137kurtosis         =  23.763                      kurtosis        =    3.014-0.15-0.10-0.050.000.050.100.150.200.250.300.350.400.45Debt Issuance/ Assets0 10 20 30 40 50 60 70 80 90 100 110 120 130Rank within firm (1983-Q1 to 2015-Q4)Debt Issuance to Assets Normally distributed shocksAverage debt issuance cross-sectional distribution. This figure is used to compare the averageof the observed firm-level debt issuance distribution (red bars) to a normally simulated counterpart(blue line). The figure is constructed using the following steps. First, for each firm, quarterly debtissuance are ranked from the highest to the lowest debt issuance into bins. Next, the simulateddebt-issuance counterparts (x j,t ) of the firm j for each bin i by solving the equation Φ j(x j,i) = i/Nb ;whereΦ j represents the cumulative density function of a normal distribution with mean and standarddeviation equal to the sample mean and standard deviation of firm j-th quarterly debt issuance. Nbdenotes the total number of bins i.e. 4× (2016− 1984+ 1). After repeating the exercise for eachfirm, I construct the averages over all firms by bin. Refer to Table 3.1 for details of the variables’definition.73Figure 3.2: First moment of firm-level debt issuance and investment rate distribution-0.50.00.51.01.52.0Fraction of Assets (%)1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1yearqNBER recessionDebt IssuanceInvestment1st. Moment Firm-Level DistributionFirst moment of firm-level debt issuance and investment rate distribution. This figure showsthe average of the first moment of the debt issuance (blue line) and investment rate (red line) cross-sectional distribution from 1984Q1 to 2016Q4. The time-series are constructed from the CRSP/-Compustat Merged Fundamentals Quarterly. Debt issuance is defined as the change of total debtscaled by total assets. Total debt is computed as the sum of long- and short-term debt. Total assetsare computed as a weighted-average of last-year quarterly assets. The investment rate, is defined ascapital expenditures to total assets. For means and pictures, I use the seasonally smoothed variables.Refer to Table 3.1 for details of the variables’ definition.74Figure 3.3: Dispersion of firm-level debt issuance and investment rate distribution2.04.06.08.0Fraction of Assets (%)1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1yearqNBER recessionDebt IssuanceInvestment2nd. Moment Firm-Level DistributionDispersion of firm-level debt issuance and investment rate distribution. Refer to Table 3.1 fordetails of the variables’ definition.75Figure 3.4: Fraction of firms exhibiting positive and negative debt issuance spikes4681012% of Firms1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1yearqNBER recessionNegative spikesPositive spikesDebt Issuance Spikes at the Firm-Level DistributionFraction of firms exhibiting positive and negative debt issuance spikes. Refer to Table 3.1 fordetails of the variables’ definition. Positive (negative) investment spikes are defined as investmentrate higher (lower) than 5% (-5%) of total assets; as in Doms and Dunne (1998), Gourio and Kashyap(2007) and Bachmann and Bayer (2014) for quarterly data. Positive (negative) debt issuance spikesare defined as debt issuance higher (lower) than 5% (-5%) of total assets.76Figure 3.5: Fraction of firms exhibiting positive investment and debt issuance spikes2.04.06.08.010.0% of Firms1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1yearqNBER recession(+) debt issuance spikes & no-$(+)$ investment spikesno-(+) debt issuance spikes & $(+)$ investment spikesDebt & Investment lumpinessFraction of firms exhibiting positive investment and debt issuance spikes. Refer to Table 3.1 fordetails of the variables’ definition. Positive (negative) investment spikes are defined as investmentrate higher (lower) than 5% (-5%) of total assets; as in Doms and Dunne (1998), Gourio and Kashyap(2007) and Bachmann and Bayer (2014) for quarterly data. Positive (negative) debt issuance spikesare defined as debt issuance higher (lower) than 5% (-5%) of total assets.77Chapter 4ConclusionThis thesis is comprised of two essays on Structural Corporate Finance. In chapter 2, the first essayexamines how asset redeployability —through its positive effect on disinvestment flexibilities andnegative effect on bankruptcy deadweight cost —affects the cross-section of financial leverage andcredit spreads. In the data, firms exhibiting more asset redeployability also show higher leverage ratiosand lower credit spreads. Moreover, in the data, the asset redeployability measure contains informa-tion that goes over and above information provided by expected recovery rates and a tangibility-basedmeasure. I investigate the economic mechanisms behind these findings by using a structural modelthat includes varying degrees of disinvestment flexibilities and bankruptcy costs. Importantly, thesetwo ingredients of the model are set to match the differences in expected returns and recovery rateshowed by extreme portfolios of firms formed based on a novel measure of asset redeployability.From the model’s simulations, I find that portfolios of firms formed based on the degree of the dis-investment flexibility and the bankruptcy costs show significant variation in terms of leverage ratiosand credit spreads along the disinvestment-flexibility dimension. Effectively, in the model, firms fac-ing high disinvestment flexibility are able to not only default less but more importantly they defaultless often in bad times; which, in the presence of a countercyclical price, allows these firms to moreand cheaper debt on average. Furthermore, within the model, differences in expected recovery ratesbetween firms are mainly explained by differences in bankruptcy costs. Then, I use this evidence toconclude that the link between asset redeployability and disinvestment flexibility can be a plausibleexplanation of why in the data, even after accounting for expected recovery rates (and a wide rangeof controls), asset redeployability still predicts higher financial leverage and lower credit spreads.More generally, this essay provides new evidence to explain the positive effect of asset redeploya-bility on the credit terms of debt. In particular, I add to the literature studying asset redeployabilityby highlighting its positive effect on firms’ value through allowing them to maneuver business cyclefluctuations more effectively. In contrast, traditional economic literature studies the asset redeploy-ability’s positive features through mainly focusing on its relation with creditors’ recovery values atcorporate default.78In chapter 3, the second essay explores time-series dynamics of the entire cross-sectional distribu-tion of debt issuance. Specifically, I add to current macroeconomic works studying debt issuances atthe aggregate level by showing that —as the cross-sectional average —, the cross-sectional dispersionof the debt issuance distribution also comoves with the business cycle. Further, I present evidence thatsuggests that the procyclical pattern of the cross-sectional dispersion of the debt issuance distributionis mainly driven by periods where firms exhibit large and positive investment and debt issuances;that is, periods of aggregate macroeconomic growth. To the extent that investment and debt issuancelumpiness result from the interaction of non-convex real and financial costs, in this essay I focus onunderstanding the contribution of both frictions on shaping the patterns of the cross-sectional disper-sion of debt issuance. To accomplish this goal, I build a DSGE model with lumpy investment anddebt financing. I use the model’s simulations to conclude that neither a non-convex real cost nor anon-convex financial cost alone can reproduce the pattern exhibited by the cross-sectional dispersionof debt issuance. In a model with countercyclical uncertainty shocks, both non-convex frictions arerequired to induce a region of inaction in bad times, while allowing high-growth firms to scale uptheir capital stock in good times through a real option effect. Interestingly, I conclude that the pro-cyclical behavior exhibited by the cross-sectional dispersion of debt issuance is not just a reflectionof the properties of the cross-sectional dispersion of investment rates.4.1 Future workBoth essays presented in this thesis could be extended along several dimensions. For instance, inthe model of the first essay, asset redeployability is modeled as an exogenous characteristic of firms’assets. While this assumption simplifies the analysis as well as the numerical solution, I believe itwould be interesting to allow firms to choose their degree of asset redeployability by either intro-ducing a second type of capital or; by differentiating new from used capital. This analysis wouldprovide a better understanding about the nature of firms’ asset redeployability and therefore, aboutits implications. Furthermore, the model predicts that differences in disinvestment flexibilities do notproduce important differences in expected recovery rates. This prediction could be tested as long asdisinvestment flexibility can be properly measured.Lastly, in the second essay, long-term bonds are assumed to have a constant average maturity.While this assumption allows the model to stay tractable, it would be interesting to explore the im-plications of the model when debt maturity decisions are also allowed. Indeed, in reality, firms issuedebt at multiple maturities. 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Section A.2 provides the details about the construction of the variables used in theestimation of panel regressions and descriptive statistics of these variables. Section A.3 describes theKMV model implemented in the data to construct the expected recovery rates and ultimately used todecompose the asset redeployability measure.A.1.1 Bond-level dataThis chapter uses a sample of U.S. non-financial and non-public-utility firms covered by the S&PCompustat and the Center for Research in Security Prices (CRSP). I obtained secondary market trans-action prices of corporate bonds from the National Association of Insurance Commissioners (NAIC).The NAIC Financial Data Repository Database for Corporate Bonds collects all holdings and transac-tions for insurance companies based on their mandatory quarterly Schedule D filings. The transactiondata includes price, date, and quantity. The data covers a specific group of investors, i.e. insurancecompanies. According to Veronesi (2016), insurances companies make up a very large fraction of themarket participants based on their holdings. To be part of the final sample, bonds must be issued by aU.S. firm and pay a fixed coupon. I also eliminate bonds with special bond features such as put, call,exchangeable, asset backed, and convertible (Campbell and Taksler (2003)).Using security-level daily transaction data, I reconstruct for each individual bond in my samplethe promised cash-flows of the corresponding corporate debt instrument. The idea is to construct thepromised sequence of cashflows {C(s) : s = 1,2, ...,S} at time t.A bond’s cashflows will consist ofthe regular coupon payments and the repayment of the principle at maturity. Importantly, the timingof the stream of cash flows is determined using information about accrued interests reported in the87NAIC database. Particularly, the next coupon date is set to replicate the reported accrued interests.Then, given the stream of cashflows determined, the (dirty) price in period t of bond k issued by firmi will satisfy the following relation,Pi,t,k =S∑s=1C(s)e−rss (A.1)where rs is the spot rate used to discount a cashflow paid at period t + s. Transactions’ yields arecomputed by equating the dirty price to the present value of cash-flows, as in equation (A.1). Then,the bond credit spreads is Si,t,k = yi,t,k−y f ,t,k, where yi,t,k denotes the benchmark treasury at the date t.To obtain the benchmark treasury for each transaction, I match the bond duration to the zero-couponTreasury yields curve provided by Gu¨rkaynak et al. (2007) - linearly interpolating if necessary.To ensure results are not driven by a small number of extreme observations, all observations withcredit spreads below 5 basis points and greater than 3,500 basis points are eliminated. Very smallcorporate issues (par value of less than $0.1 million) as well as observations with a remaining term-to-maturity of less than one year are also discarded. I also eliminate transactions that involve thethe bond issuer and those that show return reversals. These corporate securities were then matchedwith their issuer’s annual balance sheet data from Compustat and daily data on equity valuationsfrom CRSP. This procedure yielded a sample of 16,587 individual transactions over the 1995:M1-2012:M12 period.A.1.2 Variables descriptionWhile our micro-level data on credit spreads reflect month-end values1, the requisite firm-level bal-ance sheet items from are available annually whereas stock returns are obtained from CRSP file.Issuers’ accounting information are matched using the 6-digits issuer Cusip as well as stock pricesinformation. To ensure that all information is included in asset prices, stock returns and bond creditspreads from July of year t to June of year t + 1 are matched with accounting information for fiscalyear ending in year t − 1. From the annual Compustat data, I construct the following explanatoryvariables,− Market Leverage : total liabilities / book assets (at)− Total Liabilities : long-term debt (dltt)+ short-term debt (dlc)− cash (che)− Tangibility : property, plant and equipment / book assets = (ppent)/at− Book-to-Market : book value equity/market value equity− Book Equity : common/ordinary equity (ceq)+ deferred tax and inv. tax credit (txditc)− purchase of common and preferred stock (pstk)− Market Equity : shares outstanding (shrout)× market value stock price (prc)1Monthly credit spreads observations are constructing using the last transaction of the month taking into account thetime-value of money.88− ROA : (operating income after depreciation oibdp)/at− Tobin’s Q : (market equity+ at - ceq−deferred taxes (txdb))/at− Z-Score : 3.3×ROA+ 1.0× ( saleat ) + 1.4× ( reat) + 1.2× ( act-lctat )where re, act, and lct denotes retained earnings, current assets, and liabilities, respectively.All the remaining variables’ definitions are given in Section 3.2.1.A.1.3 Variables descriptive statisticsTable A.1 reports the average yield and credit spreads from the NAIC benchmark bond transactionssample described in the previous section, sorted on credit rating. In the sample, 67% of bond trans-actions lies in the A-BBB categories. Campbell and Taksler (2003) documents a similar pattern. Theaverage monthly spreads between Baa and Aaa bonds is about 144bps, which is consistent to closethe average spreads reported by Moody’s over the same period. To validate the database used, Figure2.4, I plot the time series of the average Baa yield spreads obtained from my NAIC sample along withthe spreads reported by Moody’s over the same period. Note that the two time-series show a similarpattern spiking during the 2000’s and the financial crisis. The time series correlation between the twoaggregate series is about 0.9.Table A.2 shows that the term structure of interest rate implicit in the bond sample is, in general,upward-sloping. The term structure of credit spreads shows an increasing pattern for bonds withduration larger than one year.Table A.3 Panel A reports summary statistics for the bond transaction sample used in the re-gressions. The size of issue is positively skewed, with an average (median) debt issue of 328 (250)millions. The time-to-maturity of the bonds is long, about 11 years. In general, bond characteristicsof my sample are similar to those of previous studies using public debt (see Gilchrist and Zakrajsˇek(2011)).Table A.3 Panel B shows individual firm summary statistics. The average firm size in the sampleis consistent with previous empirical works’ finding regarding the size of firms issuing public debt(Denis and Mihov (2003)). Lastly, Table A.4 reports the average asset redeployability by SIC codewhich shows similar patterns to that in Table 1 of Kim and Kung (2016).A.1.4 KMV modelTo decompose the asset redeployability measure in two components, I regress this measure on ex-pected recovery rates. Then, the first component was the one explained by expected recovery rates;whereas the residual of this regression corresponded to the second component. Importantly, expectedrecovery rates were computed based on the KMV model as explained by Bohn and Crosbie (2003),and Altman et al. (2004). In this model, the asset value of the firm VA is assumed to follow a geometricBrownian motion dVA/VA = µ dt+σA dz, where µ and σA are the firm’s asset value drift and volatilityrate and dz is a Wiener process. If the total debt at period t is denoted by Xt , default happens if at time89t the value of the firm’s assets VA,t , is lower than Xt . When default occurs, the recovery rate is givenby the ratio of the asset value to the debt, i.e. VA,t/Xt . The expected recovery rate is computed as,E(VA,tXtI{VA,t<Xt})=(VA,0ertXt)(Φ(−d1)Φ(−d2))(A.2)where r is the risk-free interest rate, Φ(·) is the standard normal cumulative distribution function, andd1 and d2 have similar interpretation as in the standard Black-Scholes formula.The model is implemented by estimating the unobservable parameters of the model regarding thefirm’s assets at time 0, i.e. VA and σA, through link them to the observable value and volatility of thefirm’s equity at time 0 denoted as VE and σE , respectively. Specifically, based on the idea that (i) thefirm’s equity can be seen as a call option on the underlying asset, (ii) debt is homogenous with timeof maturity, and (iii) debt coupon rate is zero are zero and dividends are reinvested, standard resultsshow that the value of the equity is,VE =VAΦ(d1)− e−rXtΦ(d2) (A.3)Furthermore, it is possible to show that the firm’s asset and equity volatility are related by the identity,σE = σAVAVEΦ(d1) (A.4)Given VE and σE - which are approximated by Market Equity and the annualized standard devi-ation of the last twelve monthly excess returns - this system comprised of equation (A.3) and (A.4)has a unique solution. The system is completed by using total liabilities (dltt + dlc - che)and the annualized one-month T-Bill as Xt and r, respectively.A.2 Numerical procedure appendixThis appendix provides details regarding the key elements of the quantitative model and its solutionmethod. Section B.1 describes the stationary version of the model. Section B.2 describes details of thenumerical solution method implemented. Section B.3 describes the Euler equations that characterizedthe optimal firm’s decisions. Lastly, Section B.4 provides details of the relation between debt pricesand probabilities of default as well as recovery rates used in the model’s quantitative analysis.A.2.1 Shareholders’ stationary problemAssuming that the firm does not default in the current period, and defining the following stationaryvariables: k̂t+1 = kt+1/xt , ît = it/xt , and b̂t+1 = bt+1/xt ; the stationary value function J(kt ,bt ,λt ,Γt)/xt ≡j(k̂t , b̂t ,λt ,Γt) can be written as,90j(k̂t , b̂t ,λt ,Γt) = maxkt+1,bt+1,λt+1{d̂t +Et(Mt,t+1e∆ln(xt+1) j(k̂t+1, b̂t+1,λt+1,Γt+1))}(A.5)where ∆ln(xt+1) = ln(xt+1/xt) and the stationary functions relevant to solve the program are,d̂t ≡ êt −Ψ(êt)êt ≡ (1− τ)ŷt − ît − Φ̂(̂it , k̂t ,ωt)− (λt + c(1− τ)) b̂te−∆ln(xt)+ τδ k̂te−∆ln(xt)+ P̂(k̂t+1, b̂t+1,λt+1,Γt)(b̂t+1− (1−λt)b̂te−∆ln(xt))ŷt ≡ e−α∆ln(xt)k̂αt − f zt −φ k̂te−∆ln(xt)ît ≡ k̂t+1− (1−δ )kte−∆ln(xt)Φ̂(̂it , k̂t ,ωt) ≡(e∆ln(xt)it/kt −δ)2k̂te−∆ln(xt)θ × 1 if it > 0ωt if it ≤ 0Note that the debt pricing function can also be normalized,b̂t+1× P̂(k̂t+1, b̂t+1,λt+1,Γt) = a︸︷︷︸aEt(Mt,t+1b̂t+1(λt+1+ c+(1−λt+1) · P̂(k̂t+2, b̂t+2,λt+2,Γt+1))I{zt+1<z?t+1})+Et(Mt,t+1(1−χt+1)e∆ln(xt+1) j(k̂t+1,0,0,Γt+1)I{z?t+1<zt+1<z0t+1}) (A.6)A.2.2 Numerical solution detailsThe numerical dynamic programming approach considers the joint determination of the stationaryequity value function (A.5) and the stationary bond pricing function (A.6). I use an iterative proce-dure to jointly approximate these two functions on discrete grids. Throughout the procedure, I creategrids for the shocks and the endogenous state variables, k̂t , b̂t , and λt . Given their persistent nature,we use the Rouwenhorst (1995) procedure to discretize the aggregate state and the firm-level tech-nology shocks. The aggregate Markov chain has three states and changes in the technology shockare approximated with 11 elements. I create grids for capital, the debt face value outstanding anddebt maturity parameter, with 50, 10 and 10 points respectively. The choice for tomorrow’s controlvariables is based on a dynamic searching in the original grids that consists of zooming in multipletimes around local optimal values. This methodology allows the code to spend most of the processingtime in a grid around the optimal value. Importantly, the procedure to find the maximum equity valuefunction takes as given the stochastic discount factor as well as the debt pricing function. After theequity value function converges, I solve for the bond pricing function using a value function iterationprocedure that takes the equity value function as given. Once this algorithm converges, I obtain theequity and bond value functions for each element on the state space.91A.2.3 Derivation of first-order conditionsUnder the assumption that the firm does not need to issue equity, i.e Ψ(êt) = 0, the set of first ordernecessary conditions of the original firm’s problem are,[b̂t+1] :∂ P̂t∂ b̂t+1(b̂t+1− (1−λt)b̂te−∆ln(xt))+ P̂t +EtMt,t+1e∆ln(xt+1) z?t+1∫z∂ jt+1∂ b̂t+1dZ (zt+1|zt)= 0[λt+1] :∂ P̂t∂λt+1(b̂t+1− (1−λt)b̂te−∆ln(xt))+EtMt,t+1e∆ln(xt+1) z?t+1∫z∂ jt+1∂λt+1dZ (zt+1|zt)= 0[̂it ] : −1− ∂ Φ̂t∂ ît+ γt = 0[̂kt+1] :∂ P̂t∂ k̂t+1(b̂t+1− (1−λt)b̂te−∆ln(xt))− γt +EtMt,t+1e∆ln(xt+1) z?t+1∫z∂ jt+1∂ k̂t+1dZ (zt+1|zt)= 0where γt represents the Lagrange multiplier of the capital accumulation condition, z?t+1 denotes thedefault threshold (the highest value of zt at which it is optimal to keep operating the firm), and Z (·)represents the conditional density distribution of zt+1. The derivatives of the function j(·) can beobtained by applying the envelope theorem multiple times,[b̂t ] :∂ jt∂ b̂t=−(λt + c(1− τ))e−∆ln(xt)− P̂t(1−λt)e−∆ln(xt)[λt ] :∂ jt∂λt=−b̂te−∆ln(xt)+ P̂t b̂te−∆ln(xt) =−b̂te−∆ln(xt)(1− P̂t)[̂kt ] :∂ jt∂ k̂t= (1− τ)∂ ŷt∂kt+ τδe−∆ln(xt)− ∂ Φ̂t∂ k̂t+(1−δ )e−∆ln(xt)λt(A.7)Note that the derivative of the debt price function can also be obtained from equation,b̂t+1× P̂(k̂t+1, b̂t+1,λt+1,Γt) = a︸︷︷︸aEt(Mt,t+1b̂t+1(λt+1+ c+(1−λt+1) · P̂(k̂t+2, b̂t+2,λt+2,Γt+1))I{zt+1<z?t+1})+Et(Mt,t+1(1−χt+1)e∆ln(xt+1) j(k̂t+1,0,0,Γt+1)I{z?t+1<zt+1<z0t+1})Indeed, differentiating the debt pricing function with respect to each control variable we cancompletely determined the system of equations resulted from the first-order conditions of the firm’s92problem,[b̂t+1] : P̂t + b̂t+1∂ P̂t∂ b̂t+1= Et(Mt,t+1(1−χt+1)e∆ln(xt+1) j(k̂t+1,0,0,Γ?t+1)[−dZ (z?t+1|zt)∂ z?t+1∂ b̂t+1])+Et(Mt,t+1b̂t+1(λt+1+ c+(1−λt+1) · P̂(k̂t+2, b̂t+2,λt+2,Γ?t+1))[dZ (z?t+1|zt)∂ z?t+1∂ b̂t+1])+Et(Mt,t+1(λt+1+ c+(1−λt+1) · P̂(k̂t+2, b̂t+2,λt+2,Γt+1))I{zt+1<z?t+1})+Et(Mt,t+1b̂t+1(1−λt+1) ·∇P̂b̂t+1(k̂t+2, b̂t+2,λt+2,Γt+1)I{zt+1<z?t+1})[λt+1] : b̂t+1∂ P̂t∂λt+1= Et(Mt,t+1(1−χt+1)e∆ln(xt+1) j(k̂t+1,0,0,Γ?t+1)[−dZ (z?t+1|zt)∂ z?t+1∂λt+1])+Et(Mt,t+1b̂t+1(λt+1+ c+(1−λt+1) · P̂(k̂t+2, b̂t+2,λt+2,Γ?t+1))[dZ (z?t+1|zt)∂ z?t+1∂λt+1])+Et(Mt,t+1b̂t+1(1− P̂(k̂t+2, b̂t+2,λt+2,Γt+1))I{zt+1<z?t+1})+Et(Mt,t+1b̂t+1(1−λt+1) ·∇P̂λt+1(k̂t+2, b̂t+2,λt+2,Γt+1)I{zt+1<z?t+1})[̂kt+1] : b̂t+1∂ P̂t∂ k̂t+1= Et(Mt,t+1(1−χt+1)e∆ln(xt+1) j(k̂t+1,0,0,Γ?t+1)[−dZ (z?t+1|zt)∂ z?t+1∂ k̂t+1])+Et(Mt,t+1b̂t+1(λt+1+ c+(1−λt+1) · P̂(k̂t+2, b̂t+2,λt+2,Γ?t+1))[dZ (z?t+1|zt)∂ z?t+1∂ k̂t+1])+Et(Mt,t+1b̂t+1(1−λt+1) ·∇P̂k̂t+1(k̂t+2, b̂t+2,λt+2,Γt+1)I{zt+1<z?t+1})where for any variable qt+1, the total derivative of the debt pricing function with respect to qt+1is denoted by,∇P̂qt+1t+1 ≡∂ P̂t+1∂ k̂t+2∂ k̂t+2∂qt+1+∂ P̂t+1∂ b̂t+2∂ b̂t+2∂qt+1+∂ P̂t+1∂λt+2∂λt+2∂qt+1A.2.4 Derivation of debt credit spreads as a function of pd and rrThe firm’s creditors buy corporate debt at price Pt ≡ P(kt+1,bt+1,λt+1,Γt) in exchange of collectingcoupon and principal payments until the firm defaults. If default does not occur, the bond repaymentat period t + j is CFt+ j ≡ (1−λt+1) j−1(c+λt+1). As a consequence, if the yield of the defautablebond is Yt , then Yt will relate to Pt according to the expression,Pt =∞∑j=1CFt+ j(1+Yt) j=λt+1+ cλt+1+Yt(A.8)93Similarly, if the price of a default-free debt with payments CFt+ j is Pr ft , then the yield of the default-free bond will be computed as Y r ft = (λt+1+c)/Pr ft −λt+1. Credit spreads (cst) is defined as the yielddifference between defaultable and default-free debt,cst ≡ Yt −Y r ft =λt+1+ cPt− λt+1+ cPr ft(A.9)To write credit spreads in terms of the probability of default PDt and the value of the recovery rate RRtnote that Pt is defined by an arbitrage condition such that the amount of money creditors are willingto pay for the contract must equal the expected value of future payments. Formally, this conditionimplies the following identity,Pt = Et(Mt,t+1(λt+1+ c+(1−λt+1)Pt+1)I{zt+1<z?t+1})+Et(Mt,t+1(1−χt+1)J0t+1bt+1I{z?t+1<zt+1<z0t+1}) (A.10)where J0t+1 denotes the value of the unlevered firm after default, i.e. J0t+1 ≡ J(kt+1,0,0,Γt+1). Impor-tantly, corporate bonds are held by the representative household and are thus valued using the house-hold equilibrium pricing kernel Mt,t+1. To gain some intuition about the drivers of credit spreads, forsimplicity I now consider the one-period debt case, i.e. λt+1 is set to 1. For this special case, notethat,1+ cPt=1Et(Mt,t+1)1−Et(Mt,t+1(1−χt+1) J0t+1Pt bt+1I{z?t+1<zt+1<z0t+1})1−Et(Mt,t+1Et(Mt,t+1)I{z?t+1<zt+1<z0t+1}) (A.11)similarly for the default-free bond in this special case, we have, (1+ c)/Pt = 1/Et(Mt,t+1). Con-sequently, defining the risk-neutral default probability PDt and the value of the recovery rate RRt ,asPDt ≡ Et( Mt,t+1Et(Mt,t+1)I{z?t+1<zt+1<z0t+1})RRt ≡ Et(Mt,t+1(1−χt+1)J0t+1Ptbt+1I{z?t+1<zt+1<z0t+1}) (A.12)we conclude that credit spreads can be written in terms of PDt and RRt according,cst(λt+1 = 1) =1+ cPt− 1+ cPr ft=1Et(Mt,t+1)(1−RRt1−PDt −1)(A.13)94Note that in the general case, i.e. λt+1 ∈ [0,1], the credit spreads will contain an additional termrelated to the difference between the defaultable and default-free debt price growth. Specifically,cst =1Et(Mt,t+1)(1−RRt −∆Pt1−PDt − (1−∆Pr ft ))(A.14)where ∆Pt ≡ Et(Mt,t+1(1−λt+1)Pt+1/PtI{zt+1<z?t+1})and ∆Pr ft ≡ Et(Mt,t+1(1−λt+1)Pr ft+1/Pr ft).95Table A.1: Yield data per rating categoryRating Yield (%) Yield Spread (bps) NAAA 5.01 67 477AA+ 5.04 72 274AA 5.93 89 774AA- 5.71 79 1581A+ 5.79 111 2333A 5.88 118 2847A- 6.61 133 2485BBB+ 6.46 144 2749BBB 6.45 171 3067Total 16587Yield data per rating category. This table shows the sam-ple average of corporate yields and yield spreads by creditrating. The yield spreads is obtained by subtracting from thecorporate spreads, a Treasury yield with equal duration. TheNAIC data’s sample period is from 1995 and 2012. Yieldsare in percent and yield spreads are in basis points. All bondsare in U.S. dollars and have no special features (call, put,convertibility, etc.).96Table A.2: Yield data per duration categoryYield (%) Yield Spread (bps) Nduration < 1yr 4.47 133 191yr ≤ duration < 2yr 4.49 113 14862yr ≤ duration < 4yr 5.26 116 33384yr ≤ duration < 6yr 6.23 119 36506yr ≤ duration < 8yr 6.5 110 28528yr ≤ duration < 10yr 6.83 154 142510yr ≤ duration < 12yr 7.07 160 250512yr ≤ duration < 6.52 126 131216587Yield data per duration category. For a detailed description of the variables, referto Table A.1.97Table A.3: Summary statisticsVariable Mean Median Sd Min MaxA. Bond CharacteristicsYield (%) 6.13 6.44 1.67 0.29 19.23Yield spreads (bps) 126 106 86 5 1489Coupon (%) 7.23 7.2 1.33 2 11.13Time to maturity (years) 11.02 7.39 10.64 1 100.07Issue size (millions) 328 250 268 0.01 3250Credit rating A A- - BBB AAAZ-score 2.05 1.98 0.8 -0.1 7.16B. Firm CharacteristicsAsset Redeployability 0.32 0.34 0.09 0.09 0.58Asset size (log millions) 9.59 9.69 1.09 6.18 12.4Market leverage 0.23 0.24 0.14 0.01 0.68Long-term debt to asset 0.24 0.23 0.1 0.01 0.66Book-to-Market 0.46 0.36 0.37 0.01 5.04Tangibility 0.4 0.34 0.22 0.03 0.93ROA 0.16 0.15 0.06 -0.06 0.43Tobin Q 1.99 1.66 1.14 0.69 13.01Summary statistics. This table reports summary statistics for the benchmarksample. Panel A reports bond characteristics. Yield spreads are defined as thebond yield in excess a government bond with equal duration, coupon is theannualized coupon rate, Time to maturity is the difference between the matu-rity of the bond and the transaction date, the issue size is the total principalissued for a bond. Panel B reports firm characteristics, Asset redeployabilitycomputed as in Kim and Kung (2016), Asset size is defined as total assets inCompustat, Long-term debt to asset is obtained from Compustat, the Book-to-Market ratio is defined as the ratio of book equity to the market value ofequity. The variable units are detailed in the first column.98Table A.4: Asset redeployability by two-digit sicSIC AR Industry description10 0.233 Metal, Mining13 0.1346 Oil & Gas Extraction14 0.2898 Nonmetallic Minerals20 0.3378 Food & Kindred Products21 0.3751 Tobacco Products23 0.2756 Apparel & Other Textile Prod.25 0.3463 Furniture & Fixtures26 0.2735 Paper & Allied Products27 0.4297 Printing & Publishing28 0.3556 Chemical & Allied Products29 0.3188 Petroleum & Coal Products30 0.3526 Miscellaneous Plastics Prod.32 0.3697 Stone, Clay, & Glass Products33 0.3617 Primary Metal Industries34 0.3641 Fabricated Metal Products35 0.3637 Industrial Machinery & Equip.36 0.3551 Electronic & Other Electric Equip.37 0.3064 Transportation Equipment38 0.3262 Instruments & Related ProductsSIC AR Industry description39 0.3574 Miscellaneous Manufacturing Ind.40 0.1425 Railroad Transportation42 0.3717 Trucking & Warehousing45 0.2435 Transportation by Air48 0.3465 Communications50 0.4007 Wholesale Trade - Durable51 0.4063 Wholesale Trade - Nondurable52 0.3925 Building Materials & Gardening54 0.3925 Food Stores55 0.3925 Automative dealers & Serv. Stations56 0.3922 Apparel & Accessory Stores57 0.3925 Furniture & Homefurnishings Stores58 0.3694 Eating & Drinking Places59 0.392 Miscellaneous Retail72 0.4986 Personal Services73 0.3387 Business Services75 0.4296 Auto Repair, Services, & Parking78 0.4087 Motion Pictures80 0.1289 Health ServicesAsset redeployability by two-digit SIC. This table reports the average values of asset redeployabilityfor 2-digit SIC industry. Firm-year asset redeployability are calculated as the value-weighted average ofindustry-level redeployability indices as in Kim and Kung (2016).99Appendix BAppendix to Chapter 3B.1 Data appendixThe empirical section of this chapter is based on the Compustat/CRSP merged data file. To be consis-tent with existing literature the sample used considers information from the first quarter in 1984 untilthe last quarter in 2016 from WRDS. I keep U.S incorporated firms and discard financial (SIC codes6000-6999), utility (SIC codes 4800-4999), and quasi- government (SIC codes 9000-9999) firms. Ialso drop observations with missing or negative values of assets (atq), sales (saleq), and cash andshort term investment securities (cheq). Observations that with missing liabilities (ltq) and obser-vations where cash holdings are larger than assets are also eliminated. I discard firms that violate theaccounting identity by more than 10%. Observations where leverage ratio is larger than the unity areeliminated as well as observations of those firms that where recorded in the database less than oneyear. Firms must have at least 5 observations (5 quarters) to be included into the sample. Year-to-date variables of the sale and purchase of common and preferred stock, cash dividends, and capitalexpenditures on the company’s property, plant and equipment are converted into quarterly values.B.1.1 Variables descriptionI provide the definitions of the variables used in the analysis which are conducted from the Compus-tat/CRSP merged data file,− Book Assets : total assets (at)− Book Equity : common/ordinary equity (ceq)+ deferred tax and inv. tax credit (txditc)− purchase of common and preferred stock (pstk)− Total Debt : long-term debt (dltt)+ short-term debt (dlc)− Book Leverage : total debt / book assets (at)100− Average Book Assets : average of last-three years book assets− Debt Issuance : ∆ total debt / average book assets− Investment rate : capital expenditures (capex) / average book assetsB.1.2 Robustness testIn this section, I reproduce Table B.1 for multiple variations of the original database used in theempirical analysis in order to verify that the results are not driven a specific subsample of the data.As a robustness test, Table B.1 reproduces the main results of this chapter (presented in Table 3.1)including the observations from the first year a firm appears on the data base. This in order to verify ifthe results are robust to any IPO effect. As an additional robustness test, in Table B.2, I reproduce theanalysis of this chapter from a sample where I exclude small firms, i.e. firms with total assets lowerthan $10,000. Lastly, Table B.3 reproduces the main results of the chapter by redefining firms’ totalassets as the last-year total assets observed in the database. The main results of the chapter are robustto any of these tests.B.2 Numerical procedure appendixThis appendix provides details regarding the solution method used to solve the quantitative modelproposed in this chapter. Section B.2.1 describes the stationary version of the firm’s problem. SectionB.2.2 describes the Euler equations that characterized the optimal firm’s decisions. Section B.2.3describes the recursive equilibrium that characterizes the general equilibrium. Lastly, Section B.2.4describes details of the numerical solution method implemented.B.2.1 Shareholders’ stationary problemDefining the stationary variables: k̂ j,t+1 ≡ k j,t+1/ext , î j,t ≡ i j,t/ext−1 , and b̂ j,t+1 ≡ b j,t+1/ext ; the sta-tionary value function J(k j,t ,b j,t ,z j,t ,Γt)/ext−1 ≡ Ĵ(k̂ j,t , b̂ j,t ,z j,t ,Γt) can be written as,Ĵ(k̂ j,t , b̂ j,t ,z j,t ,Γt) = maxk̂ j,t+1,b̂ j,t+1{d̂ j,t +Et(Mt,t+1e∆xt Ĵ(k̂ j,t+1, b̂ j,t+1,z j,t+1,Γt+1))}(B.1)where the stationary functions used to solve the program are,d̂ j,t ≡ ê j,t −ψ1I{ê j,t<0}ê j,t ≡ (1− τ)Π̂ j,t − î j,t − Ω̂k(̂i j,t)− (λ + c(1− τ)) b̂ j,t + τδ k̂ j,t − Ω̂b(â j,t)+P(k̂ j,t+1, b̂ j,t+1,z j,t ,Γt)(b̂ j,t+1e∆xt − (1−λ )b̂ j,t)ŷ j,t ≡ e∆xt ez j,t k̂αj,t lα̂j,t − ŵt l j,t − f k̂ j,tî j,t ≡ k̂t+1e∆xt − (1−δ )kt101Note that the debt pricing function can also be normalized,b̂ j,t+1× P̂j,t = Et(Mt,t+1b̂ j,t+1(λ + c+(1−λ ) · P̂j,t+1)I{z j,t+1<z?j,t+1})+Et(Mt,t+1(1−χ)Ĵ(k̂ j,t+1,0,z j,t+1,Γt+1)I{z?j,t+1<z j,t+1<z0j,t+1}) (B.2)B.2.2 Derivation of first-order conditionsAssuming that the firm does not need to issue equity, i.e ψe × I{e j,t<0} = 0, the set of first orderconditions that determines the optimal firms’ decisions are,[b j,t+1] :∂Pj,t∂b j,t+1(b j,t+1− (1−λ )b j,t)+Pj,t +EtMt,t+1 z¯∫z?j,t+1∂J j,t+1∂b j,t+1dZ (z j,t+1|z j,t)= ∂Ωb(a j,t)∂a j,t[i j,t ] : −1− ∂Ωk(i j,t)∂ i j,t+ γ j,t = 0[k j,t+1] :∂Pj,t∂k j,t+1(b j,t+1− (1−λ )b j,t)− γ j,t +EtMt,t+1 z¯∫z?j,t+1∂J j,t+1∂k j,t+1dZ (z j,t+1|z j,t)= 0where γ j,t represents the Lagrange multiplier of the capital accumulation condition, z?j,t+1 denotes thedefault threshold (the lowest value of z j,t+1 at which it is optimal to keep operating the firm), andZ (·) represents the conditional density distribution of z j,t+1. The derivatives of the function J(·) canbe obtained by applying the envelope theorem multiple times,[b j,t ] :∂J j,t∂b j,t=−(λ + c(1− τ))−Pj,t(1−λ )+ ∂Ωb(a j,t)∂b j,t(1−λ )[k j,t ] :∂J j,t∂k j,t= (1− τ)∂y j,t∂k j,t+ τδ − ∂Ωk(i j,t)∂k j,t+(1−δ )γ j,t(B.3)Note that the derivative of the debt price function can also be obtained from equation,b j,t+1×P(k j,t+1,b j,t+1,z j,t ,Γt) = a︸︷︷︸aEt(Mt,t+1b j,t+1(λ + c+(1−λ ) ·P(k j,t+2,b j,t+2,z j,t+1,Γt+1))I{z?j,t+1<z j,t+1})+Et(Mt,t+1(1−χ)J(k j,t+1,0,z j,t+1,Γt+1)I{z0j,t+1<z j,t+1<z?j,t+1})Finally, by differentiating the debt pricing function with respect to each control variable, the102system of equations resulted from the first-order conditions is completely determined,[b j,t+1] : Pj,t +b j,t+1∂Pj,t∂b j,t+1= Et(Mt,t+1(1−χ)J(k j,t+1,0,z?j,t+1,Γt+1)[dZ (z?j,t+1|z j,t)∂ z?j,t+1∂b j,t+1])+Et(Mt,t+1b j,t+1(λ + c+(1−λ ) ·P(k j,t+2,b j,t+2,z?j,t+1,Γt+1))[−dZ (z?j,t+1|z j,t)∂ z?j,t+1∂b j,t+1])+Et(Mt,t+1(λ + c+(1−λ ) ·P(k j,t+2,b j,t+2,z j,t+1,Γt+1))I{z?j,t+1<z j,t+1})+Et(Mt,t+1b j,t+1(1−λ ) ·∇Pb j,t+1(k j,t+2,b j,t+2,z j,t+1,Γt+1)I{z?j,t+1<z j,t+1})[k j,t+1] : b j,t+1∂Pj,t∂k j,t+1= Et(Mt,t+1(1−χ)J(k j,t+1,0,z?j,t+1,Γt+1)[dZ (z?j,t+1|z j,t)∂ z?j,t+1∂k j,t+1])+Et(Mt,t+1b j,t+1(λ + c+(1−λ ) ·P(k j,t+2,b j,t+2,z?j,t+1,Γt+1))[−dZ (z?j,t+1|z j,t)∂ z?j,t+1∂k j,t+1])+Et(Mt,t+1b j,t+1(1−λ ) ·∇Pk j,t+1(k j,t+2,b j,t+2,z j,t+1,Γt+1)I{z?j,t+1<z j,t+1})where for any variable qt+1, the total derivative of the debt pricing function with respect to qt+1represents the expression,∇Pq j,t+1t+1 ≡∂Pj,t+1∂k j,t+2× ∂k j,t+2∂qt+1+∂Pj,t+1∂b j,t+2× ∂b j,t+2∂qt+1B.2.3 Recursive equilibriumThe recursive equilibrium consists of a set of value functions, prices, household’ and firms’ optimaldecisions, aggregate quantities and the law of motion of the economy’s aggregate state satisfying thefollowing set of conditions.Policy and Value Functions1. Firm j-th’s policy functions {k∗j,t+1, l∗j,t ,b∗j,t+1} maximize its value function J(k j,t ,b j,t ,z j,t ,Γt).2. Household’s optimal decisions C∗({msj,t},mbt ,Γt), N∗({msj,t},mbt ;Γt), ms∗({msj,t},mbt ,Γt), andmb∗({msj,t},mbt ,Γt) maximize H({msj,t},mbt ,Γt).3. ms∗j,t+1 ≡ ms∗(k j,t+1,b j,t+1,z j,t ,Γt) = µt+1(k j,t+1,b j,t+1z j,t ,Γt) ∀(k j,t+1,b j,t+1z j,t) ∈ S.Market Clearing Conditions1. Commodity market clearing, C(Γt) = Y (Γt)−Θ(Γt); where,(a) Y (Γt) =∫S e(1−α)xt ez j,t (k j,t)α(l∗j,t)1−α̂µt [d(k j,t ×b j,t × z j,t)].103(b) Θ(Γt) =∫S[f × k j,t + i∗j,t +Ωk(i∗j,t)+Ωb(a∗j,t)+ψeI{e j,t<0}]µt [d(k j,t ×b j,t × z j,t)].where i∗j,t ≡ k∗j,t+1− (1−δ )k j,t , and a∗j,t ≡ b∗j,t+1− (1−λ )b j,t .2. Labor market clearing, N∗(Γt) =∫S l∗(k j,t ,b j,t ,z j,t ,Γt) µt [d(k j,t ×b j,t × z j,t)].3. The bond market clearing condition, is satisfied by Walras’ Law and the assumption that therepresentative financial intermediary participates in a competitive market.1Model’s consistent dynamic1. Law of motion for aggregate state variables Γt = µt+1 is consistent with agents’ decisions.Formally, µt+1(K ,B,Z ) =∫(k j,t ,b j,t ,z j,t)∈S[∑z j,t+1∈Z Π(z)(z j,t ,z j,t+1)]µt [d(k j,t × b j,t × z j,t)]; forall (K ,B,Z )⊂S ≡ {(k j,t ,b j,t ,z j,t) | k′∗(k j,t ,b j,t ,z j,t ,Γt)∈K and b∗j,t+1(k j,t ,b j,t ,z j,t ,Γt)∈B}; and where Π(z) denotes the transition probability of z j,t .Aggregate Prices1. The stochastic discount factor satisfies, Mt,t+1 = β(H1−γt+1Et(H1−γt+1)) 1/ψ−γ1−γ (Ĉt+1Ĉt)− 1ψ ∂Ĉt+1/∂Ct+1∂Ĉt/∂Ct; whereHt+1 ≡ H(C(Γt+1),N(Γt+1)) and Ĉt+1 ≡ Ĉ(C(Γt+1),N(Γt+1)).2. The aggregate wage equals the household marginal rate of substitution between leisure andconsumption, i.e. wt(Γt) =−(∂Ĉt/∂Nt)(∂Ĉt/∂Ct)−1.B.2.4 Numerical solution detailsThe numerical dynamic programming approach considers the joint determination of (i) the stationaryequity value function (B.1), (ii) the stationary bond pricing function (B.2), and (iii) the functions foraggregate consumption and aggregate wages (aggregate beliefs) that firms use to solve their max-imization problem. I use an iterative procedure to jointly approximate these functions on discrete1Indeed, the assumption that the representative financial intermediary participates in a competitive market implies thefollowing zero-profit condition that is satisfied at each period,0≡ Pf (Γt)×mbt+1−∫Sb j,t+1(k j,t ,b j,t ,z j,t ,Γt)×P(k j,t+1,b j,t+1,z j,t ,Γt)µt(d(k j,t ×b j,t × z j,t))+∫S∗[b j,t(1−λ )×P(k j,t+1,b j,t+1,z j,t ,Γt)+b j,t(λ + c)]µt(d(k j,t ×b j,t × z j,t))+∫SD(1−χ)J(k j,t ,0,z j,t ,Γt)µt(d(k j,t ×b j,t × z j,t))−mbtwhere the space S represents the product space R+×R+×Z ; whereZ denotes the space of the idiosyncratic technologyshock zi, j. The space S∗ and SD denote the product space that includes solvent and defaulting firms, respectively. Formally,SD ≡= S−S∗ = S∩ (S∗)′.104grids. Throughout the procedure, I create grids for the variables representing shocks and the endoge-nous state variables such as capital, and debt outstanding.For the aggregate shocks, (∆xt ,st), I use a Rouwenhorst (1995) procedure to discretize the firm-level technology shocks. The aggregate Markov chain considers five states for ∆xt and five states forst . Whereas the idiosyncratic technology shock is approximated with 19 points in the grid. I creategrids for capital and the debt face value outstanding, with 50 and 30 points respectively. The choicefor next-period control variables is based on a dynamic searching over the original grids. Specifically,in each iteration of the value function procedure, I zoom in multiple times around local optimal valuesof capital and debt. This methodology allows the code to spend most of the processing time in a gridaround the optimal value.The procedure to find the maximum equity value function takes as given the stochastic discountfactor, the debt pricing function as well as aggregate beliefs. After the equity value function con-verges, I solve for the bond pricing function using a value function iteration procedure that takes theequity value function as given. Having the firms’ decisions determined, firms’ beliefs about aggre-gate variables (e.g. aggregate consumption and wage) are updated using the model’s simulations.These beliefs are used by firms to compute the stochastic discount factor used to solve their maxi-mization problem. Importantly, in this procedure instead of assuming specific functional forms forthese beliefs, I follow a non-parametric approach where beliefs are estimated for each element ofthe aggregate state space. Finally, I use the change of the estimation of these beliefs as a metric todetermine the convergence of the entire numerical solution.105Table B.1: Moments and statistics of the cross-sectional distribution of debt issuance and in-vestment rate (excluding small firms)Panel A debt issuance investment ratemoments of firm-level distr.: average ρ(·,hp-Y) average ρ(·,hp-Y)mean 0.004 0.54 ∗∗ 0.017 0.63 ∗∗∗fraction of firms with (−) spikes 0.058 −0.42 ∗∗ 0.001 0.02fraction of firms with (+) spikes 0.079 0.61 ∗∗∗ 0.051 0.59 ∗∗∗standard deviation 0.059 0.48 ∗∗ 0.021 0.56 ∗∗Panel B ρ(·,C-S st.dev.) ρ(·,C-S st.dev.)fraction of firms with (−) spikes −0.31 ∗∗ 0.03fraction of firms with (+) spikes 0.86 ∗∗∗ 0.95 ∗∗∗Panel C average ρ(·,C-S st.dev.) ρ(·,C-S st.dev.)fraction of firms with:(+) debt issuance spikes 0.079 0.86 ∗∗∗ 0.73 ∗∗∗(+) investment spikes 0.051 0.68 ∗∗∗ 0.95 ∗∗∗(+) debt issuance spikes,and no-(+) investment spikes 0.064 0.81 ∗∗∗ 0.61 ∗∗∗no-(+) debt issuance spikes,and (+) investment spikes 0.036 0.56 ∗∗ 0.89 ∗∗∗(+) debt issuance spikes,and (+) investment spikes 0.014 0.77 ∗∗∗ 0.89 ∗∗∗Moments and statistics of the cross-sectional distribution of debt issuance and investment rate (excludingsmall firms). This table shows some empirical facts about the business dynamic of the cross-sectional distributionof debt issuance and investment rates when firms with total asset lower than $10,000 are excluded from thesample. Refer to Table 3.1 for details about variables’ definitions.106Table B.2: Moments and statistics of the cross-sectional distribution of debt issuance and in-vestment ratio (ipo firms)Panel A debt issuance investment ratemoments of firm-level distr.: average ρ(·,hp-Y) average ρ(·,hp-Y)mean 0.003 0.59 ∗∗∗ 0.017 0.63 ∗∗∗fraction of firms with (−) spikes 0.062 −0.46 ∗∗ 0.001 0.02fraction of firms with (+) spikes 0.078 0.63 ∗∗∗ 0.046 0.61 ∗∗∗standard deviation 0.062 0.48 ∗∗ 0.022 0.56 ∗∗Panel B ρ(·,C-S st.dev.) ρ(·,C-S st.dev.)fraction of firms with (−) spikes −0.21 ∗ 0.03fraction of firms with (+) spikes 0.86 ∗∗∗ 0.95 ∗∗∗Panel C average ρ(·,C-S st.dev.) ρ(·,C-S st.dev.)fraction of firms with:(+) debt issuance spikes 0.078 0.83 ∗∗∗ 0.71 ∗∗∗(+) investment spikes 0.046 0.65 ∗∗∗ 0.95 ∗∗∗(+) debt issuance spikes,and no-(+) investment spikes 0.061 0.79 ∗∗∗ 0.58 ∗∗∗no-(+) debt issuance spikes,and (+) investment spikes 0.033 0.52 ∗∗ 0.87 ∗∗∗(+) debt issuance spikes,and (+) investment spikes 0.013 0.75 ∗∗∗ 0.89 ∗∗∗Moments and statistics of the cross-sectional distribution of debt issuance and investment rate (IPOfirms). This table shows some empirical facts about the business dynamic of the cross-sectional distribu-tion of debt issuance and investment rates when the first year from each firm’s time series is included inthe sample. Refer to Table 3.1 for details about variables’ definitions.107Table B.3: Moments and statistics of the cross-sectional distribution of debt issuance and in-vestment ratio (total assets redefined)Panel A debt issuance investment ratemoments of firm-level distr.: average ρ(·,hp-Y) average ρ(·,hp-Y)mean 0.004 0.56 ∗∗ 0.016 0.64 ∗∗∗fraction of firms with (−) spikes 0.076 −0.54 ∗∗ 0.001 0.02fraction of firms with (+) spikes 0.105 0.52 ∗∗ 0.059 0.61 ∗∗∗standard deviation 0.059 0.31 ∗∗ 0.021 0.58 ∗∗∗Panel B ρ(·,C-S st.dev.) ρ(·,C-S st.dev.)fraction of firms with (−) spikes −0.32 ∗∗ 0.03fraction of firms with (+) spikes 0.81 ∗∗∗ 0.97 ∗∗∗Panel C average ρ(·,C-S st.dev.) ρ(·,C-S st.dev.)fraction of firms with:(+) debt issuance spikes 0.105 0.81 ∗∗∗ 0.73 ∗∗∗(+) investment spikes 0.059 0.59 ∗∗∗ 0.97 ∗∗∗(+) debt issuance spikes,and no-(+) investment spikes 0.088 0.81 ∗∗∗ 0.66 ∗∗∗no-(+) debt issuance spikes,and (+) investment spikes 0.042 0.47 ∗∗ 0.93 ∗∗∗(+) debt issuance spikes,and (+) investment spikes 0.017 0.71 ∗∗∗ 0.87 ∗∗∗Moments and statistics of the cross-sectional distribution of debt issuance and investment rate (totalassets redefined). This table shows some empirical facts about the business dynamic of the cross-sectionaldistribution of debt issuance and investment rates for the case where total assets are computed as last-yearassets. Refer to Table 3.1 for details about variables’ definitions.108

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