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Three essays in Macro Finance Corhay, Alexandre 2016

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Three Essays in Macro FinancebyAlexandre CorhayB.BEng., University of Lie`ge, 2008M.Sc., HEC Montre´al, 2010a 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)July 2016c© Alexandre Corhay, 2016AbstractThe present thesis is a collection of three essays in Macro Finance. The first essay examinesthe effects of industry competition on the cross-section of credit spreads and levered equityreturns. I build a quantitative model where firms make investment, financing, and defaultdecisions subject to aggregate and firm-specific risk. Firms operate in heterogeneous indus-tries that differ by the intensity of product market competition. Higher competition reducesprofit margins and increases default risk for debtholders. Equityholders are protected againstdefault risk due to the option value arising from limited liability. In equilibrium, competitiveindustries are characterized by higher credit spreads, but lower expected equity returns. Ifind strong empirical support for these predictions across concentration quintiles. Moreover,the calibrated model generates cross-sectional variation in leverage and valuation ratios inline with the data.The second essay provides new evidence that imperfect competition is an important chan-nel for time varying risk premia in asset markets. To this end, we build a general equilibriummodel with monopolistic competition and endogenous firm entry and exit. Endogenous varia-tion in industry concentration generates countercyclical markups, which amplifies macroeco-nomic risk. The nonlinear relation between the measure of firms and markups endogenouslygenerates countercyclical macroeconomic volatility. With recursive preferences, the volatilitydynamics lead to countercyclical risk premia forecastable with measures of competition. Also,the model produces a U-shaped term structure of equity returns.The final essay explores the interactions between yield curve dynamics and nominal gov-ernment debt maturity operations in a New Keynesian model with endogenous bond riskpremia. Violations of debt maturity neutrality occur when the yield curve slope is nonzero ina fiscally-led policy regime. When the risk profiles of government liabilities differ, rebalancingthe maturity structure changes the government cost of capital. In the fiscal theory, changes indiscount rates affect inflation through the intertemporal government budget equation. Whenthe yield curve is upward-sloping (downward-sloping), the fiscal discount rate channel impliesthat shortening the maturity structure has contractionary (expansionary) effects.iiPrefaceThe 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)and Lukas Schmid (Duke University). The essay in chapter 4 is based on unpublished researchwith Howard Kung and Gonzalo Morales (University of Alberta). In each of the co-authoredprojects, all authors worked on all aspects of the paper. This includes the identification ofthe research question, the theoretical analysis, the numerical implementation, the empiricalwork, and the writing of the manuscript. While hard to quantify exactly, my personal shareof contribution to chapters 3 and 4 amounts to about 1/3.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Industry Competition, Credit Spreads, and Levered Equity Returns . . . 22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 A simple model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.1 Economic environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 Individual firm’s problem . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.4 Competition, corporate policies and asset prices . . . . . . . . . . . . . 92.2.5 Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Benchmark model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.1 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.2 Industries dynamics and competition . . . . . . . . . . . . . . . . . . . . 162.3.3 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3.4 Equilibrium and aggregation . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Model parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.1 Functional forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 Quantitative results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21iv2.5.1 Aggregate moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5.2 Industry moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5.3 Decomposing the concentration premium . . . . . . . . . . . . . . . . . 242.5.4 Idiosyncratic risk and corporate spreads . . . . . . . . . . . . . . . . . . 252.6 Panel regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.6.1 Bond sample construction . . . . . . . . . . . . . . . . . . . . . . . . . . 262.6.2 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.6.3 Concentration and the cross section of corporate yield spreads . . . . . 282.6.4 Competition, firm volatility and yield spreads . . . . . . . . . . . . . . . 312.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Competition, Markups, and Predictable Returns . . . . . . . . . . . . . . . 473.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1.1 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.1 Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.2.2 Production sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.2.3 Entry & exit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.2.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3 Economic mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.3.1 Product innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.3.2 Process innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.4 Quantitative implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.4.1 Quantitative results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.4.2 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 Government Maturity Structure Twists . . . . . . . . . . . . . . . . . . . . 874.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.1.1 Related literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.2 Simple model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.2.1 Government budget equation . . . . . . . . . . . . . . . . . . . . . . . . 914.2.2 Monetary/fiscal policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.2.3 Stochastic discount factor . . . . . . . . . . . . . . . . . . . . . . . . . . 924.2.4 Fiscal discount rate channel . . . . . . . . . . . . . . . . . . . . . . . . . 934.3 Benchmark model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.3.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.4.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100v4.4.2 Yield curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.4.3 Maturity structure shocks . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.4.4 Macroeconomic fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . 1044.4.5 Market timing policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.4.6 Policy experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122A Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136A.1 A simple model: derivation details . . . . . . . . . . . . . . . . . . . . . . . . . 136A.1.1 Firm’s problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136A.1.2 Proof of proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137A.1.3 Conditional equity beta . . . . . . . . . . . . . . . . . . . . . . . . . . . 138A.2 Shareholders’ optimization problem . . . . . . . . . . . . . . . . . . . . . . . . . 139A.3 Derivation of inverse demand schedule . . . . . . . . . . . . . . . . . . . . . . . 141B Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142B.1 Data sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142B.1.1 Markup measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143B.2 Derivation of demand schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . 144B.2.1 Individual firm problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 146B.2.2 Capital producer problem . . . . . . . . . . . . . . . . . . . . . . . . . . 148C Appendix to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150C.1 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150C.2 Numerical procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151C.3 Present value relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153C.4 Simple model: approximate analytical solution . . . . . . . . . . . . . . . . . . 154C.5 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156viList of TablesTable 2.1 Quarterly calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Table 2.2 Simulated methods of moments estimates . . . . . . . . . . . . . . . . . . . . 34Table 2.3 Aggregate business cycle and asset pricing moments . . . . . . . . . . . . . . 34Table 2.4 Aggregate financing moments . . . . . . . . . . . . . . . . . . . . . . . . . . 35Table 2.5 Industry variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Table 2.6 Yield data per rating category . . . . . . . . . . . . . . . . . . . . . . . . . . 36Table 2.7 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Table 2.8 List of industries by concentration . . . . . . . . . . . . . . . . . . . . . . . . 37Table 2.9 Univariate analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Table 2.10 Competition and the cross-section of yield spreads . . . . . . . . . . . . . . 38Table 2.11 Firm-risk, competition and the cross-section of yield spreads . . . . . . . . . 39Table 2.12 Competition and the cross-section of yield spreads . . . . . . . . . . . . . . 40Table 2.13 Firm volatility, competition and the cross-section of yield spreads . . . . . . 41Table 3.1 Quarterly calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 3.2 Industry moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 3.3 Forecasts with growth of new incorporations . . . . . . . . . . . . . . . . . . 73Table 3.4 Business cycle moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 3.5 Industry cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table 3.6 Summary statistics sorted on markups . . . . . . . . . . . . . . . . . . . . . 75Table 3.7 Asset pricing moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Table 3.8 Stock return predictability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 3.9 Stock return predictability in the long sample . . . . . . . . . . . . . . . . . 77Table 3.10 Asset pricing moments: exogenous markups . . . . . . . . . . . . . . . . . . 78Table 3.11 Stock return predictability: exogenous markups . . . . . . . . . . . . . . . . 79Table 3.12 Asset pricing moments: wage markup . . . . . . . . . . . . . . . . . . . . . . 80Table 3.13 Stock return predictability: wage markup . . . . . . . . . . . . . . . . . . . . 80Table 4.1 Quarterly calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Table 4.2 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Table 4.3 Term structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111viiTable 4.4 Forecasts with the yield spread . . . . . . . . . . . . . . . . . . . . . . . . . 112viiiList of FiguresFigure 2.1 Economic environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 2.2 Aggregate impulse-response functions . . . . . . . . . . . . . . . . . . . . . 43Figure 2.3 Industries impulse-response functions . . . . . . . . . . . . . . . . . . . . . 44Figure 2.4 Idiosyncratic risk shock and industry credit spreads . . . . . . . . . . . . . 45Figure 2.5 Time-series of Baa spread from NAIC sample and Moody’s . . . . . . . . . 46Figure 3.1 Markup and number of firms . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 3.2 Impulse-response functions - productivity shock . . . . . . . . . . . . . . . . 81Figure 3.3 Impulse-response functions - productivity shock (cont.) . . . . . . . . . . . 82Figure 3.4 Business cycles asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 3.5 Business cycles and number of firms . . . . . . . . . . . . . . . . . . . . . . 84Figure 3.6 Comparative statics: industry competition . . . . . . . . . . . . . . . . . . . 85Figure 3.7 Term structure of dividend strips . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 3.8 Business cycles and volatility . . . . . . . . . . . . . . . . . . . . . . . . . . 86Figure 4.1 Average maturity of public debt . . . . . . . . . . . . . . . . . . . . . . . . 113Figure 4.2 Comparative statics: shortening maturity . . . . . . . . . . . . . . . . . . . 113Figure 4.3 Comparative statics: defaultable debt . . . . . . . . . . . . . . . . . . . . . 114Figure 4.4 Maturity restructuring with different slopes . . . . . . . . . . . . . . . . . . 114Figure 4.5 Maturity restructuring in different regimes . . . . . . . . . . . . . . . . . . 115Figure 4.6 Surplus shocks in different regimes . . . . . . . . . . . . . . . . . . . . . . . 115Figure 4.7 Lengthening maturity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 4.8 Market timing policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 4.9 Maturity restructuring at the ZLB . . . . . . . . . . . . . . . . . . . . . . . 117Figure 4.10 Maturity restructuring with market segmentation . . . . . . . . . . . . . . . 117Figure 4.11 Maturity restructuring with persistent deficits . . . . . . . . . . . . . . . . . 118Figure 4.12 Policy experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118ixAcknowledgmentsI would like to express my special gratitude and thanks my thesis advisors, Adlai Fisher andHoward Kung for their invaluable guidance throughout my graduate studies. Your advices,both on my research and my career, have been most useful to help me grow as a researcher.I am also grateful to Jack Favilukis for accepting to join my committee and providing manyconstructive suggestions. Besides my committee, I would also like to thank the rest of theUBC Finance faculty, and Lukas Schmid for their insightful comments as well as for the toughquestions that forced me to sharpen my economic intuition.I am grateful for all my fellow classmates and friends at UBC for all the fun and stimulatingdiscussions. Tzu-Ting Yang and Francis Michaud, I would never forget those nights spent onsolving and discussing economic models in front of a white board in St John’s College. Youhave been true companions through hardship.None of this would have been possible without the unconditional love and sacrifice of myfamily. Many thanks to my parents, and siblings for your relentless support through prayersand kind words. You are always there for me. I am also grateful to my parents in-law, Lyriaand Michel for believing in me and taking care of the family during my travels. My deepestthanks go to my loving, and supportive wife Laetitia. Your help taking care of our baby sonCharles was priceless, and for this I couldn’t be more thankful. I dedicate this thesis to bothof you.Finally, I would like to acknowledge the financial support provided by UBC and the SocialSciences and Humanities Research Council of Canada that funded parts of the research inthis thesis.To Laetitia and CharlesxChapter 1IntroductionThis thesis is a collection of three essays at the intersection of Finance and Macroeconomics.Although the topics are diverse, they share the common objective of studying the interplaybetween asset prices and macroeconomic fluctuations through the lens of dynamic stochasticequilibrium models. In the first essay, I examine the effects of industry competition on thecross-section of asset prices. To study this question, I build and estimate a structural modelwhere firms make optimal production and financing decisions under different competitiveenvironments. In the second essay, I investigate the effects of firm entry dynamics on stockreturn predictability and business cycle fluctuations. I build and calibrate an endogenousgrowth model where firms’ entry and exits generate time-varying competition. The third essaydocuments a novel transmission channel for open market operations targeting the averagematurity of government debt. The quantitative importance of this new mechanism is examinedthrough the lens of a calibrated New Keynesian model.Because each essay investigates a different topic, chapters were designed to be self-contained.I thus leave a more exhaustive discussion of the research question and contribution to the in-troduction specific to each chapter.1Chapter 2Industry Competition, CreditSpreads, and Levered EquityReturns2.1 IntroductionCompanies generate revenues by competing in product markets. While some firms enjoymonopoly power over the sale of their products, others face fierce competition. The intensityof competition, by affecting a firm’s profit opportunities, influences both corporate decisionsand asset prices. Recently, a growing number of studies have examined the relationshipbetween product market structure and asset prices. Yet, the existing theoretical literaturehas largely focused on linking competition to the unlevered equity risk. Also in the data, theeffect of competition on equity returns is still debated, while its impact on credit spreads islimited.1 The goal of this essay is to examine how industry competition jointly affects creditspreads and levered equity returns, and to assess the importance of these channels using aquantitative model.To analyze these issues, I develop a production based asset pricing model that capturesthe rich interaction between a firm’s competitive environment, optimal capital structure,default, and asset prices. The economy is populated by a large number of firms that operatein industries that differ in their degree of product market competition. They hire labor,accumulate capital, and compete with industry rivals in a Cournot-Nash framework. Everyperiod, each firm chooses the optimal capital structure mix by weighting the tax benefitsof debt against the costs arising from default. Industry and macroeconomic quantities areobtained by aggregating individual firm decisions. Asset prices are determined in equilibriumby a representative household assumed to have recursive preferences.1A rare exception is the recent empirical work of Valta (2012) who finds a positive relationship betweencompetition and interests charged on bank loans.2I find that industry competition increases equilibrium credit spreads and credit risk premiabut decreases equity risk. To understand the economic intuition behind this result, note thatin the model, industry competition affects asset prices in several ways. First, competitionreduces the firm’s exposure to aggregate risk. The intuition is as follows. Because competitivefirms face a more elastic demand curve, they increase current and future production morewhen productivity rises. At the industry level, the firm’s rivals also increase production, sothat total industry output increases. This leads to an increase in competition and puts adownward pressure on the firm revenues. Therefore in competitive industries, rivals’ actionscreate a procyclical negative externality that acts as a hedge against aggregate shocks. Thiscompetitive externality channel tend to reduce the risk of firms (both levered and unleveredfirms alike).Second, competition decreases the value of the firm by reducing the level of operating cashflows.2 In the model, shareholders declare bankruptcy as soon as equity becomes negative.Since competitive firms are on average less valuable, they are more likely to default. Inaddition, default is more likely to happen in recessions when firm continuation values are low.Taken together, the increased likelihood of default at times when recovery rates are low andthe price of risk is high makes corporate bonds issued by competitive firms less desirable toinvestors. Competition thus increases equilibrium credit spreads. On the other side, equityholders in competitive industries own a more valuable option to default because the limitedliability acts as an insurance against bad states of the world.3 This reduces the risk of equity.In short, the default option channel of competition increases credit spreads, but decreasesequity risk.Third, competition decreases the use of financial leverage. The intuition is readily un-derstood. Debt financing is relatively more expensive in competitive industries, thereforecompetitive firms use more equity. The lower quantity of debt mitigates the effect of competi-tion on credit spreads. However, I find that the reduction in leverage is not sufficient to makecredit spreads lower in competitive industries. This happens because the cost of default, i.e.the value lost in bankruptcy, in endogenously lower for competitive firms (these firms are lessvaluable). In the end, competitive firms issue less, but more expensive debt. The effect ofcompetition on leverage also affects equity risk. In particular, since less competitive firms usemore financial leverage, their equity risk gets higher. Consequently, the leverage channel ofcompetition leads to a further increase in equity risk in concentrated industries.To assess the quantitative importance of these channels, I calibrate the model to match abroad set of aggregate and industry moments. In the model, the only cross-sectional differenceacross industries is a parameter driving industry concentration. I estimate these to match2This holds for both equity and the unlevered firm value. In addition, although the reduction in risk tendsto increase firm valuation through a discount rate channel, I find that the cash-flow channel dominates so thatcompetition decreases the firm value. This result is consistent with empirical evidence.3This result comes from the fact that competitive firms are relatively more exposed to idiosyncratic risk,which makes default non-risky. If default was triggered by higher exposure to aggregate risk, a higher likelihoodof default risk could potentially increase shareholders’ risk.3a measure of market power obtained from industries sorted on concentration. Therefore, allremaining cross-sectional differences entirely stem from differences in industry competition.I find that competition has significant effects on corporate decisions and asset prices. In themodel, the difference in credit spreads between the high- and low-competition quintile is large,around 57bps. I test this prediction in the data using a panel of publicly traded corporatebond transactions and find strong empirical evidence. Firms in competitive industries pay25bps more on their debt.4 These results are statistically significant and are robust to variousmeasures of competition and controls. In economic terms, this represents $1.4M of additionalannual interest payments for firms in more competitive environment.5 These estimates areconsistent with Valta (2012) who finds that competitive firms pay higher interests on bankloans. The higher cost of debt leads competitive industries to use less financial leverage. Inthe model the difference in market leverage between the high- and low-competition quintileis -2.3%. These results accord with MacKay and Phillips (2005) who find that the averagebook leverage in more competitive industries is lower than in concentrated industries. Morerecently, Xu (2012) reaches similar conclusions using import penetration as an instrumentalvariables for competition. I further confirm these findings using summary statistics from mydata sample. In short, the model prediction that competition leads firms to use less, but moreexpensive debt is strongly supported in the data, both qualitatively and quantitatively.The model also provides quantitative predictions for the effects of competition on thecross-section of stock returns. I find that firms in the lowest competition quintile have a lowerequity premium (-0.76%). Also, firms in more competitive industries have lower CAPM beta(-0.14). These predictions are consistent with recent empirical evidence by Bustamante andDonangelo (2015) who find a positive relationship between excess stock returns, CAPM betasand industry concentration.6 The concentration premium arises because competition affectsthe firm’s exposure to industry rivals, the value of the option to default and the incentive touse leverage. Decomposing the concentration premium, I find that about 20% comes fromthe competitive externality effect, and 80% from the default and leverage channels. Thishighlights the importance of accounting for leverage and default in explaining the interac-tion between equity returns and industry competition. In contrast to equity risk, the modelpredicts that debt is riskier in competitive industries.7 The reason for this result is that al-though competitive firms have lower cash-flow risk, they default more. Since default occurs attimes when the price of risk is high, this effect ultimately dominates and debt in competitive4This estimate might seem low compared to the model predictions. However, as discussed later, dataestimates are likely to be a lower bound measure of the effect of competition on credit spreads because mysample is biased towards the largest firms in the population.5These values are obtained assuming a debt face value of $541M (the average face value in the sample).6In contrast, Hou and Robinson (2006) find that competition increases expected returns using the populationof firms in Compustat. A likely reason for this difference is that concentration measures based on public firmsare biased because the decision of firms to be publicly listed is affected by the structure of the industry (e.g.Bustamante and Donangelo (2015)).7The credit spread premium for competitive firms is higher by a factor of 1.2. Formally, the credit spreadspremium is defined as the difference between the yield on a risky bond minus the yield of riskless security thatpays the expected bond payoff.4industries is riskier.The previous results have highlighted the importance of idiosyncratic cash-flow shocks indriving cross-sectional differences in credit spreads across competition quintiles. I extend thebenchmark model with time-varying volatility for idiosyncratic shocks and find that creditspreads in competitive industries are more sensitive to change in idiosyncratic volatility. Tounderstand the intuition, it is useful to remember that corporate debt can be modeled asa default-free bond minus a put option on the firm assets (e.g. Merton (1974)). Toughercompetition, by reducing the firm value, brings the firm closer to default, i.e. the strike price.The sensitivity of the put option to change in volatility is thus amplified for more competitivefirms. I confirm this prediction in the data. Using a moving standard deviation of abnormalreturns as proxy for idiosyncratic volatility, I find that a 1% increase in idiosyncratic volatilityis associated to an additional 21bps increase in credit spreads in competitive industries. Interms of portfolio performance, a corporate bond portfolio of debt issued by competitive firmsloose an additional 1.49% return for each 1% increase in idiosyncratic volatility. These resultsare robust to different measures of competition and various controls, including firm fixedeffects.82.1.1 Literature reviewThe present essay contributes to the literature that links product market competition tofirm risk and stock returns. Early empirical work by Hou and Robinson (2006) finds thatcompetition increases expected stock returns using Compustat-based measures. Bustamanteand Donangelo (2015) reach opposite conclusions, using broader measures of concentrationthat include private firms. The later explain this discrepancy by noting that the decisionto be publicly listed depends on industry characteristics, which can bias concentration mea-sures. Aguerrevere (2009) examines how competition affects equity risk in a simultaneous-move oligopoly. Bena and Garlappi (2011), and Carlson, Dockner, Fisher, and Giammarino(2014) considers risk dynamics in a leader-follower equilibrium. Bustamante and Donangelo(2015), and Loualiche (2014) studies the effects of entry on the cross-section of stock returns.Corhay, Kung, and Schmid (2015) links competition to time-varying risk premia and returnpredictability. My work fills an important gap in this literature by analyzing how productmarket structure jointly affects the pricing and risk of corporate debt and levered equity.9The literature in corporate finance and IO examining the interactions between capitalstructure and product markets is vast. While most prior studies have focused on the impact ofcapital structure on firm strategies in product markets,10 a growing research (e.g. MacKay andPhillips (2005)) has highlighted the importance of industry competition on capital structure.8These calculations are obtained by computing the realized return on a bond whose characteristics are setto the sample average and assuming a 1% increase in idiosyncratic volatility.9Other related papers include Garlappi (2004), Hackbarth and Morellec (2008), Hoberg and Phillips (2010),Ortiz-Molina and Phillips (2014), Bustamante (2015).10Some examples are Brander and Lewis (1986), Bolton and Scharfstein (1990), Chevalier (1995), Phillips(1995), Lambrecht (2001), and Campello (2003).5Xu (2012) shows empirically that higher industry competition decreases the use of leverage.Valta (2012) shows that more competitive firm face a higher cost of bank loans. This essaycontributes by investigating the effects of industry competition on the quantity and pricing ofdebt in a joint framework. In addition, the quantitative model provides structural evidencethat differences in industry concentration have first order effects on corporate policies andasset prices.11My work also builds on the literature in economics and finance embedding dynamic capitalstructure decision12 into equilibrium asset pricing models. Hackbarth, Miao, and Morellec(2006) highlights the importance of macroeconomic conditions for firm financing conditionsand credit spreads in a risk-neutral framework. Building on their work, several papers havetried to rationalize the credit spread puzzle by generating variation in the market price of riskover the business cycle. Chen, Collin-Dufresne, and Goldstein (2009) accomplishes this usingthe habits formation model of Campbell and Cochrane (1999), while Bhamra, Kuehn, andStrebulaev (2009) adopts the long-run risks framework of Bansal and Yaron (2004). Chen(2010) shows how countercyclical variations in default losses helps generating a significantbond risk premia.13 In these papers, the state-price density or endowment process is assumedto be exogenous.In a recent paper, Gilchrist and Zakrajˇsek (2011) show that corporate bond risk premiacontains important information about the business cycles. Motivated by these findings, agrowing body of literature now attempts to connect corporate bond risk premium to theeconomy. This is especially important as most of the production-based asset pricing litera-ture has focused on linking the macroeconomy to equity risk premia.14 Recent contributionsinclude Gomes, Jermann, and Schmid (2013) who incorporate long-term nominal debt into astandard DSGE model to quantify the importance of nominal rigidity through a debt deflationchannel. Miao and Wang (2010) adopts a similar setup and shows how long-term debt am-plifies business cycle fluctuations. Several other papers have proved successful at generatingsignificant credit risk premium in production models: Gourio (2013) uses disaster risk, Gomesand Schmid (2010) model heterogeneous firms, and Favilukis, Lin, and Zhao (2013) highlightsthe importance of labor frictions. My work contributes to this literature by departing fromthe assumption of perfect competition and by examining how the product market structureaffects credit spreads in the cross-section.1511Also related is Miao (2005) that investigates the interaction between industry dynamics and capital struc-ture in a model with entry and exits. Other papers examine the effect of competition on other corporatedecision such as investment (e.g. Simintzi (2013), and Fre´sard and Valta (2014)).12See Strebulaev and Whited (2011) for a recent literature review.13Other related studies include Almeida and Philippon (2007), Davydenko and Strebulaev (2007), Elkamhi,Ericsson, and Jiang (2011).14Some examples are Jermann (1998), Boldrin, Christiano, and Fisher (2001), Kaltenbrunner and Lochstoer(2010), Kung and Schmid (2015)15More broadly, the essay also relates to the macroeconomic literature studying the effects of financialconstraints in quantitative general equilibrium business cycle models. Early examples in the literature areKiyotaki and Moore (1997) and Bernanke, Gertler, and Gilchrist (1999). More recent work includes Christiano,Motto, and Rostagno (2010) and Jermann and Quadrini (2012).6Finally, this essay relates to studies linking equity volatility to corporate credit spreads,e.g. Campbell and Taksler (2003). A series of recent paper documents the tight connectionbetween competition and idiosyncratic volatility (e.g. Gaspar and Massa (2006) and Irvineand Pontiff (2009)). In this essay, I contribute to the literature by showing, both theoreticallyand empirically, how competition can amplify credit spread’s exposure to idiosyncratic risk.Importantly, I also document that the increased exposure to idiosyncratic volatility translatesinto lower equity risk premium for competitive industries.The chapter is organized as follows. Section 2 develops a simple two-period model whereI derive closed form solution on the effects of competition on asset prices. Section 3 extendsthe simple model into a quantitative model. In section 4, I discuss the baseline calibration.Section 5 investigates some of the model’s quantitative implications for the cross-section ofasset prices. Section 6 presents several empirical tests and is followed by a few concludingremarks in section 7.2.2 A simple modelThis section develops a simple, two-period model to highlight some of the key economicchannels through which competition affects the pricing of equity and debt. These ingredientsare then incorporated in a more quantitative setting in the next section.2.2.1 Economic environmentConsider an oligopolistic industry that is populated by n value-maximizing firms. Thesefirms strategically compete in the product markets in a Cournot-Nash setup as in Aguerrevere(2009). In particular, it is assumed that firms play a static Cournot game in each period. Theychoose the quantity of output to maximize the value of the firm, taking production decisionsof other firms as given. For simplicity, I assume the existence of a risk-neutral representativeinvestor whose time discount factor β is used to price all securities. The timeline of eventsis as follows. In period 0, the firm hires labor after observing the realization of an aggregatetechnology shock. The firm finances itself by issuing one-period debt and equity. In period 1,the firm makes optimal production decisions after which it is hit by an idiosyncratic shock.Shareholders then have the option to declare bankruptcy. If no default occurs, the firm paysits debt obligations, and distribute all residual claim as dividend. The firm then disappearsfrom the economy.To be more specific, each firm in the industry produces an identical good yi,t. The totaldemand for the industry is given by the following downward-sloping demand curve,Yt = P−νt Yt (2.1)where ν is the elasticity of demand for the industry good, Pt is the equilibrium industry goodprice, Yt =∑ni=1 yi is the total industry output, and Yt is an aggregate demand term, taken7as given by the firm.16The firm produces output using labor lt that is rented in competitive markets at a wagerate of Wt. The production technology is assumed to be linear in labor,yt = A lt (2.2)where A is a persistent (i.e. lasts two periods) technology shock capturing all systematic riskin the economy.In period 0, the firm decides on its optimal capital structure by issuing one-period default-able debt b and equity (negative dividends). Debt is attractive because of the tax deductibilityof interest rates but is costly because default entails dead-weight costs. In particular, whenthe value of the firm becomes negative, shareholders walks away with a payoff of zero, anddebtholders get nothing. Denoting the unit price of debt by q, the value of corporate debt toinvestors is,q = βΦ(z?)(1 + C) (2.3)where Φ(z?) is the probability of survival of the firm (to be determined later), and C is thecoupon payment. Essentially, Eq. 2.3 says that the value of debt today is the expected payoff,discounted by the state-price density, β.2.2.2 Individual firm’s problemThe objective of the firm is to maximize the market value to shareholders Vj , by choosinglabor, and the optimal capital structure:Vj = maxl0,l1,i,bd0 + βE0[max {d1, 0}] (2.4)subject to the total demand for the industry good (Eq. 2.1), the market value of corporatedebt (Eq. 2.3), and production decisions of other firms. Note that the second max operatorcaptures the limited liability option of shareholders. The firm dividends are defined as thefree cash-flows generated by the firm. Because of the finite nature of the firm, there will beno debt issuance in period 1. The real dividend in each period is given by,17d0 = P0y0 −W0l0 + qb (2.5)d1 = P1y1 −W1l1 − z l¯ − (1 + C(1− τ))b1 (2.6)where (1− τ) captures the tax advantage of interest payments, and z is a mean-zero, idiosyn-cratic shock assumed to be uniformly distributed on [−a/2, a/2]. The idiosyncratic shock z16To facilitate the exposition, the i-subscript is dropped, unless it is necessary to avoid confusion.17All nominal variables, except for the output price, are normalized by the equilibrium industry price. It isassumed to be taken as given by the individual firm.8is multiplied by the average size of a firm in the industry, l¯ = 1n∑ni=1 li,t to avoid that com-petitive industries be mechanically more exposed to z shocks. In the following, I denote thecumulative distribution of z by Φ(.), and the associated probability distribution function byφ(.). The idiosyncratic cash-flow shock z captures, in a reduced form, all heterogeneity acrossfirms and is the key ingredient that drives firms to default. In particular, the bankruptcydecision consists of a threshold rule where shareholders declare bankruptcy as soon as z islarger than a default threshold z?, where z? is such that d1(z?) = EquilibriumIn the model, all firms are the same except for their idiosyncratic shock realization. Becausethis cost enters as a fixed cost, all firms make identical decisions. Therefore the model admits aunique symmetric Nash equilibrium, where all firms maximize their firm value, taking rivals’actions as given. To close the labor market, I assume that the total labor supply in theindustry is equal to 1. I leave the derivation of the solution to the appendix.The equilibrium is described by a set of three equations, one optimality condition forlabor, one for debt, and an optimal default threshold. This implies the following equilibriumprofit margin:PM =hν(2.7)where h =∑ni=1(yi,t/Yt)2 is the industry Herfindahl-Hirschman concentration index. h−1 isa measure of industry competition. Note that the firm profit margin is increasing in industryconcentration. Intuitively, when competition is tougher, a single firm has less control on theindustry price Pt, and faces a more elastic demand curve.18 Therefore higher competitiondrives each individual firm to produce more. At the industry level, all firms produce moreso that the increased industry production puts a downward pressure on revenues and reducesthe firm profits.2.2.4 Competition, corporate policies and asset pricesThis section examines the effect of industry competition on equilibrium corporate policies,credit spreads and equity. Proposition 1 summarizes several key results.Proposition 1. An increase in industry competition: (i) increases the expected default prob-ability, (ii) decreases financial leverage, (iii) decreases equity value, and (iv) increases creditspreads.19Proof. See appendix18To be more specific, the elasticity of demand for an individual firm is ηyj ,P =νh.19Note that I’m working under the assumption that β > 0, C > 0, τ > 0, ν > 1. Also, note that theseresults hold quite generally for all distribution functions Φ(.) such that Φ(z)φ(z)is increasing in z. This is the casefor most standard distribution function such as normal, uniform, etc.9To understand the intuition behind these results note that, as shown in Eq. 2.7, competi-tion erodes firms’ profit margins. This makes competitive firms more exposed to idiosyncraticcash-flows shocks and increases the expected probability of default. Creditors are rationaland discount the value of corporate bonds issued by competitive firms. Consequently, equi-librium credit spreads rise. In response to the more expensive cost of debt, shareholders cuton leverage. However, the reduction in leverage is not sufficient to decrease credit spreads be-cause equity holders in competitive industries endogenously face a lower cost of default. Thishappens because the cost of default is determined by the value of the firm lost in bankruptcyand competitive firms are, on average, less valuable. In the end, competitive firms earn lowerprofits, default more, and generate less tax shield from leverage, making their equity valuelower.Another measure of interest is equity risk. More formally, equity risk can be measured bythe firm conditional beta βi, calculated as the elasticity of equity with respect to the systematicshock A.20 It can be shown that the conditional beta is composed of three components (seeappendix for details),βi = 1−β∫ zz? z dΦ(z)Vj︸ ︷︷ ︸Default option+βτC1 + (1− τ)CΦ(z?)z?Vj︸ ︷︷ ︸Tax shield(2.8)The first term is the equity beta of an unlevered firm without idiosyncratic shocks. It is equalto one because in this case, the firm value is linear in A. The second term captures the effectof default on equity risk. This term is negative, that is, the option to default decreases equitybeta. The intuition is that the limited liability of shareholders acts as an insurance againstbad states of the world, making equity safer. Finally, the third term captures the risk comingfrom the expected tax-shield. This term contributes positively to βi because the net benefitof debt is procyclical.In contrast to credit spreads, industry competition decreases equity risk. The reason forthis result is two-fold. First, because competitive firms face a higher likelihood of default,their limited liability option is more valuable. This decreases equity risk through a defaultoption channel. Second, because competition reduces the use of debt, they are less exposedto the risk stemming from the expected tax-shield. This further decreases equity risk througha leverage channel. So far, we have abstracted from investment, a key ingredient in thebenchmark model. Allowing firms to invest in extra capacity leads to an additional effectof competition which I refer to as the competitive externality channel. I discuss this thirdchannel in the next section.20To be more precise, the risk premium on the asset is βi × λ, where λ is the market price of the systematicrisk. In this simple model, the price of risk is null because of the risk-neutrality assumption. Therefore exposureto the A shock is not risky per se. The model could easily be augmented to have a positive price of risk withoutchanging the qualitative results. To keep exposition as simple as possible I abstract from this and keep referringto βi as capturing equity risk.102.2.5 InvestmentThe previous section illustrates how competition, by reducing the level of profits, makes firmmore exposed to idiosyncratic cash-flow shocks. Competition increases credit spreads becausethe likelihood of default is higher. Yet, it reduces equity risk because the default optionbecomes more valuable and competitive firms use less financial leverage. In this section, Idiscuss how allowing for investment gives rise to another effect of competition on asset prices;namely, competition decreases the riskiness of the firm cash flows.The intuition is as follows. Firms in competitive industries face a more elastic demandcurve. Consequently, they increase investment relatively more in response to positive newsabout productivity. At the industry level, all firms adopt a similar strategy such that totalindustry output increases. This puts a downward pressure on the output price (see Eq. 2.1).In the end, competitive firms produce more and sell at a cheaper price. Because the marginalproduct of capital is decreasing, competitive industries are characterized by less procyclicalprofits. Therefore when investment is allowed, feedback effects from industry rivals curtailpotential profit opportunities from investment, and decreases the firm exposure to aggregaterisk. I refer to this effect as the competitive externality channel.21The simple model has highlighted several channels through which competition affectslevered equity returns and credit spreads. In the next section, I build a production-basedasset pricing model to quantitatively assess the strengths of each these channels.2.3 Benchmark modelI now extend the simple two-period model into a quantitative dynamic stochastic generalequilibrium model. The economy is composed various industries in which firms compete inproduct markets. These firms issue debt and equity and are owned by risk-averse investors.Figure 2.1 gives an overview of the economic environment. The goal here is to test whetherthe channels highlighted previously are quantitatively sufficient to explain the cross-sectionaldifferences in industries sorted on industry concentration.2.3.1 FirmsThis section describes the economic environment faced by an individual firm i operating in anindustry j. The industry is composed of nj firms which compete for the sale of an identicalindustry good. As before, competition in product markets is captured by assuming that firmsplay a Cournot game in each period. The number of firms nj is the only difference acrossindustries and captures differences in industry competition. In particular, higher nj industriesare characterized by tougher competition. For simplicity, I assume that nj is fixed. The total21The idea that rivals’ actions can reduce own-firm risk arises in other setups. For instance, Carlson, Dockner,Fisher, and Giammarino (2014) obtain similar results in dynamic duopoly model where firms have the optionto invest in additional capacity (intensive margin). More recently, Bustamante and Donangelo (2015) usesprocyclical entry threat (extensive margin).11demand for industry goods, Yj,t, obeys the following inverse demand curve,Yj,t = P˜−νj,t Yt (2.9)where Yt is an aggregate demand term, Yj,t =∑nji=1 yi,j,t is the total industry output, P˜j,t =Pj,t/Pt is the price of the industry good, relative to the economy price index Pt, and ν is theelasticity of demand for industry goods. For now, I take this demand function as given. Atthe end of the section, I provide an industry structure to rationalize this specification.Technology Intermediate firm i in industry j uses capital ki,j,t and labor li,j,t as input in aCobb-Douglas production technology:yi,j,t = kαi,j,t (Atli,j,t)1−α (2.10)where At represents an aggregate productivity shock common across firms, and is composedof a short- and long-run risk components:22∆at+1 = µ+ gt + σaa,t+1 (2.11)gt = ρggt−1 + σggt (2.12)where ∆at = ln(At)− ln(At−1), and at and gt are uncorrelated standard normal shocks i.i.d.shocks. The low-frequency component in productivity, gt, is used to generate sizeable riskpremia as in Bansal and Yaron (2004).Firm’s operating profit The firm hires li,j,t units of labor from households at a competitivewage of WtPt. Each unit of goods is sold to customers at a unit price of Pj,t. FollowingGomes, Jermann, and Schmid (2013), heterogeneity accross firms is captured by assumingthat operating profits are hit by an idiosyncratic, mean zero, i.i.d. shock zi,j,t. These shockssummarize, in a reduced form, all idiosyncratic risk affecting a firm’s cash flows. The realoperating profit before tax isΠi,j,t = P˜j,t yi,j,t −Wt li,j,t − zi,j,t k¯j,t (2.13)where k¯j,t is the average capital stock in the industry.23 In the following, I denote by Φ(.)and φ(.) the cumulative and density distribution function of the idiosyncratic shock z whichis defined over the support [z, z¯]. Eq. 2.13 means that operating profits are equal to totalsales, minus the total cost of labor, minus a firm-specific shock, assumed to be uncorrelated22Other studies using this type of productivity process include Croce (2014), Kung (2015), and Kung andSchmid (2015).23One needs to multiply zi,j,t by some non-stationary variables to avoid that idiosyncratic risk becomestrivially small along the balanced growth path. Furthermore, multiplying by the average size of a firm avoidsthat competitive industries be mechanically more exposed to idiosyncratic shocks.12both serially and cross-sectionally.Financing Each period, after observing realizations of all shocks, the owner of the inter-mediate firm decides on whether to default or not. If no default occurs, the firm chooses itsoptimal capital structure by issuing new debt, bi,j,t+1, and equity to finance its operations. Incase of default, the owner walks away with a payoff of zero24 and creditors take over the firmafter paying some bankruptcy cost.Before issuing new debt, the firm is required to pay the interest and the principal due onits outstanding one-period debt,((1− τ)C + 1) bi,j,t (2.14)where bi,j,t is the total amount of real corporate debt issued at t−1, C is the coupon paymenton existing debt, and τ is the corporate tax rate. When no default occurs, the firm issuesnew debt bi,j,t+1 at a market price of qi,j,t per unit of debt. Finally, all costs associated withadjustments to leverage are captured by a cost function ψb(bi,j,t, bi,j,t+1).25 Therefore the netcash flow from debt financing activities isbi,j,t+1qi,j,t − ((1− τ)C + 1) bi,j,t − ψb(bi,j,t, bi,j,t+1) (2.15)Investment The firm accumulates capital for production in the next period through capitalinvestment, Ii,j,t. The stock of productive capital accumulates as follow,ki,j,t+1 = (1− δk)ki,j,t + Γ(Ii,j,tki,j,t)ki,j,t (2.16)where δk is the depreciation rate of capital, and Γ (.) captures the idea that capital accumu-lation is subject to adjustment costs. As in reality, it is assumed that the firm can deductdepreciated capital from taxable income. The net cash flows from investment activities is−Ii,j,t + τδkki,j,t (2.17)Equity value Equity holders have the right to the firm dividends so long as the firm is inoperation. The dividend is equal to firm free cash-flows that is, the operating profit, net of24In practice, shareholders can receive a positive amount in case of default (e.g. Garlappi and Yan (2011)).Accounting for this has no bearing on the main results.25One could obtain financing frictions in other ways. For instance Jermann and Quadrini (2012) assumequadratic adjustment costs for dividends, and Gomes, Jermann, and Schmid (2013) use long-term nominaldebt.13cash flows from financing and investment activities,Di,j,t = (1− τ)Πi,j,t − Ii,j,t + τδkki,j,t − ((1− τ)C + 1) bi,j,t + qi,j,tbi,j,t+1 − ψb,i,j,t (2.18)The objective of the firm manager is to maximize the equity value defined as the presentvalue of dividends, subject to the capital accumulation equation and the inverse demand forthe firm goods. Denoting the vector of aggregate state variables and production decisions ofrivals by Υj,t ≡{k¯j,t,Yt, gt,∆at, {yk,j,t}njk=1,k 6=j}, the firm problem isE (bi,j,t, ki,j,t, zi,j,t,Υj,t) = max{maxzi,j,tDi,j,t + Et [Mt,t+1E (bi,j,t+1, ki,j,t+1, zi,j,t+1,Υj,t+1)] , 0}s.t. ki,j,t+1 = (1− δk)ki,j,t + Γ(Ii,j,tki,j,t)ki,j,tYj,t = P˜−νj,t Yt(2.19)where zi,j,s ≡ {bi,j,s+1, Ii,j,s, ki,j,s+1, li,j,s} is a vector containing all the firm controls, andMt,t+s is the equilibrium stochastic discount factor. Note that the first max operator capturesthe limited liability of shareholders, and the second max operator relates to the optimaldecision of the manager.Default decision When the value of the firm becomes negative, shareholders declarebankruptcy and leave with a payoff of zero. Let’s define V (bi,j,t, ki,j,t, zi,j,t,Υj,t) to be thepresent discounted value of dividends (the term inside the first max in Eq. 2.19). The defaultdecision consists in finding the threshold value z?i,j,t such that V(bi,j,t, ki,j,t, z?i,j,t,Υj,t)= 0and declaring bankruptcy when zi,j,t > z?i,j,t. The assumption that zi,j,t enters as an i.i.d.fixed cost makes the value of the firm additive in zi,j,t26 and we can solve easily for z?i,j,t,z?i,j,t =V (bi,j,t, ki,j,t, 0,Υj,t)(1− τ)k¯j,t(2.20)Eq. 2.20 highlights the fact that the optimal default threshold depends on the firm valuation.This will be important to generate countercyclical default rates as in the data.Debt value When the firm defaults, creditors gain control over the firm assets after payinga one time cost of ξt% of the firm value. They become owner of an unlevered firm andcollect the firm’s profit in the current period. Corporate bonds are held by the representativehousehold and are thus valued using the household equilibrium pricing kernel Mt,t+1. Thevalue of newly issued debt to creditors is26 In particular, V (bi,j,t, zi,j,t,Υj,t) = V (bi,j,t0,Υj,t)− (1− τ)zi,j,tk¯j,t.14(2.21)qi,j,tbi,j,t+1 = EtMt,t+1{Φ(z?j,t+1)(C + 1)bi,j,t+1+(1− ξt)∫ zz?j,t+1V (0, zj,t+1,Υt+1) dΦ(zj,t+1)}The first term inside the brackets is the payment when the firm survives multiplied by theprobability of survival. It is equal to the coupon payment plus the principal. The second termis the bondholders payoff when the firm defaults, multiplied by the probability of default.Optimal firm decisions The objective of the manager is to make a series of operating,financing and investment decisions to maximize the value of the firm. The Lagrangian andderivations of the first order necessary conditions are detailed in the appendix.Let’s first examine the optimal capital structure decision. The leverage decision is givenby the first order condition with respect to bi,j,t+1,qi,j,t +∂qi,j,t∂bi,j,t+1bi,j,t+1 = EtMt,t+1Φ(z?j,t+1) [(1− τ)C + 1] + ∆ψb,t (2.22)where ∆ψb,t27 is the net cost associated with issuing an amount bi,j,t+1 of debt. This conditionmeans that in equilibrium, the firm equates the marginal benefits (left-hand side) to themarginal costs (right-hand side) of debt. More specifically, issuing an additional unit of debtprovides shareholders with an additional payoff equal to qi,j,t, adjusted to take account ofthe decrease in debt value due to the increased probability of default. The cost of issuingan additional unit of debt is the after-tax interest rate, plus the principal due in the nextperiod, plus the change in issuance cost. These costs are multiplied by the probability ofsurvival as shareholders have the option to walk away in the next period. Worth noticing isthat equity holders rationally take account of the impact of their choices on the cost of debt,i.e. ∂qi,j,t/∂bi,j,t+1.The optimal investment decision is obtained by equating the marginal benefits to themarginal costs of an additional unit of capital,ΛKt = EtMt,t+1 (1 + ϑi,j,t+1){D′k,i,j,t+1 + ΛKt+1[1− δk + Γi,j,t+1 − Γ′i,j,t+1(it+1kt+1)]}(2.23)where ϑi,j,t+1 = φ(z?i,j,t+1)bi,j,t+1(1−τ)k¯j,t (τC + ξt+1[(1 − τ)C + 1]) − ξt+1(1 − Φ(z?i,j,t+1)) and ΛKtis the Lagrange multiplier on the capital accumulation equation and represents the shadowvalue of an additional marginal unit of capital (Tobin’s Q). The two terms inside the bracketsin Eq. 2.23 represents the expected increase in dividend and capital gains from investing amarginal unit of capital today.28 The multiplicative term (1 + ϑi,j,t+1) captures the distortionarising from the leverage decision. More specifically, investing today increases future dividendsand thereby decreases the probability of default (first term in ϑi,j,t+1). Besides, because27In particular, ∆ψb,t =∂ψb,t∂bi,jt+1+ EtMt,t+1Φ(z?j,t+1)∂ψb,t+1∂bi,jt+1.28Specifically, D′k,i,j,t = (1− τ)P˜j,t[1− 1νytYj,t]α ytkt+ τδk15bankruptcy is costly, there is a chance that the invested unit is going to be lost partiallyin the next period (second term). Note that the standard investment Euler equation is aparticular case where ϑi,j,t+1 = Industries dynamics and competitionThe final consumption good is produced by a representative firm operating in a perfectlycompetitive market. The firm uses a continuum of industry goods Yj,t as input in a CESproduction technology. To keep the number of industries finite, it is assumed that the economyis composed on N different industries equally distributed on the [0, 1] interval,Yt =(∫ 10Yν−1νj,t dj) νν−1=(1NN∑i=1Yν−1νj,t) νν−1(2.24)where ν is the elasticity of substitution between goods of different industries.Solving the profit maximization problem for the final good firm (see the appendix) yieldsthe following inverse demand function for goods in industry j,Yj,t = P˜−νj,t Yt (2.25)where P˜j,t = Pj,t/Pt, and Pt =(∫ 10 P1−νj,t) 11−νis the aggregate price index. Note that this isthe same inverse demand function as the one specified in Eq. HouseholdsThe model is closed by specifying the household industry. I assume the existence of a repre-sentative household with recursive utility over a bundle of consumption Ct and leisure (1−Lt)as in Croce (2014),Ut =C˜1− 1ψt + βEt [U1−γt+1 ]1− 1ψ1−γ11− 1ψ(2.26)C˜t = Ctϕ(At−1(1− Lt))1−ϕ (2.27)where γ is the coefficient of relative risk aversion, ψ is the elasticity of intertemporal substi-tution, β is the subjective discount factor, and ϕ drives the total amount of hours worked.Note that leisure is multiplied by productivity At−1 to ensure balanced growth.To finance her consumption stream, the representative household collects wages by sup-plying specialized labor Lj,t to industry j. In addition, the household has access to financialmarkets where she can invest in stocks, and corporate bonds in all industries as well as gov-ernment bonds. The total position held in equities is denoted by Qt, while the total amountinvested in corporate and government bonds is denoted by Bct+1 and Bgt+1, respectively. The16real (normalized by Pt) budget constraint of the household isCt +[Bct+1 + Bgt+1 +Qt]︸ ︷︷ ︸Position in securities=WtLt +[RctBct +RftBgt +RdtQt−1]︸ ︷︷ ︸Proceeds from securities−Tt(2.28)where WtLt = 1N∑Nj=1Wj,tLj,t is the total labor income, Rft is the risk-free return on gov-ernment bonds bought in the previous period, and Rdt and Rct are the total returns on theequity and corporate debt portfolio. These returns are defined in the next section. Tt arelump-sum government taxes.29Solving the household problem yields a set of Euler equation to price all the securities inthe economy. The equilibrium one-period pricing kernel isMt,t+1 = β(Ct+1Ct)−1( C˜t+1C˜t)1− 1ψ Ut+1Et(U1−γt+1) 11−γ1ψ−γ(2.29)The household labor supply for each industry is,Wj,t =(1ϕ− 1) Ct(1− Lt) (2.30)Because the household works indifferently in all industries, the aggregate wage will be thesame across all industries.2.3.4 Equilibrium and aggregationAs in the simple model, the fixed cost specification for the idiosyncratic risk makes all firmsex-ante identical. Besides, in case of bankruptcy, the firm is transferred to debt-holders whomake the same decisions as surviving firms. Therefore, the only cross-sectional differenceacross firms comes from the realization of the firm-specific shock zi,j,t. In the aggregate, thelaw of large numbers applies to each type of industry j = 1, ..., N and we only need to keeptrack of the measure of defaulting firms each period, 1 − Φ(z?j,t).30 Therefore each industryadmits a symmetric Nash equilibrium and the i-subscript can be dropped. In the symmetricequilibrium, the model has 2×N+2 state variables; two endogenous state variables for eachindustry (k¯j,t, bj,t), and two exogenous variables (gt, ∆at) for the economy.29To close the model, I assume the existence of a government whose objective is to set Tt to maintain azero deficit. Therefore the net supply of government debt is zero and household taxes amounts to the totalcorporate tax subsidy of interests net of corporate tax collection.30A big advantage of this specification is that one can obtain an exact aggregation for the firm distributionswithout having to rely on the more involved Krusell and Smith (1998) algorithm (e.g. Miao and Wang (2010),Gomes, Jermann, and Schmid (2013)).17Asset returns The return on equity and corporate debt in industry j are defined in astandard way and account for the proportion of firms that defaults,Rdj,t =∫ z?j,tz [Dj,t +Qj,t] dΦ(z)Qj,t−1Rcj,t =Φ(z?j,t)(C + 1)bj,t +∫ zz?j,t+1(1− ξt)V Uj,t dΦ(z)Bcj,t−1(2.31)where Qj,t = Vj,t −Dj,t is the ex-dividend value of equity in industry j, and V Uj,t is the equityvalue cum-dividend of an unlevered firm.Resource constraint Using the definition for the returns (2.31) earned in financial marketsand imposing market clearing on all markets.31 The aggregate resource constraint (2.28)becomes,Yt = Ct + It + Ψb,t + Ξt (2.32)where It = 1N∑Ni=1 Ij,t is aggregate investment, Ψb,t =1N∑Ni=1 ψb(bi,j,t, bi,j,t+1) is the amountof resources spent in debt adjustments, and Ξt =1N∑Ni=1(∫ zz?j,t+1ξtVj,t (0, z) dΦ(z))is theaggregate resource lost in bankruptcy.Industry pricing In the symmetric Nash equilibrium, the industry price is defined as amarkup over the industry marginal cost. In particular, denoting the real marginal cost ofproduction by MCj,t =Wt(1−α) yj,tlj,t,P˜j,t = MCj,t(1− hjν)−1︸ ︷︷ ︸Price markup(2.33)where hj is the Herfindahl-Hirschman index in industry j. Note that P˜j,t is increasing inindustry concentration. The intuition is that when less players compete in product markets,firms behave more like monopolist and charge a higher markup.2.4 Model parametrizationThis section describes the benchmark model calibration and provides details on the functionalforms for the adjustment costs and idiosyncratic shocks distribution. The model is solvedusing a second order perturbation method about the steady state after normalizing all non-31In particular, I impose that the representative household holds all equity claims, buys all corporate debtissued by corporations: Bct+1 = 1N∑Nj=1 qj,tbj,t+1, that the net supply of government bonds is zero: Bgt+1=0,and that the labor and goods supply equal their respective demands.18stationary variables by At− Functional formsThe capital adjustment costs function Γ(.) is modeled following Jermann (1998),Γ(x) =α11− 1/ζk x1−1/ζk + α2,k (2.34)where α1,k and α2,k are determined such that there is no adjustment costs in the deterministicsteady state. The debt adjustment cost is assumed to be quadratic,ψ(b˜t+1, b˜t) =χb2(b˜t+1 − b˜t)2k¯j,t (2.35)where b˜t+1 is corporate debt normalized by the average industry capital Kj,t+1, and χb is aparameter capturing the magnitude of the cost to change leverage. Note that this specificationensures that the debt adjustment cost has no impact on the deterministic steady state.In a similar spirit as Chen (2010), I model the cost of bankruptcy ξt to be a function ofthe productivity process ∆at,ξt = ξ + ξ1∆aˆt (2.36)where ∆aˆt = ∆at − µ. Finally, the firm specific shock z is assumed to follow a normaldistribution with a mean of zero and a variance σz.2.4.2 CalibrationThe model parameters are picked in two ways. First, standard real business cycles parametersas well as preference parameters are set to values from the existing literature. The remainingparameters are estimated by minimizing the distance between moments simulated from themodel and empirical targets. All parameters values are summarized in Table 2.1.The preference parameters are standard in the long-run risk literature (e.g. Croce (2014),Kung (2015)). The elasticity of intertemporal substitution ψ is set to 2 and the coefficientof relative risk aversion γ is set to 10. The subjective discount factor β is equal to 0.99.The relative preference for labor, ϕ, is set such that the household works 1/3 of her timeendowment in the steady state. On the technology side, the capital share α is set to 0.33,and the depreciation rate of capital δk is set to 2.0% (e.g. Comin and Gertler (2006)). Theproductivity process is calibrated following Croce (2014). The persistence of the long runrisk is set to imply a annual persistence of 0.85. The conditional annualized volatility of theshort- and long-run productivity shocks are σa = 4.5% and σx = 0.335%, respectively. Theelasticity of substitution across industries ν does not affect model dynamics much, I set it to1.32 Finally, I set the quarterly coupon payment, C to 7%/4 to match the average coupon32Note that when ν < 1, industry goods are complements while when ν > 1, they are substitute. ν = 1 is19payment of my sample (see Table 2.7).The remaining parameters, namely Θ =[σz, ξ, χb, ζk, τ, µ, α1, {hj}Nj=1]are chosen to min-imize the distance between a vector of identifying moments from the data and the samemoments generated from model simulations.33 Mathematically, I obtain the parameter esti-mates by solving,Θˆ = arg minΘ[mˆ−m(Θ)]′ W˜−1 [mˆ−m(Θ)] (2.37)where W˜ is a weighing matrix set to the identity matrix, mˆ is a vector of empirical moments,and m(Θ) is the vector of model-implied moments obtained assuming a value of Θ for thestructural parameters.To ensure a successful identification, the empirical targets need to be carefully chosen.Table 2.2 reports the estimated structural parameters along with the eight identifying modeland empirical moments. All targets are at the aggregate level except for the profit margin,net of investment that is at the industry level. More specifically, I target a quarterly averagedefault rate of 0.25% in order to match match the Moody’s average annual default rateof 1% per year. In the model, default is triggered by the idiosyncratic shock, thereforethis moment provides a good identification for σz. To identify the parameters governing ξt,namely ξ, and α1, I follow Chen (2010) and target a mean recovery rate in default of 45%,a volatility of recovery rates of 10%, a correlation between recovery rates and default of -0.82, and a correlation between recovery rates and output growth of 0.58. I also target anaverage annualized credit spreads of 90bps which is the average spread between Baa and Aaayields used in previous studies (e.g. Gourio (2013)). τ captures the tax-benefits of debt, itis identified using the mean aggregate book-to-asset ratio, set to 0.40 (e.g. Gourio (2013)).Next, I obtain the capital adjustment cost curvature ζk by targeting an investment to outputvolatility of 4.50 (Croce (2014)). The mean growth rate in productivity, µ is chosen to generatean annualized growth rate of output of 1.80%. To obtain χb, I aim a standard deviation ofbook-leverage of 9% (Gourio (2013)).The last parameters to identify are the degree of concentration in each industry, hj . Tomake the model close to the empirical section where I use quintiles sorted on competition, Iassume the existence of N = 5 representative industries.34 I further assume that the intensityof competition h−1j linearly increases between h−11 = h−1low and h−15 = h−1hig. This leaves me withhhig and hlow to estimate. Because hj is directly linked to measures of market power, I followa measure similar to Allayannis and Ihrig (2001) that I adjust to take capital expendituresthe Cobb-Douglas case.33Moments from the model are computed on a long sample simulation of 25,000 observations, with a burningperiod of 1,000 quarters.34Theoretically, the model can accommodate any number of industries N . The cost of having more industriesis the increased in computing time. None of the results in this chapter depends on the particular assumptionfor N .20into account. Specifically, market power is defined asMPIj,t =Salesj,t + ∆Inventoryj,t − Costsj,t − Investmentj,tSalesj,t + ∆Inventoryj,t(2.38)where ∆Inventoryj,t is the change in inventory, Costsj,t is the sum of payroll, cost of material,and energy, and j-t are industry-year subscripts. The data is obtained from the NBER-CESManufacturing Industry Database. Each year, I sort industries into quintiles based on theirlagged measure of concentration. I then compute the average MPIj,t in the highest and lowestconcentration quintile each year and get the average of these series. The resulting two targetmoments are 0.299 and 0.263.The SMM estimates are reported in Table 2.2. Overall, the estimation matches the targetmoments fairly well. The value for σz is 0.97 and allows me to exactly match the averagequarterly default rate of 0.25%. The estimate value for ξ is estimated at 11.8%, which is inthe range of estimates in van Binsbergen, Graham, and Yang (2010). The bankruptcy costcyclicality parameter α1 replicates quite well key dynamics of recovery rates reported in Chen(2010). The tax benefits of debt, τ , is about 13.76%. The degree of concentration acrossindustries, hj ’s implies a demand elasticity for the firm’s product of 3.87 (4.37) for the low-(high-) competition quintile. The value for χb generates a relatively stable financial leverageas in the data, i.e. σ(b˜) = 8.3%.2.5 Quantitative resultsThis section quantitatively assesses the importance of competition as a determinant of thecross-section of asset prices. First, I examine how the model matches key macroeconomicsand asset pricing moments at the aggregate level. This is important as most of the parametersare calibrated at the economy-wide level. Next, I disaggregate moments by industries. Theobjective is to evaluate whether differences in industry competition are sufficient to explainthe cross-sectional differences we observe in the data. Finally, I generate additional empiricalpredictions on the relationship between credit spreads, competition and idiosyncratic volatilitythat I test empirically in the next section.2.5.1 Aggregate momentsTable 2.3 reports key business cycle moments from the calibrated model and the associateddata moments. The calibrated model generates an average investment-output ratio of 21%,in line with its 20% empirical counterpart. The output volatility and relative macro volatilityare quite close to the data. The model also replicates the correlations across key businesscycle variables, namely the procyclicality of consumption, labor, and stock returns. Also, theimplied persistence in consumption and output growth is low, as in the data.Figure 2.2 describes the model dynamics in response to a positive productivity shock bymeans of impulse response functions. An increase in productivity leads to sustained growth21and persistently increases firms’ profits opportunities. Because the elasticity of substitutionis greater than one, the substitution effect dominates so that positive productivity leads to anincrease in firm valuation proxies, such as the market-to-book ratio (MB). Simultaneously,the excess return on the aggregate stock market rises (re − rf ). As the continuation valueof companies increases, less firms find it optimal to declare bankruptcy leading to a fall inaggregate default and a persistent drop in credit spreads (cs). In the model, agents exhibitpreference for early resolution of uncertainty and are therefore averse to the long-run riskgenerated by low-frequency variations in productivity growth. As a consequence, financialassets that co-move with the business cycle will command a risk premium.Table 2.3 also reports some key asset pricing moments from simulations. The modelgenerates a large equity risk premium of about 6.80% per annum, and produces substantialvariations in excess returns. The annualized standard deviation of excess stock returns isabout 9.27%. The strong demand for precautionary savings drives the risk-free rate downto 2.14%, somewhat higher than in the data. The volatility of the risk free rate is also low(1.18%). The model generates a sizable credit spreads of 89bps which exhibits substantialtime-series variation. The standard deviation in the model is 24bps and about 42bps inthe data. As in the data, credit spreads are counter-cyclical. In particular, the correlationbetween credit spread and GDP growth is -0.36 in the data and -0.44 in the model. Thecountercyclicality of credit spreads leads to a bond risk premium. In the model, the creditspread premium is around 20bps, that is 22% of the total credit spread.35 Although empiricalestimates are quite noisy, the credit risk premium in the model is on the lower range of valuesreported in the literature. Two reasons can explain this. First there exists strong empiricalevidence suggesting that other factors contribute to this spread such as taxation (e.g. Elton,Gruber, Agrawal, and Mann (2001)), or liquidity (e.g. Ericsson and Renault (2006), andChen, Lesmond, and Wei (2007)). Second, the model abstracts from ingredients that haveproved useful to generating a large credit risk premia. For instance, Gourio (2013) assumethe existence of disaster risk, while Chen (2010) and Bhamra, Kuehn, and Strebulaev (2010)use long-term debt and time-varying uncertainty. In unreported results, I find that allowingfor countercyclical idiosyncratic risk helps raise the credit risk premium to 30bps withoutchanging any of the model implications.Table 2.4 reports several key aggregate corporate financing moments. The model generatesan annual market leverage of about 0.11 and a frequency of equity issuance of 0.10 (0.09 inthe data). The unconditional probability of default is 0.25% per quarter as in the data.Also, and consistent with recent evidence by Jermann and Quadrini (2012) and Covas andHaan (2011), equity payout are pro-cyclical while debt repayment are countercyclical. Forinstance, the correlation between equity payout (debt repayment) and GDP is 0.55 (-0.59) insimulated data. Jermann and Quadrini (2012) reports a correlation with GDP of 0.45 and-0.70, respectively.35Formally, the credit spreads premium is defined as the difference between the yield on a risky bond minusthe yield of riskless security that pays the expected bond payoff.22Overall, the model does a good job matching unconditional moments and key dynamicsof both macro aggregates and asset prices. The next section investigates how competitionaffects these decisions by disaggregating moments at the industry-level.2.5.2 Industry momentsIn this section, I disaggregate the moments and impulse response functions per industryto study the effects of competition on the cross-section of asset prices. It is important toremember that the only difference across industries is a calibrated proxy for market power.Therefore all cross-sectional differences will be induced by heterogeneity in hj ’s.Table 2.5 reports various model moments for the high- and low-competition quintile. In themodel and in the data, more competitive industries are characterized by lower profit margin.The intuition is that competition erodes profits, making a unit of asset less productive in acompetitive industry. This result is consistent with previous empirical studies (e.g. MacKayand Phillips (2005)). Because competition erodes firm’s growth opportunities by creating anegative externality from rival’s actions, competitive firms have lower Book-to-Market ratio.The last two columns compare the difference between the high and low competition quintilesin the model and in the data. The profit margin (as measured by market power) is 3.60%higher in concentrated industries. Moreover, the cross-sectional difference in Book-to-Marketratio is 0.032 closely match its empirical counterpart of 0.040.The model predicts that concentrated industries use more financial leverage. What hap-pens is that more concentrated industries have higher firm valuation and enjoy a better bufferagainst idiosyncratic cash-flow shocks. This lowers the probability of default, and increasesthe expected tax benefits of debt making leverage more attractive. Also, because default iscountercyclical, bonds issued by concentrated firms are safer. This further increases the mar-ket value of debt and the incentive to use leverage. In the model, market leverage is 2.30%lower in competitive industries.36 By comparison, summary statistics from my data samplereveal a similar pattern: market leverage is 1.4% lower in the lowest concentration quintile.These results accords with a recent study by Xu (2012) who documents a strong negativerelationship between competition and leverage, using import penetration as an instrumentalvariable. Therefore, the model prediction that competition decreases financial leverage seemssupported in the data.37Table 2.5 also reports several asset pricing moments. Equilibrium credit spreads are higherin competitive industries (119bps) than in concentrated industries (62bps). The magnitudeof the difference in the model is 57bps, higher than its empirical counterpart of 25bps. Thereare at least two reasons that explains this larger difference. First, the data sample is biasedtowards larger firms. Valta (2012) shows that the spread on bank loans is twice as high forsmaller firms. This would bring us much closer to the 57bps. Secondly, firms in the sample36Market leverage is obtained as the ratio of the market value of debt divided by sum of the market valuesof equity and debt.37MacKay and Phillips (2005) also find that competition decreases book leverage by about 3.6%.23varies across many more dimensions that in the model. Therefore a univariate analysis maynot capture well the cross-sectional difference in credit spreads. In the data section, I runpanel regression to alleviate some of these later concerns.The model generates substantial differences in equity risk across industries. The averageexcess return is 7.20% in concentrated vs. 6.43% in competitive industries. This leads to aconcentration premium of 0.76%. In the data, this premium is 2.54%, with a standard error of1.30%. Therefore the difference between model premium and the data estimate is not differentat the usual confidence level. The estimated CAPM beta is also higher in less competitiveindustries by 0.14 (vs. 0.21 in the data). A series of recent empirical studies are supportiveof these predictions. For instance Bustamante and Donangelo (2015) document a positiverelationship between excess returns, CAPM betas, and measures of industry concentration.To understand why the risk premium on equity is lower in competitive industries, it is usefulto look at some impulse response functions. Figure 2.3 compares the response to a positivelong-run productivity shock in the high- vs. low-competition industry. Firms in competitiveindustries face a more elastic demand curve and increase production more when productivityrises. At the industry level, supply gets higher and industry competition increases. This putsa downward pressure on the output price and makes dividends less procyclical in competitiveindustries. At the same time, firm values rise, and the conditional probability of default drops.Because competitive firms are closer to bankruptcy, the value of their default option fallsrelatively more. This further dampens the effect of productivity on equity value. Finally, firmsin concentrated industries have higher financial leverage which renders cash flows even moreprocyclical. Taken together, these three forces make equity value in concentrated industriesmore sensitive to productivity shocks. Since investors are averse to long-run risks, this givesbirth to a concentration premium.In short, the model predicts that competition decreases leverage, increases credit spreads,and decreases the equity premium. These predictions are in line with earlier studies andmatches the data quantitatively. This is quite surprising given that the only source of hetero-geneity in the model is hj .2.5.3 Decomposing the concentration premiumThe prior literature has largely focused on linking competition to the unlevered equity riskpremia. This essay shows that competition also affects optimal capital structure and default.These two decisions in turn affect equity risk. To assess the contribution of leverage anddefault to the concentration premium, I decompose the premium into two components. Thefirst component measures the effect of competition on equity risk that arises from industryrivals’ actions. It relates to how competition affects the firm’s assets in place and growthoptions. This premium is positive because in competitive industries, competitors create aprocyclical negative externality that acts as a hedge against aggregate shocks. The second24component measures the contribution of leverage and default.38To obtain this decomposition, I proceed in two steps. First, I compute the equity premiumon a security that pays the same cash-flows as the benchmark firm, but has no debt nor optionsto default. More specifically, the value of that synthetic security is,V Aj,t = Et∞∑s=tMt,s [(1− τ)Πj,s − Ij,s + τδkkj,s] (2.39)The difference in equity premium between the low- and high-competition quintile measuresthe rival’s externality effect. Next, the remainder of the concentration premium unexplainedby cash-flows from real assets is attributed to the default and leverage effects.39Estimating these components for the benchmark calibration reveals that the rivals’ ex-ternality effect generates a premium of 15bps (see Table 2.5). In other words, about 80% ofthe concentration premium comes from the “levered” component of returns. This highlightsthe importance of accounting for leverage and default in explaining the interaction betweenequity returns and industry competition.2.5.4 Idiosyncratic risk and corporate spreadsThe importance of idiosyncratic volatility for credit spreads dates back to at least Merton(1974). In his paper corporate debt is modeled as a default-free bond minus a put option onthe firm assets. A rise in firm volatility increases the value of the put option to default. Thislowers the value of debt and leads to an increase in corporate spreads. This section investigateshow competition can amplify debtholders’ exposure to idiosyncratic volatility shocks. To thatend, the model is augmented to allow for time-varying volatility in the firm-specific shock zj,tσzj,t = ρσzσzj,t−1 + σσzσ,j,t (2.40)where eσ,j,t are standard normal i.i.d. shocks.As we saw earlier, firms in competitive industries operate on a lower profit margin. As such,an increase in idiosyncratic volatility is more likely to drive competitive firms to default. InMerton (1974) context, competitive firms are more likely to exercise their default put option.Therefore we expect that the effects of a persistent increases in σzj,t on debt value to bestronger for more competitive firms. Figure 2.4 presents the impulse response fuctions to anincrease in idiosyncratic volatility.40 In response to the higher idiosyncratic risk, default ratesand credit spreads increase. To alleviate the increase in risk, firms try to cut on debt butadjusting leverage is costly. This leads to a small, persistent decrease in debt-to-assets that38I consider these two effects jointly because the probability of bankruptcy drives both the value of thedefault option and the cost of leverage and are therefore hard to disentangle.39The premium are obtained by building synthetic securities that are priced using the benchmark calibrationpricing kernel to avoid that the pricing of risk changes across specifications.40The idiosyncratic risk process is calibrated as follows; ρσz = 0.6, and σσz = 4% which implies an annualizedstandard deviation of idiosyncratic industry volatility of 10% (e.g. Campbell, Lettau, Malkiel, and Xu (2001)).25is not sufficient to avoid the sharp increase in default probability. Importantly, while creditspreads in both industries rise, the reaction in competitive industries is larger by around 33%.Testing this prediction empirically is challenging because idiosyncratic volatility shocksare not as easily identified as in the model. In the empirical section of the chapter, I goaround this problem by using proxies based on stock market prices.2.6 Panel regressionIn this section, I test two empirical implications of the model using a data set of publicly tradedbonds: (i) credit spreads in competitive industries are higher, and (ii) shocks to idiosyncraticvolatility are amplified in competitive industries.2.6.1 Bond sample constructionBond sample construction I obtain corporate bond prices from the National Associationof Insurance Commissioners (NAIC) bond transaction file. The NAIC file records all publiccorporate bond transactions by life insurance companies, property and casualty insurancecompanies, and Health Maintenance Organizations (HMOs). The database starts in 1994 butthe coverage of disposal transactions (e.g. sales) only begins in 1995, leaving a sample periodof 1995 to 2012. While not exhaustive, the NAIC database represents a substantial portionof the corporate bond market. Schultz (2001) and Campbell and Taksler (2003) for instancenote that insurance companies hold between one-third and 40% of issued corporate bonds.Bessembinder, Maxwell, and Venkataraman (2006) estimate that they represent a substantialproportion (≈12.5%) of total bond trading volume.The NAIC bond transactions table is linked to the Mergent Fixed Income SecuritiesDatabase (FISD) to obtain bond specific information such as the maturity, coupon rate, etc.To be part of the sample, bonds must be issued by a U.S. firm and pay a fixed coupon. Fol-lowing Campbell and Taksler (2003), I also eliminate bonds with special bond features such asput, call, exchangeable, asset backed, and convertible. I only keep bonds with an investment-grade rating because insurance companies are often forbidden to invest in speculative-gradebonds. The transaction data for these bonds are thus likely to be unrepresentative of themarket.41 I follow a common practice in the finance literature and remove from the samplefirms that belongs to the regulated utilities industry (SIC codes 49) and financial institutions(SIC codes in the 60-69 range).Following Bessembinder, Kahle, Maxwell, and Xu (2009), I eliminate transactions smallerthan $100,000 or those that involve the bond issuer, i.e. transactions labelled as cancelled,corrected, cancelled, corrected, issuer, direct, called, conversion, exchanged, matured, put, re-deemed, sinking fund, tax-free, exchange, or tendered. To eliminate potential data-entry errors,41When an issue is rated by more than one agency at a given date, the average rating is computed, otherwisethe last rating in date is used.26I also remove return reversals. A return reversal is defined as a return of more than 15% inmagnitude immediately followed by a more than 15% return in the opposite direction. BesidesI exclude observations with obvious data errors such as negative price or transaction datesoccurring after maturity. In case there are several bond transactions in a day, the daily bondprice is obtained by weighting each transaction price by its volume (in face value).Reported price in the NAIC file are clean bond price and accrued interests are added toget the full settlement price (i.e. the bond dirty price). Yields are computed by equating thedirty price to the present value of cash-flows and yield spreads are defined in excess of thebenchmark treasury at the date of transaction. To get the benchmark treasury, I match thebond duration to the zero-coupon Treasury yields curve from Gu¨rkaynak, Sack, and Wright(2007), linearly interpolating if necessary. Treasury yields with a maturity lower than 1 yearare obtained from the CRSP risk-free series. Matching duration instead of maturity providesa more robust benchmark as coupon payment can vary greatly across issuers. As a final checkand following Gilchrist and Zakrajˇsek (2011), I truncate the yield spreads in the sample to bebetween 5bps and 3,500bps and restrict the bond remaining maturity to be below 30 years.Issuers’ accounting information are from Compustat and are matched using the 6 digitsissuer CUSIP. Stock prices information are obtained in a similar way from the CRSP file. Toensure that all information is included in asset prices, stock returns and bond yield spreadsfrom July of year t to June of year t+1 are matched with accounting information for fiscal yearending in year t−1, following Fama and French (1992). Monthly yield spread observations areconstructed using the last transaction of the month. The sample consists of an unbalancedmonthly panel of 12,198 different bond-month transactions. The final number of observationsdepends on the definition of competition.Industry competition measures In the model, the degree of competition is capturedby industry concentration. A direct empirical proxy is the sales-based Herfindahl-Hirschmanindex (HHI) published by the U.S. Census of Manufactures. I use this measure as my bench-mark. More formally, the sales-based HHI is defined as follows,HHIj =Nj∑i=1s2i,j (2.41)where si,j is the sales market share of firm i in industry j. The U.S. Census data is updatedevery five years and covers only manufacturing industries. Following Ali, Klasa, and Yeung(2009), I use the HHI for a given year, and assume this is also a good proxy for concentrationfor the one or two years immediately before and after it. An advantage of the U.S. Censusdata is that it covers both public and private firms and it has been shown in a prior literaturethat it is a good proxy for actual industry concentration (e.g. Ali, Klasa, and Yeung (2009)).Throughout the rest of the chapter, I define an industry by using the 4-digit SIC industryclassification.27To check the robustness of my results, I use several other well-used measures of competi-tion. The first is a measure based on markup power used in Allayannis and Ihrig (2001):Market powerj,t =Salesj,t + ∆Inventoryj,t − Payrollj,t − Cost of Materialj,tSalesj,t + ∆Inventoryj,t(2.42)The data are obtained at the industry level from the NBER-CES Manufacturing IndustryDatabase. The second measure is the Fitted SIC-based Industry concentration data used inHoberg and Phillips (2010). This fitted measure has the advantage of capturing the influenceof both public and private firms, and to be available for all industries.422.6.2 Descriptive statisticsIn Table 2.6, I report the average yield and yield spread from my NAIC benchmark bondtransactions sample, sorted on credit rating. To facilitate notation, I report credit ratingusing the Moody’s rating scale only. In the sample, the majority of bond transactions (≈79%) lies in the A-Baa categories, a pattern consistent with earlier studies (e.g. Campbelland Taksler (2003)). The average monthly spread between Baa and Aaa bonds is about 113bps, close to the average spread reported by Moody’s over the same period (101 bps). InFigure 2.5, I plot the time series of the average Baa yield spread obtained from my NAICsample along with the spreads reported by Moody’s over the same period. The two seriesfollow a similar pattern with pikes occurring during the 2000’s and the financial crisis. Thetime series correlation between the two series is high (≈ 0.91). In Panel A of Table 2.7, Ireport summary statistic for my bond sample. The size of issue is positively skewed, withan average (median) debt issue of 541 (350) millions. The time-to-maturity of the bonds islong, about 10 years. The summary statistics are similar to those of previous studies usingpublic debt (e.g. Gilchrist and Zakrajˇsek (2011)). Panel B reports individual firm summarystatistics. The average firm size in the sample is fairly large. This is consistent with previousempirical work that finds that firms issuing public debt are larger than firms using bank loans(e.g. Denis and Mihov (2003)). Finally, I report the average 4-digit SIC HHI by 2-digit SICindustries inTable 2.8. The resulting sort of industries is similar to that in Table 5 of Ali,Klasa, and Yeung (2009).Overall these results suggest that my bond transaction sample is quite representative ofthe investment-grade bond market. My firm sample is biased towards the largest, safestfirms. As a consequence, my empirical results should be a lower bound of the true effects ofcompetition on credit spreads.2.6.3 Concentration and the cross section of corporate yield spreadsThis section investigates the first empirical prediction of the model, namely credit spreads incompetitive industries are higher. Following the litterature I define competition as a dummy42Many thanks to the authors for making the data available on their website.28equal to one if HHI is in the lowest quintile of the yearly sample distribution and zero other-wise. This specification will facilitate the economic interpretation of the coefficient and alsomitigate measurement errors.Univariate analysis I start my investigation by looking at univariate sorts on industryconcentration. Table 2.9 reports the mean, and median bond yield spread for the highest andlowest competition quintile. Consistent with the model predictions, credit spreads in morecompetitive industries are higher by 25bps. The difference in mean and median are bothstatistically significant. Also and perhaps surprisingly, the estimate is quite close to the bankloan spread difference between low and high competition industry reported in Valta (2012)(22bps for large firms). Table 2.9 also reports the mean and median stock excess return acrosscompetition quintiles. Excess stock returns are lower in competitive industries (-2.54% for themean and -3.29% for the median). These results are statistically significant and consistentwith the model prediction that equity is safer in more competitive industries.Multivariate analysis Using my monthly panel data, I investigate whether measures ofconcentration have any predictive power on corporate yield spreads for public debt. In par-ticular, I run the following regression model,csi,t = δ × Compi,t−1 + β Xi,t−1 + i,t (2.43)where (i, t) denotes a specific firm-month observation, Compi,t−1 is equal to one if the firmis in the highest competition quintile and zero otherwise, and Xi,t−1 is a vector of controls,potentially including time, or industry fixed effects. The parameter of interest is δ. It capturesthe difference in credit spreads for firms operating in competitive industries.I group my set of controls into three categories: equity characteristics, bond characteristics,and macroeconomic variables. It is important to control for all these characteristics because,in contrast to the model, the bond data set exhibits vast heterogeneity in both bond and firmcharacteristics. In the equity controls category, I include the mean of the firm abnormal equityreturns (net of the market return), for the 180 days prior to the month when the transactionoccurs. I also control for leverage (total debt to capitalization), the firm size (log-asset) andasset tangibility (e.g. Ortiz-Molina and Phillips (2014)). I also add the log-book-to-marketratio and the log-market value of equity, two well-known determinants of the cross-section ofequity returns.43I also control for a series of bond specific characteristics. I include bond ratings to takeinto account the overall risk of the firm. Moody’s ratings are converted to numerical values by43Total debt to capitalization is [total long-term debt (DLTT) + debt in current liabilities (DLC) - cashholdings (CHE)] to [total liabilities (LT) + market value of equity (CRSP)]. The book-to-market ratio is definedas [book value of stockholders’ equity (CEQ), plus balance sheet deferred taxes (TXDITC) - book value ofpreferred stock (PST)] to [market equity (CRSP) at the end of June of the year following the fiscal year.29creating an index starting at 12 (Baa3) and linearly increasing by one for each credit ratingnotch. I control for the bond years-to-maturity because longer maturity bonds are likely tobe risker (e.g. Leland and Toft (1996)). I also include the coupon rate since bonds that payhigher coupon suffers from higher taxation (e.g. Elton, Gruber, Agrawal, and Mann (2001)).Corporate bonds exhibit various degree of trading frequency which can lead to the presence ofan illiquidity premium (e.g. Ericsson and Renault (2006), and Dick-Nielsen, Feldhu¨tter, andLando (2012)). To control for bond-specific illiquidity I include a measure of trading turnoverdefined as the average, over the past twelve months, of trading volume as a proportion oftotal amount outstanding. I also add the log amount outstanding because smaller issue arelikely to be less liquid.Finally, I include a series of macroeconomic variables to capture the level (3-month Trea-sury Bill), and the slope (10-year minus 1-year Treasury Bond yields) of the yield curve. Ialso use the 1-month Euro-Dollar spread as a proxy for aggregate demand for liquidity (e.g.Longstaff (2004)). I also include the 180-day moving average and standard deviation of theaggregate market return. Finally, I control for the aggregate labor share obtained from Bureauof Labor Statistics (Favilukis, Lin, and Zhao (2013)). In the regressions, bond yield spreadsfrom July of year t to June of year t + 1 are matched with accounting information for fiscalyear ending in year t−1. Equity and macroeconomic data are lagged one month. This ensuresthat all information is included in asset prices at the time the transaction takes place. Alsoall reported t-statistics are calculated using standard errors clustered at the industry level.Table 2.10 reports the main regression results (see for Table 2.12 for the detailed regressionoutput) estimated both from the NAIC bond transaction panel and from simulated modeldata.44 Columns (1) presents coefficient estimates without any controls. The coefficient ofinterest, δ, is estimated to be around 23bps and is statistically significant. In other words,a firm operating in the highest competition quantile is expected to have its corporate debtdiscounted by about 23bps on financial markets. Columns (2) presents the same regressionusing simulated data from the calibrated model. As expected, the model overestimates theeffects of competition on credit spreads. This is due to the fact that the empirical data setis biased towards the largest, safest firms. The coefficient of interest is estimated at 37bpsand is statistically significant. The last three columns present robustness checks. Column(3) checks whether these results are robust to the inclusion of the battery of controls definedearlier. I also add industry fixed effects. While δ slightly drops from 23bps to 18bps, it isstrongly significant at the usual confidence level. Columns (4)-(5) present results from thesame regression as column (3) but using alternative measures for competition and show thatthe model predictions are also robust across those dimensions. Note that the estimates are inline with findings in Valta (2012) who find that competitive firms pay about 15bps more onbank loans.In short, this section shows that firms operating in more competitive industries have less44Simulated panel are such that the total number of observations is equal to the data. For more details seethe table description.30valuable corporate debt. The value discount is estimated to be between 15bps and 24bps. Interms of cash flow, it means that firms facing tougher competition pay on average betweenUSD811,500 and USD1,298,000 of additional interest payments on their debt, per year.45 Themagnitude is also comparable to the effect of a one- to three-notch downgrade in credit rating.2.6.4 Competition, firm volatility and yield spreadsIn the model, competitive firms are more sensitive to changes in idiosyncratic risk (e.g. seeFigure 2.4). In this section, I test this prediction in the data. While shocks to firm-levelvolatility are well-identified in the model, they are quite challenging to identify in the data.To go around this problem, I use the 180-day moving standard deviation of abnormal excessreturns as a proxy for σz,t. In particular, I run the following regression model,csi,t = δ0 × σrxi,t−1 + δ1 × Compi,t−1 × σrxi,t−1 + β Xi,t−1 + i,t (2.44)where (i, t) denotes a specific firm-month observation, Compi,t−1 is equal to one if the firm isin the highest competition quintile and zero otherwise, σrxi,t−1 is a 180-day backward movingaverage of the market-adjusted stock return volatility, and Xi,t−1 is a vector of controls,potentially including time, industry or firm fixed effects.46 The parameter of interest is theinteraction coefficient δ1. It captures the extent to which competition increases the sensitivityof credit spreads to change in idiosyncratic risk.Table 2.11 presents the main regression output. The full detailed panel is reported in Table2.13. Column (1) reports the coefficient estimates without controls, except for industry fixedeffects. The interaction term coefficient has the expected sign, companies in more competitiveindustries are more sensitive to change in firm-specific volatility. The coefficient falls short ofstatistical significance, which is not surprising given the degree of heterogeneity in bond andfirm characteristics. Column (2) reports the coefficient estimates from model simulations. δ1is estimated at around 13bps which is slightly lower than in the data (19bps). In column(3) I control for firm and bond characteristics and δ1 becomes significant while keeping thesame magnitude of around 21bps. In economic terms, a 1% increase in idiosyncratic volatilityincreases corporate yield spreads by an additional 21bps in a more competitive industry. Interms of portfolio performance, a bond portfolio of debt issued by competitive firms lose anadditional 1.49% return for each 1% increase in idiosyncratic volatility.47 These results stayseconomically and statistically significant, even after controlling for firm fixed effects in column(4), or using the alternative measures of competition in columns (5)-(6).45These values are obtained assuming a debt face value of $541M (the average face value in the sample).46I also include in the controls the Compi,t−1 dummy.47These calculations are obtained by computing the realized return on a bond whose characteristics are setto the sample average and assuming a 1% increase in idiosyncratic volatility.312.7 ConclusionThis chapter develops a production-based asset pricing model to explore the effects of indus-try competition on the cross-section of credit spreads and levered equity returns. The modelfeatures two main sources of risks: aggregate and idiosyncratic. In equilibrium, competitionaffects asset prices by affecting the firm exposure to these risks. First, the competitive exter-nality channel creates an externality from peers’ actions that makes the firm cash flows lessprocyclical. This effect reduces firm risk. Second, competition increases the firm exposure toidiosyncratic risk and leads to a default option effect. This further reduces the risk of equityand leads corporate debt to be both less valuable and riskier. As a result of their competi-tive disadvantage in issuing debt, firms in competitive industries substitute equity for debt.Ultimately, competitive firms issue less, but more expensive debt.The model is calibrated to match a set of aggregate moments and to replicate cross-sectional differences in market power across concentration quintiles. Because the only differ-ence across industries is the intensity of competition, the model offers a compelling laboratoryto quantify the importance of product market structure. I find that competition has largeeffects on corporate decisions and asset prices. The magnitudes across competition quintilesfor equity returns and financial leverage accords with the existing empirical literature. I ver-ify additional predictions using a panel of publicly traded corporate bond transactions andfind that product market competition increases average credit spreads by 15bps. Also, creditspreads in more competitive industries are 40% more sensitive to idiosyncratic risk. Theseresults are robust to the inclusions of various controls and alternative measures of competition.32Table 2.1: Quarterly calibrationParameter Description ModelA. Preferencesβ Subjective discount factor 0.99ψ Elasticity of intertemporal substitution 2.00γ Risk aversion 10.00B. Productionα Capital share 0.33δk Depreciation rate of capital stock 2.00%ζk Capital adjustment cost parameter 10.54†C. Productivity4µ Mean of ∆at 1.72%†ρ4 Persistence of ∆at 0.85√4σa Conditional volatility of at 4.50%√4σg Conditional volatility of gt 0.34%D. FinanceC Coupon payment 7%/4ξ0 Bankruptcy costs 11.81%†ξ1 Bankruptcy costs cyclicality -10.89†σz Volatility idiosyncratic shock 0.97†τ Corporate tax rate 13.76%†χb Debt adjustment cost parameter 0.28†E. Industry parametersν Elasticity of substitution across industries 1hlow Elast. of subst. in low concentr. industry 0.2287†hhig Elast. of subst. in high concentr. industry 0.2583†This table reports the parameter values used in the benchmark quarterly calibration of the model. † denotesa parameter estimated by SMM.33Table 2.2: Simulated methods of moments estimatesTarget moment Data Model EstimatesQuarterly default rate 0.25% 0.25% σz = 0.9685Baa-Aaa yields spread 90bps 89bps ξ = 11.812%Average bond recovery 0.40 0.41 ξ1 = -10.89Volatility bond recovery 0.10 0.21Corr(Bond recovery,Default) -0.82 -0.52Corr(Bond recovery,Profit growth) 0.58 0.96Book leverage 0.40 0.35 τ = 13.76%Standard deviation book leverage 0.09 0.08 χb = 0.2816Investment-to-output vol. 4.50 5.99 ζk= 10.544Mean growth rate of output 1.80% 1.85% µ = 0.430%Profit margin high concentration 0.299 0.299 hhig = 0.2583Profit margin low concentration 0.263 0.263 hlow = 0.2287This table reports the empirical targets, model moments, and corresponding parameters estimates obtainedfrom the simulated method of moments procedure.Table 2.3: Aggregate business cycle and asset pricing momentsMoment Data Model Moment Data ModelA. Business cycleE(∆y) 1.80 1.85† corr(∆c,∆y) 0.39 0.82E(I/Y ) 0.20 0.21 corr(∆l,∆y) 0.75 0.53σ(∆y) 3.56 3.44 corr(∆c, re − rf ) 0.25 0.82σ∆c/σ∆y 0.71 0.85 ACF1(∆y) 0.35 0.10σ∆i/σ∆y 4.50 5.99† ACF1(∆c) 0.32 0.13σ∆l 1.70% 1.31% ACF1(i− k) 0.86 0.89B. Asset pricesE(re − rf ) 7.23 6.80 σ(re − rf ) 16.54 9.27E(rf ) 1.51 2.14 σ(rf ) 2.25 1.18E(cst) 90bps 89bps† σ(cst) 42bps 24bpsThis table reports aggregate macroeconomics and asset pricing moments from the model and the data. ∆y,∆c, ∆l, ∆i denotes output growth, consumption growth, labor growth, and investment growth respectively.I/Y is investment over GDP, i− k is the log investment-to-capital ratio, re − rf is the aggregate stock marketexcess return, rf is the one-period real risk-free rate, and cst is the aggregate credit spread. Model momentsare calculated by simulating the model for 25,000 quarters, with a 1,000 quarters burning period. Aggregatequantities are obtained by summing up industry-level data, aggregate returns and credit spreads are equally-weighted. Growth rates, and returns moments are annualized percentage, credit spreads are in annualizedbasis point units. † denotes a SMM target moment.34Table 2.4: Aggregate financing momentsData ModelMarket leverage 0.18 0.11Frequency of equity issuance 0.09 0.10Default rate 0.25% 0.25%†corr(Equitypay,GDP) 0.45 0.55corr(DebtRep,GDP) -0.70 -0.59corr(cs,∆y) -0.36 -0.44This table reports aggregate financing moments from the model and from the data. Debt repayment (DebtRep)and Equity payout (Equitypay) are normalized by output. Data moments are obtained from Jermann andQuadrini (2012) and Chen, Collin-Dufresne, and Goldstein (2009). Model moments are calculated by simulatingthe model for 25,000 quarters, with a 1,000 quarters burning period. The data are aggregated by summingup industry-level data. Growth rates, and returns moments are annualized percentage, credit spreads are inannualized basis point units. † denotes a SMM target moment.Table 2.5: Industry variablesSimulated moments High minus LowHigh comp. Low comp. Model DataMarket power 0.263† 0.299† -0.036† -0.036Book-to-Market 0.377 0.345 0.032 0.040Market Leverage 0.100 0.124 -0.023 -0.014Default rate 0.35% 0.15% 0.20% -E(cs) 119bps 62bps 57bps 25bpsE(ri − rf ) 6.43% 7.20% -0.76% -2.54%βCAPM 0.93 1.07 -0.14 -0.21E(rAi − rf ) 3.73% 3.88% -0.15% -This table reports several key moments sorted by competition quintiles. Model moments are calculated bysimulating the model for 25,000 quarters, with a 1,000 quarters burning period. The data are then aggregatedby competition quintiles. Data moments are obtained as follows: market power is calculated following Eq. 2.38;excess returns, market leverage, and credit spreads moments are obtained from my panel data set where com-petition is defined as the U.S. Census 4-digit SIC HHI; CAPM beta, and Book-to-Market are from Bustamanteand Donangelo (2015). Market leverage is obtained as the ratio of the market value of debt divided by sumof the market values of equity and debt. The market value of debt is defined as total debt times the marketvalue of 1$ of debt obtained from my data sample. ri − rf is the return on equity in excess of the risk-freerate, rAi − rf is the excess return on a security that receives the same operating cash flows as the benchmarkfirm with no idiosyncratic risk nor debt (see Eq. 2.39). † denotes a SMM target moment.35Table 2.6: Yield data per rating categoryRating Yield Yield Spread NAaa 5.31 64.72 304Aa 5.17 74.61 716A 5.87 123.63 1958Baa 6.44 198.05 1842This table presents the sample average of corporate yields and yield spreads by credit rating for the benchmarkdata set (Manufacturing Census HHI measure). The yield spread is obtained by subtracting from the corporatespread, a Treasury yield with equal duration. The sample period of the NAIC data is from 1995 and 2012.Yields are in percent and yield spreads are in basis points. All bonds are in U.S. dollars and have no specialfeatures (call, put, convertibility, etc.).Table 2.7: Summary statisticsVariable Mean Median SD Min MaxA. Bond characteristicsYield (%) 5.95 6.20 1.70 0.38 15.72Yield spread (bps) 141 110 113 6 1,276Coupon (%) 7.00 6.99 1.23 2.13 12.63Time to maturity (years) 9.78 7.30 7.62 0.01 29.98Issue size (Millions) 541 350 604 25 4,800Credit rating A A - Baa AaaB. Firm characteristicsCensus HHI (log) 5.13 5.16 1.05 1.24 7.07Asset size (log Millions) 9.21 9.19 1.12 6.33 12.27Long-term debt to asset 0.22 0.21 0.11 0.02 0.91Book-to-Market 0.40 0.34 0.32 -0.04 2.35This table reports summary statistics for the benchmark sample. Panel A reports bond characteristics. Yieldspreads are defined as the bond yield in excess a government bond with equal duration, coupon is the annualizedcoupon rate, Time to maturity is the difference between the maturity of the bond and the transaction date, theissue size is the total principal issued for a bond. Panel B reports firm characteristics, Census HHI is the U.S.Census Herfindhal Index computed at the 4-digit SIC industry level using the same methodology as Ali, Klasa,and Yeung (2009), Asset size is defined as total assets in Compustat, Long-term debt to asset is obtained fromCompustat, the Book-to-Market ratio is defined as the ratio of book equity to the market value of equity. Thevariable units are detailed in the first column.36Table 2.8: List of industries by concentrationSIC HHI Description24 13.23 Lumber and wood products34 46.20 Fabricated metal products35 139.11 Industrial and commercial machinery and computer equipment25 172.17 Furniture and fixtures26 182.94 Paper and allied products28 224.81 Chemicals and allied products36 234.47 Electronic, electrical equipment38 235.04 Measuring instruments29 335.99 Petroleum refining20 344.65 Food and kindred products30 540.61 Rubber and plastic products37 607.97 Transportation equipment33 790.06 Primary metal industries21 806.12 Tobacco products32 891.21 Stone, clay, glass, and concrete productsThis table reports the average values of HHI-Census for 4-digit SIC industries within a 2-digit SIC industry.4-digit SIC industries HHI are calculated by weighting the HHI-Census values of component 6-digit NAICSindustries by the square of their share of the broader 4-digit SIC industry as in Ali, Klasa, and Yeung (2009).Table 2.9: Univariate analysisHigh Competition Low Competition Test of differencesMean Median Mean Median t-test Wilcoxon testYield spread 163 bps 123 bps 138 bps 108 bps 4.41*** 4.48***E[ri − rf ] 8.59% 10.09% 11.14% 13.38% -1.96** -1.78*This table reports the means and medians aggregated across all firms/months for subsamples of the datasorted on the U.S. Census 4-digit HHI concentration measure. The High Competition corresponds to thelowest concentration quintile and Low Competition to the highest concentration quintile. The yield spread isdefined as the bond yield in excess of a government bond with equal duration and ri − rf is the annualizedrealized stock return over the following year in excess of the daily bill. The last two columns of the tablepresent test statistics of the t-test and the Wilcoxon test of the differences in mean and median across the twosamples. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.37Table 2.10: Competition and the cross-section of yield spreadsHHI Model HHI Fit HHI Markup(1) (2) (3) (4) (5)Competition 22.75** 37.39*** 18.18** 31.67*** 31.34***(1.86) (9.39) (1.92) (2.89) (3.12)Controls No No Yes Yes YesObservations 4814 5000 4814 10000 4529R2 0.01 0.13 0.49 0.36 0.50Industry FE No No Yes Yes YesThis table presents point estimates from the panel regressions examining the effects of competition on industrycredit spreads. Columns 1 and 3 are estimated using the U.S. Census HHI index at the 4-digit SIC level.Column 2 is estimated from simulated model data across 5 industries, with a time series length such thatthe total number of observations in the panel is 5,000. Columns 4 and 5 present robustness checks using FitHHI from Hoberg and Phillips (2010) and the empirical measure of markup in Eq. 2.42, respectively. Productmarket competition is measured as a dummy equal to 1 if the firm is in the lowest quintile of concentration ormarket power measures in the year previous to the transaction date. All control variables are lagged by onemonth for monthly variables and 12 months for yearly variables. Definitions of the variables included in thecontrols category is detailed in the sample description. Twelve month dummies are included in the regressionsto control for any unobserved monthly time effects, and were omitted from the table. The detailed coefficientestimates are reported in Table 2.12. I report t-statistics calculated over standard errors clustered at the 48Fama-French industries level in parentheses below the coefficient estimates. Significance at the 10%, 5%, and1% level is indicated by *, **, and ***, respectively.38Table 2.11: Firm-risk, competition and the cross-section of yield spreadsHHI Model HHI Fit HHI Markup(1) (2) (3) (4) (5) (6)Competition × Ex. ret. volatility 18.90 12.81* 22.04*** 21.25*** 44.96* 15.77*(1.21) (1.83) (3.28) (2.74) (1.79) (1.86)Volatility excess return 50.32*** 29.15*** 48.74*** 39.89*** 42.81*** 47.73***(6.28) (5.65) (4.69) (5.93) (5.68) (3.77)Controls No No Yes Yes Yes YesObservations 4814 5000 4814 4814 10000 4529R2 0.24 0.87 0.54 0.64 0.44 0.56Industry FE Yes Yes Yes No Yes YesFirm FE No No No Yes No NoThis table presents point estimates from the panel regressions examining how competition amplifies the effectsof firm-specific risk on credit spreads. Columns 1 and 3-4 are estimated using the U.S. Census HHI index atthe 4-digit SIC level. Column 2 is estimated from simulated model data across 5 industries, with a time serieslength such that the total number of observations in the panel is 5,000. Columns 5-6 presents robustness checksusing Fit HHI from Hoberg and Phillips (2010) and the empirical measure of markup in Eq. 2.42. Productmarket competition is measured as a dummy equal to 1 if the firm is in the lowest quintile of concentration ormarket power measures in the year previous to the transaction date. All control variables are lagged by onemonth for monthly variables and 12 months for yearly variables. The volatility of excess return is calculatedas the moving standard deviation of the individual stock return in excess of the market return over the past180 days. Idiosyncratic volatility in the model is measured by σz,t (see Eq. 2.40). Definitions of the variablesincluded in the different control categories is detailed in the sample description. Comp. × Ex. ret. volatility isthe interaction term between the competition dummy and excess return volatility. A dummy for competition isalso included in the regression but omitted from the table. Definitions of the variables included in the controlscategory is detailed in the sample description. Twelve month dummies are included in the regressions andomitted from the table. The detailed coefficient estimates are reported in Table 2.13. I report t-statisticscalculated over standard errors clustered at the 48 Fama-French industries level in parentheses below thecoefficient estimates. Significance at the 10%, 5%, and 1% level is indicated by *, **, and ***, respectively.39Table 2.12: Competition and the cross-section of yield spreadsCensus HHI Fit HHI Markup(1) (2) (3) (4)Competition 22.75** 18.18** 31.67*** 31.34***(1.86) (1.92) (2.89) (3.12)Mean excess return -67.40*** -119.84*** -82.46***(-2.60) (-4.36) (-3.72)Total debt to capitalization -40.26 113.60 -64.31(-0.72) (1.25) (-1.20)Tangibility 1.49 -52.27*** -4.87(0.06) (-2.60) (-0.31)Book-to-market (log) 70.57*** 51.23** 72.20***(5.18) (1.94) (3.56)Size (log) -4.10 -6.11*** -2.37(-1.15) (-2.00) (-0.48)Bond characteristicsCredit rating -13.03*** -8.43*** -10.98***(-5.30) (-5.43) (-4.46)Years to maturity 1.82*** 1.94*** 1.91***(4.82) (7.62) (4.70)Coupon rate (in %) 14.69*** 6.68*** 12.24***(5.35) (2.30) (5.68)Issue size (log) -6.37 -3.70 -8.46(-1.00) (-0.90) (-1.14)Trading turnover -77.72*** -54.61*** -43.50***(-2.95) (-2.97) (-2.44)Macroeconomic variables3m T-Bill (in %) -11.96*** -12.15*** -9.49**(-3.60) (-4.15) (-2.07)Term spread (in %) -3.59 -8.53 0.37(-0.52) (-1.42) (0.05)1m Eurodollar spread (in %) 25.85*** 10.57 22.00***(7.05) (1.59) (5.89)Labor share -1.39 7.80*** -0.79(-0.72) (5.93) (-0.49)Vol. of daily index ret. (in %) 60.72*** 21.56*** 56.02***(3.87) (2.30) (4.11)Mean daily index ret. (in %) -238.52*** -346.55*** -216.95***(-4.08) (-6.72) (-4.26)Constant 129.96*** 526.17*** -423.93*** 443.58***(9.80) (2.72) (-2.91) (2.99)Observations 4814 4814 10000 4529R2 0.01 0.49 0.36 0.50Industry FE No Yes Yes YesFor a detailed description, refer to Table 2.10.40Table 2.13: Firm volatility, competition and the cross-section of yield spreadsCensus HHI Fit HHI Markup(1) (2) (3) (4) (5)Competition × Ex. ret. volatility 18.90 22.04*** 21.25*** 44.96* 15.77*(1.21) (2.88) (2.72) (1.71) (1.86)Mean excess return -50.69*** -46.16*** -97.51*** -66.97***(-3.77) (-4.13) (-5.20) (-5.53)Equity characteristicsVolatility excess return 50.32*** 48.74*** 39.89*** 42.81*** 47.73***(6.28) (4.69) (5.93) (5.68) (3.77)Total debt to capitalization -53.06 11.50 102.27 -50.37(-1.34) (0.20) (1.57) (-1.17)Tangibility -22.25 22.74 -45.73*** -40.14(-0.87) (0.35) (-2.80) (-1.45)Book-to-market (log) 56.51*** 46.51*** 45.62* 54.24***(4.01) (2.96) (1.91) (3.44)Size (log) -7.25* -37.29*** -8.44*** -8.39(-1.78) (-3.09) (-3.42) (-1.43)Bond characteristicsCredit rating -10.31*** -2.76 -5.34*** -6.69***(-3.97) (-0.59) (-3.09) (-2.32)Years to maturity 1.86*** 1.47*** 2.00*** 1.96***(5.07) (6.36) (8.91) (4.66)Coupon rate (in %) 14.84*** 15.79*** 7.96*** 13.69***(5.83) (3.76) (3.96) (5.56)Issue size (log) -5.80 -11.62*** -1.41 -5.45(-1.45) (-2.94) (-0.52) (-1.02)Trading turnover -70.58*** -63.50*** -50.80*** -47.43***(-3.22) (-2.80) (-3.31) (-2.45)Macroeconomic variables3m T-Bill (in %) -17.68*** -29.36*** -20.80*** -16.70***(-6.43) (-5.92) (-6.18) (-3.49)Term spread (in %) -6.95 -25.47*** -15.08*** -6.85(-1.50) (-3.76) (-2.76) (-1.10)1m Eurodollar spread (in %) 29.73*** 24.79*** 11.75*** 25.36***(8.51) (7.22) (1.99) (8.80)Labor share -6.41*** -4.96*** 2.65* -6.18***(-2.94) (-2.83) (1.69) (-3.16)Vol. of daily index ret. (in %) 11.84 17.93 -27.67* 10.07(1.05) (1.58) (-1.83) (0.79)Mean daily index ret. (in %) -259.50*** -247.97*** -321.26*** -233.59***(-5.03) (-4.78) (-8.09) (-5.75)Competition -29.76 -29.12*** -41.74*** -74.91 0.35(-0.95) (-2.37) (-2.41) (-1.46) (0.02)Constant 42.03*** 1050.70*** 1436.00*** 67.45 982.92***(3.06) (4.16) (3.71) (0.40) (4.42)Observations 4814 4814 4814 10000 4529R2 0.24 0.54 0.64 0.44 0.56Industry FE Yes Yes No Yes YesFirm FE No No Yes No NoFor a detailed description, refer to Table 2.11.41Figure 2.1: Economic environmentThis figure depicts the economic environment of the benchmark model assuming two industries in the economy.42Figure 2.2: Aggregate impulse-response functions0 5 10 15 20012∆a [%]0 5 10 15 20012∆c [%]0 5 10 15 2000.050.1Market to Book0 5 10 15 20024re − rf [%]0 5 10 15 20−0.1−0.050Default [%] 0 5 10 15 20−10−50cs [bps]0 5 10 15 20−15−10−50Debt payout [%]quarters0 5 10 15 20051015Equity payout [%]quarters  LRSRThis figure plots the impulse-response function to a positive long-run (red solid) and short-run (blue dashed)productivity shock for productivity growth (∆a), consumption growth (∆c), the aggregate Market to Bookratio, the aggregate stock market excess return (re − rf ), the aggregate default probability (Default), theaggregate credit spread (cs), and the aggregate debt and equity payout. The plots are calculated as deviationfrom the steady state. Units, when applicable, are specified next to the plot title.43Figure 2.3: Industries impulse-response functions0 5 10 15 2000.10.2∆a [%]0 5 10 15 200.1E[∆y] [%]0 5 10 15 20−0.0200.02price [%]0 5 10 15 20051015x 10−3 Dividend 0 5 10 15 2000. to Book0 5 10 15 200123ri − rf [%]0 5 10 15 20−0.06−0.04−0.020quartersDefault [%] 0 5 10 15 20−10−50quartersCredit spread [bps]   Low comp.High comp.This figure plots the impulse-response functions to a positive long-run productivity shock for industries thatdiffer in their degree of product market competition. The responses in the low-competition industry are plottedin red solid while those in the high-competition industry are plotted in dashed blue. ∆a denotes productivitygrowth, E[∆y] is the expected production growth in the industry, price is the industry output price relative tothe aggregate price index, and ri− rf is the industry stock excess return. The plots are calculated as deviationfrom the steady state. Units, when applicable, are specified next to the plot title.44Figure 2.4: Idiosyncratic risk shock and industry credit spreads0 5 1000.010.020.03σz   Low comp.High comp.0 5 1000.050.1Default [%] 0 5 10024quartersCredit spread [bps] 0 5 10−2−10x 10−3quartersDebt−to−asset This figure plots the impulse-response functions to a positive idiosyncratic volatility shock for industries thatdiffer in their degree of product market competition. The responses in the low-competition industry are plottedin red solid while those in the high-competition industry are plotted in dashed blue. σz denotes the volatilityof the idiosyncratic shock. The plots are calculated as deviation from the steady state. Units, when applicable,are specified next to the plot title.45Figure 2.5: Time-series of Baa spread from NAIC sample and Moody’s100200300400500600yield spread (bps)1995 1997 1999 2001 2002 2004 2006 2008 2010 2012yearsNAIC Baa spread Moody’s Baa spreadThis figure compares the quarterly time series of average Baa bond spreads reported by Moody’s and the sameseries obtained from the NAIC bond transaction file between 1995 and 2012. Yield spreads are in basis points.Bonds from NAIC are in U.S. dollars and have no special features (call, put, convertibility, etc.).46Chapter 3Competition, Markups, andPredictable Returns3.1 IntroductionEconomists have long argued that the creation of new businesses is an important engine ofgrowth. In fact, careful measurement reveals that the vast majority of productivity growthoccurs as new establishments enter product markets (for recent evidence, see, e.g. Gourio,Messer, and Siemer (2014)). The flipside of entry is that old establishments face increasedcompetitive pressure that may eventually drive them out of business. Going back at least toSchumpeter, economists have referred to this process as ‘creative destruction’. One strikingstylized fact about the intensity of net business creation is that it is highly procyclical.1 Whileprocyclical variation in the number of competitors is related to changes in profit opportunities,it also suggests that competitive pressure and the price elasticity of demand, should adjustaccordingly. Indeed, a long list of contributions documents empirically that markups arecountercyclical2 and that the degree of competitiveness in industries is strongly procyclical.3In this essay, we quantitatively link variation in industry concentration to the predictablecomponent in equity risk premia. We show theoretically and empirically that measures of netbusiness formation and markups forecast the equity premium. To this end, we build a generalequilibrium asset pricing model with monopolistic competition and endogenous firm entry andexit. There are two endogenous components of measured productivity in the model, productinnovation and process innovation. Product innovation refers to resources expended for thecreation of new products and firms (e.g., Atkeson and Burstein (2011)). Process innovationrefers to incumbent firms investing to upgrade their technology in response to the entry threat.1See, e.g., Chatterjee and Cooper (2014), Devereux, Head, and Lapham (1996), Jaimovich and Floetotto(2008), Bilbiie, Ghironi, and Melitz (2012)2See, for example, Bils (1987), Rotemberg and Woodford (1991) and Rotemberg and Woodford (1999),Chevalier, Kashyap, and Rossi (2003).3Some examples include Bresnahan and Reiss (1991) and Campbell and Hopenhayn (2005)47Due to spillover effects from process innovation, process innovation provides a powerful low-frequency growth propagation mechanism that leads to sizable endogenous long-run risks asin Kung (2015) and Kung and Schmid (2015).Product innovation, on the other hand, implies a novel amplification mechanism for shocksat business cycle frequencies. A positive technology shock raises profits and increases firmcreation, and vice versa (e.g., firm creation is procyclical). Also, the price elasticity of demandis positively related to the number of competitors in a particular industry. Thus, markups arecountercyclical, which magnifies short-run risks. In booms (downturns), markups fall whichexpands (contracts) production more. Consequently, short-run dividends are very risky andthe model produces a U-shaped term structure of equity returns, consistent with the empiricalevidence from van Binsbergen, Brandt, and Koijen (2012).We show that in equilibrium the relation between the number of firms and markups isnonlinear. In economic downturns, profits fall, firms exit and industry concentration rises.As a consequence, surviving producers enjoy elevated market power and face steeper demandcurves. While this allows firms to charge higher markups in our model, it also makes themmore sensitive to aggregate shocks and implies that the amplification mechanism is asymmet-ric. Markups increase more in recessions than it decreases in booms. Consequently, the modelendogenously produces countercyclical macroeconomic volatility. With recursive preferences,these volatility dynamics generate a countercyclical equity premium that can be forecastedby measures of industry concentration.The calibrated model generates an equity premium of around 5% on an annual basis, whilesimultaneously fitting a wide-range of macroeconomic moments, including those relating tomarkup and business creation dynamics. The sizable equity premium is primarily compen-sation for the endogenous long-run risks (e.g., Bansal and Yaron (2004) and Croce (2014))generated by the process innovation channel as in Kung (2015) and Kung and Schmid (2015).The countercyclical equity premium is attributed to the product innovation channel due tononlinearities in markup dynamics. The model generates quantitatively significant endoge-nous variation in risk premia. For example, excess stock return forecasting regressions usingthe price-dividend ratio produces a R2 of 0.22 at a five-year horizon. The model also pre-dicts that excess stock returns can be forecasted by markups, profit shares, and net businessformation, which we find strong empirical support for. In short, this essay highlights howfluctuations in competitive pressure are an important source of time-varying risk premia.3.1.1 LiteratureOur work belongs to several strands of literature. First, the essay is related to the emergingliterature linking risk premia and imperfect competition. Second, it connects to research onsources of endogenous return predictability. Third, it contributes to the literature on generalequilibrium asset pricing with production.Our starting point is an innovation-driven model of stochastic endogenous growth follow-48ing Kung (2015) and Kung and Schmid (2015). Also, Ward (2015) uses a similar framework asKung and Schmid (2015) to estimate the transition dynamics of the IT revolution. Method-ologically, this work builds on the literature on medium-term cycles pioneered by Comin andGertler (2006) and Comin, Gertler, and Santacreu (2009). More generally, these papers area stochastic extension of the endogenous growth models developed by Romer (1990), Aghionand Howitt (1990), and Peretto (1999). We extend the framework from Kung (2015) andKung and Schmid (2015) to account for entry and exit along the lines of Bilbiie, Ghironi, andMelitz (2012) and Jaimovich and Floetotto (2008), and examine the asset pricing implica-tions. We follow the multisector approach from Jaimovich and Floetotto (2008), which yieldsendogenous countercyclical markups. Opp, Parlour, and Walden (2014) obtain time-varyingmarkups in a model of strategic interactions at the industry level.This essay is related to a growing literature studying the link between product marketcompetition and stock returns. Hou and Robinson (2006), Bustamante and Donangelo (2015),van Binsbergen (2015), and Loualiche (2014) examine the impact of competition on the crosssection of stock returns. This essay is closely related to Loualiche (2014) who also considersa general equilibrium asset pricing model with recursive preferences and entry and exit. Hefinds that aggregate shocks to entry rates are an important factor priced in the cross-sectionof returns. Our work differs from these papers by focusing on the time-series implications andespecially on how changes in competition endogenously generate time-varying risk premia.Our approach therefore provides distinct and novel empirical predictions.This essay shares its focus with the growing literature on asset pricing in general equi-librium models with production. Papers that use habit preferences include Jermann (1998)and Boldrin, Christiano, and Fisher (2001). More recently, Tallarini (2000), Campanale, Cas-tro, and Clementi (2010), Kuehn (2008), Ai (2010) and Kaltenbrunner and Lochstoer (2010)explore endogenous long-run consumption risks in real business cycle models with recursivepreferences. Gourio (2012) and Gourio (2013) examine disaster risks. Particularly closelyrelated are recent papers by Croce (2014), Backus, Routledge, and Zin (2007), Backus, Rout-ledge, and Zin (2008), Gomes, Kogan, and Yogo (2009), Kogan and Papanikolaou (2010),Garleanu, Kogan, and Panageas (2009), Papanikolaou (2011), and Ai, Croce, and Li (2013)who examine the implications of long-run productivity risk and technological innovation forequity market returns. Our approach differs from their work as technological progress andproductivity growth is endogenous in our model through process and product innovation.Furthermore, these papers focus on unconditional asset pricing moments, while we considerreturn predictability.Our work is related to papers examining mechanisms that generate return predictability.Dew-Becker (2014) and Kung (2015) generate return predictability by assuming exogenoustime-varying processes in risk aversion and the volatility of productivity, respectively. Anumber of papers show how predictability can be generated endogenously. Favilukis and Lin(2016) and Favilukis and Lin (2015), Kuehn, Petrosky-Nadeau, and Zhang (2012), Santos and49Veronesi (2006) work through frictions in the labor markets. In these papers, wages effectivelygenerate operating leverage and they identify variables related to labor market conditions thatcan forecast stock returns. Gomes and Schmid (2010) explicitly model financial leverage ingeneral equilibrium and find that credit spreads forecast stock returns through countercyclicalleverage. Our channel, which operates through endogenous time-varying markups, is noveland allows us to empirically identify a new set of predictive variables for stock returns linkedto time-varying competitive pressure.Finally, this essay relates to models that try to explain the declining term structure ofequity returns documented in van Binsbergen, Brandt, and Koijen (2012) and van Binsber-gen, Hueskes, Koijen, and Vrugt (2013). Belo, Collin-Dufresne, and Goldstein (2015) show,in an endowment economy, that imposing a stationary and procyclical leverage ratio ampli-fies short-run risks and increases the procyclicality of short-term dividends, which leads to adownward sloping term structure. Croce, Lettau, and Ludvigson (2014) also generate this re-sult using an endowment economy with limited information. Ai, Croce, Diercks, and Li (2012)and Favilukis and Lin (2016) show how vintage capital and wage rigidities, respectively, arealternative channels in a production-based framework. In contrast to these papers, endoge-nous countercyclical markups in our model provide a distinct but complimentary amplificationmechanism for short-run risks that helps to explain the equity term structure.The chapter is organized as follows. We describe our model in section 2 and examine themain economic mechanisms in section 3. The next section discusses quantitative implicationsby means of a calibration, and presents empirical evidence supporting our model predictions.Section 5 offers a few concluding remarks.3.2 ModelIn this section, we present a general equilibrium asset pricing model with imperfect com-petition and endogenous productivity growth. Endogenous innovation impacts productivitygrowth because of imperfect competition, as markups and the associated profit opportunitiesprovide incentives for new firms to enter (product innovation) and for incumbent firms toinvest in their own production technology (process innovation). Cyclical movements in profitopportunities affect the mass of active firms and thus competitive pressure and markups. Wealso assume a representative household with recursive preferences.Overall the model is a real version of the endogenous growth framework of Kung (2015),extended to allow for entry and exit with multiple industries and time-varying markups. Westart by briefly describing the household sector, which is quite standard. Then we explainin detail the production sector and the innovation process in our economy, and define thegeneral equilibrium. Also, note that we use calligraphic letters to denote aggregate variables.503.2.1 HouseholdThe representative agent is assumed to have Epstein-Zin preferences over aggregate consump-tion Ct and labor Lt4Ut = u (Ct,Lt) + β(Et[U1−θt+1 ]) 11−θwhere θ = 1− 1−γ1−1/ψ , γ captures the degree of risk aversion, ψ is the elasticity of intertemporalsubstitution, and β is the subjective discount rate. The utility kernel is assumed to beadditively separable in consumption and leisure,u (Ct,Lt) = C1−1/ψt1− 1/ψ + Z1−1/ψt χ0(1− Lt)1−χ1− χwhere χ captures the Frisch elasticity of labor5, and χ0 is a scaling parameter. Note that wemultiply the second term by an aggregate productivity trend Z1−1/ψt to ensure that utilityfor leisure does not become trivially small along the balanced growth path.When ψ 6= 1γ , the agent cares about news regarding long-run growth prospects. We willassume that ψ > 1γ so that the agent has a preference for early resolution of uncertainty anddislikes uncertainty about long-run growth rates.The household maximizes utility by participating in financial markets and by supplyinglabor. Specifically, the household can take positions Ωt in the stock market, which pays anaggregate dividend Dt, and in the bond market Bt. Accordingly, the budget constraint of thehousehold becomesCt +QtΩt+1 + Bt+1 =WtLt + (Qt +Dt)Ωt +Rf,tBt, (3.1)where Qt is the stock price, Rf,t is the gross risk free rate and Wt is the wage rate.These preferences imply the stochastic discount factor (intertemporal marginal rate ofsubstitution)Mt+1 = β Ut+1Et(U1−θt+1 )11−θ−θ (Ct+1Ct)− 1ψAdditionally, the labor supply condition states that at the optimum the household trades4Traditionally, Epstein-Zin preference are defined as U˜t ={u (Ct,Lt)1−1/ψ + β(Et[U˜1−γt+1 ]) 1−1/ψ1−γ} 11−1/ψwhere γ is the coefficient of relative risk aversion and ψ is the intertemporal elasticity of substitution. Thefunctional form above is equivalent when we define Ut = U˜1−1/ψt and θ = 1− 1−γ1−1/ψ but has the advantage ofadmitting more general utility kernels u (Ct,Lt) (see Rudebusch and Swanson (2012)).5Given our assumption that the household works 1/3 of his time endowment in the steady state, the steadystate Frisch labor supply elasticity is 2/χ.51off the wage rate against the marginal disutility of providing labor, so thatWt = χ0(1− Lt)−χC−1/ψtZ1−1/ψt .3.2.2 Production sectorThe production sector is composed of three entities: final goods production, intermediategoods production, and the capital producers. The final good aggregates inputs from a con-tinuum of industries, and each industry uses a finite measure of differentiated intermediategoods as inputs. Stationary shocks drive stochastic fluctuations in the profits on interme-diate goods. Higher profit opportunities induce new intermediate goods producers to enter(product innovation) and incumbent firms respond by upgrading their technology throughR&D (process innovation). The capital sector produces and accumulates both physical andintangible capital and rents it out to the intermediate goods firms.Final Goods The final goods sector is modeled following Jaimovich and Floetotto (2008).The final good is produced by aggregating sectoral goods which are themselves compositesof intermediate goods. We think of each sector as a particular industry and use these labelsinterchangeably.More specifically, a representative firm produces the final (consumption) goods in a per-fectly competitive market. The firm uses a continuum of sectorial goods Yi,t as inputs in thefollowing CES production technologyYt =(∫ 10Yν1−1ν1i,t di) ν1ν1−1where ν1 is the elasticity of substitution between sectorial goods. The profit maximizationproblem of the firm yields the isoelastic demand for sector j goods,Yj,t = Yt(Pj,tPY,t)−ν1where PY,t =(∫ 10 P1−ν1j,t dj) 11−ν1 is the final goods price index (and the numeraire). We providethe derivations in the appendix.In turn, each industry j produces sectoral goods using a finite number Nj,t of differentiatedgoods Xi,j,t. Importantly, the number of differentiated goods in each industry is allowed tovary over time. Because each industry is atomistic, sectorial firms face an isoelastic demandcurve with constant price elasticity ν1. The sectoral goods are aggregated using a CES52production technologyYj,t = N1− ν2ν2−1j,tNj,t∑i=1Xν2−1ν2i,j,tν2ν2−1where Nj,t is the number of firms and ν2 is the elasticity of substitution between intermediategoods. The multiplicative term N1− ν2ν2−1j,t is added to eliminate the variety effect in aggregation.The profit maximization problem of the firm yields the following demand schedule forintermediate firms in industry j (see the appendix for derivations):Xi,j,t =Yj,tNj,t(Pi,j,tPj,t)−ν2where Pi,j,t is the price of intermediate good i in industry j and Pj,t = N−11−ν2j,t(∑Nj,ti=1 P1−ν2i,j,t) 11−ν2is the sector j price index. In the following, we assume that the elasticity of substitution withinindustry is higher than across industries, i.e. ν2 > ν1.Intermediate Goods Intermediate goods production in each industry is characterized bymonopolistic competition. In each period, a proportion δn of existing firms becomes obsoleteand leaves the economy. The specification of the production technology is similar to Kung(2015). Intermediate goods firms produce Xi,j,t using a Cobb-Douglas technology defined overphysical capital Ki,j,t, labor Li,j,t, and technology Zi,j,t. We think of technology as intangiblecapital, such as patents. Firms rent their physical and technology from capital producers ata period rental rate of rkj,t and rzj,t, respectively. Labor input is supplied by the household.We assume that technology is only partially appropriable and that there are spillovers acrossfirms. The production technology isXi,j,t = Kαi,j,t(AtZηi,j,tZ1−ηt Li,j,t)1−αwhere Zt ≡∫ 10(∑Nj,ti=1 Zi,j,t)dj is the aggregate stock of technology in the economy and theparameter η ∈ [0, 1] captures the degree of technological appropriability. These spillover effectsare crucial for generating sustained growth in the economy (e.g. Romer (1990)). Technologyincreases the efficiency of intermediate good production, so that we interpret that input asprocess innovation. The variable At represents an aggregate technology shock that is commonacross firms and evolves in logs as an AR(1) process:at = (1− ρ)a? + ρat−1 + σtwhere at ≡ log(At), t ∼ N(0, 1) is i.i.d., and a? is the unconditional mean of at.53Dividends for an intermediate goods firm is then given byDi,j,t =Pi,j,tPY,tXi,j,t −Wj,tLi,j,t − rkj,tKi,j,t − rzj,tZi,j,t.The demand faced by an individual firm depends on its relative price and the sectoraldemand which in turn depends on the final goods sector. Expressing the inverse demand asa function of final goods variables,Xi,j,t =YtNj,t(P˜i,j,t)−ν2 (P˜j,t)ν2−ν1where tilde-prices are normalized by the numeraire, i.e. P˜i,j,t ≡ Pi,j,tPY,t and P˜j,t ≡Pj,tPY,t.The objective of the intermediate goods firm is to maximize shareholder’s wealth, takinginput prices and the stochastic discount factor as given:Vi,j,t = max{Li,j,t,Ki,j,t,Zi,j,t,P˜i,j,t}t≥0E0[ ∞∑s=0Mt,t+s(1− δn)sDi,j,s]s.t. Xi,j,t =YtNj,t(P˜i,j,t)−ν2 (P˜j,t)ν2−ν1where Mt,t+s is the marginal rate of substitution between time t and time t+ s.This market structure yields a symmetric equilibrium in the intermediate goods sector.Hence, we can drop the i subscripts in the equations above. As derived in the appendix, thecorresponding first order necessary conditions arerkj,t =αøj,tXj,tKj,trzj,t =η(1− α)øj,tXj,tZj,tWj,t =(1− α)øj,tXj,tLj,tøj,t =−ν2Nj,t + (ν2 − ν1)−(ν2 − 1)Nj,t + (ν2 − ν1)where øj,t is the price markup reflecting monopolistic competition. Note that the price markupdepends on the number of active firms Nj,t in each industry, and so can be time-varying. Wedescribe how the evolution of the mass of active firms is endogenously determined below.Capital producers Capital producers operate in a perfectly competitive environment andproduce industry-specific capital goods. They specialize in the production of either physicalcapital or technology.Physical capital producers lease capital Kcj,t to sector j for production in period t at a54rental rate of rkj,t. At the end of the period, they retrieve (1− δk)Kcj,t of depreciated capital.They produce new capital by transforming Ij,t units of output bought from the final goodsproducers into new capital via the technology6:Φk,j,tKcj,t = α1,k1− 1ζk(Ij,tKcj,t)1− 1ζk+ α2,kKcj,tTherefore, the evolution of aggregate physical capital in industry j isKcj,t+1 = (1− δk)Kcj,t + Φk,j,tKcj,tand the dividend is defined as rkj,tKcj,t − Ij,t.The optimization problem faced by the representative physical capital producer is to chooseKcj,t+1 and Ij,t in order to maximize shareholder value:V kj,t = max{Ij,t,Kcj,t+1}t≥0E0[ ∞∑s=0Mt,t+s(rkj,sKcj,s − Ij,s)]s.t. Kcj,t+1 = (1− δk)Kcj,t + Φk,j,tKcj,tAs shown in the appendix, this optimization problem yields the following first order con-ditions:Qkj,t = Φ′−1k,j,tQkj,t = Et[Mt,t+1(rkj,t+1 +Qkj,t+1(1− δk − Φ′k,j,t+1(Ij,tKcj,t)+ Φk,j,t+1))]where Qkt is the Lagrange multiplier on the capital accumulation constraint.The structure of the technology capital producer is similar. More specifically, this sectorproduces new intangible capital by transforming Sj,t units of output bought from the finalgoods producers into new technology via the technology7:Φk,j,tZcj,t = α1,z1− 1ζz(Sj,tZcj,t)1− 1ζz+ α2,zZcj,t.We think of Sj,t as investment in R&D. In the model, therefore, technology accumulatesendogenously.6This functional form for the capital adjustment costs is borrowed from Jermann (1998). The parame-ters α1,k and α2,k are set to values so that there are no adjustment costs in the deterministic steady state.Specifically, α1,k = (∆Z − 1 + δk)1ζk and α2,k =1ζk−1 (1− δk −∆Z).7Similarly, the parameters α1,z and α2,z are set to values so that there are no adjustment costs in thedeterministic steady state. Specifically, α1,z = (∆Z − 1 + δz)1ζz and α2,z =1ζz−1 (1− δz −∆Z).55As with physical capital producers, the optimization problem of the representative tech-nology producer is to maximize shareholder value, so that the first conditions are,Qzj,t = Φ′−1z,j,tQzj,t = Et[Mt,t+1(rzj,t+1 +Qzj,t+1(1− δz −(Sj,t+1Zcj,t+1)Φ′z,j,t+1 + Φz,j,t+1))]Zcj,t+1 = (1− δz)Zcj,t + Φz,j,tZcj,t.3.2.3 Entry & exitEach period, new firms contemplate entering the intermediate goods sector. Entry into theintermediate goods sector entails the fixed cost FE,j,t ≡ κjZt. A newly created firm will startproducing in the following period. Note that these costs are multiplied by the aggregate trendin technology to ensure that the entry costs do not become trivially small along the balancedgrowth path.The evolution equation for the number of firms in the intermediate goods sector isNj,t+1 = (1− δn)Nj,t +NE,j,twhere NE,j,t is the number of new entrants and δn is the fraction of firms, randomly chosen,that become obsolete after each period. The entry condition is:Et[Mt+1Vj,t+1] = FE,j,t (3.2)where Vj,t = Dj,t + (1 − δn)Et[Mt+1Vj,t+1] is the market value of the representative firm insector j. Movements in profit opportunities and valuations thus lead to fluctuations in themass of entering firms.3.2.4 EquilibriumSymmetric Equilibrium We focus on a symmetric equilibrium, in which all sectors andintermediate firms make identical decisions, so that the i and j subscripts can be dropped.Given the symmetric equilibrium, we can express aggregate output asYt = NtXtXt = Kαt (AtZηt Z1−ηt Lt)1−αAggregation Aggregate macro quantities are defined as: It ≡∫ 10 Ij,t dj = It, St ≡∫ 10 Sj,t dj =St, Zt ≡∫ 10∑Nti=1 Zi,j,t dj = NtZt, Kt ≡∫ 10∑Nti=1Ki,j,t dj = NtKt. The aggregate dividend56coming from the production sector is defined asDt = NtDt + (rktKt − It) + (rztZt − St)Note that the aggregate dividend includes dividends from the capital and technology sectors.Market Clearing Imposing the symmetric equilibrium conditions, the market clearingcondition for the final goods market is:Yt = Ct + It + St +NE,t · FE,tThe market clearing condition for the labor market is:Lt =Nt∑j=1Lj,tImposing symmetry, the equation above impliesLt =LtNtThe market clearing condition for the capital markets implies that the amount of capitalrented by firms equals the aggregate supply of capital:Kt = KctZt = ZctEquilibrium We can thus define an equilibrium for our economy in a standard way. Ina symmetric equilibrium, there is one exogenous state variable, At, and three endogenousstate variables, the physical capital stock Kt, the intangible capital stock Zt, and the numberof intermediate good firms, Nt. Given an initial condition {A0,K0,Z0,N0} and the law ofmotion for the exogenous state variable At, an equilibrium is a set of sequences of quantitiesand prices such that (i) quantities solve producers’ and the household’s optimization problemsand (ii) prices clear markets.We interpret the stock market return as the claim to the entire stream of future aggregatedividends, Dt.3.3 Economic mechanismsOur model departs in two significant ways from the workhorse stochastic growth model inmacroeconomics. First, our setup incorporates imperfect competition and the entry and exitof intermediate goods firms. Product innovation, or the variation in the number of firms57in a particular sector, changes the degree of industry competitiveness. Second, rather thanassuming an exogenous trend in aggregate productivity, the long-run growth is endogenouslydetermined by firms’ investment in their technology, which we refer as process innovation.In this section, we qualitatively examine how both product and process innovation producerich model dynamics with only a single homoscedastic technology shock. In particular, inthe language of Bansal and Yaron (2004), we document that product innovation providesan amplification mechanism for short-run risks while process innovation provides a growthpropagation mechanism that generates long-run risks. Further, the product innovation channelgenerates conditional heteroscedasticity in macroeconomic quantities due to nonlinearities inmarkups.While we focus on a qualitative examination of our setup here, we provide a detailedquantitative analysis of the model in the next section.3.3.1 Product innovationThis subsection describes how business creation combined with imperfect competition providesan short-run amplification mechanism that is asymmetric. This channel is important forgenerating return predictability and a U-shaped term structure of equity returns.Entry & Exit We start by examining the business creation process through the free entrycondition, equation (3.2). Suppose there is a positive technology shock. As firms becomemore productive, the value of intermediate goods firms increases. Attracted by higher profitopportunities, new firms enter the market. Firms will enter the market up until the entrycondition is satisfied, implying procyclical entry. On the other hand, as the number of firmsin the economy grows, product market competition intensifies. Thus, the model is consistentwith the empirical evidence that the degree of competitiveness in industries is procyclical,as documented, for example, in Bresnahan and Reiss (1991) and Campbell and Hopenhayn(2005).Next, we show that in our model how changes in the number of competitors in an industrylead to time-varying markups.Markups In the classic Dixit-Stiglitz CES aggregator, an individual firm is atomistic.Therefore, a single firm will not affect the sectoral price level, Pj,t. The firm faces a con-stant price elasticity of demand and charges a constant markup equal to ν2ν2−1 .In contrast, in our model the measure of firms within each sector is finite. Consequently,the intermediate producer takes into account its effect on the sectoral price index. This impliesthat the price elasticity of demand in a sector depends on the number of firms. As we show inthe appendix, intermediate firms’ cost minimization problem implies that the price markup58is8øt =−ν2Nt + (ν2 − ν1)−(ν2 − 1)Nt + (ν2 − ν1) .Thus, equilibrium markups depend on the number of active firms and thus, the degree ofcompetition. Taking the derivative of the markup with respect to Nt, we find∂øt∂Nt =ν1 − ν2[−(ν2 − 1)Nt + (ν2 − ν1)]2< 0. (3.3)Assuming that the elasticity of substitution within industries is higher than across sectors(ν2 > ν1) implies that markups decrease as the number of firms increases, and thus arecountercyclical in the model. This implication is consistent with the empirical evidence doc-umented e.g. in Bils (1987), Rotemberg and Woodford (1991) and Rotemberg and Woodford(1999) and Chevalier, Kashyap, and Rossi (2003). Moreover, countercyclical markups amplifiyshort-run risks as in booms (downturns), markups are higher which expands (contracts) pro-duction more. Riskier short-run cash flows allows the model to generate a downward slopingequity term structure initially.The expression for the derivative of the markup with respect to the number of firms Ntimplies that the sensitivity of markups to a marginal entrant depends on the number of firmsin the industry. The nonlinear relation between markups and Nt is illustrated in figure 3.1.Adding a new firm to an already highly competitive industry (high Nt) will have little impacton product market competition. In contrast, a marginal entrant will have a large impact onmarkups when the number of firms are low. Consequently, markups will rise more recessionsthan it falls in booms, which leads to countercyclical macroeconomic volatility.3.3.2 Process innovationThis subsection illustrates the long-run growth propagation mechanism through process in-novation. This channel generates endogenous long-run risks.Endogenous Productivity The aggregate production technology can be expressed asYt = NtKαt (AtZηt Z1−ηt Lt)1−α= Nt(KtNt)α [At(ZtNt)ηZ1−ηt(LtNt)]1−α= Ktα [Zp,tLt]1−αwhere Zp,t ≡ AtZtN−ηt is measured TFP, which is composed of three components. At is anexogenous component while Zt, the stock of intangible capital, is endogenously accumulatedthrough process innovation (i.e., R&D), and the mass of active firms Nt, endogenously created8The standard constant markup specification is a particular case in which Nt →∞.59through product innovation. Due to the spillover effect from process innovation, Zt grows andis the endogenous trend component.To filter out the cyclical components of productivity, we can take conditional expectationsof the log TFP growth rate:Et[∆zp,t+1] = E[∆at+1 + ∆zt+1 − η∆nt+1]≈ ∆zt+1,where the second approximation is recognizing that at+1 and nt+1 are persistent stationaryprocesses, so ∆at+1 and ∆nt+1 are approximately iid. Thus, as in Kung (2015) and Kung andSchmid (2015), low-frequency components in growth are driven by the accumulation of intan-gible capital, which they also find strong empirical support for. With recursive preferences,these low-frequency movements in productivity lead to sizable risk premia in asset markets.3.4 Quantitative implicationsIn this section, we present quantitative results from a calibrated version of our model. Wecalibrate it to replicate salient features of industry and business cycles and use it to gaugethe quantitative significance of our mechanisms for risk premia. We also provide empiricalevidence supporting the model predictions.In order to quantitatively isolate the contributions of process innovation, product inno-vation and time-varying markups on aggregate risk and risk premia, we find it instructive tocompare our benchmark model to another nested model. In the following, we refer to thebenchmark model as model A. Model B features a CES aggregator, and abstracts away fromentry and exit, so that the mass of firms and hence markups are constant.The models are calibrated at quarterly frequency. The empirical moments correspond tothe U.S. postwar sample from 1948 to 2013. The model is solved using third-order perturbationmethods.9Calibration We begin with a description of the calibration and the construction of the keyempirical data series, such as entry rates, markups, R&D, and intangible capital stock.Following Bils (1987), Rotemberg and Woodford (1999) and Campello (2003), we constructan empirical price markup series by exploiting firms’ first order condition with respect to Lt,imposing the symmetry condition,øt = (1− α) YtLtWt = (1− α)1SL,tand adjusting for potential nonlinearities in the empirical counterparts. Here, SL,t is the labor9We prune simulations using the Kim, Kim, Schaumburg, and Sims (2008) procedure to avoid generatingexplosive paths in simulations.60share in the model. We discuss further details about the construction of the markup measurein the appendix.For entry rates, we use two empirical counterparts. First, we use the index of net businessformation (NBF). This index is one of the two series published by the BEA to measure thedynamics of firm entry and exit at the aggregate level. It combines a variety of indicators intoan approximate index and is a good proxy for nt. The other is the number of new businessincorporations (INC), obtained from the U.S. Basic Economics Database. Both series havesimilar dynamics. Below, we provide a number of robustness checks with respect to bothmeasures.Finally, our empirical series for St measures private business R&D investment and comesfrom the National Science Foundation (NSF). The Bureau of Labor Statistics (BLS) constructsthe R&D stock by accumulating these R&D expenditures and allowing for depreciation, muchin the same way as the physical capital stock is constructed. We thus use the R&D stock asour empirical counterpart for the stock of technology Zt. For consistency, we use the samedepreciation rate δn in our calibration as does the BLS in its calculations. The remainingempirical series are standard in the macroeconomics and growth literature. Additional detailsare collected in the appendix.Table 3.1 presents the quarterly calibration. Panel A reports the values for the preferenceparameters. The elasticity of intertemporal substitution ψ is set to 1.8 and the coefficient ofrelative risk aversion γ is set to 10.0, both of which are standard values in the long-run risksliterature (e.g. Bansal, Kiku, and Yaron (2008)). The labor elasticity parameter χ, is set to 3.This implies a Frisch elasticity of labor supply of 2/3, which is consistent with estimates fromthe microeconomics literature (e.g. Pistaferri (2003)). χ0 is set so that the representativehousehold works 1/3 of her time endownment in the steady state. The subjective discountfactor β is calibrated to 0.995 to be consistent with the level of the real risk-free rate.Panel B reports the calibration of the technological parameters. The capital share α is setto 0.33, and the depreciation rate of capital δk is set to 2.0%. These two parameters are cali-brated to standard values in the macroeconomics literature (e.g. Comin and Gertler (2006)).The parameters related to R&D are calibrated following Kung (2015). The depreciation rateof the R&D capital stock δz is set to 3.75%, implying an annualized depreciation rate of 15%.The physical and R&D capital adjustment cost parameters ζk and ζz are both set at 0.738 tobe consistent with the relative volatility of R&D investment growth to physical investmentgrowth. The degree of technological appropriability η is calibrated to 0.065, in line with Kung(2015). The exogenous firm exit shock δn is set to 1%, slightly lower than in Bilbiie, Ghironi,and Melitz (2012). The price elasticity across (ν1) and within (ν2) industries are calibratedto 1.05 and 75, respectively to be consistent with estimates from Jaimovich and Floetotto(2008). κ is set to ensure an aggregate price markup of 20% in the deterministic steady state.Panel C reports the parameter values for the exogenous technology process. The volatilityparameter σ is set at 1.24% to match the unconditional volatility of measured productivity61growth. The persistence parameter ρ is calibrated to 0.985 to match the first autocorrelationof expected productivity growth. a? is chosen to generate an average output growth of 2.0%.3.4.1 Quantitative resultsWe now report quantitative results based on our calibration. We start by discussing the natureof macroeconomic dynamics and then present quantitative predictions for asset returns andempirical tests.Implications for growth and cyclesAggregate cycles in the model reflect movements at the industry level. New firms enter,obsolete products exit, competitive pressure and markups adjust, and measured productivityfluctuates. Productivity dynamics in turn shape macroeconomic cycles.Industry Cycles Table 3.2 reports basic industry moments from the benchmark model.The average markup and the mean profit share are broadly consistent with the data. Similarly,the model quantitatively captures industry cycles well by closely matching the volatilities andfirst autocorrelations of markups, intangible capital growth, profit shares and net entry rates.The last panel confirms the negative relation between the mass of firms and entry rates.Figure 3.2 illustrates the underlying dynamics by plotting the responses of key variablesto a positive one standard deviation exogenous technology shock. We focus on two modelspecifications, namely the benchmark model and model B (constant mass of firms and aconstant markup). In the benchmark model, a positive technology shock raises valuationsand thus triggers entry, as shown in the top left panel, and the mass of firms increases,as documented in the top right panel. In our benchmark model, firms take their effect oncompetitor firms into account when setting prices, so that increasing competitive pressureleads to falling markups, as shown in the lower left panel. Importantly, as the lower rightpanel illustrates, the entry margin significantly amplifies investment in technology. This isbecause in response to falling markups, demand for intermediate goods increase. To satisfythe higher demand, firms produce more and increase demand for both physical and technologycapital.In table 4.4, we report results from predictive regressions of aggregate growth rates onentry rates. Qualitatively, the model predicts that a rise in entry rates forecasts highergrowth. Indeed, we empirically find that entry positively forecasts higher growth rates ofoutput, consumption, and investment. While the signs are consistent with the model predic-tion throughout, statistical significance obtains only for shorter horizons, consistent with thenotion that entry rates are highly cyclical. This suggests that variations in entry rates are animportant determinant of business cycles fluctuations, which we examine next.62Business Cycles Table 3.4 reports the main business cycle statistics for models A, and B.While all of them are calibrated to match the mean and volatility of consumption growth, thecyclical behavior across models differs considerably.The benchmark model quantitatively captures basic features of macroeconomic fluctua-tions in the data well. It produces consumption volatility, investment volatility and R&Dvolatility that are similar to their empirical counterparts. While investment volatility fallsa bit short of the empirical analogue, Kung (2015) shows that incorporating sticky nomi-nal prices and interest rate shocks in such a framework can help to explain the remainingvolatility. The model generates volatile movements in labor markets, even overshooting thevolatility of hours worked slightly. This is noteworthy, as standard macroeconomic modelstypically find it challenging to generate labor market fluctuations of the orders of magnitudeobserved in the data.The quantitative success of the benchmark model contrasts starkly to the simulated mo-ments from the nested model B. Without entry and exit investment and R&D volatility aresignificantly reduced. Thus, entry and exit combined with countercyclical markups serve asa quantitatively significant amplification mechanism for shocks at business cycle frequencies.The amplification mechanism is illustrated in figure 3.3, which plots the impulse responsefunctions of aggregate quantities. Upon impact of a positive exogenous productivity shock,output, investment and consumption all rise, and significantly more so than in a specificationwithout the entry margin. The lower two panels show that both the responses of realizedand and expected consumption growth are amplified in the benchmark model. Accordingly,the amplification mechanism increases the quantity of priced risk in the economy, since thestochastic discount factor in the model reflects both realized and predictable movements inconsumption growth, given the assumption of Epstein-Zin preferences.The intuition for the amplification result is as follows. With procyclical entry, the modelpredicts countercyclical markups, so that falling markups in expansions triggers higher de-mand for intermediate goods from the final good producer, further stimulating investment incapital and technology, and thus output. Similarly, rising markups in downturns dampen thedemand for intermediate goods, and deepens recessions further.Table 3.5 provides empirical support for the model predictions regarding the cyclical be-havior of entry rates, number of firms, and markups. The correlation of aggregate quantitiesand our empirical markup series is negative while the number of firms and entry rates areprocyclical.Asymmetric Cycles Fig. 3.4 plots the difference between the response of quantities to apositive shock and to a negative shock of the same magnitude. Any deviation from a zerodifference reflects an asymmetry in responses at some horizon. Observe that model B, withconstant firm mass and markups, generates no differential response at any horizon. Thatspecification thus predicts symmetric cycles. This is quite different in our benchmark model.63It features differential responses at all horizons. The number of firms increases relatively morein expansions than it falls in recessions. Similarly, markups fall relatively more in upswingsthan they rise in downturns. On the other hand, investment, consumption and output rise byrelatively less in good times than they fall in bad times, so that recessions are deeper in ourbenchmark economy.The source of asymmetry in the model comes from the nonlinear relation between markupsand the number of firms, which is highlighted in figure 3.5. This figure plots responses ofquantities in the benchmark conditional on high and low number of firms. Note that thefigure shows that both realized and expected consumption growth fall by relatively more ina scenario with a low mass of incumbent firms (i.e., during a recession). Consequently, thisasymmetry implies conditional heteroscedasticity in fundamentals, including consumptiongrowth. If we fit our simulated data to the consumption process of Bansal and Yaron (2004),we obtain:zt+1 = 0.961 zt + 0.433 σtet+1gt+1 = zt + σtηt+1σ2t+1 = 0.00462 + 0.975 (σ2t − 0.00462) + 0.184× 10−6 wt+1where gt+1 is the realized consumption growth, zt is the expected consumption growth, σt isthe conditional volatility of gt+1 and et+1, ηt+1, and wt+1 are i.i.d. shocks. To compare withBansal and Yaron (2004), we time aggregate their model to a quarterly frequency, and obtain:zt+1 = 0.939 zt + 0.151 σtet+1gt+1 = zt + σtηt+1σ2t+1 = 0.00222 + 0.962 (σ2t − 0.00222) + 8.282× 10−6 wt+1Note that our endogenous consumption volatility dynamics closely matches the exogenousspecification of Bansal and Yaron (2004). Quantitatively, our model generates significanttime-varying volatility. Consistent with Kung (2015) and Kung and Schmid (2015), the modelalso generates significant long-run risks through the process innovation channel.Table 3.6 highlights that our time-varying macroeconomic volatility is also countercyclical.Using our markup series, we split the data sample into high and low markup episodes. Thisprocedure allows us to compute moments conditional on markups. Given the countercycli-cality of our markup measure, it is perhaps not surprising that average output, consumptionand investment is lower in high markup episodes. More interestingly, however, we find thatthe volatilities conditional on high markups are also higher. In line with the discussion above,the model is consistent with these findings.64Asset pricing implicationsIn our production economy, the endogenous consumption and cash flow dynamics will be re-flected in aggregate risk premia and their dynamics. Intuitively, we expect two effects. First,the entry margin endogenously amplifies movements in realized consumption growth. Second,R&D decisions of firms propagates technology shocks to long-run consumption growth, whichgenerates endogenous persistence in expected consumption growth. With Epstein-Zin prefer-ences, both shocks to realized and expected consumption growth are priced, hence we expectthat the amplification and propagation mechanisms will give rise to a sizable unconditionalequity premium. Second, since quantity of risk is time-varying and depends negatively on themass of firms, we expect a countercyclical conditional equity premium.We now use our calibration to assess the quantitative significance of these dynamics forrisk premia and to generate empirical predictions. We discuss and quantify these implicationsin turn and present empirical evidence supporting the model predictions.Equity Premium Table 3.7 reports the basic asset pricing implications of the benchmarkmodel and the alternative specification. Absent entry and exit, the risk free rate is aboutdouble its empirical counterpart (model B), while the benchmark model (model A) replicatesa low and stable risk free rate. While we calibrate the endogenous average growth rate tocoincide across all models, the amplification mechanism working through the entry margincoupled with countercyclical markups creates higher persistent uncertainty. Higher uncer-tainty increases the precautionary savings motive, driving down interest rates to realisticlevels in our benchmark economy.The higher uncertainty also leads to a significantly higher and realistic equity premium.This is because product innovation provides an amplification mechanism for short-run riskswhile process innovation provides a growth propagation mechanism that generates endogenouslong-run risks. While stock return volatility falls short of the empirical target, Ai, Croce, andLi (2013) report that empirically, the productivity driven fraction of return volatility is aroundjust 6%, which is close to our quantitative finding.Consistent with the existence of sizeable risk premia, the benchmark model also generatesquantitatively realistic implications for the level and the volatility of the price-dividend ratio.Competition and asset prices Imperfect competition and variations in competitive pres-sure is a key mechanism driving risk premia in our setup. We now provide some comparativestatics of risk and risk premia with respect to average competitive pressure. We do this byreporting some sensitivity analysis of simulated data with respect to the sectoral elasticity ofsubstitution between goods, ν2. Fig. 3.6 reports the results by plotting key industry, macroand asset pricing moments for different values of ν2.Raising the sectoral elasticity of substitution between goods, ν2, has two main effects onmarkups. First, by facilitating substitution between intermediate goods, it increases compe-65tition and therefore, holding all else constant, lowers markups. Second, by the virtue of ourexpression for the markup, equation (3.3), it raises the sensitivity of markups with respect tothe number of incumbent firms, and thus, all else equal, makes markups more volatile. Thefirst effect is an important determinant of the average growth rate of the economy, while thelatter affects the volatility of growth.With respect to the first effect, increasing ν2 has two opposing implications. First, decreas-ing the average markup, holding all else equal, lowers monopoly profits in the intermediatesector. Second, a lower average markup increases the demand for intermediate goods inputs,which raises monopoly profits. In our benchmark calibration, the second effect dominates,and therefore more intense competition, and a higher average markup raises steady-stategrowth. On the other hand, a more volatile demand for intermediate goods inputs triggeredby increasingly volatile markups leads to a more volatile growth path. This effect is exacer-bated by increasingly cyclical entry as profit opportunities become more sensitive to aggregateconditions. The net effect is a riskier economy, which translates into a higher risk premium.Term structure of equity returns An emerging literature starting with van Binsbergen,Brandt, and Koijen (2012) provides evidence that the term structure of expected equityreturns is downward sloping, at least in the short-run. This is in contrast to the implicationsof the baseline long-run risks model (Bansal and Yaron (2004)) or the habits model (Campbelland Cochrane (1999)). The empirical finding reflects the notion that dividends are very riskyin the short-run.Our benchmark model is qualitatively consistent with these findings. We compute the cur-rent price Qt,t+k of a claim to the aggregate dividend at horizon k as Qt,t+k = E[Mt,t+kDt+k]and compute its unconditional expected return accordingly.The left panel of figure 3.7 shows that the term structures of (unlevered) equity returns forthe benchmark model and the model without entry and exit. Consistent with the standardlong-run risks model, the model absent entry and exit produces an upward sloping termstructure. In the benchmark model, countercyclical markups substantially amplify short-runrisks and increase the procyclicality of short-term cash flows, which leads to a downward-sloping equity term structure for roughly the first five years. Note also that the risk premiaon the very short-term strips are significantly higher than those at medium to long horizons,consistent with the data.These cash flow dynamics are illustrated in the right panel of figure 3.7, which plotsthe impulse response function of the aggregate dividend growth rate to a positive exogenoustechnology shock in the benchmark model and the model without entry and exit. Both modelsgenerate a persistent increase in dividend growth at longer maturities through the processinnovation channel. Thus, long-run cash flows are risky as reflected by the high long-horizonrisk premia. On the other hand, industry and markup dynamics render short-run dividendssignificantly more risky in the benchmark model. Intuitively, dividends spike upwards on66impact as new firms enter more slowly in response to attractive profit opportunities. Whencompetitive pressure rises, markups and dividends start falling until the aggregate demandfor capital and R&D increases, triggering low-frequency movements in productivity that driveup dividends again.Return predictibility The previous sections establish how the endogenous short- andlong-run risks in our benchmark model produce a realistic unconditional equity premium.This section documents that the endogenous countercyclical volatility due to nonlinearities inmarkups implies countercyclical variation in the conditional equity premium consistent withthe data. We show that excess equity returns are forecastable by measures of markups andnet business formation, which we verify empirically.Table 3.8 presents our main predictability results. Panel A first verifies standard long-horizon predictability regressions projecting future aggregate returns on current log price-dividend ratios in our data sample, and shows statistically significant and negative slopecoefficients, and R2’s increasing with horizons up to five years. Perhaps more interestingly,we run the same regressions with simulated data from our benchmark model using a sampleof equal length as the empirical counterpart. The top right panel reports the results. Consis-tent with the data, we find statistically significant and negative slope coefficients, with R2’sincreasing with horizons up to five years and of similar magnitude as the data. Notably, theR2’s in our model simulations match their empirical counterparts remarkably well.These predictability results in the model imply that the model generates endogenous con-ditional heteroscedasticity, as shocks to the forcing process, At, are assumed to be homoscedas-tic. Figure 3.8 confirms this. It shows the impulse response functions of the conditional riskpremium and the conditional variance of excess returns to a positive exogenous technologyshock, both in the benchmark model and in model absent entry and exit. While in model Bneither the risk premium nor the conditional variance respond, they both persistently fall onimpact in the benchmark model. With the entry margin and countercyclical markups, therisk premium and its variance are countercyclical, mirroring the endogenous countercyclicalconsumption volatility.Our predictability results are related to the degree of competition, which we confirm inthe remaining panels in table 3.8. Moreover, we present novel empirical evidence supportingthis prediction. We use two measures of entry, our markup series, and the profit share aspredictive variables. Panels B to E report the results from projecting future aggregate returnson these variables for horizons up to 5 years, in the model and in the data. In the model,the proxies for entry forecast aggregate returns with a statistically significant negative sign,while markups and profit shares forecast them with a statistically significant positive sign. Weverify this empirical prediction in the data. The empirically estimated slope coefficients allhave the predicted sign, and except for the profit share regressions, are statistically significant.We thus provide novel evidence on return predictability related to time-varying competitive67pressure.It is well-known that statistical inference in predictive regressions is complicated throughsmall sample biases. To illustrate that the sources of predictability in our model is robust tothese concerns, we repeat the predictability regressions in a long sample of 200,000 quarters.For simplicity, we only report evidence from projecting returns on log price-dividend ratios.Table 3.9 shows the results from these regressions across model specifications. In case of themodel without entry and exit, the explanatory power of the regressions are identically equalto zero. In contrast, the benchmark model produces R2 that are still sizeable and increasingwith horizon.3.4.2 ExtensionsGiven the importance of markup dynamics for our asset pricing results, we next considertwo extensions of the model that address properties of markups recently emphasized in theliterature. Countercyclical movements in both price and wage markups are often recognized asthe main source of fluctuations at higher frequency (e.g. Christiano, Eichenbaum, and Evans(2005)). The objective of this section is to investigate which features of markups appearrelevant through the lens of asset pricing. In a first extension, we consider price markupshocks, in a way often considered in the DSGE literature (e.g. Smets and Wouters (2003),Justiniano, Primiceri, and Tambalotti (2010)). Second, in addition to price markups, weconsider wage markups, whose relevance has recently been pointed out in the context of NewKeynesian macroeconomic models (e.g. Gali, Gertler, and Lopez-Salido (2007)). The twoextensions also allow us to gain further intuition about the mechanisms underlying the riskpremia and predictability results in the benchmark model.Markup shocksIn this section, we show that we need two ingredients to jointly generate a countercyclical riskpremium: markups need to be countercyclical and conditionally heteroskedastic.We start by considering exogenously stochastic price markups. To that end, we solve theversion of the model without entry and exit and specify the markup process aslog(øt) = (1− ρø) log(ø) + ρø log(øt−1) + σøutwhere ut is a standard normal i.i.d. shock that has a contemporaneous correlation of % witht. We investigate three cases, (i) constant price markups, (ii) uncorrelated time-varyingmarkups, and (iii) countercyclical markups. We set ø, ρø, and σø to match the unconditionalmean, first autocorrelation, and unconditional standard deviation of øt in the benchmarkmodel.Panels A, B, and C in table 3.10 report the main quantitative implications for asset re-turns and price-dividend ratios. The results are instructive. Panel B shows that introducing68uncorrelated stochastic markups has a 40 bps impact on the risk premia and increases sig-nificantly the volatility of the price dividend ratio. Consistent with the intuition developedearlier, the additional risk raises the precautionary savings motive and lowers the risk-freerate. When markups are exogenously countercyclical, panel C shows that the risk premiumgoes up by close to one percent. In line with the intuition explained in the benchmark case,countercyclical markups amplifiy uncertainty.While countercyclical markups increase uncertainty, it does not generate predictability ifthe dynamics are symmetric. Table 3.11 illustrates this point by reporting the results fromprojecting future returns on log price-dividend ratios in models with exogenous markups. Theresults in panels A, B, and C show that none of these specifications generate any predictability.The missing ingredient is the asymmetry or conditional heteroscedasticity in markups that isgenerated endogenously in our benchmark model.To illustrate the importance of this asymmetry for predictibility, we solve a version ofthe model where the volatility of technology shocks is affected by the level of markups. Inparticular, we assumeat = (1− ρa)a? + ρaat−1 + σttσt = σ(1 + κøøˆt)where κø > 0 captures the effects of markups on the conditional volatility of productivityshocks. We choose κø to approximately replicate the asymmetry generated by the benchmarkmodel. Results from the simulation are reported in Tables 3.10 and 3.11, panel D. While theaverage risk premium is barely affected, markup induced heteroskedasticity generates excessstock return predictability.Wage markupsIn addition to price markups, imperfect competition in labor markets reflected in wagemarkups plays an important role in current DSGE models. The dynamics of wage markupsis currently subject to a debate after an influential paper by Gali, Gertler, and Lopez-Salido(2007) which argues that they should be countercyclical. In this section, we quantitativelyexplore the implications of dynamic wage markups for asset returns.Formally, the wage markup is defined as the ratio of the real wage to the householdsmarginal rate of substitution between labor and consumption,log(øwt ) = log(Wt)− log(χ0(1− Lt)−χC−1/ψtZ1−1/ψt)reflecting imperfect competition in the labor supply market. We specify the wage markup69process exogenously as an AR(1) process in logslog(øwt ) = (1− ρwø ) log(øw) + ρwø log(øwt−1) + σwø uwtwhere uwt is a standard normal i.i.d. shock that has a contemporaneous correlation of %w witht.We augment the benchmark model with wage markups and compare asset pricing mo-ments and predictability results for two additional specifications: (i) uncorrelated time-varyingmarkups, and (ii) countercyclical wage markup. We calibrate the markup process to match thestandard deviation and first autocorrelation of the wage markup reported in Gali, Gertler, andLopez-Salido (2007): ρwø = 0.96, and σwø = 2.88%. Whenever applicable, we set %w = −0.45in order to replicate the −0.79 correlation between wage markups and output documentedin Gali, Gertler, and Lopez-Salido (2007). The steady state markup is set to 1.2 (see e.g.,Comin and Gertler (2006)).The main asset pricing implications are collected in table 3.12 and predictability results arereported in table 3.13. Accounting for wage markups in addition to endogenous countercyclicalprice markups amplifies priced risk and raises risk premia. On the other hand, introducingwage markups only sharpens predictability when the dynamics are countercyclical.3.5 ConclusionWe build a general equilibrium model with monopolistic competition and endogenous firmentry and exit. Endogenous R&D accumulation (process innovation) generates substantiallong-run risks and therefore, a sizable equity premium. Also, our model structure implies anegative and nonlinear relation between the number of firms and markups. Consequently,variation in entry and exit of firms (product innovation), generates countercyclical and asym-metric markups. Countercyclical markups amplifiy short-run risks, which allows the modelto generate a downward sloping equity term structure up to roughly five years. Asymmetricmarkup dynamics produce countercyclical consumption volatility, and with recursive prefer-ences, this implies a countercyclical equity premium. The model also predicts that the equitypremium is forecastable with measures of markups and the intensity of new firm creation,which we verify in the data. In short, this essay highlights how fluctuations in competitivepressure is an important source of time-varying risk premia.70Table 3.1: Quarterly calibrationParameter Description ModelA. Preferencesβ Subjective discount factor 0.995ψ Elasticity of intertemporal substitution 1.8γ Risk aversion 10χ Labor elasticity 3B. Productionα Capital share 0.33η Degree of technological appropriability 0.065δk Depreciation rate of capital stock 2.0%δk Depreciation rate of R&D stock 3.75%δn Firm obsolescence rate 1.0%ζk Capital adjustment cost parameter 0.738ζz R&D capital adjustment cost parameter 0.738ν1 Price elasticity accross industries 1.05ν2 Price elasticity within industries 75C. Productivityρ Persistence of at 0.985σ Conditional volatility of at 1.24%This table reports the parameter values used in the benchmark quarterly calibration of the model. The tableis divided into three categories: Preferences, Production, and Productivity parameters.71Table 3.2: Industry momentsData ModelA. MeansE[log(ø)] (%) 13.39 15.92E[Profit Share] (%) 7.04 10.98B. Standard deviationsσ[log(ø)] (%) 2.30 2.69σ[∆zp] (%) 1.74 2.55σ[∆z] (%) 1.05 0.87σ[Profit Share] (%) 2.18 2.37σ[NE] 0.06 0.05C. AutocorrelationsAC1[log(ø)] 0.900 0.998AC1[∆zp] 0.159 0.107AC1[∆z] 0.958 0.985AC1[Profit Share] 0.955 0.998AC1[NE] 0.701 0.696D. Correlationscorr(log(ø), N) -0.139 -0.213corr(log(ø), NE) -0.101 -0.023This table presents the means, standard deviations, autocorrelations, for key macroeconomic variables fromthe data and the model. The model is calibrated at a quarterly frequency using the benchmark calibration.The growth rate of technology has been annualized (∆zp). To obtain a stationary, unit-free measure of entry,log(NE) is filtered using a Hodrick-Prescott filter with a smoothing parameter of 1,600.72Table 3.3: Forecasts with growth of new incorporationsData ModelHorizon (in quarters)1 4 8 1 4 8A. Outputβ 0.235 0.429 0.108 1.224 4.784 9.585S.E. 0.034 0.107 0.165 0.725 2.603 5.464R2 0.242 0.118 0.004 0.010 0.029 0.044B. Consumptionβ 0.071 0.206 0.157 3.310 12.041 21.516S.E. 0.013 0.049 0.064 0.293 1.782 4.476R2 0.012 0.125 0.036 0.247 0.265 0.237C. Investmentβ 1.277 1.980 0.225 1.625 5.819 10.761S.E. 0.213 0.549 0.785 1.084 3.606 7.136R2 0.268 0.119 0.001 0.009 0.025 0.036This table presents output growth, consumption growth, and investment growth forecasts for horizons of one,four, and eight quarters using the growth in net business formation from the data and the model. The n-quarterregressions, 1n(xt,t+1 + · · · + xt+n−1,t+n) = α + β∆nt + t+1, are estimated using overlapping quarterly dataand Newey-West standard errors are used to correct for heteroscedasticity.Table 3.4: Business cycle momentsData A. B.First MomentE(∆c) 2.00 2.00 2.00Second Momentσ∆c/σ∆y 0.64 0.49 1.11σ∆i/σ∆c 4.38 3.00 0.99σ∆s/σ∆c 3.44 2.77 0.92σ(∆c) 1.10 1.10 1.10σ(l) 1.52 2.24 0.98This table reports simulated moments for two specifications of the model. Column A reports model momentsfor the benchmark model. Column B reports model moments for the model without entry and exit. To keepthe comparison fair, we recalibrate a? and σ to match the first and second moments of realized consumptiongrowth. The risk premiums are levered following Boldrin, Christiano, and Fisher (2001). Growth rate momentsare annualized percentage. Moments for log-hours (l) are reported in percentage of total time endownment.73Table 3.5: Industry cyclesData ModelA. Markupscorr(ø, Y ) -0.174 -0.137corr(ø, C) -0.283 -0.213corr(ø, I) -0.164 -0.134B. Number of firmscorr(N,Y ) 0.708 0.656corr(N,C) 0.638 0.944corr(N, I) 0.701 0.634C. Entrycorr(NE, Y ) 0.449 0.838corr(NE,C) 0.397 0.255corr(NE, I) 0.487 0.851This table reports correlations for key macro variables with aggregate markups (ø), the number of firms (NBF:Index of net business formation, and entry (INC: total number of new incorporations) for the data and themodel. The model is calibrated at a quarterly frequency and all reported statistics are computed after applyingan Hodrick-Prescott filter with a smoothing parameter of 1,600 to the log of all non-stationary variables.74Table 3.6: Summary statistics sorted on markupsData Modellow øt high øt low øt high øtA. Outputmean 0.436 -0.019 0.199 -0.303std 1.030 1.970 1.336 1.433min -1.275 -3.798 -5.197 -5.919max 2.319 3.536 5.076 5.399B. Consumptionmean 0.450 -0.158 0.202 -0.301std 0.748 0.805 0.600 0.831min -0.543 -1.406 -2.023 -3.413max 1.820 1.083 2.258 2.696C. Investmentmean 1.335 -0.753 0.288 -0.448std 4.434 9.411 1.881 2.455min -9.264 -21.177 -7.219 -10.329max 8.562 11.827 7.026 8.815This table presents summary statistics for output, consumption, and investment by sorting the data on the levelof markup. All non-stationary data are detrended using a Hodrick-Prescott filter with a smoothing parameterof 1,600. All units are percentage deviation from trend.Table 3.7: Asset pricing momentsData A. B.First MomentE(rf ) 1.62 1.34 2.89E(rd − rf ) 5.84 5.16 0.55E[pd] 3.43 3.77 4.43Second Momentσ(rf ) 0.67 0.60 0.06σ(rd − rf ) 17.87 6.57 2.62σ[pd] 0.37 0.29 0.02This table reports simulated moments for two specifications of the model. Column A reports model momentsfor the benchmark model. Column B reports model moments for the model without entry and exit. To keepthe comparison fair, we recalibrate a? and σ to match the first and second moments of realized consumptiongrowth. The risk premiums are levered following Boldrin, Christiano, and Fisher (2001). Returns are inannualized percentage units.75Table 3.8: Stock return predictabilityData ModelHorizon (in years)1 2 3 4 5 1 2 3 4 5A. Log Price-Dividend Ratioβ(n) -0.132 -0.231 -0.292 -0.340 -0.430 -0.062 -0.120 -0.172 -0.221 -0.265S.E. 0.041 0.078 0.099 0.112 0.135 0.022 0.039 0.054 0.066 0.076R2 0.090 0.157 0.193 0.214 0.254 0.051 0.097 0.140 0.179 0.215B. Net Business Formationβ(n) -0.770 -1.006 -1.059 -1.255 -1.790 -0.054 -0.103 -0.148 -0.189 -0.227S.E. 0.248 0.385 0.375 0.411 0.590 0.017 0.031 0.042 0.050 0.058R2 0.121 0.122 0.108 0.121 0.166 0.062 0.117 0.167 0.212 0.252C. Growth in New Incorporationsβ(n) -0.396 -0.866 -1.049 -1.219 -1.323 -0.666 -1.271 -1.828 -2.333 -2.798S.E. 0.248 0.449 0.634 0.656 0.717 0.216 0.386 0.520 0.632 0.728R2 0.008 0.024 0.028 0.031 0.024 0.060 0.115 0.164 0.208 0.248D. Markupβ(n) 1.516 2.571 2.747 3.529 4.185 0.303 0.580 0.834 1.068 1.284S.E. 0.651 1.052 1.301 1.577 2.016 0.112 0.199 0.269 0.328 0.379R2 0.043 0.075 0.071 0.102 0.116 0.048 0.091 0.131 0.167 0.201E. Profit Shareβ(n) 0.298 0.733 0.943 1.678 2.135 0.340 0.651 0.937 1.199 1.442S.E. 0.620 1.056 1.554 2.375 3.060 0.126 0.224 0.302 0.369 0.426R2 0.001 0.005 0.007 0.018 0.022 0.048 0.091 0.130 0.167 0.201This table reports excess stock return forecasts for horizons of one to five years, i.e. rext,t+n − y(n)t = αn + β xt + t+1, where xt is the predicting variables. Thedifferent panels present forecasting regressions using different predicting variables: the log price-dividend ratio (panel A), the linearly detrended index of netbusiness formation (panel B), the growth in new incorporations (panel C), price markups (panel D), and the profit share (panel E). The forecasting regressions useoverlapping quarterly data. Newey-West standard errors are used to correct for heteroscedasticity. The estimates from the model regression are averaged across100 simulations that are equivalent in length to the data sample. The sample is 1948-2013 for Panel A and E, 1948-1993 for panel B and C, and 1964-2013 forpanel D. The risk premiums are levered following Boldrin, Christiano, and Fisher (2001).76Table 3.9: Stock return predictability in the long sampleHorizon (in years)1 2 3 4 5A. Benchmarkβ(n) -0.039 -0.075 -0.108 -0.139 -0.168R2 0.032 0.062 0.089 0.114 0.138B. No Entry/Exitsβ(n) -0.018 -0.029 -0.043 -0.051 -0.051R2 0.000 0.000 0.000 0.000 0.000This table reports excess stock return forecasts in the long sample for horizons of one to five years using thelog-price-dividend ratio: rext,t+n−y(n)t = αn+β log(Pt/Dt)+ t+1. Panel A presents the forecasting regressionsfor the benchmark model with time-varying markup, panel B presents the regression results for the modelwithout entry and exit and constant price markup. The forecasting regressions use overlapping quarterly data.The risk premiums are levered following Boldrin, Christiano, and Fisher (2001).77Table 3.10: Asset pricing moments: exogenous markupsA. B. C. D.First MomentE(rf ) 2.89 2.55 2.22 2.15E(rd − rf ) 0.55 0.98 1.51 1.53E(pd) 4.43 4.40 4.30 4.28Second Momentσ(rf ) 0.06 0.17 0.19 0.33σ(rd − rf ) 2.62 2.92 3.40 3.45σ(pd) 0.02 0.17 0.16 0.22This table reports asset pricing moments for four specifications of the model with exogenous markups. ColumnA reports model moments for the model with constant markups (ρø = 0, σø = 0, % = 0, and κø = 0). ColumnB reports model moments for the time-varying markup model (ρø = 0.997, σø = 0.17%, % = 0, and κø = 0).Column C reports model moments for the model with countercyclical markups (ρø = 0.997, σø = 0.17%,% = −0.5, and κø = 0). Column D reports moment for the model with countercyclical markups and businesscycle asymmetry (ρø = 0.997, σø = 0.17%, % = −0.5, and κø = 15). The risk premiums are levered followingBoldrin, Christiano, and Fisher (2001).78Table 3.11: Stock return predictability: exogenous markupsHorizon (in years)1 2 3 4 5A. Constant markupβ(n) -0.018 -0.029 -0.043 -0.051 -0.051R2 0.000 0.000 0.000 0.000 0.000B. Time-varying, uncorrelated øtβ(n) 0.001 0.002 0.003 0.004 0.005R2 0.000 0.000 0.000 0.000 0.000C. Countercyclical øtβ(n) 0.002 0.004 0.005 0.007 0.009R2 0.000 0.000 0.000 0.000 0.000D. Countercyclical and heteroskedastic øtβ(n) -0.022 -0.044 -0.066 -0.087 -0.109R2 0.015 0.029 0.043 0.057 0.070This table reports long sample excess stock return forecasts in the model with exogenous price markup forhorizons of one to five years using the log-price-dividend ratio: rext,t+n − y(n)t = αn + β log(Pt/Dt) + t+1.Panel A reports the forecasting regressions for the model with constant markups (ρø = 0, σø = 0, % = 0,and κø = 0). Panel B reports the forecasting regressions for the time-varying markup model (ρø = 0.997,σø = 0.17%, % = 0, and κø = 0). Panel C reports the forecasting regressions for the model with countercyclicalmarkups (ρø = 0.997, σø = 0.17%, % = −0.5, and κø = 0). Panel D reports the forecasting regressions for themodel with countercyclical markups and business cycle asymmetry (ρø = 0.997, σø = 0.17%, % = −0.5, andκø = 15). The risk premiums are levered following Boldrin, Christiano, and Fisher (2001).79Table 3.12: Asset pricing moments: wage markupA. B. C.First MomentE(rf ) 1.34 0.62 0.00E(rd − rf ) 5.16 5.63 6.94E(pd) 3.77 3.59 3.32Second Momentσ(rf ) 0.60 0.72 0.90σ(rd − rf ) 6.57 7.02 7.90σ(pd) 0.29 0.33 0.37This table reports asset pricing moments for four specifications of the model with wage markups as wellas the benchmark model. Column A reports moments for the benchmark model. Column B reports modelmoments for the benchmark model with time-varying, uncorrelated wage markup (σwø = 2.88%, ρwø = 0.96, and%w = 0). Column C reports moments for the benchmark model with countercyclical wage markup (σwø = 2.88%,ρwø = 0.96, and %w = −0.45). Column D reports model moments for the model with constant price markupand countercyclical wage markup (σwø = 2.88%, ρwø = 0.96, and %w = −0.45). The risk premiums are leveredfollowing Boldrin, Christiano, and Fisher (2001).Table 3.13: Stock return predictability: wage markupHorizon (in years)1 2 3 4 5A. Benchmarkβ(n) -0.039 -0.075 -0.108 -0.139 -0.168R2 0.032 0.062 0.089 0.114 0.138B. Time-varying, uncorrelated øwtβ(n) -0.054 -0.105 -0.152 -0.196 -0.238R2 0.043 0.082 0.119 0.153 0.184C. Countercyclical øwtβ(n) -0.173 -0.333 -0.480 -0.615 -0.740R2 0.119 0.215 0.294 0.357 0.408This table reports long sample excess stock return forecasts in the model with exogenous wage markup forhorizons of one to five years using the log-price-dividend ratio: rext,t+n−y(n)t = αn+β log(Pt/Dt)+t+1. Panel Areports the forecasting regressions for the benchmark model. Panel B reports the forecasting regressions for thebenchmark model with time-varying, uncorrelated wage markup (σwø = 2.88%, ρwø = 0.96, and %w = 0). PanelC reports the forecasting regressions for the benchmark model with countercyclical wage markup (σwø = 2.88%,ρwø = 0.96, and %w = −0.45). Panel D reports the forecasting regressions for the model with constant pricemarkup and countercyclical wage markup (σwø = 2.88%, ρwø = 0.96, and %w = −0.45). The risk premiums arelevered following Boldrin, Christiano, and Fisher (2001).80Figure 3.1: Markup and number of firms11.051.11.15οtMeasure of firms (Nt)−1.5−1−0.50∂οt/∂NtMeasure of firms (Nt)This figure plots the markup (left) and the first derivative of the markup with respect to Nt (left) as a functionof the number of firms (Nt) for the benchmark calibration of the model.Figure 3.2: Impulse-response functions - productivity shock10 20 30 40−  BenchmarkNo Entry/Exit10 20 30 4000.51n10 20 30 40−2−1.5−1−0.50markupquarters10 20 30 4000.∆zquartersThis figure plots the impulse response functions for entry (NE), the number of firms (n), the price markup,and the growth of technology (∆z) to a positive one standard deviation productivity shock for the benchmarkmodel (dashed line), and the model without entry and exit (solid line). The parameters used to solve the noentry/exit model are the same as the benchmark model except for a? that is modified to ensure an averagegrowth rate of 2%, and σ that is modified to get a consumption growth volatility of 1.10%. All values on they-axis are in annualized percentage log-deviation from the steady state.81Figure 3.3: Impulse-response functions - productivity shock (cont.)10 20 30 4002468I/K  BenchmarkNo Entry/Exit10 20 30 400246∆y10 20 30 400123∆cquarters10 20 30 4000.[∆c]quartersThis figure plots the impulse response functions for the investment-to-capital ratio (I/K), output growth (∆y),consumption growth (∆c), and expected consumption growth (E[∆c]) to a positive one standard deviationproductivity shock for the benchmark model (dashed line), and the model without entry and exit (solid line).The parameters used to solve the no entry/exit model are the same as the benchmark model except for a?that is modified to ensure an average growth rate of 2%, and σ that is modified to get a consumption growthvolatility of 1.10%. All values on the y-axis are in annualized percentage log-deviation from the steady state.82Figure 3.4: Business cycles asymmetry10 20 30 40−0.2−0.15−0.1−0.050n  BenchmarkNo Entry/Exit10 20 30 40−1−0.500.5markup0 10 20 30 4000. 20 30 4000.020.040.06∆z0 10 20 30 4000.[∆y]quarters10 20 30 4000.050.1E[∆c]quartersThis figure plots the asymmetry in impulse response functions for the number of firms (nt), the price markup,the investment-to-capital ratio (I/K), the growth in technology (∆z), and the expected growth rate of output(E[∆y]) and consumption (E[∆c]) in the benchmark model (dashed line), and the model without entry andexit (solid line). The graphs are obtained by taking the difference between minus the response to a twostandard deviation negative productivity shock and the response to a positive two standard deviation shock.The parameters used to solve the no entry/exit model are the same as the benchmark model except for a?that is modified to ensure an average growth rate of 2%, and σ that is modified to get a consumption growthvolatility of 1.10%. All values on the y-axis are in annualized percentage log-deviation from the steady state.83Figure 3.5: Business cycles and number of firms10 20 30 40−1.5−1−0.50n  Low NHigh N10 20 30 400123markup10 20 30 40−8−7−6−5−4I/K10 20 30 40−0.35−0.3−0.25−0.2−0.15∆z10 20 30 40−0.4−0.3−0.2−0.10E[∆y]quarters10 20 30 40−0.8−0.6−0.4−0.20E[∆c]quartersThis figure plots the impulse response functions for the number of firms (nt), the price markup, the investment-to-capital ratio (I/K), the growth in technology (∆z), and the expected growth rate of output (E[∆y]) andconsumption (E[∆c]) in the benchmark model to a negative one standard deviation technology shock as afunction of the number of firms in the economy, Nt. The high N (low N ) case corresponds to the averageresponses across 250 draws in the highest (lowest) quintile sorted on Nt. The data for the sorting is obtainedby simulating the economy for 50 periods prior to the realization of the negative technology shock. All valueson the y-axis are in annualized percentage log-deviation from the steady state.84Figure 3.6: Comparative statics: industry competition65 70 75 80 851214161820E[markup]65 70 75 80 8511.522.53E[∆c]65 70 75 80 853.544.555.5E[rd − rf]ν265 70 75 80 851.σ[∆c]ν2This figure plots the impact of varying the degree of competition within industry ν2 on the average markup,the average output growth, the average equity premium, and the volatility of output growth. Values on y-axisare in annualized percentage units for expected consumption growth and the equity premium and in percentageunits for the price markup.Figure 3.7: Term structure of dividend strips0 5 10 15 returnsyears−3−11310 20 30 40−20246∆dquarters  BenchmarkNo Entry/ExitThis figure plots the term structure of equity returns (left) and the response of dividend growth to a positivetechnology shock (right) in the benchmark model and in the model without entry and exit (constant markups).The parameters used to solve the no entry/exit model are the same as the benchmark model except for a?that is modified to ensure an average growth rate of 2%, and σ that is modified to get a consumption growthvolatility of 1.10%. All values on the y-axis are in annualized percentage.85Figure 3.8: Business cycles and volatility10 20 30 40−0.1−0.050Et[rd − rf]quarters  BenchmarkNo Entry/Exit10 20 30 40−0.06−0.04−0.020σt[rd − rf]quartersThis figure plots the impulse response functions for the conditional risk premium (Et[rd − rf ]), and the con-ditional variance of the risk premium (σ2[rd − rf ]) to a positive one standard deviation productivity shock forthe benchmark model (dashed line), and the model without entry and exit (solid line). The parameters usedto solve the no entry/exit model are the same as the benchmark model except for a? that is modified to ensurean average growth rate of 2%, and σ that is modified to get a consumption growth volatility of 1.10%. Allvalues on the y-axis are in annualized percentage log-deviation from the steady state.86Chapter 4Government Maturity StructureTwists4.1 IntroductionDuring the global financial crisis, central banks, constrained by the zero lower bound (ZLB)on nominal interest rates, conducted open market operations on an unprecedented scale. Theseries of quantitative easing (QE) operations between 2008 and 2014 reduced the averageduration of U.S. government liabilities (including reserve balances) held by the public by over20%. Fig. 4.1 illustrates the impact of the QE operations on average maturity.1 Given thatthe risk profiles of bonds vary by maturity, rebalancing the maturity structure also changesthe expected return on the government bond portfolio. In the fiscal theory of the pricelevel, variation in government discount rates affect the price level through the intertemporalgovernment budget equation. In this essay, we explore the role of this fiscal discount ratechannel for open market maturity restructuring operations. We also highlight the importanceof the term structure of interest rates, in the fiscal theory, as a transmission channel for openmarket maturity operations.To quantitatively examine these issues we build a small-scale New Keynesian model thathas several distinguishing features. First, households have recursive preferences (e.g., Epsteinand Zin (1989)) which allows the model to generate realistic term premia. Second, the supplyof nominal government bonds over various maturities is time-varying (e.g., Greenwood andVayanos (2014)). Third, the monetary/fiscal policy mix is subject to regime shifts betweenmonetary- and fiscally-led regimes (e.g., Davig and Leeper (2007a), Bianchi and Ilut (2014),and Bianchi and Melosi (2014)). In the monetary-led regime, the Taylor principle is satisfiedand the monetary authority controls inflation while the fiscal authority stabilizes the real valueof debt. In the fiscally-led regime, the fiscal authority determines the price level through1When calculating the average maturity of privately-held public debt we include reserve balances withFederal Reserve Banks. Reserve balances are included since the Federal Reserve started to pay interests onreserves in October 2008 making them, effectively, government debt.87the government budget equation while the monetary authority stabilizes debt and anchorsexpected inflation.We show that in the presence of a fiscally-led regime, a nonzero slope of the nominal yieldcurve implies that debt maturity restructuring affects inflation. To isolate the effects of debtmaturity, we consider self-financing shocks to the maturity structure that keep the marketvalue of total government bonds the same immediately after the operation (e.g., MaturityExtension Program), but is allowed to adjust freely afterwards. When the financing costs ofbonds vary by maturity, changing the financing mix also alters the government cost of capital.In the fiscally-led regime, the price level is determined by the ratio of nominal debt to thepresent value of surpluses. Thus, variation in the government discount rate changes the fiscalbacking, and the price level adjusts to revalue debt to satisfy the present value condition.Sticky prices are required for this channel to have real effects. Interpreted more generally,these results illustrate how accounting for heterogeneity in expected returns across differentassets in the fiscal theory breaks Wallace (1981) neutrality.The slope of the nominal yield curve dictates the effects of maturity restructuring for thefiscal discount rate channel. When the yield curve is upward-sloping (downward-sloping),shortening the maturity structure in a self-financing operation is contractionary (expansion-ary). Taking interest rates as given, increasing the proportion of short-term debt in thematurity structure when the yield curve is upward-sloping implies that the government is re-financing at a lower rate. Lowering the government discount rate puts upward pressure on thereal value of debt. In anticipation of this, households increase demand for bonds and decreasedemand for consumption goods, which drives down the price level. With sticky prices, thefall in the price level is sluggish, so that prices are temporarily too high, which leads to acontraction in production and output. The opposite results are obtained when the yield curveis downward-sloping. Furthermore, the endogenous yield curve reactions reinforce our fiscaldiscount rate channel.Under persistent deficits, the discount rate effects from maturity restructuring are atten-uated, and can potentially be reversed if the deficit is particularly severe. Consider the casewhere the yield curve is upward-sloping, then shortening the maturity lowers the discountrate persistently. With a budget deficit today, discounting temporarily negative surpluses ata lower rate has a negative effect on the present value of the fiscal backing. One the otherhand, since the deficit is temporary, discounting positive future surpluses at a lower rate hasa positive effect on the present value. Hence, if the deficit today is particularly severe orpersistent, the discount rate effects from the deficit component can potentially dominate.When the yield curve is flat, debt maturity operations are neutral even in the presence of afiscally-led regime since the cost of financing is the same across maturities. In a monetary-ledregime without the possibility of regime shifts, the economy is insulated from fiscal distur-bances as surplus policy will completely offset changes to the debt burden. Thus, maturityrestructuring is also neutral in this case regardless of the slope of the yield curve. However,88with regime shifts and rational expectations, the possibility of entering the fiscally-led regimeand a nonzero slope is also sufficient for debt maturity non-neutrality in the monetary-ledregime.Since the nominal yield curve provides the key transmission channel for the maturitystructure shocks, we also calibrate our model to explain key term structure facts. Supplyshocks in the model drive countercyclical real marginal costs which generate negative co-movement between consumption growth and inflation similar to Kung (2015). With recursivepreferences, these dynamics produce sizable bond risk premia (e.g., Piazzesi and Schneider(2007) and Bansal and Shaliastovich (2013)) and the model matches the average five-yearterm spread. The model also replicates the persistence in yields and the forecasting ability ofthe term spread for macroeconomic aggregates in the data.We consider an extended version of the model to assess the quantitative importance ofthe fiscal discount rate channel for QE operations involving maturity twists. In the extendedmodel, we incorporate market segmentation, short-term liquidity demand shocks, and a zerolower bound (ZLB) constraint to capture other relevant features for these maturity operations.Also, we start the economy off in the monetary-led regime (with a possibility of entering thefiscally-led regime) and a budget deficit. During the Great Recession, the yield curve wassignificantly upward-sloping, and we find that the fiscal discount rate channel implies con-tractionary effects from shortening debt maturity. Indeed, using an estimated process forthe maturity structure of debt and assuming that the economy starts off in the monetary-ledregime, we find that the fiscal channel significantly dampened expansionary effects from in-creasing short-term liquidity. In particular, the fiscal channel dampened inflation responses by53% and output by 60% during QE2. Thus, we highlight a potential “cost” of QE operations.4.1.1 Related literatureThe literature examining how the interactions between monetary and fiscal policy determinethe price level begins with Sargent and Wallace (1981) who show that permanent fiscal deficitshave to eventually be financed by seignorage when the government only issues real debt.Further, the money creation leads to inflation. Building on this paper, the fiscal theory of theprice level (FTPL) shows that when the government issues nominal debt and does not providethe necessary fiscal backing, deficits are linked to current and expected inflation throughthe intertemporal government budget equation, without necessarily relying on seignoragerevenues (e.g., Leeper (1991), Sims (1994), Woodford (1994), Woodford (1995), Woodford(2001), Schmitt-Grohe´ and Uribe (2000), Cochrane (1999), Bassetto (2002), Bassetto (2008),Cochrane (2005), and Cochrane (2011)).Our essay relates to the literature examining the role of the government maturity structurefor policy. Angeletos (2002) and Buera and Nicolini (2004) demonstrate how a portfolio ofnon-state-contingent real debt of different maturities can replicate the complete markets allo-cation with state-contingent securities. Lustig, Sleet, and Yeltekin (2008), Leeper and Zhou89(2013), and Faraglia, Marcet, Oikonomou, and Scott (2013) analyze optimal maturity struc-ture of nominal debt in DSGE models with distortionary taxes and market incompleteness.Greenwood and Vayanos (2014), Chen, Curdia, and Ferrero (2012), and Guibaud, Nosbusch,and Vayanos (2013) analyze nominal maturity restructuring polices in models with preferredhabitats. Reis (2015) studies maturity operations in a framework that features an exogenousfiscal limit and endogenous default. We differ from these papers by highlighting a distinctbut complementary mechanism for maturity structure non-neutralities. Notably, we demon-strate how accounting for heterogeneity in risk across nominal bonds in the context of thefiscal theory provides a channel for the maturity structure to affect inflation without marketsegmentation or distortionary taxation.Our essay is most closely related to Cochrane (2001) who also considers the maturitystructure in the fiscal theory. In a partial equilibrium setting with a constant interest rate,Cochrane illustrates how restructuring the face value of nominal government debt alters thetiming of inflation. In contrast, we focus on market value restructuring operations (i.e.,holding the market value of debt constant initially), and highlight how a nonzero yield curveslope is essential for such open market procedures to affect inflation through the fiscal discountrate channel. Furthermore, we also evaluate our mechanism in a Dynamic Stochastic GeneralEquilibrium (DSGE) framework with an estimated process for the average duration of publicdebt to quantitatively examine effects of maturity restructuring policies.The Markov-switching Dynamic Stochastic General Equilibrium (DSGE) framework buildson Davig and Leeper (2007a), Davig and Leeper (2007b), Farmer, Waggoner, and Zha (2009),Bianchi and Ilut (2014), and Bianchi and Melosi (2014). In particular, Bianchi and Ilut (2014)and Bianchi and Melosi (2014) also consider stochastic shifts between monetary- and fiscally-led policy regimes. However, our focus is on how the interaction between risk compositionand the fiscally-led policy regime (or expectations of entering the regime) propagates maturityrestructuring shocks.Our essay connects to the theoretical literature studying the effects of unconventional mon-etary policy and transmission channels. Cu´rdia and Woodford (2010), Gertler and Karadi(2011), and Arau´jo, Schommer, and Woodford (2015) analyze the role of financial frictionsfor central bank purchases of risky assets. Correia, Farhi, Nicolini, and Teles (2013) demon-strate how distortionary tax policy can deliver an economic stimulus when monetary policy isconstrained at the zero lower bound. Reis (2015) explores QE operations in an environmentwith an exogenous fiscal limit, default risk, and a fiscal regime. Gomes, Jermann, and Schmid(2013) illustrate how incorporating nominal corporate debt in a DSGE framework providesan important source of monetary non-neutrality. We offer an alternative transmission channelfor thinking about unconventional monetary policy that relies on the interaction between thefiscal theory and bond risk premia to break Wallace neutrality.More broadly, this essay relates to general equilibrium models that link policy to riskpremia. For example, Rudebusch and Swanson (2012), Palomino (2012), Dew-Becker (2014)90Campbell, Pflueger, and Viceira (2014), and Kung (2015) link asset prices to monetary policy.Croce, Kung, Nguyen, and Schmid (2012), Pastor and Veronesi (2012), Gomes, Michaelides,and Polkovnichenko (2013), and Belo, Gala, and Li (2013) look at fiscal policy and assetprices.The chapter is organized as follows. Section 2 provides a simple partial equilibrium modelto qualitatively illustrate the basic mechanisms. Section 3 presents the benchmark model.Section 4 examines the quantitative implications of the model and considers a policy experi-ment relating to the QE operations. Section 5 concludes.4.2 Simple modelIn this section we propose a simple partial equilibrium model to illustrate how the risk com-position of the government portfolio affects inflation. Using approximate analytical solutions,we explicitly show how the impact of changing debt maturity on inflation depends on theslope of the yield curve. These concepts are then formalized and quantified in the benchmarkgeneral equilibrium model.4.2.1 Government budget equationWe assume that the government finances nominal surpluses by issuing one- and two-periodnominal debt. The flow government budget constraint at time t is therefore given by:B(1)f,t +Q(1)t B(2)f,t = Q(1)t B(1)f,t+1 +Q(2)t B(2)f,t+1 + St, (4.1)where B(n)f,t is the nominal face value of debt issued by the treasury with a maturity of nperiods, Qnt is the corresponding nominal bond price, and St ≡ Tt − Gt is the nominalprimary surplus. The relative supply of government bonds (portfolio weights) is assumed tobe exogenous and constant. In particular, we define the relative supply of the one-periodbond (in terms of market values) as:Q(1)t B(1)f,t+1Q(1)t B(1)f,t+1 +Q(2)t B(2)f,t+1≡ wt = w, (4.2)which we assume to be constant.4.2.2 Monetary/fiscal policyWe assume that the monetary/fiscal policy mix is permanently characterized by a fiscally-ledpolicy regime (without regime shifts). We consider a particular policy mix that allows foranalytical tractability.91Fiscal policyFiscal policy sets the real surplus independently of debt. We assume that st ≡ St/Pt, followsan exogenous stochastic process:st = (1− ρs)s¯+ ρsst−1 + σss,t, (4.3)where s,t ∼ iid N(0, 1).Monetary policyMonetary policy sets the short-term nominal interest rate independently of inflation. Specif-ically, the nominal short rate is determined by an exogenously specified nominal stochasticfactor Mt via the Euler equation:rt ≡ log(Rt) = − log (Et[Mt+1]) .4.2.3 Stochastic discount factorThe log nominal stochastic discount factor, mt ≡ log(Mt), is assumed to follow an ARMA(1,1)as in Backus and Zin (1994b):−mt = (1− ρ)δ − ρmt−1 + t + θt−1, (4.4)where t ∼ iid N(0, σ2). This specification of the pricing kernel allows for various averageslopes of the yield curve.Bond pricingThe nominal price of a n-period nominal zero-coupon bond can be written recursively usingthe Euler equation:Q(n)t = Et[Mt+1Q(n−1)t+1], (4.5)where Q(0) ≡ 1 and Q(1)t ≡ 1/R(1)t+1. The corresponding yield-to-maturity for the n-periodbond is defined as:y(n)t ≡ −1nlogQ(n)t . (4.6)When yields are persistent, there is tight relation between the yield spread and the corre-sponding return spread:E[log(R(2)t )− log(R(1)t )] ≈ 2 · E[y(2)t − y(1)t ], (4.7)92where R(2)t ≡ Q(1)t /Q(2)t−1 and R(1)t ≡ 1/Q(1)t− Fiscal discount rate channelWe can rewrite the flow government budget constraint in terms of market values of debt andreturns:R(1)t B(1)t +R(2)t B(2)t = B(1)t+1 +B(2)t+1 + St, (4.8)where B(i)t ≡ Q(i)t−1B(i)f,t, R(2)t ≡ Q(1)t /Q(2)t−1, R(1)t ≡ 1/Q(1)t−1, Bt ≡ B(1)t + B(2)t , Rgt ≡ wR(1)t +(1−w)R(2)t . Iterating Eq. (4.8) forward and imposing the transversality condition, we obtainthe present value formula relating the real value of government liabilities to the present valueof future surpluses (see C.3 for derivation):bt ≡ BtPt= Et∞∑i=0 st+i∏ij=0{Rgt+j/Πt+j} . (4.9)In the fiscally-led regime, the price level, Pt, is determined by the intertemporal governmentbudget equation (Eq. (4.9)). Any current or expected fiscal disturbances directly affect theprice level.The slope of the nominal yield curve determines the relative cost of debt financing acrossmaturities. When the yield curve is not flat, rebalancing the maturity structure changesthe government cost of capital, Rg, which directly affects the price level through Eq. (4.9).Importantly, the sign of effect on the price level depends on the sign of the slope of the nominalyield curve. Suppose the yield curve is downward-sloping, then shortening the maturitystructure increases Rg. To satisfy the intertemporal government budget equation, the increasein discount rates is compensated by a devaluation of the debt portfolio through inflation(increases in Pt). The effects are reversed when the yield curve is upward-sloping and neutralwhen the yield curve is flat. If we add sticky prices (and the slope is nonzero), rebalancing thematurity structure will also have real effects, so that the fiscal discount rate channel violatesWallace neutrality.Fig. 4.2 illustrates comparative statics from shortening the maturity structure (i.e., in-creasing w) on the government discount rate (top figure) and inflation (bottom figure). Weshow these comparative statics for parameterizations of the SDF where the nominal yieldcurve is upward-sloping (solid line), flat (line with circles), downward-sloping (dashed line).Consistent with the intuition above, the sign of the slope determines the sign of the responsesto changes in maturity restructuring.2Note that log(R(2)t ) = 2y(2)t−1−y(1)t and log(R(1)t ) = y(1)t−1. Thus, if yields are persistent, then E[R(2)t −R(1)t ] ≈E[2y(2)t − 2y(1)t ] = 2 · E[y(2)t − y(1)t ].93Approximate analytical solutionWe can directly link the impact of debt maturity changes on inflation to the slope by meansof an approximate analytical solution. Define Bt ≡ B(1)t + B(2)t as the total nominal marketvalue of the debt portfolio. Substituting this definition in the government budget equation(Eq. (4.8)), we can write the return on the government bond portfolio as:Rgt =Bt+1 + StBt. (4.10)Rewriting this return in terms of real surpluses and debt:RgtΠt=bt+1 + stbt,where lowercase variables denote real variables. Define log(x) ≡ x˜, and take logs of Eq. (4.11):R˜gt − Π˜t = b˜t+1 + log(1 +stbt+1)− b˜t. (4.11)Since surpluses can be negative, substitute st = τt−gt (τt and gt are real taxes and governmentexpenditures, respectively) into Eq. (4.11) and rearrange:R˜gt − Π˜t = b˜t+1 − b˜t + log(1 + exp(τ˜t − b˜t+1)− exp(g˜t − b˜t+1)). (4.12)Following Berndt, Lustig, and Yeltekin (2012), log-linearize Eq. (4.12) with respect to thelog tax-to-debt and the log government expenditure-to-debt ratios around the steady-state:R˜gt − Π˜t = θ1b˜t+1 − b˜t + θ0 + (1− θ1)(µτ τ˜t − µg g˜t), (4.13)where θ1, θ0, µτ , and µg are parameters of linearization that are defined in C.4. IteratingEq. (4.13) forward and imposing the transversality condition:b˜t =θ01− θ1 +∞∑j=0θj1((1− θ1)(µτ τ˜t+j − µg g˜t+j)− R˜gt+j + Π˜t+j). (4.14)Take expectations of Eq. (4.14), solve for expected inflation, and substitute R˜gt = ωR˜(1)t +(1− ω)R˜(2)t :E[Π˜t]1− θ1 = E[b˜t]− θ01− θ1 − E [µτ τ˜t − µg g˜t] +E[R˜(2)t − ω(R˜(2)t − R˜(1)t )]1− θ1 . (4.15)Taking derivative of expected inflation with respect to ω we see that the sign and magnitudefrom shortening maturity on inflation depends negatively on the average slope of the nominal94yield curve:dE[Π˜t]dω= −E[R˜(2)t − R˜(1)t]≈ −2 · E[y(2)t − y(1)t ]. (4.16)where the last approximate equality uses Eq. (4.7). Thus, the impact of shortening maturityon expected inflation is negatively related to the slope of the nominal yield curve.Other asset classesThe fiscal discount rate channel also extends beyond maturity restructuring operations toother asset classes with different risk profiles. Accounting for differences in expected returnsacross financing instruments, regardless of maturity, in the fiscal theory provides a directchannel for changes in the government portfolio to affect inflation. Assume now that thegovernment issues one-period riskless nominal debt B(1)t and one-period defaultable nominaldebt Dt:R(1)t B(1)t +R(d)t Dt = B(1)t+1 +Dt+1 + St. (4.17)The return of the defaultable bond is:R(d)t ≡ 1/Q(d)t−1, (4.18)where the price, Q(d)t , is given by the Euler equation:Q(d)t = Et[Mt+1Πt+1e−κt+1], (4.19)and κt+1 is the fraction of debt that is defaulted at time t, which follows an exogenous process:κt = (1− ρκ)κ+ ρκκt−1 + σκεκ,t. (4.20)The discount rate of the government is given by:R(g)t = (1− wd)R(1)t + wdR(d)t . (4.21)Given default risk, we can show that E[R(d)t ] > E[R(1)]. Therefore, increasing the financingweight on risky debt will increase the government discount rate and generate inflation. Thesecomparative statics are illustrated in Fig. Benchmark modelThis section presents the benchmark model which builds on and quantifies the insights fromthe simple model.954.3.1 HouseholdsThe representative household is assumed to have Epstein-Zin preferences over streams ofconsumption Ct and labor Lt:Ut ={(1− β) (C?t )1−1/ψ + β(Et[U1−γt+1]) 1θ} θ1−γ, (4.22)C?t = Ct(L¯Lt)ϕ, (4.23)where γ is the coefficient of risk aversion, ψ is the elasticity of intertemporal substitution,θ ≡ 1−γ1−1/ψ is a parameter defined for convenience, β is the subjective discount rate, and L¯ isthe agent’s time endowment. The time t budget constraint of the household isPtCt +Bt+1 = PtDt +WtLt +RtBt − Tt, (4.24)where Pt is the aggregate price level, Bt is the nominal market value of a portfolio of gov-ernment bonds, Dt represents real dividends received from the intermediate firms, Rt is thegross nominal interest rate on the bond portfolio, Wt is the nominal competitive wage, andTt are lump sum taxes from the government. The household chooses sequences of Ct, Lt, andBt to maximize lifetime utility subject to the budget constraints.4.3.2 FirmsProduction in our economy is comprised of two sectors: the final goods sector and the inter-mediate goods sector.Final goodsA representative firm produces the final consumption goods Yt in a perfectly competitivemarket. The firm uses a continuum of differentiated intermediate goods Xit as input in aconstant elasticity of substitution (CES) production technology:Yt =(∫ 10Xν−1νi,t) νν−1, (4.25)where ν is the elasticity of substitution between intermediate goods. The profit maximizationproblem of the final goods firm yields the following isoelastic demand schedule with priceelasticity ν:Xi,t = Yt(Pi,tPt)−ν, (4.26)96where Pt is the nominal price of the final goods and Pi,t is the nominal price of the interme-diate goods i. The inverse demand schedule isPi,t = PtY1νt X−1νi,t . (4.27)Intermediate goodsThe intermediate goods sector is characterized by a continuum of monopolistic firms. Eachintermediate goods firm produces Xi,t using labor Li,t:Xi,t = ZtLi,t − ΦZt, (4.28)where Zt represents an aggregate productivity shock common across firms, and is composedof both transitory and permanent components (e.g., Croce (2014) and Kung and Schmid(2015)):Zt = ez?+at+nt , (4.29)at = ρaat−1 + σaat, (4.30)∆nt = ρn∆nt−1 + σnnt, (4.31)where z? is the unconditional mean of log(Zt), ∆nt = nt−nt−1, at and nt are standard normalshocks with a contemporaneous correlation equal to ρan. The low-frequency component inproductivity, ∆nt, generates long-run risks and sizeable risk premia (i.e., Bansal and Yaron(2004)). The fixed cost of production Φ is multiplied by Zt to ensure that it does not becometrivially small along the balanced growth path.Using the inverse demand function from the final goods sector, nominal revenues forintermediate firm i can be expressed asPi,tXi,t = PtY1νt [ZtLi,t − ΦZt]1−1ν . (4.32)The intermediate firms face a cost of adjusting the nominal price a` la Rotemberg (1982),measured in terms of the final good asG(Pi,t, Pi,t−1) =φR2(Pi,tΠssPi,t−1− 1)2Yt, (4.33)where Πss ≥ 1 is the steady-state inflation rate and φR is the magnitude of the costs.The source of funds constraint isPtDi,t = Pi,tXi,t −WtLi,t − PtG(Pi,t, Pi,t−1;Pt, Yt), (4.34)97where Di,t is the real dividend paid by the firm. The objective of the firm is to maximizeshareholder’s value V(i)t = V(i)(·) taking the pricing kernel Mt, the competitive nominal wageWt, and the vector of aggregate state variables Υt = (Pt, Zt, Yt) as given:V(i)t (Pi,t−1; Υt) = maxPi,t,Li,t{Di,t + Et[Mt+1 V(i) (Pi,t; Υt+1)]}, (4.35)subject toDi,t =Pi,tPtXi,t −WtLt −G(Pi,t, Pi,t−1;Pt, Yt), (4.36)Pi,tPt=(Xi,tYt)− 1ν. (4.37)The corresponding first-order conditions are listed in C.1.GovernmentThe flow budget constraint of the government is given by:N∑i=1B(i)t+1 =N∑i=1R(i)t B(i)t − St, (4.38)where B(i)t+1 is the nominal debt of maturity i issued at the end of period t, R(i)t is thenominal interest paid on debt of maturity i, St denotes the nominal value of primary surpluses.For parsimony, we assume that the government only levies lump-sum taxes and governmentexpenditures are excluded. Thus, the primary surplus equals lump-sum taxes. Denoting thetotal market value of public debt by Bt and scaling the budget constraint by nominal outputPtYt,bt+1 =RgtΠt∆Ytbt − st, (4.39)where bt+1 ≡ Bt+1/(PtYt), st ≡ St/(PtYt) and Rgt =∑Ni=1w(i)t R(i)t is the nominal grossinterest paid on the portfolio of government debt. The government issues nominal debt at Ndifferent maturities and we assume that each period the government retires outstanding debtand issues new debt over the N maturities. The proportion of the debt financed with bondsof maturity i is given by:w(i)t = w¯(i) + β(i)xmt, (4.40)where the constants w¯(i)’s determine the steady state maturity structure of debt and the β(i)’sdetermine the sensitivity to xmt, a stochastic process drives the dynamics of the maturity98structure. The evolution of xmt is given by:xmt = ρmxmt−1 + σmmt, (4.41)subject to∑Ni=1 w¯(i)t = 1. Note that these shocks are self-financing so that the total marketvalue of debt Bt+1 is unaffected initially, but is allowed to adjust freely afterwards.Monetary and fiscal rulesThe central bank follows an interest rate feedback rule:ln(R(1)tR(1))= ρr ln(R(1)t−1R(1))+ (1− ρr)(ρpi,ζt ln(ΠtΠ)+ ρy ln(ŶtŶ))+ σrrt, (4.42)where R(1)t+1 is the gross one-period nominal interest rate, Πt is inflation, Ŷt is detrendedoutput, and rt is a normal i.i.d. shock. Note that the coefficient ρpi,ζt is indexed by ζt, whichdetermines the policy mix at time t.The fiscal authority adjusts the primary surplus-to-GDP ratio, st ≡ St/(PtYt), accordingto the following rule:st − s = ρs(st−1 − s) + (1− ρs) δb,ζt(bt − b) + σsst . (4.43)The coefficient δb,ζt is also indexed ζt and is therefore depends on the policy mix at time t.Monetary/Fiscal Policy MixLeeper (1991) distinguishes four policy regions in a model with fixed policy parameters. Two ofthe parameter regions admit a unique bounded solution for inflation. One of the determinacyregions is what Leeper refers to as the Active Monetary/Passive Fiscal (AM/PF) regime,which is the familiar textbook case (e.g., Woodford (2003) and Gal´ı (2015)). The Taylorprinciple is satisfied (ρpi > 1) and the fiscal authority adjusts taxes to stabilize debt (δb >(β∆Y1− 1ψ)−1−1). In this policy mix, monetary policy determines inflation while fiscal policypassively provides the fiscal-backing to accommodate the inflation targeting objectives of themonetary authority. We refer to this regime as the monetary-led regime.The other determinacy region is the Passive Monetary/Active Fiscal (PM/AF) regime.The fiscal authority is not committed to stabilizing debt (δb <(β∆Y1− 1ψ)−1−1), but insteadthe monetary authority passively accommodates fiscal policy (ρpi < 1) by allowing the pricelevel to adjust (to satisfy the government budget constraint). In this setting, fiscal policydetermines inflation while monetary policy stabilizes debt and anchors expected inflation.Importantly, in this regime, fiscal disturbances, including non-distortionary taxation, havea direct impact on the price level via the government budget constraint because households99know that changes in taxes will not be offset by future tax changes.3 We refer to this regimeas the fiscally-led regime.When both the fiscal and monetary authorities are active (AM/AF), no stationary equi-librium exists. When both authorities are passive, there exist multiple equilibria. In ourregime-switching specification, we follow Bianchi and Melosi (2014) and assume that the pol-icy mix alternates between monetary- and fiscally-led regimes according to a two-state Markovchain with the following transition matrix:M =(pMM 1− pFF1− pMM pFF),where pij ≡ Pr(ζt+1 = i|ζt = j) and M denotes the monetary-led regime and F denotes thefiscally-led regime.4.4 ResultsThis section presents the key results of the model. We begin with a description of the cali-bration of the model followed by a quantitative analysis. The model is solved using a globalprojection method that is outlined in C. CalibrationTable 4.1 presents the quarterly calibration. Panel A reports the values for the preferenceparameters. The elasticity of intertemporal substitution ψ is set to 1.5 and the coefficient ofrelative risk aversion γ is set to 10.0, which are standard values in the long-run risks literature(e.g., Bansal and Yaron (2004)). The subjective discount factor β is calibrated to 0.9935 tobe consistent with the average return on the government bond portfolio (see Panel A of Table4.2). The relative preference for leisure ϕ is set so that the household works one-third of thetime in the steady-state.Panel B reports the calibration of the technological parameters. The price elasticity ofdemand ν is set to 2. The fixed cost of production Φ is set such that the dividend is zero inthe deterministic steady state. The price adjustment cost parameter φR is set to 10.4 Themean growth rate of productivity z? is set to obtain a mean growth rate of output of 2%. Theparameters ρa and σa are set to be consistent with the standard deviation and persistence ofoutput growth, respectively (see Panel B of Table 4.2). The parameters ρn and σn are set tomatch the standard deviation and persistence of expected productivity growth.For parsimony, we assume that shocks to the short-run and long-run components of pro-3In this regime, the government budget constraint is an equilibrium condition rather than a constraint thathas to hold for any price path, which Cochrane (2005) refers to as the government debt valuation equation.4For example, in a log-linear approximation, the parameter φR can be mapped directly to a parameter thatgoverns the average price duration in a Calvo pricing framework. In this calibration, φR = 10 corresponds toan average price duration of 3.7 quarters, a standard value in the macroeconomics literature (e.g. Ferna´ndez-Villaverde, Gordon, Guerro´n-Quintana, and Rubio-Ramı´rez (2012)).100ductivity are perfectly correlated (a,t = n,t). Indeed, Kung and Schmid (2015) and Kung(2015) show that a stochastic endogenous growth framework produces a very strong positivecorrelation between these components (i.e., around 0.98). Kung (2015) illustrates that theseproductivity dynamics help to generate countercyclical real marginal costs, which implies anegative relation between inflation and expected growth. Further, these inflation and growthdynamics imply an upward sloping nominal yield curve (see Table 4.3).Panel C reports the calibration of the policy rule parameters. We set the steady state debt-to-GDP ratio to match the empirical average. The persistence and volatility parameters, ρsand σs, are chosen to match primary surplus dynamics. The surplus rule parameter, δb, isset to 0.05 and 0.00 in the AM/PF and PM/AF regimes, respectively. The interest rate ruleparameter, ρpi, is set to 1.5 and 0.4 in the AM/PF and PF/AM regimes, respectively. Thecalibration of these policy parameters, conditional on regime, are consistent with structuralestimation evidence from Bianchi and Ilut (2014). The persistence of the interest rate ruleρR is calibrated to 0.5. For parsimony, we abstract from monetary policy shock and outputsmoothing. Steady-state inflation Πss is calibrated to match the average level of inflation.Following Bianchi and Melosi (2014), we assume that the transition matrix governing thedynamics of the policy/mix is symmetric: pMM = pFF ≡ p is set to 0.9875, implying that theeconomy stays on average 20 years in a given regime.Panel D reports the calibration of the government bond supply dynamics. Fig. 4.1 plots theaverage maturity of net government liabilities, including reserves, from Q1:2005 to Q3:2013.Note that the three QE operations and the Maturity Extension Program (MEP), show upquite visibly as each of these operations significantly shortened the maturity structure of debt.5We calibrate the bond supply process to capture salient features of the maturity structuredynamics. We set N = 40, so that we include bonds up to a maturity of 10 years, as in ourdata sample. The steady state maturity structure {w¯(i)} is set to match the sample average.To calibrate the dynamics of the process driving the duration of government liabilities, xmt,we proceed as follows. First, we run a principal component analysis on the panel data ofmaturity structure. Next, we extract the first principal component (PC1) and fit the timeseries to an AR(1) process.6 The estimates for ρm and σm are 0.9513 and 1.28%, respectively.The loadings {β(i)} for bonds of each maturity are also obtained from the first principalcomponent.4.4.2 Yield curveThe dynamics of the nominal yield curve provide the key transmission channel for maturityrestructuring operations in the fiscal theory. In this section, we show that the model endoge-nously generates realistic term structure implications. Table 4.3 reports the mean, standarddeviation, and first autocorrelation of nominal yields for maturities of one quarter to five5Details on the data construction are described in C.5.6The first principal component explains about 62% of the cross-sectional dynamics of the debt maturitystructure101years. The model does a fairly good job in explaining the level and persistence of yields.In particular, the negative link between inflation and expected consumption growth impliesthat long nominal bonds are riskier than short nominal bonds, which helps the model explainthe upward-sloping average yield curve (five-year minus one-quarter yield spread is 0.55%).The volatility of yields falls short of the empirical moments, however Kung (2015) shows thatincorporating volatility shocks to productivity and interest rate rule shocks in a similar DSGEframework helps to fit the second moments better.The model can explain the joint dynamics between bond yields and macroeconomic vari-ables. Table 4.4 shows that the slope of the nominal yield curve can positively forecastconsumption and output growth while negatively forecast inflation as in the data. The inter-est rate rule plays an important role in these forecasting regressions. Suppose that inflationfalls persistently today, then the monetary authority responds by lowering the short rate. Atemporary fall in the short rate steepens the slope of the yield curve. Further, due to thenegative inflation-growth link, a fall in inflation is also associated with higher expected growthrates.4.4.3 Maturity structure shocksAs described in the simple model, the combination of a fiscally-led regime and a non-zero slopeimplies that rebalancing the maturity structure affects inflation. We again can derive a similarpresent value relation by iterating forward the government budget equation (Eq. (4.38)) fromour benchmark model (see C.3 for the derivation):bt ≡ BtPt= Et[ ∞∑i=0st+i∏ij=0Rgt+j/(Πt+j∆Yt+j)]. (4.44)In the fiscally-led regime, Eq. (4.44) is an equilibrium condition that determines the pricelevel. This equation is similar to the present value relation derived in the simple model exceptthat there is now debt issued up to N -periods and the equation accounts for growth. Whenthe yield curve is not flat, changing the financing mix alters the government cost of capital,Rg, which leads to an adjustment in inflation (and expected inflation) to satisfy Eq. (4.44).The addition of sticky prices in the benchmark model implies that the fiscal discount ratechannel has real effects and therefore violates Wallace neutrality. We show that the directionof these effects is determined by the slope of the nominal yield curve.Fig. (4.4) plots impulse response functions, conditional on staying in the fiscally-led regime,to a shock that reduces average maturity by 0.18 years (similar magnitude as in QE2). Weillustrate the effects of the maturity shock for when the yield curve is upward-sloping (solidline), flat (line with circles), and downward-sloping (dashed line). Since the average slope inthe model is positive, for the downward-sloping case we look at maturity structure shocksconditional on periods when the slope is negative. For the upward-sloping case, we considerthe average effects from maturity restructuring (without conditioning on the realized slope).102For the flat yield curve scenario, we assume that the monetary authority implements aninterest rate peg.In the positive slope case, shortening the maturity structure implies that the governmentis refinancing at a lower rate. In the fiscally-led regime, a persistent decline in the governmentdiscount rate leads requires that inflation fall persistently to revalue nominal debt obligationsto satisfy the intertemporal government equation. A heuristic interpretation of the discountrate-inflation link is as follows (e.g., Cochrane (2011)). A fall in the government discount rateputs upward pressure on the real value of debt. Households, in anticipation of the apprecia-tion in their debt portfolio, increase demand for debt and decrease demand for consumptiongoods. The fall in aggregate demand leads to a decline in the price level. Without stickyprices, the fall in prices will be sufficient to leave households content with their original con-sumption allocation. However, with sticky prices, the fall in prices is sluggish, so that pricesare temporarily too high relative to the flexible price case, which depresses production (out-put) and increases the real rate. Thus, when the yield curve is upward-sloping, the fiscalchannel implies a potential “cost” of QE operations.The endogenous yield curve responses to the maturity structure shocks provide a feedbackchannel that amplifies the fiscal channel. For example, the fall in inflation (in the upward-sloping case) leads to a decline in the short rate due to the interest rate rule. A temporaryfall in the short rate steepens the slope of the nominal yield curve, which deepens the fall inthe government discount rate from shortening maturity. Furthermore, the fall in the overalllevel of the yields from falling inflation further depresses the nominal bond portfolio return.In the negative slope case, shortening the maturity structure gives the opposite effectscompared to when the slope is positive, which is illustrated in Fig. (4.4). In particular,reducing maturity in this case means that the government is refinancing at a higher rate.In the fiscal regime, an increase in the discount rate requires a devaluation in the real valueof the bond portfolio via higher inflation to satisfy the intertemporal government budgetconstraint. With sticky prices, the increase in inflation stimulates an expansion in output.Also, flattening of the yield curve due to the increase in the short rate amplifies the maturityrestructuring effects, following a similar logic as above. Finally, when the yield curve is flat,our fiscal channel is neutral even in the fiscally-led regime, as the financing costs are the sameacross maturities. These results illustrate how monetary policy is important for open marketoperations even when it is “passive”. Overall, we highlight the importance of the yield curvefor maturity restructuring in the fiscal theory.Due to the recurrent regime shifts and rational expectations, maturity restructuring alsohas non-neutral effects in the monetary-led regime when the yield curve is nonzero. Fig. (4.5)displays impulse response functions, conditional on staying in the fiscally-led (dashed line) andthe monetary-led (solid line) regimes for the relevant period, to a shock to maturity structurethat reduces average maturity by 0.18 years. We show these plots for the upward-slopingcase. Without regime shifts, changes in fiscal discount rates are neutral in the monetary-led103regime due to offsetting surplus policy. However, the possibility of entering the fiscally-ledregime propagates the restructuring effects, through agent’s expectations, to the monetary-ledregime.Indeed, the responses in the monetary-led regime are qualitatively similar to the reactionsin the fiscally-led regime. However, since the probability of changing regimes is small, theresponses of macroeconomic quantities in the monetary-led regime are significantly smaller.For example, output drops by 33 basis points in the fiscal regime compared to 5 basis pointsin the monetary-led regime. Note that the responses of the short rate and yield spreadare of similar magnitude despite the much smaller response of inflation in the monetary-ledregime. This is because the short rate responds more aggressively to inflation deviations inthe monetary-led regime than in the fiscally-led regime.4.4.4 Macroeconomic fluctuationsTable 4.2 reports basic macroeconomic summary statistics from the data and the model coun-terparts. The ‘model’ column reports the unconditional moments while ‘fiscal’ and ‘mone-tary’ columns report the moments conditional on the regime. Macroeconomic volatility issignificantly higher in the fiscally-led regime because the economy is less insulated from fis-cal disturbances than in the monetary-led regime (e.g., Bianchi and Ilut (2014)). This washighlighted in the previous section when we compared responses from changes in governmentdiscount rates due to maturity restructuring operations in the two regimes.Fig. 4.6 plots impulse response functions to a positive one standard deviation shock toreal surpluses, conditional on staying in the monetary-led (solid line) and fiscally-led (dashedline) regimes for the relevant period. In the fiscally-led regime, an increase in real surplusesraises the fiscal-backing for debt. To satisfy the intertemporal government budget constraint,the price level needs to fall to increase the real value of debt. In the monetary-led regimewithout regime shifts, surplus shocks are offset by stabilizing future surplus policy whichimplies that surplus shocks are neutral. However, the possibility of entering the fiscally-ledregime propagates the effects to the monetary regime. Qualitatively, the responses are similarin the two regimes, but quantitatively, the responses are significantly larger in the fiscally-ledregime since the regimes are persistent.4.4.5 Market timing policiesFig. 4.7 plots impulse response functions from a shock that lengthens average maturity, con-ditional on staying in the fiscally-led regime, for various slopes as in Fig. 4.4. The effectsof lengthening maturity are the opposite to shortening maturity. When the yield curve isupward-sloping (downward-sloping), lengthening maturity is expansionary (contractionary).These results suggest that there might be a role for market timing maturity operations basedon the slope of the nominal yield curve.Consider a maturity restructuring policy that depends directly on the slope of the nominal104yield curve:xm,t = ρmxm,t−1 + φ(y5Yt − y1Qt)+ σmm,t. (4.45)A positive coefficient (φ > 0) implies that the government shortens the maturity structurewhen yield curve is upward-sloping and lengthens the maturity structure when the yield curveis downward-sloping. A negative coefficient implies the opposite policy. Fig. 4.8 plots com-parative statics for varying φ from -1 to 1. Note that more negative values of φ smoothmacroeconomic fluctuations, reduce risk premia, and improve welfare through the fiscal dis-count rate channel. In contrast, more positive values of φ increase consumption and inflationvolatility, and, in turn, increase welfare costs. Negative values of φ shorten the maturity struc-ture when the yield curve is downward sloping, which stimulates the economy and generatesfiscal inflation exactly during low expected growth states. Using similar logic, positive valuesfor φ deepen recessions and increase deflationary pressure.4.4.6 Policy experimentIn this section we explore the quantitative significance of the fiscal discount rate channelfor quantitative easing operations during the Great Recession. To enrich this analysis, weaugment the benchmark model with a zero lower bound (ZLB) constraint on nominal interestrates and include market segmentation through transaction costs. We also assume that theeconomy starts in the monetary-led regime (with the possibility of entering the fiscally-ledregime) along with a government budget deficit calibrated to match the data during the GreatRecession.At the onset and during the aftermath of the Great Recession, interest rates were nearzero, and therefore the monetary authority was unable to prevent deflationary/contractionarypressure by lowering interest rates using conventional measures. Consequently, policymakersresorted to unconventional monetary policy, such as maturity twist operations (e.g., the Ma-turity Extension Program and QE2). One motivation for implementing the maturity twistoperations is because of market segmentation, so that government purchases of long-term debtwould lower long-term borrowing costs. Indeed, there is empirical evidence suggesting thatthe QE operations were effective in flattening the yield curve in the short-run.7 We analyzeeach new feature before we combine these elements in our policy experiment.7See, for example, Gagnon, Raskin, Remache, and Sack (2011), Krishnamurthy and Vissing-Jorgensen(2011), Swanson (2011), d’Amico, English, Lo´pez-Salido, and Nelson (2012), Hamilton and Wu (2012), Green-wood and Vayanos (2014).105ZLBTo capture periods where the ZLB constraint is binding for multiple periods, we also incor-porate time preference shocks (e.g., Eggertsson and Woodford (2003)):ln(βt) = (1− ρβ) ln(β) + ρβ ln(βt−1) + σββ. (4.46)The ZLB constraint is given by:ln(R(1)tR(1))= max{0, ρr ln(R(1)t−1R(1))+ (1− ρr)(ρpi,ζt ln(ΠtΠ)+ ρy ln(ŶtŶ))+ σrrt}.(4.47)As in Aruoba, Cuba-Borda, and Schorfheide (2013), Ferna´ndez-Villaverde, Gordon, Guerro´n-Quintana, and Rubio-Ramı´rez (2012), and Gust, Lo´pez-Salido, and Smith (2012), we useglobal projection methods and rational expectations (as in our bechmark model) to approxi-mate the policy functions with the ZLB constraint.Fig. 4.9 plots impulse response functions for a shock that reduces average maturity by0.18 years (e.g., QE2), conditional on starting in the monetary-led regime, for when the ZLBbinds (dashed line) and when the ZLB is not binding (solid line). For the binding case, weuse a time preference shock to send the economy to the ZLB for an average of four quartersas in Ferna´ndez-Villaverde, Gordon, Guerro´n-Quintana, and Rubio-Ramı´rez (2012). Also, weconsider the benchmark case where the yield curve is, on average, upward-sloping.The effects of maturity restructuring are amplified at the ZLB. This is because the demandshock that temporarily sends the economy to the ZLB steepens the slope of the nominalyield curve. Indeed, during the aftermath of the Great Recession when interest rates wereclose to zero (2008 - 2015), the average slope was about 50% larger than the longer sample(1953 - 2015). With a steeper slope, shortening debt maturity decreases the governmentdiscount rate more than being away from the ZLB. Consequently, a binding ZLB enhancesthe contractionary effects of the fiscal discount rate channel when the yield curve is upward-sloping. More broadly, this example with the ZLB illustrates how the magnitude of the slopedictates the magnitude of the effects from the fiscal channel.Market segmentationWhile this essay highlights a potential cost of QE through the fiscal discount rate channel,for our policy experiment, we also account for a key proposed benefit of maturity operations- lowering long-term borrowing costs. To this end, we incorporate market segmentation viatransaction costs for bonds of different maturities (e.g., Bansal and Coleman (1996)).The transaction costs captures, in a reduced-form, a preferred habitat motive (e.g., Vayanosand Vila (2009)). These costs imply that operations shortening debt maturity flattens theyield curve by reducing the risk premium of bonds at a specific maturity. More specifically,the household pays an additional fee χ(i)t for each unit of bond of maturity i purchased. We106modify the budget constraint of the representative household in the following way:PtCt +n∑i=1B(i)t+1(1 + χ(i)t ) = PtDt +WtLt +n∑i=1Q(i−1)tQ(i)t−1B(i)t − St. (4.48)Solving the household problem, the nominal price of a i-maturity bond isQ(i)t = Et[Mt+1Πt+1Q(i−1)t+11 + χ(i)t]. (4.49)Note that the existence of transaction costs gives rise to a liquidity premium that depends onχ(i)t . Following the literature on preferred habitats, it is assumed that the liquidity premiumdepends on the aggregate supply of bonds:χ(i)t = χ¯(i)e(B(i)t+1Bt+1−B(i)B), (4.50)= χ¯(i)e(β(i)xm,t), (4.51)where χ¯(i) > 0 is the steady state transaction cost, and χ¯(i) ≥ χ¯(i−1) that is, longer-term bondare relatively more costly to trade than shorter-term bonds.Fig. 4.10 shows impulse response functions from shortening maturity with (solid line) andwithout (dashed line) market segmentation. To isolate the effects of the new ingredients,we shut down the fiscal discount rate channel by assuming the economy can only be in themonetary-led regime without the possibility of entering the fiscally-led regime. The marketsegmentation parameters are calibrated such that a QE2-type operation reduces the five-yearnominal yield spread, on average, by around 15 basis points on impact to be consistent withempirical estimates from Krishnamurthy and Vissing-Jorgensen (2011), while still matchingthe average yields implied by the benchmark model (Table 4.3).Without the fiscal discount rate channel or market segmentation, maturity restructuringpolicies are neutral. However, with market segmentation, shortening maturity drives downlong-term interest rates while stimulating economic activity (e.g., increasing inflation andoutput).Persistent deficitsFig. 4.11 explores the impact of persistent budget deficits on maturity restructuring policies atthe zero lower bound. This figure displays impulse response functions, conditional on startingin the monetary-led regime and an upward-sloping nominal yield curve, to a shock that reducesaverage maturity by 0.18 years under positive surpluses around the steady-state level as inthe benchmark (solid line), a budget deficit shock calibrated to the data during the GreatRecession (line with circles), and a severe deficit shock that is eight times the magnitude of the107deficit during the Great Recession (dashed line).8 Restructuring under a deficit attenuates thefiscal discount rate effects on inflation. In the case where the yield curve is upward-sloping,shortening the maturity lowers the discount rate persistently. For the negative surpluses todayand in the immediate future, lowering the discount rate has a negative effect on the presentvalue of the fiscal backing. Since the surplus process is mean-reverting, surpluses will bepositive at some point in the future, and a lower discount rate applied to these cash flowshas a positive effect on the present value.9 Hence, if the deficit today is particularly severeor persistent, the discount rate effects from the deficit component can potentially dominate.Quantitatively, when the magnitude of the deficit is calibrated to the recent U.S. data, wehave similar responses as the positive surplus case (benchmark), albeit somewhat weakened.For the responses to be reversed (i.e., negative component dominates), it requires a deficitthat is almost an order of magnitude larger than the current deficit.Full analysisWe analyze these responses with (solid line) and without (dashed line) the fiscal discount ratechannel. In the latter case, we shut down the fiscal channel by eliminating regime changesand assuming policy is always characterized by the monetary-led regime. Given that the yieldcurve is upward-sloping, we find that the fiscal discount rate channel significantly dampens theexpansionary effects, due to market segmentation, from maturity restructuring. Comparingthe impulse response functions, we find that the fiscal discount rate channel dampens inflationresponses by 21% after 5 quarters, and 53% after 10 quarters. Similarly, the fiscal channeldampens output responses by 17% after 5 quarters, and 60% after 10 quarters. The increasingeffects by horizon reflect that the cumulative probability of switching to the fiscally-led regimeincreases over time. In addition, the fiscal channel also partially undoes the flattening of theyield curve from market segmentation. Interpreting these results, accounting for the fiscaldiscount rate channel provides a potential explanation for why there was not a strong responsein inflation after the QE operations.4.5 ConclusionThis essay explores the interactions between yield curve dynamics and nominal governmentdebt maturity operations through the fiscal discount rate channel. Self-financing debt ma-turity operations are non-neutral when the slope of the nominal yield curve is nonzero inthe fiscal theory. When the risk profile of bonds varies by maturity, rebalancing the maturitystructure affects the cost of government financing. Changes in government discount rates thendirectly affect inflation through the intertemporal government budget equation. With stickyprices, the fiscal discount rate channel has real effects and therefore breaks Wallace neutrality.8During the onset of crisis, the surplus dropped sharply, which corresponds to a negative 3.5-sigma shockto the surplus process. In the severe deficit case, the shock is set to be eight times the magnitude of the deficitshock at the onset of the crisis.9This is implicitly assuming that the maturity structure shock is more persistent than the deficit.108When the yield curve is upward-sloping (downward-sloping) the effects of maturity restruc-turing implied by the fiscal channel are contractionary (expansionary). In contrast, the effectsare neutral when the slope is zero. Thus, when the yield curve is upward-sloping, we illustratea potential cost for QE operations.We quantitatively assess the fiscal discount rate channel in a DSGE framework with astochastic maturity structure and policy regime changes between monetary-led and fiscally-led regimes. Without regime shifts, the effects of maturity restructuring are neutral in themonetary-led regime. However, with regime shifts, the possibility of entering in the fiscally-ledregime along with a nonzero slope also implies violations of nominal debt maturity neutralityin the monetary-led regime. Using an estimated process for the maturity structure of publicdebt, we show that the fiscal discount rate channel had substantial dampening effects oninflation and output responses to QE2, given an upward-sloping yield curve. Overall, thisessay highlights the importance of the term structure of interest rates as a transmissionchannel for quantitative easing policies in the fiscal theory.109Table 4.1: Quarterly calibrationParameter Description ModelA. Preferencesβ Subjective discount factor 0.9935ψ Elasticity of intertemporal substitution 1.5γ Risk aversion 10B. Productionν Price elasticity for intermediate goods 2φR Magnitude of price adjustment costs 10z? Unconditional mean growth rate 0.5%ρa Persistence of at 0.95σa Volatility of transitory shock eat 0.7%ρn Persistence of ∆nt 0.99σn Volatility of permanent shock ent 0.015%C. Policyρs Persistence of government surpluses 0.92σs Volatility of government surpluses est 0.05%δb(M/F ) Sensitivity of taxes to debt 0.05 / 0.0ρr Degree of monetary policy inertia 0.5 / 0.5ρpi(M/F ) Sensitivity of interest rate to inflation 1.5 / 0.4p Switching probability 0.9875D. Bond Supplyb¯ Steady state Debt-to-GDP ratio 0.5ρm Persistence of xmt 0.958σm Volatility of emt 1.28%This table reports the parameter values used in the quarterly calibration of the model. The table is dividedinto four categories: Preferences, Production, Policy, and Bond Supply parameters.110Table 4.2: Summary statisticsData Model Monetary FiscalA. MeansE(y(20) − y(1)) (in %) 1.02 0.55 0.89 0.18E (rg) (in %) 5.47 6.06 5.95 6.21B. Standard Deviationsσ(∆y) (in %) 2.22 2.90 1.47 4.07σ(∆c) (in %) 1.42 2.85 1.44 4.02σ(pi) 1.64 1.20 0.32 1.62σ(∆l)/σ(∆y) 0.92 0.51 0.21 0.57σ (rg) (in %) 4.53 1.22 0.81 1.52C. Correlationscorr(pi,∆c) (low-frequency) -0.85 -0.91 -0.91 -0.92This table presents the means, and standard deviations for key macroeconomic variables from the data andthe model. The model is calibrated at a quarterly frequency and the reported statistics are annualized.Table 4.3: Term structureMaturity1Q 1Y 2Y 3Y 4Y 5Y 5Y - 1QMean (Model) (in %) 5.68 5.91 6.03 6.11 6.17 6.23 0.55Mean (Data) (in %) 5.03 5.29 5.48 5.66 5.80 5.89 1.02Std (Model) (in %) 1.20 1.00 0.90 0.80 0.70 0.60 0.70Std (Data) (in %) 2.97 2.96 2.91 2.83 2.78 2.72 1.05AC1 (Model) 0.95 0.90 0.90 0.90 0.90 0.92 0.95AC1 (Data) 0.93 0.94 0.95 0.95 0.96 0.96 0.74This table presents the mean, standard deviation, and first autocorrelation of the one-quarter, one-year, two-year, three-year, four-year, and five-year nominal yields and the 5-year and one-quarter spread from the modeland the data. The model is calibrated at a quarterly frequency and the moments are annualized.111Table 4.4: Forecasts with the yield spreadData ModelHorizon (in quarters)1 4 8 1 4 8A. Outputβ 1.023 0.987 0.750 1.694 1.211 0.820S.E. 0.306 0.249 0.189 0.413 0.217 0.169R2 0.067 0.148 0.147 0.045 0.147 0.176B. Consumptionβ 0.731 0.567 0.373 1.650 1.179 0.800S.E. 0.187 0.163 0.153 0.398 0.211 0.165R2 0.092 0.136 0.088 0.045 0.145 0.173C. Inflationβ -1.328 -1.030 -0.649 -2.370 -1.784 -1.266S.E. 0.227 0.315 0.330 0.154 0.215 0.237R2 0.180 0.157 0.071 0.484 0.355 0.235This table presents output growth, consumption growth, and inflation forecasts for horizons of one, four, andeight quarters using the five-year nominal yield spread from the data and the model. The n-quarter regressions,1n(xt,t+1 + · · ·+ xt+n−1,t+n) = α+ β(y(5)t − y(1Q)) + t+1, are estimated using overlapping quarterly data andNewey-West standard errors are used to correct for heteroscedasticity.112Figure 4.1: Average maturity of public debt2006 2008 2010 20123.43.63.844. (years)average maturity (years)QE1↓QE2↓MEP↓QE3↓This figure plots the average maturity structure of government debt held by the public from Q1-2005 toQ3-2013.Figure 4.2: Comparative statics: shortening maturity0 0.2 0.4 0.6 0.8 1E[r g]w  Slope>0Slope=0Slope<00 0.2 0.4 0.6 0.8 1E[pi]wThis figure plots the average effect from increasing the portfolio weight on short-term debt, w, on the gov-ernment discount rate Rg (top figure) and log inflation pi (bottom figure) for when the average yield curve isupward-sloping (solid line), downward-sloping (dashed line), and flat (line with circles).113Figure 4.3: Comparative statics: defaultable debt0 0.2 0.4 0.6 0.8 1E[r g]wd0 0.2 0.4 0.6 0.8 1E[pi]wdThis figure plots the average effect from increasing the portfolio weight on risky debt, wd, on the governmentdiscount rate Rg (top figure) and log inflation pi (bottom figure).Figure 4.4: Maturity restructuring with different slopes0 10 20−0.2−0.10maturity  Slope>0Slope=0Slope<00 10 20−0.100.1E[r g] 0 10 20−0.500.5E[pi] 0 10 20−0.0500.05yield spread quarters0 10 20−0.100.1FFRquarters0 10 20−0.500.51yquartersThis figure plots conditional impulse response functions for the government discount rate, expected inflation,the 5-year minus 1-quarter nominal yield spread, the fed funds rate, and output to a decrease in the averagematurity of government debt (similar in magnitude as QE2) in the fiscal regime. Results are reported for whenthe yield curve is upward-sloping (solid line), flat (line with circles), and downward-sloping (dashed line). Theunits of the y-axis are annualized percentage deviations from the steady-state, except for the average durationthat is in years.114Figure 4.5: Maturity restructuring in different regimes0 10 20−0.2−0.10maturity   MonetaryFiscal0 10 20−0.100.1E[r g] 0 10 20−0.500.5E[pi] 0 10 20−0.0500.05yield spread quarters0 10 20−0.100.1FFRquarters0 10 20−0.4−0.20yquartersThis figure plots the conditional impulse response functions for the government discount rate, expected inflation,the 5-year minus 1-quarter nominal yield spread, the fed funds rate, and output to a decrease in the averagematurity of government debt (similar magnitude as QE2) in the monetary regime (solid line) and fiscal regime(dashed line). The units of the y-axis are annualized percentage deviations from the steady-state, except forthe average duration that is in years.Figure 4.6: Surplus shocks in different regimes0 10 20−0.0500.05s  MonetaryFiscal0 10 20−0.4−0.20E[r g] 0 10 20−0.8−0.6−0.4−0.20E[pi] 0 10 2000.20.4yield spread quarters0 10 20−0.4−0.20FFRquarters0 10 20−4−20yquartersThis figure plots conditional impulse response functions of the government discount rate, expected inflation,the 5-year minus 1-quarter nominal yield spread, the fed funds rate, and output to a positive one standarddeviation surplus shock in the monetary (solid line) and fiscal (dashed line) regime. The units of the y-axisare annualized percentage deviations from the steady-state, except for the surplus that is in levels.115Figure 4.7: Lengthening maturity0 10 2000.10.2maturity  Slope>0Slope=0Slope<00 10 20−0.200.2E[r g] 0 10 20−0.500.5E[pi] 0 10 20−0.100.1yield spread quarters0 10 20−0.200.2FFRquarters0 10 20−2−101yquartersThis figure plots conditional impulse response functions of the government discount rate, expected inflation,the 5-year minus 1-quarter nominal yield spread, the fed funds rate, and output to an increase in the averagematurity of government debt in the fiscal regime. Results are reported for when the yield curve is upwardsloping (solid line), flat (line with circles), and downward sloping (dashed line). The units of the y-axis areannualized percentage deviations from the steady-state, except for the average duration that is in years.Figure 4.8: Market timing policies−1 −0.5 0 0.5 1−101welfare cost −1 −0.5 0 0.5 100.51yield spread −1 −0.5 0 0.5 1234std(E[∆c]) φ−1 −0.5 0 0.5 111.52std(pi)φThis figure plots comparative statics for the welfare cost, average yield spread, standard deviation of consump-tion growth, and the standard deviation of inflation when the market timing sensitivity to the yield spreadvaries.116Figure 4.9: Maturity restructuring at the ZLB0 10 20−0.2−0.10maturity   away ZLBat ZLB0 10 20−0.02−0.010E[r g] 0 10 20−0.02−0.010E[pi] 0 10 2000.010.020.03yield spread quarters0 10 20024FFRquarters0 10 20−0.4−0.20yquartersThis figure plots the conditional impulse response functions of the government discount rate, expected inflation,the 5-year minus 1-quarter nominal yield spread, the fed funds rate, and output to a decrease in the averagematurity of government debt (similar magnitude as QE2) when in the monetary regime. The dashed linerepresents the response at the zero lower bound and the solid line represents the response away from the zerolower bound. The units of the y-axis are annualized percentage deviations from the steady-state, except forthe average duration that is in years and the fed funds rate that is in levels.Figure 4.10: Maturity restructuring with market segmentation5 10 15 20−0.2−0.10maturity  SegmentationNo segmentation5 10 15 20−0.1−0.050E[r g] 5 10 15 20−[pi] 5 10 15 20−0.200.2yield spreadquarters5 10 15 20−0.500.5FFRquarters5 10 15 2000.10.2yquartersThis figure plots the impulse response functions of the government discount rate, expected inflation, the5-year minus 1-quarter nominal yield spread, the fed funds rate, and output to a decrease in the averagematurity of government debt (similar magnitude as QE2) in the monetary regime (without regime shifts). Thedashed line represents the response without market segmentation and the solid line, the response with marketsegmentation. The units of the y-axis are annualized percentage deviations from the steady-state, except forthe average duration that is in years.117Figure 4.11: Maturity restructuring with persistent deficits0 10 20−0.15−0.1maturity  Positive surplusLess severe deficitMore severe deficit0 10 20−10−50x 10−3E[r g] 0 10 20−20−100x 10−3E[pi] 0 10 2000.02yield spread quarters0 10 2024FFRquarters0 10 20−0.1−0.050yquartersThis figure plots the conditional impulse response functions of the government discount rate, expected inflation,the 5-year minus 1-quarter nominal yield spread, the fed funds rate, and output to a decrease in the averagematurity of government debt (similar magnitude as QE2) when the economy starts initially in the monetaryregime at the zero lower bound. The solid line represents the response under positive surpluses. The linewith circles represents the response under a deficit shock (-3.5 sigma) calibrated to the data during the GreatRecession (2008-2010). The dashed line represents a severe deficit shock that is eight times the magnitude ofthe deficit during the Great Recession. The units of the y-axis are annualized percentage deviations from thesteady-state, except for the average duration that is in years and the fed funds rate that is in levels.Figure 4.12: Policy experiment0 10 20−0.18−0.16−0.14−0.12−0.1−0.08maturity  SwitchingNo switching0 10 20−0.1−0.08−0.06−0.04−0.02E[r g] 0 10 2000.050.10.15E[pi] 5 10 15 20−0.2−0.10yield spreadquarters0 10 200246FFRquarters0 10 2000.10.20.3yquartersThis figure plots the conditional impulse response functions of the government discount rate, expected inflation,the 5-year minus 1-quarter nominal yield spread, the fed funds rate, and output to a decrease in the averagematurity of government debt (similar magnitude as QE2) when the economy starts initially in the monetaryregime at the zero lower bound. These plots come from the augmented model that also incorporates marketsegmentation and a short-term liquidity demand. The solid line represents the response with switching tothe fiscal regime and the dashed line represents the response without the possibility of switching to the fiscalregime. The units of the y-axis are annualized percentage deviations from the steady-state, except for theaverage duration that is in years and the fed funds rate that is in levels.118Chapter 5ConclusionThis thesis is a collection of three essays on Macro Finance. The first essay, chapter 2, ex-amines how industry competition affects the cross-section of asset prices. Empirically, morecompetitive industries are characterized by higher credit spreads, but lower expected returns.I reconcile these two facts within a structural model that captures the rich interaction betweena firm’s competitive environment, optimal capital structure, and asset prices. In the model,tougher competition erodes profit margins and reduces the firm value. Consequently, com-petitive firms are more exposed to idiosyncratic cash-flow shocks which increases credit riskand leads to higher credit spreads. In contrast, equityholders in competitive industries owna more valuable option to default. Effectively, the limited liability feature acts as an insur-ance for bad states of the world. This makes equity safer and decreases expected returns. Inequilibrium, competitive industries issue less, but more expensive debt, and have a lower costof equity. I find substantial empirical evidence for these predictions. Besides, the calibratedmodel generates cross-sectional variation in leverage and valuation ratios close to the data.More generally, this essay provides new evidence that competition is a key determinant ofthe cross-section of asset prices, both equity returns and credit spreads. It also shows theimportance to account for leverage and default in explaining the interaction between equityreturns and industry competition.In chapter 3, I explore the implications of firm entry dynamics for asset prices and macroe-conomic fluctuations. The model features two sources of innovation. First, process innovationrefers to incumbent firms investing to upgrade their current technology in response to thethreat of entry. In equilibrium, R&D investment by incumbents drives a small, but persistentcomponent in productivity growth that leads to sizable endogenous long-run risks. With re-cursive preferences, households are very averse to such persistent movements and commandhigh risk premia in asset markets that help the model match key asset price data, such as ahigh equity premium and a low riskfree rate. The second type of innovation is product inno-vation and refers to resources spent on the creation of new products and firms. In the model,entry is procyclical and leads to countercyclical markups. Novelly, these entry dynamics makeshort-term dividends very risky and the model produces a U-shaped term structure of equity119returns, consistent with the data. Firm entry is also endogenously asymmetric which pro-duces countercyclical macroeconomic volatility. With recursive preferences, these volatilitydynamics generate a countercyclical equity premium that can be forecasted by measures ofindustry concentration. These predictions are tested and confirmed in the data. Overall, thischapter presents new theoretical and empirical evidence that fluctuations in competition isan important determinant of time-varying risk premia.The last essay, chapter 4, studies the impact of government policy on asset prices and theeconomy. In this chapter, I document a novel transmission channel for open market operationstargeting the average maturity of government debt. I emphasize two key ingredients for thischannel to work. First, the risk profiles of bonds vary by maturity, i.e. the slope of thenominal yield curve is nonzero. In this case, varying the maturity structure changes theexpected return on the government bond portfolio and affects its market value through adiscount rate channel. When the monetary policy is passive and fiscal authorities are notcommitted to stabilize government liabilities, changes in government debt value impact theprice level through a fiscal inflation channel. This is the second key ingredient. In short, I showthat in the presence of a fiscally-led regime and a nonzero slope of the nominal yield curve,government debt maturity restructurings affect inflation. More specifically, when the nominalyield curve is upward-sloping, this channel implies that shortening the maturity structure hascontractionary effects. The quantitative importance of these effects are assessed in a modelcalibrated to replicate the second round of Quantitative Easing (QE) and I find that this newfiscal channel significantly dampened the inflation and output responses to QE2. Therefore,this essay shows the importance of the term structure of interest rates as a transmissionchannel for quantitative easing policies in the fiscal theory and highlights a new potential costof QE operations.5.1 Future workThe three essays presented in this thesis could be extended along several dimensions. In thefirst essay, for instance, all industries are assumed to be similar except for the number offirms, which is exogenously specified. While this assumption allows the model to stay rela-tively tractable, it would be interesting to allow for endogenous, and potentially time-varyingindustry competition. In addition, the model provides new predictions on the cross-sectionalrelationship between competition and expected bond returns that could be tested empirically.In the second essay, I assume the existence of a perfectly liquid capital market from whichfirms rent their technology. It would be interesting to see how allowing firms to innovate“in-house” and to sell their patents in imperfect markets would impact the quantitative re-sults. Finally, in the third essay, firms produce output using labor and finance themselvesonly through equity markets. Thus the model abstracts from key corporate decisions suchas capital expenditures and capital structure. 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Elsevier. → pages 89, 2001, Fiscal requirements for price stability, Journal of Money, Credit and Banking33, 669–728. → pages 89, 2003, Interest and prices: foundations of a theory of monetary policy, PrincetonUniversity Press, New Jersey. → pages 99Xu, Jin, 2012, Profitability and capital structure: Evidence from import penetration, Journalof Financial Economics 106, 427–446. → pages 4, 6, 23135Appendix AAppendix to Chapter 2A.1 A simple model: derivation detailsA.1.1 Firm’s problemFirst note that shareholders declare default as soon as the value of the firm turns negative.In period 1, the value of the firm is simply d1. Therefore the default threshold is the value z?that solves d1(z?) = 0, that isz? = (P1y1 −W1l1 − (1 + (1− τ)C)b) l¯−1 (A.1)Substituting the price using the inverse demand schedule (Eq. 2.1), and using the valuationof corporate debt (Eq. 2.3), and the default threshold (Eq. A.1) into the firm’s problem, theobjective of the firm becomesVj = maxl0,l1,b1Y1ν0(n∑i=1yi,0)− 1νyi,0 −W0l0 − (1 + (1− τ)C)b0 + βΦ(z?)(1 + C)b1 (A.2)+ β∫ z?z(z? − z) dΦ(z) l¯ (A.3)Applying Leibniz’ rule, the first order necessary conditions with respect to lt, and b1 areWt = Y1ν0(n∑i=1yi,0)− 1ν yi,0li,0(1− 1νyi,0∑ni=1 yi,0)Φ(z?)τC = φ(z?)(1 + (1− τ)C)(1 + C)bl¯(A.4)Each firm in the industry faces the same problem and differs only by the realization of theidiosyncratic shock z. Because this cost enters as a fixed cost, it doesn’t affect individualfirm decisions so that the industry admits a unique symmetric Nash equilibrium in which136all firms make identical decisions. The i-subscript can be dropped and l¯ = l. Imposing themarket clearing on the goods market that demand must equal supply in equilibrium, we havenyt = Yt = Yt. Imposing market clearing on the labor market, i.e. nlt = 1, the set of FOCsbecomesW =(1− hν)AΦ(z?)τC = φ(z?)(1 + (1− τ)C)(1 + C)b˜(A.5)where h =∑ni=1(yi,t/Yt)2 = 1/n is the Herfindahl-Hirschman index of the industry, andb˜ = b/l¯ is a measure of leverage (debt over the firm size).The price-elasticity of demand ηy,P in the symmetric equilibrium is obtained using Eq. 2.1,ηy,P = −∂yi,tyi,t∂PtPt=νh(A.6)A.1.2 Proof of proposition 1Proof. First, note that I assume that z? is an interior solution on the interval [−a/2, a/2].1 Inaddition, under the assumption that z is uniformly distributed on [−a/2, a/2], the cumulativedistribution function isΦ(x) =0 x < −a/21a(x+ a2) −a/2 ≤ x ≤ a/21 x < a/2(A.7)and the associated probability density function is φ(x) = 1a . Using the set of equilibriumconditions (A.5), and the default threshold (A.1), the equilibrium default threshold is givenbyz? =(hAν− a2τC(1 + C))(1 +τC(1 + C))−1(A.8)To prove the effects of competition on the expected default probability, I take the partialderivative of z? with respect to h,∂z?∂h=Aν(1 +τC1 + C)−1(A.9)which is positive. Therefore an increase in competition (decrease in h) decreases the optimaldefault threshold and the survival probability of the firm, Φ(z?).1This is without loss of generality as one can always find a value for a such that it holds.137To see the effect on debt, note that equilibrium leverage is given byb˜ =(z? +a2) τC(1 + (1− τ)C)(1 + C) (A.10)The result follows from the fact that z? is increasing in h.Next, the equilibrium firm value over labor isV˜ (A) =hAν− (1 + (1− τ)C)b˜0 + β [Φ(z?)(1 + C)] b˜1(z?) + β∫ z?z[z? − z] dΦ(z) (A.11)where b˜1(z?) is the optimal leverage. Plugging the optimal policy for b˜(z?) and taking thepartial derivative with respect to h,∂V˜ (A)∂h=Aν+ β{τCΦ(z?)(1 + (1− τ)C)[2− Φ(z?)φ′(z?)φ2(z?)]+ Φ(z?)}∂z?∂h=Aν(1 + βΦ(z?)1 + C1 + (1− τ)C) (A.12)where the second line is obtained using the expression for ∂z?∂h in Eq. A.9. The term insidethe parentheses is strictly positive, implying that the firm value is a increasing function ofconcentration and therefore a decreasing function of competition.Finally, the credit spread is defined as cs = (1 + C)/q − β−1, therefore∂cs∂h= −(1 + C)q2∂q∂h= −βφ(z?)(1 + C)2q2∂z?∂h< 0 (A.13)where the inequality sign follows from Eq. A.9.A.1.3 Conditional equity betaProof. Formally, the conditional equity beta is measured as the elasticity of Vj with respectto A,βi =d log V˜j(A)d logA=Ahν(1 + βΦ(z?)1 + C1 + (1− τ)C)1V˜ (A)=1 + βΦ(z?) 1+C1+(1−τ)C1 + νhAaβ2 Φ2(z?)(τC+1+C1+(1−τ)C) (A.14)Taking the partial derivative of βi with respect to h is somewhat more involved, however,it can be shown that a sufficient condition for ∂βi∂h > 0 is τ < 1, which is always the case.Therefore an increase in competition decreases the firm conditional beta.To obtain the expression for the conditional equity beta in Eq. 2.8, note that the normalized138value of the firm can be rewritten asV˜j(A) =Ahν(1 + β)− (1 + (1− τ))b˜0 + β[Φ(z?)b˜1τC − (1− Φ(z?))Ahν]− β∫ z?zz dΦ(z)(A.15)Rewriting the expression for the conditional equity beta (Eq. A.14), I getβi = 1 +(1 + (1− τ)C)b0Vj(A)+βτC1 + (1− τ)CΦ(z?)z?Vj(A)− β∫ zz? z dΦ(z)Vj(A)(A.16)A.2 Shareholders’ optimization problemTo keep notation readable, the (i, j)-subscript is omitted, unless necessary but all lower casevariables should be understood as firm-specific variables.Optimization problem Assuming that the firm doesn’t default in the current period,and replacing for P˜j,t using the inverse demand schedule, the recursive representation of theLagrangian for the shareholders’ problem isL (bt, kt, zt,Υt) = (1− τ)(Y1νt(Y −j,t + yt)−1νyt −Wtlt − zi,j,tk¯j,t)− it + τδkkt− ((1− τ)C + 1) bt + qtbt+1 − ψb(bt, bt+1)+ ΛKt((1− δk)kt + Γ(itkt)kt − kt+1)+ EtMt,t+1∫ z¯zL (bt+1, kt+1, z′,Υt+1) dΦ(z′)(A.17)where Y −j,t =∑njk=1,k 6=i yk,j,t is the total industry output produced by the firm’s rivals, andΛKt is the Lagrange multiplier on the capital accumulation equation. The set of first ordernecessary conditions are:[it] : ΛKt Γ′t = 1[lt] : P˜j,t[1− 1νytYj,t](1− α)ytlt−Wt = 0[kt+1] : q′k,tbt+1 − ΛKt + EtMt,t+1∫ z?t+1zL′k,t+1dΦ(z′) = 0[bt+1] : q′b,tbt+1 + qt − ψ′b,2,t + EtMt,t+1∫ z?t+1zL′b,t+1dΦ(z′) = 0(A.18)where I use the following notation: Γ′t = ∂Γt/∂(it/kt), q′k,t = ∂qt/∂kt+1, q′b,t = ∂qt/∂bt+1,L′k,t = ∂Lt/∂kt, L′b,t = ∂Lt/∂bt, ψ′b,1,t = ∂ψb,t/∂bt, and ψ′b,2,t = ∂ψb,t/∂bt+1. L′k,t and L′b,t are139obtained by applying the enveloppe theorem,L′k,t = (1− τ)P˜j,t[1− 1νytYj,t]αytkt+ τδk + ΛKt(1− δk + Γt − Γ′titkt)L′b,t = − ((1− τ)C + 1)− ψ′b,1,t(A.19)Finally, q′k,t and q′b,t are obtained by taking partial derivatives of total debt value qtbt+1 withrespect to bt + 1 and kt+1,2q′b,tbt+1 + qt = EtMt,t+1[(C + 1)Φ(z?t+1) + z?′b,t+1φ(z?t+1)bt+1(τC + ξt+1[(1− τ)C + 1])]q′k,tbt+1 = EtMt,t+1[z?′k,t+1φ(z?t+1)bt+1(τC + ξt+1[(1− τ)C + 1]) + (1− ξt+1)∫ z¯z?t+1L′k,t+1 dΦ(z′)](A.20)wherez?′k,t =L′k,t(1− τ)k¯j,tz?′b,t =L′b,t(1− τ)k¯j,t(A.21)Note that Eq. 2.23 is obtained by replacing for z?′k,t and q′k,t in the capital FOC.Symmetric equilibrium Because each firm is ex-ante identical and the i.i.d. shock entersas a fixed costs, all firms make the same decisions and the model admits a symmetric Nashequilibrium in each industry. In particular, we have yi,j,t = yj,t, Yj,t = njyj,t, li,j,t = lj,t,ki,j,t = kj,t = k¯j,t, and bi,j,t = bj,t.Price markups Using the first order condition with respect to labor, and the symmetricproperty of the equilibrium,P˜j,t(1− hjν)=Wt(1− α)yj,tlj,t(A.22)where hj = 1/nj is the Herfindahl-Hirschman index. The right-hand-side is the firm realmarginal cost of production. Defining the price markup to be the price set by the firm over2It is implicitly assumed that although creditors inherit an unlevered firm in bankruptcy, the debt adjust-ment cost is paid on the leverage level at the time of bankruptcy.140marginal cost, the price markup is,µj,t =(1− hjν)−1(A.23)A.3 Derivation of inverse demand scheduleThe final goods firm solves the following profit maximization problemmaxYj,t∈[0,1]Pt(∫ 10Yν−1νj,t dj) νν−1−∫ 10Pj,tYj,t dj (A.24)where Pt is the price of the final good (taken as given), Yj,t is the amount of input boughtfrom industry j, and Pj,t is the unit price of that input, j ∈ [0, 1].The first-order condition with respect to Yj,t isPt(∫ 10Yν−1νj,t dj) νν−1−1Y− 1νj,t − Pj,t = 0 (A.25)which can be rewritten asYj,t = Yt(Pj,tPt)−ν(A.26)Using the expression above, for any two industries j, k ∈ [0, 1],Yj,t = Yk,t(Pj,tPk,t)−ν(A.27)Raising the expression above to the power of ν−1ν , integrating over j and raising the expressionto the power of νν−1 ,Yj,t = Yt Pj,t(∫ 10 P1−νj,t) 11−ν−ν(A.28)Using (A.26), I obtain the expression for the price indexPt =(∫ 10P 1−νj,t) 11−ν(A.29)141Appendix BAppendix to Chapter 3B.1 Data sourcesQuarterly data for consumption, capital investment, and GDP are from the Bureau of Eco-nomic Analysis (BEA). Annual data on private business R&D investment are from the surveyconducted by the National Science Foundation. Annual data on the stock of private businessR&D are from the Bureau of Labor Statistics. Real annual capital stock data is obtainedfrom the Penn World Table. Quarterly productivity data are from Fernald (2012) (FederalReserve Bank of San Francisco) and is measured as Business sector total factor productivity.The labor share and average weekly hours are obtained from the Bureau of Labor Statistics(BLS). The monthly index of net business formation (NBF) and number of new business in-corporations (INC) are from the U.S. Basic Economics Database. Consumption is measuredas expenditures on nondurable goods and services. Capital investment is measured as privatefixed investment. Output is measured as GDP. The labor share is defined as the businesssector labor share. Average weekly hours is measured for production and nonsupervisoryemployees of the total private sector. The variables are converted to real using the ConsumerPrice Index (CPI), which is obtained from the Center for Research in Security Prices (CRSP).Annual data are converted into quarterly data by linear interpolation. The inflation rate iscomputed by taking the log return on the CPI index. The sample period is for 1948-2013,except for the average weekly hours series which starts in 1964 and the NBF and INC seriesthat were discontinued in 1993.Monthly nominal return and yield data are from CRSP. The real market return is con-structed by taking the nominal value-weighted return on the New York Stock Exchange(NYSE) and American Stock Exchange (AMEX) and deflating it using the CPI. The realrisk-free rate is constructed by using the nominal average one-month yields on treasury billsand taking out expected inflation1. Aggregate market and dividend values are from CRSP.The price dividend ratio is constructed by dividing the current aggregate stock market value1The monthly time series for expected inflation is obtained using an AR(4).142by the sum of the dividends paid over the preceding 12 months.B.1.1 Markup measureSolving the intermediate producer problem links the price markup to the inverse of themarginal cost of production MCt,øt =1MCtIn equilibrium, MCt is equal to the ratio of marginal cost over marginal product of eachproduction input (see the cost mininization problem). Since data on wages are available atthe aggregate level, the labor input margin has been the preferred choice in the literature.Using the first order condition with respect to Lt and imposing the symmetry condition,øt = (1− α) YtLtWt = (1− α)1SL,twhere SL,t is the labor share.The inverse of the labor share should thus be a good proxy for the price markup. However,there are many reasons why standard assumptions may lead to biased estimates of the markup(see Rotemberg and Woodford (1999)). In this paper, we follow Campello (2003) by focusingon non-linearities in the cost of labor2. More specifically, when deriving the cost function, weassumed that the firm was able to hire all workers at the marginal wage. In practice however,the total wage paid W (Lt), is likely to be convex in hours (e.g. Bils (1987)). This creates awedge between the average and marginal wage that makes the labor share a biased estimateof the real marginal cost. Denoting this wedge by ωt = W′(Lt)/(W (Lt)/Lt), the markupbecomes,øt = (1− α) 1SL,tω−1tLog-linearizing this expression around the steady state,øˆt = −sˆL,t − ωL lˆtwhere ωL is the steady state elacticity of ωt with respect to average hours. Bils (1987) proposesa simple model of overtime. Assuming a 50% overtime premium3 he estimates the elasticityωL to be 1.4. We use this value to build our overtime measure of the price markups. We setthe steady state values for Lt and SL,t to 40 hours and 1004, respectively and linearly detrend2Rotemberg and Woodford (1999) presents several other reasons that makes marginal costs more procyclicalthan the labor share (e.g. non-Cobb-Douglas production technology, overhead labor, etc.). For robustness, wetried additional corrections. Overall, they make markups even more countercyclical, and further strengthenour empirical results.3This is the statutory premium in the United States.4The Bureau of labor statistics use 100 as the index for the labor share in 2009. Our results stay robust to143the series.B.2 Derivation of demand scheduleFinal goods sector The final goods firm solves the following profit maximization problemmax{Yj,t}j∈[0,1]PY,t(∫ 10Yν1−1ν1j,t dj) ν1ν1−1 −∫ 10Pj,tYj,t djwhere PY,t is the price of the final good (taken as given), Yj,t is the input bought from sectorj and Pj,t is the price of that input j ∈ [0, 1],The first-order condition with respect to Yj,t isPY,t(∫ 10Yν1−1ν1j,t dj) ν1ν1−1−1Y− 1ν1j,t − Pj,t = 0which can be rewritten asYj,t = Yt(Pj,tPY,t)−ν1(B.1)Using the expression above, for any two intermediate goods j, k ∈ [0, 1],Yj,t = Yk,t(Pj,tPk,t)−ν1(B.2)Since markets are perfectly competitive in the final goods sector, the zero profit conditionmust hold:PY,tYt =∫ 10Pj,tYj,t dj (B.3)Substituting (B.6) into (B.3) givesYj,t = PY,tYtP−ν1j,t∫ 10 P1−ν1j,t dj(B.4)Substitute (B.5) into (B.4) to obtain the price indexPY,t =(∫ 10P 1−ν1j,t dj) 11−ν1Since each sector is atomistic, their actions will not affect Yt nor PY,t. Thus, each of thesechange in this value.144sectors will face an isoelastic demand curve with price elasticity ν1.Sectorial goods sector The representative sectorial firm j solves the following profit max-imization problemmax{Xi,j,t}i=1,Nj,tPj,tN1− ν2ν2−1j,tNj,t∑i=1Xν2−1ν2i,j,tν2ν2−1−Nj,t∑i=1Pi,j,tXi,j,twhere Pj,t is the aggregate price in sector j (taken as given by the firm), Xi,j,t is intermediategood input produced by firm i in sector j, and Nj,t is the number of firms in sector j.The first-order condition with respect to Xi,j,t isPj,tN1− ν2ν2−1j,tNj,t∑i=1Xν2−1ν2i,j,tν2ν2−1−1X− 1ν2i,j,t − Pi,j,t = 0which can be rewritten asXi,j,t =Yj,tNj,t(Pi,j,tPj,t)−ν2(B.5)Using the expression above, for any two intermediate goods i, and k,Xi,j,t = Xk,j,t(Pi,j,tPk,j,t)−ν2(B.6)Now, raising both sides of the equation to the power of ν2−1ν2 , summing over i and raising bothsides to the power of ν2ν2−1 , we getNj,t∑i=1Xν2−1ν2i,j,tν2ν2−1= Xk,j,t(∑Nj,ti=1 P1−ν2i,j,t) ν2ν2−1P−ν2k,j,t(B.7)Substituting for the production function in the left-hand side and rearranging the terms,Yj,tNtP−ν2k,j,tXk,j,t= N−ν2ν2−1tNj,t∑i=1P 1−ν2i,j,t−ν2ν2−1(B.8)145Using the first order condition with respect to Xi,j,t, the left-hand side is equal to P−ν2j,t .Therefore, the sectoral price index isPj,t = N−11−ν2j,tNj,t∑i=1P 1−ν2i,j,t 11−ν2B.2.1 Individual firm problemUsing the demand faced by an individual firm i in sector j, and the demand faced by sectorj, the demand faced by firm (i,j) can be expressed asXi,j,t =YtNj,t(Pi,j,tPj,t)−ν2 ( Pj,tPY,t)−ν1(B.9)=YtNj,t(P˜i,j,t)−ν2 (P˜j,t)ν2−ν1(B.10)where P˜i,j,t ≡ Pi,j,tPY,t and P˜j,t ≡Pj,tPY,t.The (real) source of funds constraint isDi,j,t = P˜i,j,tXi,j,t −Wj,tLi,j,t − rktKi,j,t − rztZi,j,tTaking the input prices and the pricing kernel as given, intermediate firm (i,j)’s problem isto maximize shareholder’s wealth subject to the firm demand emanating from the rest of theeconomy:Vi,j,t = max{Li,j,t,Ki,j,t,Zi,j,t,P˜i,j,t}t≥0E0[ ∞∑s=0Mt,t+s(1− δn)sDi,j,s]s.t. Xi,j,t =YtNj,t(P˜i,j,t)−ν2 (P˜j,t)ν2−ν1where Mt,t+s is the marginal rate of substitution between time t and time t + s. Note thateach sector is atomistic and take the final goods price as given. However, the measure of eachfirm within a sector is not zero and individual firms will take into account the impact of theirprice setting on the sectorial price. Further, note that there is no intertemporal decisions.The objective of the firm thus simplifies to a profit maximixation problem with constraint.The Lagrangian of the problem isVi,j,t = P˜i,j,tKαi,j,t(AtZηi,j,tZ1−ηt Li,j,t)1−α −Wj,tLi,j,t − rkj,tKi,j,t − rzj,tZi,j,t+Λdj,t(Kαi,j,t(AtZηi,j,tZ1−ηt Li,j,t)1−α − YtNj,t(P˜i,j,t)−ν2 (P˜j,t)ν2−ν1)146The corresponding first order necessary conditions arerkj,t = αXi,j,tKi,t(P˜i,j,t + Λdt )rzj,t = η(1− α)Xi,j,tZi,j,t(P˜i,j,t + Λdt )Wj,t = (1− α)Xi,j,tLi,j,t(P˜i,j,t + Λdt )Xi,j,t = Λdj,tYtNj,t[−ν2P˜−ν2−1i,j,t P˜ ν2−ν1j,t + (ν2 − ν1)P˜−ν2i,j,t P˜ ν2−ν1−1j,t∂P˜j,t∂Pi,j,t]where Λdj,t is the Lagrange multiplier on the inverse demand function.In the standard Dixit-Stiglitz aggregator,∂P˜j,t∂Pi,j,t= 0. This happens because each individualfirm is atomistic and has no influence on the aggregate price. In our setup, it will be non-zerobecause the the measure of firm within an industry is strictly positive. Using the definitionof the price index,∂P˜j,t∂Pi,j,t=1Nj,t(Pi,j,tPj,t)−ν2Imposing the symmetry condition, i.e. P˜j,t = P˜i,j,t = 1, and Yt = Nj,tXj,t, our set ofequilibrium conditions simplifies to:rkj,t = αXj,tKj,t(1 + Λdj,t)rzj,t = η(1− α)Xj,tZj,t(1 + Λdj,t)Wj,t = (1− α)Xj,tLj,t(1 + Λdj,t)Λdj,t =[−ν2 + (ν2 − ν1) 1Nj,t]−1The price markup is defined as the ratio of the optimal price set by the firm over themarginal cost of production. The marginal cost of production is obtained by solving thefollowing cost minimization problem:minKi,j,t,Zi,j,t,Li,j,trkj,tKi,j,t + rzj,tZi,j,t +Wj,tLi,j,ts.t. Kαi,j,t(AtZηi,j,tZ1−ηt Li,j,t)1−α = X?147In Lagrangian form,Vi,j,t = rkj,tKi,j,t + rztZi,j,t +WtLi,j,t + λi,j,t(X? −Kαi,j,t(AtZηi,j,tZ1−ηt Li,j,t)1−α)where λi,j,t is the Lagrange multiplier on the production objective. It is also the marginalcost of production of intermediate firms. Taking the first order conditions,rkj,t = αλi,j,tXi,j,tKi,j,trzj,t = η(1− α)λi,j,tXi,j,tZi,j,tWj,t = (1− α)λi,j,tXi,j,tLi,j,tFrom the individual firm problem (FOC w.r.t. Li,j,t), we know thatWj,t = (1− α)Xi,j,tLi,j,t(P˜i,j,t + Λdi,j,t)Putting the two FOCs w.r.t. to labour together and defining the price markup øi,j,t asP˜i,j,t/λi,j,t,øi,j,t =(1 +Λdi,j,tP˜i,j,t)−1Imposing the symmetry condition P˜j,t = 1 and using the expression for Λdj,t, the price markupisøi,j,t =−ν2Nj,t + (ν2 − ν1)−(ν2 − 1)Nj,t + (ν2 − ν1)B.2.2 Capital producer problemThe period profit of capital producers is rkj,tKcj,t − Ij,t. The optimization problem faced bythe representative physical capital producer is to choose Kcj,t+1 and Ij,t in order to maximizethe present value of revenues, given the capital accumulation constraint:V kj,t = max{Ij,t,Kcj,t+1}t≥0E0[ ∞∑s=0Mt,t+s(rkj,sKcj,s − Ij,s)]s.t. Kcj,t+1 = (1− δk)Kcj,t + Φk,j,tKcj,tThe Lagrangian in recursive form is,Vj,t = rkj,tKcj,t − Ij,t + Et [Mt,t+1Vj,t+1] +Qkj,t((1− δk)Kcj,t + Φk,j,tKcj,t −Kcj,t+1)148The first order conditions are:Qkj,t = Φ′k( Ij,tKj,t)−1Qkj,t = Et[Mt,t+1∂Vj,t+1∂Kcj,t+1]Using the enveloppe theorem,∂Vj,t∂Kcj,t=(rkj,t +Qkj,t(1− δk −(Ij,tKcj,t)Φ′k,j,t + Φk,j,t))The set of equilibrium conditions for the representative capital producer isQkj,t = Φ′−1k,j,tQkj,t = Et[Mt,t+1(rkj,t+1 +Qkj,t+1(1− δk −(Ij,t+1Kcj,t+1)Φ′k,j,t+1 + Φk,j,t+1))]Kcj,t+1 = (1− δk)Kcj,t + Φk,j,tKcj,tThe equilibrium conditions for the technology sector are derived is the same way,Qzj,t = Φ′−1z,j,tQzj,t = Et[Mt,t+1(rzj,t+1 +Qzj,t+1(1− δz −(Sj,t+1Zcj,t+1)Φ′z,j,t+1 + Φz,j,t+1))]Zcj,t+1 = (1− δz)Zcj,t + Φz,j,tZcj,twhere Sj,t is the aggregate investment in R&D in sector j.149Appendix CAppendix to Chapter 4C.1 EquilibriumThe equilibrium is given by the sequence {Yt, Ct, Ut, Lt, wt,Λt, bt,Mt, Zt, at,∆nt, st, xt,w(i)t , R(1)t ,Πt}∞t=0 determined by:1. Household’s first-order conditions:1 = Et[Mt+1Πt+1R(i)t+1], (C.1)Mt+1 = βCt+1(L¯Lt+1)ϕCt(L¯Lt)ϕ1−1ψ (Ct+1Ct)−1 U1−γt+1Et[U1−γt+1]1− 1θ , (C.2)wt =ϕCtLt. (C.3)2. Household’s utility:Ut ={(1− β)(Ct(L¯Lt)ϕ)1−1/ψ+ β(Et[U1−γt+1]) 1θ} θ1−γ. (C.4)3. Intermediate firm’s first-order conditions:wt =(1− 1ν)Zt + Λt(1ν)ZtYt, (C.5)Λt = φR(ΠtΠss− 1)ΠtYtΠss− Et[Mt+1 φR(Πt+1Πss− 1)Yt+1Πt+1Πss]. (C.6)1504. Government policy:ln(R(1)tR(1))= ρr ln(R(1)t−1R(1))+ (1− ρr)(ρpi,%t ln(ΠtΠ)+ ρy ln(ŶtŶ))+ σrrt,(C.7)st − s = ρs(st−1 − s) + (1− ρs) δb,%t(bt − b) + σsst , (C.8)bt+1 =RgtΠt∆Ytbt − st, (C.9)Rgt =N∑i=1(w¯(i) + β(i)xmt)R(i)t . (C.10)5. Output:Yt = ZtLt − ΦZt. (C.11)6. Market clearing:Yt = Ct +φR2(ΠtΠss− 1)2Yt. (C.12)7. Stochastic processes:ln(Zt) = z? + at + nt, (C.13)at = ρaat−1 + σaat, (C.14)∆nt = ρn∆nt−1 + σnnt, (C.15)xmt = ρmxmt−1 + σmmt. (C.16)C.2 Numerical procedureThe model is solved using a global method following Judd, Maliar, and Maliar (2012) andJudd, Maliar, Maliar, and Valero (2014). A subset of the policy functions are approximatedby piece-wise ordinary polynomials of the state variables. The state variables are:St = (rt−1, at−1, st−1, bt−1, xmt, Yt−1,∆nt−1, βt,+at, nt, st, {Q(n)t−1}Ni=2), (C.17)where rt−1 is the nominal one-period risk-free rate, at−1 is the transitory productivity shock,st−1 is the governments’ surplus, bt−1 is the total debt of the government, xmt is the stochasticprocess driving the maturity structure, Yt−1 is the final consumption goods, ∆nt−1 is thepermanent productivity shock, βt is the subjective discount rate, eat is the innovation to thetransitory productivity shock, ent is the innovation to the permanent productivity shock, estis the innovation to the government’s surplus, and {Q(i)t−1}Ni=2 are the nominal bond prices.151The approximated policy functions are:G = (Ft, Ct,Ut, {Q(i)t }Ni=2, E∆Ct, Epit), (C.18)whereFt =(ΠtΠss− 1)ΠtΠss, (C.19)Ct is consumption, Ut is household utility, {Q(i)t }Ni=2 are nominal bond prices, E∆Ct is ex-pected consumption growth, and Epit is expected inflation.Let L be a policy function, the policy function is approximated as:L̂ = 1F pF + 1MpM , (C.20)where 1j is an indicator function equals to one in regime j and zero otherwise, and pj is apolynomial. Note that a different polynomial is used in each regime as indicated by the F ,and M subscript.The model is solved by finding the set of polynomial coefficients Θ that minimizes themean squared residuals for the approximated decision rules over a fixed grid. For each pointj on the grid the residuals {Rjk}N+4k=1 are calculated as:Rj1 = φRFjt Yjt − Ejt [Mt+1 φRFt+1Yt+1]− Λt, (C.21)Rj2 = Ejt[Mt+1RWt+1]− 1, (C.22)Rj3 = Ujt −{(1− β)(Cj?t)1−1/ψ+ β(Ejt[U1−γt+1]) 1θ} 11−1/ψ, (C.23)Rj4 = Ejt [Cgt+1]− ECgjt , (C.24)Rj5 = Ejt [pit+1]− Epijt , (C.25)Rji+4 = Ejt[Mt+1Πt+1Q(i−1)t+1]−Qj,(i)t ∀i = 2..N. (C.26)Rj1 is calculated using the first order condition (in equilibrium) of the firms in the intermediategoods sector, Rj2 is calculated using the Euler equation for the return on the wealth portfolio,Rj3 is computed using the value function equation. Rj4 and Rj5 are calculated directly fromtheir definition. Finally, {Rji}N+4i=6 are computed using the Euler equations for the nominalbonds.The grid on the state variables space is calculated in 5 steps. First, for each of the regimesthe model is solved using a second-order perturbation approximation to obtain an initial guessfor the set of coefficients Θ. Second, the regime-specific model is simulated and the principalcomponents of the state variables are calculated. Third, an auxiliary grid on the principalcomponents space is calculated using the Smolyak algorithm. Fourth, the regime-specific152grid on the state variables space is calculated by performing a linear transformation of theauxiliary grid calculated in the previous step. Finally, the grid is calculated as the union ofthe two single regime grids (fiscally-led regime and monetary-led regime).The Smolyak algorithm is used for the auxiliary grid because it is a highly efficient methodto calculate a sparse grid in a hypercube. The drawback of the Smolyak algorithm is thatthe points are not chosen to maximize the number of points on the region of the state spacewhere the ergodic distribution of the model is located. The Smolyak algorithm is improved byadapting it to the characteristics of the model using the principal components transformation.Second-order standard ordinary polynomials are used for each of the regime-specific poly-nomials. The nominal bond prices are approximated as linear combinations of variables thatare known to be important to understand the dynamics of the yield curve (see Bansal andShaliastovich (2013) and Kung (2015)), namely, expected consumption growth and expectedinflation. These approximations can be thought of as being second-order approximations onthe state variables where the coefficients are restricted to be linear combinations of the coef-ficients for expected consumption growth and expected inflation. The minimization is doneusing a numerical optimizer. To improve the speed of the code, an analytical gradient andmonomial integration are used. The mean square error is of the order of 10−6.C.3 Present value relationsThe flow budget constraint of the government for the simple model Eq. (4.8) can be writtenasBtPt−1=ΠtRgt(Bt+1Pt+ st), (C.27)where Bt = B(1)t +B(2)t is the total nominal value of government debt, st is the real surplus,and Rgt = R(1)tB(1)tBt+ R(2)tB(2)tBtis the nominal gross interest rate paid on the portfolio ofgovernment debt. In real terms we have:bt =ΠtRgt(bt+1 + st). (C.28)Leading Eq. (C.28) for one period and taking the conditional expectation at time t,Et[bt+1] = Et[Πt+1Rgt+1bt+2]+ Et[Πt+1Rgt+1st+1]. (C.29)Iterating forward on Et[bt+1] using the law of iterated expectations and assuming a transver-sality condition on real debt, we haveEt[bt+1] = Et[ ∞∑i=1Pt+iPt−11∏ij=1Rgt+jst+i]. (C.30)153Using Eq. (C.28) and Eq. (C.30) together, the present value of government surpluses isbt = Et ∞∑i=0st+i∏ij=0{Rgt+j/Πt+j} . (C.31)The present value relation for the benchmark model can be calculated in a similar way.Leading Eq. (4.39) for one period and taking the conditional expectation at time t we get:Et[bt+1] = Et[Πt+1∆Yt+1Rgt+1bt+2]+ Et[Πt+1∆Yt+1Rgt+1st+1]. (C.32)Iterating forward on Et[bt+1] using the law of iterated expectations and assuming a transver-sality condition on real debt,Et[bt+1] = Et[ ∞∑i=1Pt+i Yt+iPt−1 Yt−11∏ij=1Rgt+jst+i]. (C.33)Simplifying, we get that the present value of government surpluses isbt = Et[ ∞∑i=0st+i∏ij=0 Π−1t+j∆Y−1t+jRgt+j]. (C.34)C.4 Simple model: approximate analytical solutionThe real return of the government portfolio is:RgtΠt=bt+1 + stbt, (C.35)where lowercase variables denote real variables. Define log x ≡ x˜, and take logs of Eq. (C.35):R˜gt − Π˜t = log (bt+1 + st)− log (bt) , (C.36)= b˜t+1 + log(1 +stbt+1)− b˜t. (C.37)Since surpluses can be negative, substitute st = τt−gt (τt and gt are real taxes and governmentexpenditures, respectively) into Eq. (C.36) and rearrange:R˜gt − Π˜t = b˜t+1 + log(1 +τt − gtbt+1)− b˜t, (C.38)= b˜t+1 − b˜t + log(1 + exp(τ˜t − b˜t+1)− exp(g˜t − b˜t+1)). (C.39)Following Berndt, Lustig, and Yeltekin (2012), we log-linearize the last term in Eq. (C.39)with respect to the log tax-to-debt and the log government expenditures-to-debt ratios around154the steady-state:log(1 + exp(τ˜t − b˜t+1)− exp(g˜t − b˜t+1))' log(1 + exp(τ˜ − b˜)− exp(g˜ − b˜))+exp(τ˜ − b˜)1 + exp(τ˜ − b˜)− exp(g˜ − b˜) (τ˜t − b˜t+1 − (τ˜ − b˜))−exp(g˜ − b˜)1 + exp(τ˜ − b˜)− exp(g˜ − b˜) (g˜t − b˜t+1 − (g˜ − b˜)) . (C.40)Collecting constant terms and rearranging:log(1 + exp(τ˜t − b˜t+1)− exp(g˜t − b˜t+1))' θ0 + (1− θ1)(µτ τ˜t − µg g˜t − b˜t+1), (C.41)whereµτ =exp(τ˜ − b˜)exp(τ˜ − b˜)− exp(g˜ − b˜) , µg = exp(g˜ − b˜)exp(τ˜ − b˜)− exp(g˜ − b˜) ,θ1 =11 + exp(τ˜ − b˜)− exp(g˜ − b˜) ,and θ0 = log(1 + exp(τ˜ − b˜)− exp(g˜ − b˜))−exp(τ˜ − b˜)1 + exp(τ˜ − b˜)− exp(g˜ − b˜) (τ˜ − b˜)+exp(g˜ − b˜)1 + exp(τ˜ − b˜)− exp(g˜ − b˜) (g˜ − b˜) .Eq. (C.39) can be written as:R˜gt − Π˜t = θ1b˜t+1 − b˜t + θ0 + (1− θ1)(µτ τ˜t − µg g˜t). (C.42)Iterating Eq. (C.42) forward and imposing the transversality condition:b˜t =θ01− θ1 +∞∑j=0θj1((1− θ1)(µτ τ˜t+j − µg g˜t+j)− R˜gt+j + Π˜t+j), (C.43)taking unconditional expectations:E[b˜t]=θ01− θ1 +∞∑j=0θj1((1− θ1)E [µτ τ˜t+j − µg g˜t+j ]− E[R˜gt+j]+ E[Π˜t+j]). (C.44)155Since the unconditional expectation is the same for all t, we can simplify the expression:E[b˜t]=θ01− θ1 + (1− θ1)E [µτ τ˜t+j − µg g˜t]1− θ1 −E[R˜gt]1− θ1 +E[Π˜t]1− θ1 , (C.45)=θ01− θ1 + E [µτ τ˜t − µg g˜t]−E[R˜gt]1− θ1 +E[Π˜t]1− θ1 . (C.46)Solving for E[Π˜t]:E[Π˜t]1− θ1 = E[b˜t]− θ01− θ1 − E [µτ τ˜t − µg g˜t] +E[R˜gt]1− θ1 , (C.47)= E[b˜t]− θ01− θ1 − E [µτ τ˜t − µg g˜t] +E[ωR˜(1)t + (1− ω)R˜(2)t]1− θ1 . (C.48)In Eq. (C.48) we substituted R˜gt for ωR˜(1)t + (1− ω)R˜(2)t . Reordering the last term we have:E[Π˜t]1− θ1 = E[b˜t]− θ01− θ1 − E [µτ τ˜t − µg g˜t] +E[R˜(2)t − ω(R˜(2)t − R˜(1)t )]1− θ1 . (C.49)Finally, we can calculate the derivative of expected inflation with respect to the weight of the1-period bond ω:dE[Π˜t]dω= −E[R˜(2)t − R˜(1)t]. (C.50)C.5 DataWe obtain quarterly data for consumption and output from the Bureau of Economic Analysis(BEA). Consumption is measured as real personal consumption expenditures(DPCERX1A020NBEA). Output is measured as real gross domestic product (GDPC1). In-flation is computed by taking the log return on the Consumer Price Index for All UrbanConsumers (CPIAUCSL), obtained from the Bureau of Labor Statistics (BLS). Monthly yielddata are from CRSP. Nominal yield data for maturities of 4, 8, 12, 16, and 20 quarters arefrom the CRSP Fama-Bliss discount bond file. The one-quarter nominal yield is from thethe CRSP Fama risk-free rate file. Finally we build our bond supply maturity structure datausing the same methodology as Doepke and Schneider (2006) and Greenwood and Vayanos(2014). In particular, in each month we collect the complete history of U.S. government bondsissued from the CRSP historical bond database. We then break the stream of each bonds cashflows into principal and coupon payments. Summing the streams from each outstanding bondvintage over their respective maturity give us the monthly maturity structure of government156debt. The sample period runs from Q1-1964 to Q3-2013. We obtain the maturity distributionof privately-held Treasury marketable securities from Table FD-5 of the Treasury Bulletin.We supplement the information on the Treasury Bulletin by including reserve balances withFederal Reserve Banks from the Federal Reserve H.4.1.157


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