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Essays on firm heterogeneity and entrepreneurship Galindo da Fonseca, João Alfredo 2018

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Essays on Firm Heterogeneity and EntrepreneurshipbyJoa˜o Alfredo Galindo da FonsecaB.Sc. Economics, Universite´ de Montre´al, 2011M.A. Economics, University of Toronto, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Economics)The University of British Columbia(Vancouver)December 2018c© Joa˜o Alfredo Galindo da Fonseca, 2018The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Essays on Firm Heterogeneity and Entrepreneurshipsubmitted by Joa˜o Alfredo Galindo da Fonseca in partial fulfillment of the re-quirements for the degree of Doctor of Philosophy in Economics.Examining Committee:Henry Siu, EconomicsSupervisorJesse Perla, EconomicsSupervisory Committee MemberFlorian Hoffmann, EconomicsUniversity ExaminerSanghoon Lee, BusinessUniversity ExaminerAdditional Supervisory Committee Members:Paul Beaudry, EconomicsSupervisory Committee MemberGiovanni Gallipoli, EconomicsSupervisory Committee MemberiiAbstractWhat determines firm heterogeneity? What are the consequences of this hetero-geneity for the macroeconomy? Traditionally, economists have considered a rep-resentative firm as an approximation for reality. Although such a restriction canbe useful to study some questions, in reality there is a great deal of heterogeneityin firm behavior. In this work, I look at different dimensions of heterogeneity inoutcomes for firms, their sources and their implications for the macroeconomy.In Chapter 1, I propose a rich general equilibrium model of entrepreneurship,where I allow both wage workers and unemployed to start firms. I show that inthis framework, the lower opportunity cost of entrepreneurship for the unemployedinduces the formation of lower quality firms relative to wage workers. Using anew confidential owner-employer-employee matched dataset from Canada I testthese predictions by verifying that firms created by the unemployed are on averagesmaller and die faster. I test the mechanism behind this result, by verifying thatworkers are more responsive to wage changes in their decision to start a firm rel-ative to the unemployed. Finally, I use this framework to evaluate the impact onthe economy of a public policy that promotes entrepreneurship among the unem-ployed.In the model presented in Chapter 2, we study the choice of an individual tostart a firm as a function of their outside option as an unemployed and the im-plications for the efficient allocation in the economy. We show that by simplyadding this additional margin to an otherwise standard general equilibrium theo-retical framework, wage comparative statics become richer and the efficient allo-cation chosen by a benevolent social planner has a new interpretation. The chapterhighlights the importance of modelling the entry margin into firm ownership iniiidetermining firm heterogeneity as well as wage dynamics.In the last chapter, we turn to the study of determinants of a firm’s decisionof which contract to offer a worker and the implications for wage dynamics andworker retention. We verify empirically that, due to a worker retention motive,match quality affects contract choice and wage cyclicality.ivLay SummaryHow do we explain the differences we see in firm behaviour? Why are certainsfirms more productive than others? Why are some larger? Why are there differ-ences in wages firms offer to workers? How does the answer to these questionsaffect our understanding of the labor market?In this dissertation I provide evidence that making sense of an individual’s deci-sions to start a firm can play a key role in our understanding of wage determinationand firm dynamics. Furthermore, I show that these might have important implica-tions for our understanding of the firm productivity distribution and the impact ofpublic policy. Finally, I show that match quality is important in determining thecontract a firm choses to offer a worker and as a result the wage.vPrefaceChapter 1 of this thesis ”Unemployment, Entrepreneurship and Firm Outcomes” ismy original work. The empirical section of this chapter uses data from StatisticsCanada’s Candian Employment Employee Dynamic Database (CEEDD).The second chapter, ”Entrepreneurship Outside options and Constrained Effi-ciency”, is an unpublished working paper that I co-authored with Iain Snoddy. Theauthors contributed equally to the project overall.In Chapter 3, ”Match Quality, Contractual Sorting and Wage Cyclicality” is anunpublished working paper that I co-authored with Giovanni Gallipoli and YanivYedid-Levi. The authors contributed equally to the project overall.Any views expressed in the thesis are mine alone and do not reflect the viewsof Statistics Canada or the Government of Canada.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Unemployment, Entrepreneurship and Firm Outcomes . . . . . . . 51.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2.1 Static Profit Optimization . . . . . . . . . . . . . . . . . 111.2.2 Dynamic Problem of the Business Owner . . . . . . . . . 121.2.3 Problems of the Unemployed and the Wage worker . . . . 131.2.4 Market Clearing . . . . . . . . . . . . . . . . . . . . . . 141.2.5 Equilibrium Measure of Unemployed Individuals . . . . . 15vii1.2.6 Characterizing the Equilibrium . . . . . . . . . . . . . . . 151.3 Empirical Section . . . . . . . . . . . . . . . . . . . . . . . . . . 191.3.1 Data and Measurement . . . . . . . . . . . . . . . . . . . 191.3.2 Identification . . . . . . . . . . . . . . . . . . . . . . . . 211.3.3 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . 241.3.4 Main Empirical Results . . . . . . . . . . . . . . . . . . 251.4 Additional Model Implication . . . . . . . . . . . . . . . . . . . 311.4.1 Identification . . . . . . . . . . . . . . . . . . . . . . . . 321.4.2 Exogeneity . . . . . . . . . . . . . . . . . . . . . . . . . 341.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 351.5 Policy Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . 361.5.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . 381.5.2 Policy Analysis . . . . . . . . . . . . . . . . . . . . . . . 391.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432 Entrepreneurship, Outside options and Constrained Efficiency . . . 452.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482.3 Model Exploration . . . . . . . . . . . . . . . . . . . . . . . . . 522.4 The Constrained Efficient Solution: Deriving the Hosios Condition 552.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 Match Quality, Contractual Sorting and Wage Cyclicality . . . . . . 603.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.2 A Simple Model of Worker Pay . . . . . . . . . . . . . . . . . . . 633.2.1 Participation Constraints and Performance Pay Contracts . 673.2.2 Contract Choice and Wage Cyclicality . . . . . . . . . . . 703.3 Data and Measurement . . . . . . . . . . . . . . . . . . . . . . . 763.3.1 Empirical Wage Processes . . . . . . . . . . . . . . . . . 773.3.2 Measuring Match Quality . . . . . . . . . . . . . . . . . 783.3.3 Data on Work Histories . . . . . . . . . . . . . . . . . . . 803.3.4 Performance Pay in the NLSY79 . . . . . . . . . . . . . . 833.4 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . 83viii3.4.1 Match Quality and Performance Pay Adoption . . . . . . 843.4.2 Match Quality and Wage Cyclicality . . . . . . . . . . . . 863.4.3 Evidence from Occupation Groups . . . . . . . . . . . . . 903.4.4 Performance Pay and Job Durations . . . . . . . . . . . . 933.4.5 Extensions and Robustness . . . . . . . . . . . . . . . . . 943.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 114A.1 Appendix to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . 114A.1.1 Proofs Benchmark Model . . . . . . . . . . . . . . . . . 114A.1.2 Controlling for learning by doing mechanism . . . . . . . 126A.1.3 Model with multiple sectors and testable prediction . . . . 127A.1.4 Robustness of Testable Prediction to allow for Worker Mo-bility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136A.1.5 Details on Instrument and Wage Measure . . . . . . . . . 137A.1.6 Proofs Calibration section . . . . . . . . . . . . . . . . . 138A.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142A.3 Alternative Calibration . . . . . . . . . . . . . . . . . . . . . . . 144A.3.1 Firms created by Laid off versus not Laid-off individuals(without Fixed Effects) . . . . . . . . . . . . . . . . . . . 147A.3.2 Data Appendix . . . . . . . . . . . . . . . . . . . . . . . 149A.3.3 Supplemental Appendix I : Solving for Multi-Industry Econ-omy model. . . . . . . . . . . . . . . . . . . . . . . . . 150A.3.4 Supplemental Appendix II : Solving for model with searchfrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . 159A.4 Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . 171A.4.1 Deriving the Endogenous Productivity Distribution . . . . 176A.4.2 Deriving the Job Creation Curve . . . . . . . . . . . . . . 177A.5 Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . 178A.5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178ixA.5.2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180A.5.3 Results with K(m) = K, ∀m . . . . . . . . . . . . . . . . 189A.6 An alternative assumption on period 1 aggregate productivity: P1 =PL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190A.7 Proof for Empirical Wage Processes section . . . . . . . . . . . . 199xList of TablesTable 1.1 Tests for Randomness of displacement shock . . . . . . . . . . 23Table 1.2 Summary Statistics Firms . . . . . . . . . . . . . . . . . . . . 24Table 1.3 Summary Statistics Individuals . . . . . . . . . . . . . . . . . 25Table 1.4 Log number of employees . . . . . . . . . . . . . . . . . . . 27Table 1.5 Exit Probability . . . . . . . . . . . . . . . . . . . . . . . . . 28Table 1.6 Entry Probability . . . . . . . . . . . . . . . . . . . . . . . . 30Table 1.7 Additional Implication Results . . . . . . . . . . . . . . . . . 36Table 1.8 Policy outcomes . . . . . . . . . . . . . . . . . . . . . . . . . 42Table 3.1 Performance Pay and Match Quality: Fixed Effects Logits . . . 85Table 3.2 Pooled wage regression . . . . . . . . . . . . . . . . . . . . . 88Table 3.3 Wage regressions: PPJ vs non-PPJ. . . . . . . . . . . . . . . . 89Table 3.4 Occupation heterogeneity: share of jobs with (i) above medianmatch quality and (ii) performance pay, by occupation group. . 91Table 3.5 Wage Regressions: Cyclicality by Occupation Group. . . . . . 92Table 3.6 Summary statistics of job durations in different occupation groups. 94Table 3.7 Performance Pay and Match Quality: Fixed Effects Logits (menand women) . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Table 3.8 Pooled wage regression (men and women) . . . . . . . . . . . 97Table 3.9 Wage regressions: PPJ vs non-PPJ (men and women) . . . . . 98Table 3.10 Performance Pay and Match Quality: Linear Probability Re-gressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Table 3.11 Wage regressions using GDP as a cyclical proxy. . . . . . . . . 102Table 3.12 Proportion of performance pay jobs (PPJ) by education group. . 103xiTable 3.13 Wage Regressions: Cyclicality by Education Group. . . . . . . 104Table A.1.1 Log number of employees . . . . . . . . . . . . . . . . . . . 127Table A.2.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Table A.3.1 Model Extension - Different ψ values . . . . . . . . . . . . . . 144Table A.3.2 Policy outcomes . . . . . . . . . . . . . . . . . . . . . . . . . 146Table A.3.3 Log number of employees . . . . . . . . . . . . . . . . . . . 148xiiList of FiguresFigure 3.1 Employment Cycles: an Example. . . . . . . . . . . . . . . . 82xiiiGlossaryIV Instrumental VariableOLS Ordinary Least SquaresUI Unemployment InsurancexivAcknowledgmentsI am indebted to my supervisor Henry Siu and my supervisory committee JessePerla, Giovanni Gallipoli, Paul Beaudry. I would also like to thank Yaniv Yedid-Levi and David Green for the advice and help during the PhD process.A special acknowledgment goes to Iain Snoddy for his friendship and support.I also want to mention my PhD colleagues : Pierluca Pannella, Nouri Najjar, BradHackinen, Jose´ Pulido, Tom Cornwall and Alastair Fraser.Gostaria de agradecer a minha famı´lia, meu pai, minha ma˜e, Ivanzoco e Kekeu.Voceˆs me ensinaram a alegria de viver. I also want to thank Rik Van Bogart andSophine Johnsson for the days in Ottawa. Finally, I want to thank Emilie Johnsson.Sem a felicidade que voceˆ me trouxe, nada disso teria sido possı´vel.xvThis work is dedicated to min a¨lskling, Emilie.xviIntroductionHow do firms vary in behaviour, performance and how is this linked to the aggre-gate economy? The answer to these questions are crucial for our understanding offirm dynamics, wage formation and unemployment.In this thesis I study different components of firm heterogeneity, investigatetheir sources and how they relate to the macroeconomy. One recurring and crucialcomponent of the analysis will be the study of the individual’s decision to starta firm. By investigating the sources of these decisions, we can investigate howchanges in the economy for the household impact the firm productivity distribu-tion. This channel has often been understudied. Most recent papers consider someform or another of a free entry condition. This condition can be stated as the as-sumption that there is an infinite amount of potential firms that will enter the marketas long as the value of doing so is positive. On the other hand, in a framework withentrepreneurship this decision to operate as a firm will depend on the individualoutside option to entrepreneurship.In the first chapter entitled Unemployment, Entrepreneurship and Firm Out-comes, I investigate whether there are differences between firms created by un-employed individuals relative to otherwise identical employed individuals. I thenshow that these patterns are important for our understanding on whether policiespromoting entrepreneuship among the unemployed are warranted strategies to pro-mote job creation. This is relevant given the widespread usage of these policiesacross the world.To shed light on these issues I propose a general equilibrium model of en-trepreneurship that allows for different choices by the unemployed and the em-ployed. In the model the only difference between the unemployed and wage worker1is their outside option. Due to poorer outside options, the unemployed are less se-lective on which business projects to implement. In equilibrium, this implies thatthe unemployed are more likely to start a firm but conditional on doing so, hirefewer workers and are more likely to exit entrepreneurship relative to an individualwho started a business (implemented a business project) from wage work.These implications of the model hold in the data. I use firm closures to iden-tify random assignments of an individual to unemployment (via layoff). I find thatunemployment doubles the probability of an individual to start a firm, and condi-tional on starting, the individual hires 26% fewer workers and is 30% more likelyto exit firm ownership. The data being used is composed of the entire universe oftax filers linked to privately owned incorporated firms in Canada. It improves onemployer-employee datasets by having also the link between each firm and theircorresponding owner.1 This makes it fitting for studies in entrepreneurship. Withan extension of the theory to a multi sector environment I derive the additional im-plication that higher wages decrease the entry rate into entrepreneurship of wageworkers by more than that of unemployed. Wages represent the opportunity costof entrepreneurship for wage workers but not for the unemployed. As a result,wage workers are more responsive to wage variation than the unemployed in theirdecision to open a firm. Using city wage variation and a Bartik style IV strategyfor wages, I show that a 1% drop in wages increases by 3.2 percentage points theentry rate into entrepreneurship for wage workers and has no impact for laid offindividuals.Finally, I quantify the impact on the aggregate economy of a policy that sub-sidizes entry into entrepreneurship among the unemployed. The result is a 2.14%drop in average firm productivity and a 1% drop in the unemployment rate. Thepolicy induces the creation of low productivity firms by the unemployed. With alarger mass of firms, the equilibrium cost of labour increases. This induces highproductivity firms to hire fewer workers and wage workers to be more selective onbusiness projects. This employment drop among high productivity firms offsets job1The three most used employer-employee linked datasets, the LEHD for the US, the DADS forFrance and the LIAB for Germany, all lack information on individual owners of firms. With theexception of registry data from Sweden and Denmark, this is the first dataset to allow the tracking ofall linkages between a firm and its employees and owners across time.2gains from firms created with the subsidy. The result is a shift in resources fromhigh productivity firms created by wage workers to low productivity firms createdby the unemployed.In the second chapter entitled Entrepreneurship, Outside options and Con-strained Efficiency we study a theoretical framework with search frictions in whichthe free entry condition is replaced by the decision of individuals to start a firmor not. We show that the outside options of a firm owner and a worker are nowthe same since both always have the option of reverting to unemployment. Thecorollary of this is that the direction of wage responses to shocks now becomesambiguous. Wages are no longer necessarily increasing with the value of beingunemployed. While a higher value of unemployment allows the worker to nego-tiate a higher wage, it also increases entrepreneurs’ outside options. As a result,how wages respond to a higher value of unemployment now depends on whichparty has more bargaining power the worker or the entrepreneur. It follows that thebargaining parameter determining each party’s bargaining strengh becomes crucialfor wage response to exogenous shocks.We next evaluate the conditions for which this economy attains the constrainedefficiency allocation.2 We find that the condition is the same as that found by Ho-sios ([Hosios, 1990] for an economy with search frictions but without entrepreneurs.But despite a similar condition the implication for the economy is now different. Inparticular, under this efficient allocation, dynamics of the model following a shockremain sensitive to the degree of friction in the labor market. In particular, wagesdo not necessarily exert a dampening effect in response to exogenous shocks.In Chapter 3 entitled, Match Quality, Contractual Sorting and Wage Cycli-cality, the focus shifts from firm formation to the contract choice by firms. Westudy the role of match quality for contractual arrangements, wage dynamics andworkers retention. We develop a model in which profit maximizing firms offer aperformance-based pay arrangement to retain workers with relatively high match-specific productivity. The key implications of our model hold in the data, whereinformation about job histories and performance pay is available. We verify em-pirically that firms are more prone to offering performance pay based contracts to2The constrained efficient allocation is defined as that which is equivalent to that chosen by abenevolant social planner constrained by all the market frictions of the decentralized economy.3workers for which match quality is higher. We also verify that wage cyclicality iscoming from performance pay jobs, with those offering different contracts exhibit-ing no cyclicality. Finally we also show that match quality has a direct effect evenafter we control for contract choice and we relate our findings to the literature onoccupation heterogeneity.4Chapter 1Unemployment,Entrepreneurship and FirmOutcomes1.1 IntroductionHow does unemployment affect an individual’s decision to open a firm and theoutcomes of that firm relative to employment? The answer to this question is cru-cial for understanding the determinants of entrepreneurship, firm dynamics and theappropriate policies to promote job creation.Across the world, countries have established policies to promote entrepreneur-ship among the unemployed.1 Examples include the expenditure of 37.5 millioneuros by France in 2009 alone, with 40% of new businesses being started by theunemployed (Commission [2010]). In Germany in 2004, spending on these poli-cies totalled 2.7 billion euros, representing 17.2% of expenditures in active labourmarket policies (Baumgartner and Caliendo [2007]). In the UK, such a policy has1Policies vary from extended unemployment benefits to direct financial assistance and coachingin the startup process. Examples of such policies are the Back to Work Enterprise Allowance inIreland and the Self-employment assistance program in the US, both of which allow individuals tokeep welfare benefits while they start their own business. A list of policies across Europe, Australia,Canada and the US as well as coverage in the press are available upon request.5been responsible for the creation of nearly 2,000 new businesses per month sinceits reintroduction in 2011 (Burn-Callender [2013]). In Canada in 2012, these poli-cies cost 118 million Canadian dollars, representing 10% of expenditures in activelabour market policies (CEIC [2014]).Although there is a large literature on entrepreneurship and firm dynamics2, thelabour status of the potential entrepreneur has often been overlooked.3 To analyzethese issues, I propose a general equilibrium model of entrepreneurship that allowsfor different choices by the unemployed and the employed. In the framework, theonly difference between the unemployed and wage workers is their outside option.As a result, the unemployed are less selective on which business projects theyimplement. In equilibrium, this implies that the unemployed are more likely tostart a firm but, conditional on doing so, hire fewer workers and are more likely toexit entrepreneurship relative to an individual who started a business (implementeda business project) from wage work.In the model, workers and unemployed draw business opportunities at a samerate ψ and from a same exogenous distribution F . Each business project is associ-ated to an initial firm productivity. Upon drawing a business project each individualmakes the endogenous decision to implement it or not. Individuals go into and outof unemployment from and to wage work at an exogenous rate.4 Since there are nosearch frictions, at each instant an entrepreneur maximizes firm profits by choosingthe optimal firm size given the productivity of the firm and the equilibrium wagerate.5 However, the entrepreneur also faces a dynamic problem. Once the firmstarts operating the productivity of the firm starts moving according to a brown-ian motion with a drift. This in turn results in a optimal stoppping problem forthe entrepreneur, which gives us a optimal threshold productivity below which the2Lucas Jr [1978], Holtz-Eakin et al. [1994], Fonseca et al. [2001], Hurst and Lusardi [2004],Cagetti et al. [2006], Quadrini [2000], Beaudry et al. [2011], Hamilton [2000] and Haltiwanger et al.[2013]3The tradition in the literature on entrepreneurship has been to use models in which differences inoutcomes arise due to differences in innate entrepreneurial ability of individuals. This chapter pro-poses a framework in which differences in outcomes between unemployed and employed individualsarise in the absence of ex-ante heterogeneity.4This assumption is later relaxed in the extension of the model, in which the job finding ratebecomes an equilibrium object determined by labor market tightness.5Entrepreneurs hire from the pool of available workers, all individuals that did not open a firmand did not receive the exogenous unemployment shock.6individual exits entrepreneurship.In equilibrium, because wage workers are more selective on which businessprojects to implement, conditional on entering, their initial productivity level ishigher. This in turn translates to higher average size for firms created by wageworkers. Furthermore, since the threshold below which an entrepreneur exits en-trepreneurship is the same for wage worker and entrepreneur, this higher initialproductivity also implies a lower average exit rate for firms created by wage work-ers.These implications of the model hold in the data. The data being used is com-posed of the entire universe of tax filers linked to privately owned incorporatedfirms in Canada. It improves on employer-employee datasets by linking firms totheir corresponding owner.6 This makes it fitting for studies of entrepreneurship. Iuse firm closures to identify the random assignment of an individual to unemploy-ment (via lay-offs). Furthermore, due to the use of individual fixed effects, I amusing within individual variation. I find that unemployment doubles the probabilityof an individual to start a firm, and conditional on starting, an individual hires 26%fewer workers and is 30% more likely to exit firm ownership.Next, I consider an extension of the model that adds congestion externalities infirm hiring to the baseline framework. This allows the job finding rate to becomean equilibrium object. Using this extension, I quantify the impact on the aggre-gate economy of a policy that redistributes a share of total Unemployment Insur-ance (UI) income to those that are unemployed and starting a firm. In my numericalpolicy counterfactual, 5% of total UI income is redistributed to new entrepreneurshaving entered from unemployment. This corresponds to an entrepreneur receiving30% of her previous UI benefits during the first year of business. This is similarin magnitude to the subsidy program in British Columbia, Canada in which en-trepreneurs entering from unemployment receive their full UI benefits for the first38 weeks of a business operation.76The three most used employer-employee linked datasets, the Longitudinal Employer-HouseholdDynamics (LEHD) for the US, the De´claration annuelle de donne´es socials (DADS) for France andthe Linked Employer-Employee-Data of the IAB (LIAB) for Germany, all lack information on indi-vidual owners of firms. With the exception of registry data from Sweden and Denmark, this is thefirst dataset to allow the tracking of all linkages between a firm and its employees and owners acrosstime.7For a period in which the average provincial unemployment rate is up to 8%, the total duration7The main metric for measuring the success of the policy is taken as its effecton job creation. The reason being that this is the most common argument for theuse of such policies. The result is a 2.14% drop in average firm productivity andonly a 1% drop in the unemployment rate.8 The policy induces the creation of lowproductivity firms by the unemployed. This increases the share of firms created bythe unemployed and decreases the share of firms created by the employed. With alarger mass of firms, the equilibrium cost of labour increases.9 This induces firmsto hire fewer workers. With higher wages, the value of being a worker increasesand the value of being a business owner decreases for a given productivity level. Asa consequence, the employed become more selective on which business projects toimplement which further increases the share of firms created by the unemployed.Since, on average, the unemployed create lower productivity firms, average firmproductivity drops. In the quantitative exercise, the employment drop among highproductivity firms offsets job gains from firms created with the subsidy. The resultis a shift in resources from high productivity firms created by the employed to lowproductivity firms created by the unemployed.The model abstracts from learning. One possibility is to allow for learningduring the entrepreneurial spell just like models on learning on the job (Jovanovic[1979]). In the presence of learning there might be gains associated to the gov-ernment subsidizing entrepreneurship. However, to the extent that this informationfriction is not different between the unemployed and the wage worker, there shouldbe no additional benefit of the government targetting the unemployed with the sub-sidy.In the theoretical framework, the unemployed and wage workers are ex-anteidentical. In that sense, I investigate the difference between firms created by un-employed and employed individuals that have the same level of innate ability. Al-of unemployment insurance (UI) benefits is a maximum of 40 weeks. This implies that the programin British Columbia allows individuals to receive virtually the entirety of the UI benefits they wereeligible for in that year.8I focus on productivity and job creation, instead of welfare, as these are often the key variablestargeted by policy makers.9This increase in the ”cost of labour” comes via a tighter market, that makes it harder to findworkers, and a rise in wages. The model in the next section abstracts from congestion externalitiesbut they are incorporated in the model used to evaluate policy, with the ”cost of labour” for anentrepreneur being affected by the equilibrium wage as well as the tightness in the market.8though not the focus of this chapter, negative selection into unemployment shouldincrease the differences in outcomes between unemployed and employed individu-als. As a result, if negative selection were added to the model, the negative impactsof the policy would be amplified. It follows that the policy outcomes here can bethought of as lower bounds.10Finally, an additional implication of the theory is that higher wages decreasethe entry rate into entrepreneurship of the employed by more than that of the unem-ployed. Wages represent the opportunity cost of entrepreneurship for the employedbut not for the unemployed. As a result, the employed are more responsive to wagevariation than the unemployed in their decision to open a firm. With an extensionof the theory to a multi-sector environment, I formally derive this additional impli-cation and the Bartik style Instrumental Variable (IV) (Bartik [1993]) used to testit. Using region-wage variation and my instrumental variable strategy for wages, Ishow that a 1% drop in wages increases by 3.2 percentage points the entry rate intoentrepreneurship for wage workers and has no impact for unemployed individuals.While there are papers looking at the empirical relationship between unem-ployment and entrepreneurship (see Donovan [2014], Block and Wagner [2010]and Evans and Leighton [1989]), this is the first research to evaluate the impact ofexogenous variation in unemployment. Using firm closures, I isolate the impactof unemployment on individual choice from the negative selection associated withunemployment.Previous papers have investigated the impact of policies that subsidize en-trepreneurship among the unemployed (see Caliendo and Ku¨nn [2011], Baumgart-ner and Caliendo [2007] and Hombert et al. [2014]), but the interplay between thedecision of the wage worker and the unemployed to open a firm has not been stud-ied before. Here, I show that these margins are important for the crowding outeffects of the policy via a redistribution of resources from firms created by wage10In the model, I abstract from credit constraints. Since workers are more likely to start higherproductivity firms, adding capital and borrowing constraints to the model would imply that, con-ditional on wealth, workers are more likely to be liquidity constrained relative to the unemployed.Therefore, it is not obvious why the unemployed would be differentially more liquidity constrainedand more misallocated relative to wage workers when it comes to entrepreneurship. This argument isconsistent with Karaivanov and Yindok [2015] who find that, although ”involuntary” entrepreneurshave lower average wealth, they are less likely to be credit constrained. I leave such an extension forfuture work.9workers towards firms created by the unemployed.This chapter also relates to the development literature looking at subsistenceentrepreneurship in developing economies. The measure of involuntary entrepreneur-ship is often ad-hoc, such as self-employed with no employees (Earle and Sakova[2000]) and de Mel et al. [2008]) or education (Poschke [2013]). Here, instead ofconcentrating on the notion of involuntary entrepreneurship, I focus on the role ofinvoluntary unemployment for entrepreneurial outcomes. Karaivanov and Yindok[2015] also evaluate the importance of involuntary unemployment but concentrateon its interplay with credit frictions in partial equilibrium. Here, instead, I considera general equilibrium framework without credit frictions.This chapter also links to papers showing that firms started in recessions aresmaller (Sedla´cˇek and Sterk [2017] and Moreira [2015]) by providing microeco-nomic evidence that laid-off individuals create smaller firms.The structure of the chapter is the following. Section 2 develops the baselinemodel. Section 3 describes the data and the empirical differences between firmscreated by the unemployed and wage workers. Section 4 develops the multi-sectormodel extension, the new additional testable implication and presents the resultsin the data. Section 5 develops the model extension with congestion externalities,explains the calibration and reports the policy counterfactual result. Section 6 con-cludes.1.2 ModelIn this section, I propose a theoretical framework to shed light on the interactionbetween individual decisions to open a business and the differences in outcomesbetween firms created by ex-ante homogeneous individuals and the implicationsfor the labour market. In particular, the model generates predictions concerningdifferences in outcomes between firms created by the unemployed and the em-ployed (hereafter, wage workers). In equilibrium, due to a higher value of beingemployed, W , relative to being unemployed, U , workers are more selective aboutwhich business projects to implement. As a result, despite ex-ante homogeneityamong individuals, ex-post, firms created by the unemployed are different fromthose created by wage workers. In the next section I test these implications in the10data. 11The population in the economy is of measure 1. At each instant an individualis in one of three states : business ownership, unemployed or employed.The economy can be thought of as being composed of two islands : on oneisland a Walrasian market exists, with a unique wage that equates the supply anddemand of workers. Demand is made up by all the jobs created by the individ-ual business owners on that island. Supply is made up of all individuals on theWalrasian island who do not operate a firm. A second island is composed of theunemployed, who can transition to the Walrasian island by becoming a worker ata fixed exogenous rate, or alternatively, by deciding to operate a business opportu-nity. 12Workers can either be forced to move to the unemployment island by an ex-ogenous shock or decide to operate a business opportunity and become a businessowner. Business owners decide at each instant whether or not they should continueto operate their firm or transition to the unemployment island. Business oppor-tunities arrive at a constant rate ψ , which is the same for both workers and theunemployed.1.2.1 Static Profit OptimizationLet Z be the productivity of the firm, then, define z ≡ log(Z). Conditional onfirm survival, at each instant business owners maximize their profits. Productionis given by y = eznα where n is the number of employees. The static profit maxi-mization problem for a firm ispi∗(z)≡maxneznα −wn. (1.1)The firm problem above impliespi∗(z) = (1−α)(αw)α1−α ez1−α . (1.2)11An assumption is that there is no market for business opportunities. Wage workers are unable totrade with unemployed individuals opportunities they do not desire.12This version of the model ignores the general equilibrium effects of the entrepreneurship marginon the rate at which the unemployed can become employed. In the section considering counterfactualpolicy scenarios, I develop a simple extension of the model that endogenizes this transition rate.111.2.2 Dynamic Problem of the Business OwnerAlthough the profit maximization problem at any point in time is static, the en-trepreneur faces a dynamic problem, which is whether or not they should continueto operate. If the firm is shut down, the individual has to pay a cost of χ andbecomes unemployed with value U .Once firm production starts, Z follows a geometric Brownian Motion with driftµ < 0 and variance parameter σdZ(t) = (µ+σ22)Z(t)dt+σZ(t)dΩ(t) (1.3)where Ω(t) is a standard Brownian Motion. Then,dz(t) = µdt+σdΩ(t). (1.4)It follows that entrepreneurs face the following optimal stopping problem :rJ(z) = pi∗(z)+µJ′(z)+σ22J′′(z) if z≥ zˆ (1.5)J(z) =U−χ if z≤ zˆ (1.6)J′(zˆ) = 0. (1.7)Where µ is assumed to be negative, otherwise there would be an accumulationof firms that never exit the market. zˆ is the productivity threshold chosen by theentrepreneur below which it is optimal to shut down the firm and exit entrepreneur-ship.The cost of shutting down, χ , makes the algebra tractable by guaranteeing thatthe expressions for the distributions of both types are of the same functional form,with the only difference coming from the difference in selection of projects uponentry, zu versus zw, and the unemployment to employment transition rate, f , versusthe employment to unemployment transition rate, s.121.2.3 Problems of the Unemployed and the Wage workerOnce unemployed, an individual receives a flow payment of bw, where b < 1 andw is the equilibrium wage. At rate f , the unemployed transitions to the Walrasianisland as a wage worker. At exogenous rate ψ a business opportunity is drawn.Business opportunities are drawn from a distribution F . Let F be exponential ofshape β .13 For integrals to be well defined, assume β > 11−α and−2µσ2 >11−α . Inequilibrium we must have W >U , otherwise the individual would choose to remainon the unemployment island and markets would not clear on the Walrasian island.This is a direct consequence of the assumption that individuals at any moment canchoose not to work.If the productivity of the potential firm is sufficiently high, the individual makesthe choice to become a business owner and receives J(z). It follows the valuefunction of the unemployed individual can be written asrU = bw+ f (W −U)+ψ∫zu(J(z)−U)dF(z) (1.8)where zu is the threshold productivity above which the unemployed individual de-cides to implement the business project.14Once employed, an individual receives flow payment w, the equilibrium wage.At exogenous rate s, the person transitions onto the unemployment island and re-ceives value U . At rate ψ , the same as for the unemployed, a business opportunityis drawn. If the opportunity is sufficiently productive, in other words, if z is highenough, the wage worker enters business ownership with value J(z). The valuefunction of the employed can be written asrW = w+ s(U−W )+ψ∫zw(J(z)−W )dF(z) (1.9)where zw is the threshold productivity above which the working individual decides13Note that F is defined over z ≡ log(Z), as such, to assume F is exponential is equivalent todefining a distribution G defined over Z, from which individuals draw from, where G is Pareto ofscale 1 and shape β .14The event in which the unemployed individual obtains a job and a business opportunity simulta-neously is measure zero.13to implement the business project.15 zu and zw are defined byJ(zu) =U (1.10)J(zw) =W. (1.11)The rate and distribution from which unemployed and employed workers re-ceive business opportunities are the same. If they were allowed to be different,given the closer contact of wage workers with the labour market and currently op-erating firms, the arrival rate would be higher and the distribution shifted to theright for the employed. This would only reinforce the predictions of the model thatfirms created by employed individuals should last longer and hire more.161.2.4 Market ClearingLet η be the measure of business owners in the population, u the measure of un-employed and n(z,w) the optimal number of employees for a business owner witha firm of productivity z facing wage w. Then market clearing is determined by(1−u−η) =∫n(z,w)Λ(z)dz. (1.12)The equilibrium wage is linked to the average marginal product of labor as thisis in turn linked to the distribution of projects implemented, Λ(z).In frameworks such as these, where all jobs are being created by firms oper-ated by individuals of that economy, demand and supply are tightly linked beyondthe price mechanism. Supply and demand are jointly determined by individuals’choices over which side of the market to operate in. This is due to the fact thatboth job creators and workers come from the same pool. It follows that, beyondthe general equilibrium price effect, anything that affects the supply of labor, di-rectly affects labor demand and vice versa, since they are co-determined by theindividual’s decision to open a business or not.15The event in which the worker is placed on the unemployment island and receives an opportunitysimultaneously is measure zero.16This choice of a similar distribution and rate of arrival of business projects is also motivated bythe fact that when taking the model to the data, we explicitly control for the characteristics of theprevious employer of the individual which controls partially for any learning mechanisms.141.2.5 Equilibrium Measure of Unemployed IndividualsTo close the model, we need the law of motion of the measure of unemployed inthe economy, which is given byu˙ = s(1−u−η)− f u−ψ(1−F(zu))u+E (1.13)and the law of motion of the measure of firms/business owners,η˙ = ψ(1−F(zu))u+ψ(1−F(zw))(1−u−η)−E (1.14)where u is the measure of unemployed individuals, η the measure of business own-ers and E the measure of individuals exiting business ownership. Setting equations1.13 and 1.14 to zero and replacing the expression for E in equation 1.13 givesu =(s+ψ(1−F(zw)))(1−η)f + s+ψ(1−F(zw)). (1.15)1.2.6 Characterizing the EquilibriumProposition 1. The solution to the firm’s optimal stopping problem impliesJ(z) =Br− µ1−α − σ22 (11−α )2(ez1−α +1a(1−α)e−a(z−zˆ)+ zˆ1−α ) (1.16)whereB≡ (1−α)(αw)α1−α (1.17)a =µ+√µ2+2rσ2σ2> 0. (1.18)Unsurprisingly, the value function of the business owner J(z) is increasing inproductivity for the range of values for which the business operates z ∈ [zˆ,∞[. 17Let Λw(z) denote the measure of business owners operating a business project of17To see this note that∂ 2J(z)∂ z2=C(11−α )(ez1−α1−α +ae−a(z−zˆ)+ zˆ1−α )> 0 (1.19)15productivity z that were employed when they received the current business oppor-tunity. Let Λu(z) be the measure of business owners operating a business projectof productivity z that were unemployed at the moment they received the currentbusiness opportunity.18Proposition 2. For all i ∈ {u,w}, the measure of business owners running a firmof productivity z is given by• For z ∈ [zˆ,zi]Λi(z) = Λi1(z) =Mi−µ (1− e2µσ2(z−zˆ)) (1.23)• For z ∈]zi,∞[Λi(z) =Λi2(z) =βMi σ2−2µ e2µσ2(z−zi)(µ+ σ2β2 )− Mi−µ e2µσ2(z−zˆ)− Mie−β ze−β zi(µ+ σ22 β )(1.24)whereMi = ψue−β zu if i = u (1.25)Mi = ψ(1−u−η)e−β zw if i = w. (1.26)Corollary 2.1. The measure of business owners, η , and the fraction that wereunemployed when they entered entrepreneurship, ηuη , are given byη =ψ(1−η)s+ f +ψe−β zw[Au(s+ψe−β zw)e−β zu +Aw f e−β zw ] (1.27)and for z = zˆ∂J(z)∂ z= 0. (1.20)This implies for z≥ zˆ,∂J(z)∂ z≥ 0. (1.21)18In other words, this is equivalent to saying that Λw(z) and Λu(z) are defined such that∫zˆΛu(z)dz+∫zˆΛw(z)dz+u+ e = 1 (1.22)where e is the measure of workers.16ηuη=Au(s+ψe−β zw)e−β zuAu(s+ψe−β zw)e−β zu +Aw f e−β zw(1.28)whereAi = [1+β (zi− zˆ)−µβ ] for i ∈ {u,w}. (1.29)We are now ready to define a Stationary competitive equilibrium.Definition 1. A Stationary competitive equilibrium is defined by zu,zw,w,η ,ηu,Λu(z),Λw(z),usuch that• W >U• J(zw) =W• J(zu) =U• J(zˆ) = J(zu)−χ• The expression for J(z) is given by Proposition 1• The expression for Λu(z) and Λw(z) are given by Proposition 2• u is given byu =(s+ψ(1−F(zw)))(1−η)f + s+ψ(1−F(zw))(1.30)• η and ηu are defined by Corollary 2.1•w = α[1(1−u−η)(∫zˆez1−αΛu(z)dz+∫zˆez1−αΛw(z)dz)]1−α (1.31)The first condition states that the value of being an employed worker is higherthan the value of unemployment. Otherwise, no individual would ever chooseto transition to wage work and markets would not clear. The second and thirdconditions guarantee that individuals’ decisions to open a business are optimal and17the last condition comes from market clearing. The next proposition states that theequilibrium can be characterized by a system of 4 equations and 4 unknowns.Proposition 3. A Stationary equilibrium can be characterized by 4 variables (w, zˆ,zu,zw)and 4 equations :•rJ(zu) = bw+ f (J(zw)− J(zu))+ψ∫zu(J(z)− J(zu))dF(z) (1.32)•rJ(zw) = w+ s(J(zu)− J(zw))+ψ∫zw(J(z)− J(zw))dF(z) (1.33)•J(zˆ) = J(zu)−χ (1.34)•w = α[1(1−u−η)(∫zˆez1−αΛu(z)dz+∫zˆez1−αΛw(z)dz)]1−α (1.35)where J(z) is given by Proposition 1 and Λu(z),Λw(z) are given by Proposition 2Now I turn to examining the key proposition arising from the model, whichgenerates the patterns documented in the data. It states that in equilibrium, wageworkers are more selective about which business opportunities to implement. Thenecessary and sufficient condition for it to hold is simply that the income receivedwhile unemployed is lower than that received while employed. Were it not thecase, the equilibrium would not exist as markets would not clear.Proposition 4. In equilibrium, zw > zu⇔ b < 1The following corollaries result from the difference in selection on businessprojects between unemployed and wage workers.Corollary 4.1. In equilibrium, businesses created by employed workers have alower exit rate than those created by unemployed individuals.Corollary 4.1 results from business owners exiting at the same threshold whilehaving different levels of selection in the entry into business creation.18Corollary 4.2. In equilibrium, businesses created by employed workers have ahigher firm size and larger profits relative to those created by unemployed individ-uals.Corollary 4.2 is a direct consequence of the fact that both profits and firm sizeare monotonically increasing in productivity.Corollary 4.3. In equilibrium, the entry rate into business ownership of unem-ployed individuals is higher than that of employed workers.Finally, as it is often the case with selection mechanisms, an increased averageproductivity is associated with a lower entry rate.The theory predicts that even when we compare ex-ante identical individuals,we should observe differences in outcomes for entrepreneurs that were unemployedwhen they opened their firm versus those that were working. In the next section, Itest the following predictions• Firms created when the individual was unemployed, are smaller.• If the firm was started during a period of unemployment, the entrepreneur ismore likely to exit entrepreneurship.• Being unemployed makes an individual more likely to enter firm ownership.1.3 Empirical Section1.3.1 Data and MeasurementThe data used for the empirical analysis is the Canadian Employer-Employee Dy-namics Database (CEEDD). It contains the entire universe of Canadian tax filers,and privately owned incorporated firms. The dataset links employees to firms andfirms to their corresponding owners across space and time. This is achieved bylinking individual tax information (T1 files, individual tax returns), with linked19employer-employee information (T4 files)19 and firm ownership and structure in-formation (T2 files).20 The data is annual and is available from 2001 to 2010.This constitutes an advantage relative to employer-employee firm population datafrom the US, since this firm-level data does not allow the researcher to identify theowners of the firm.The data is annual with information on all employers and any businesses anindividual owned in a given year. Using this database, I can examine the character-istics of both the business owner and the firm. I concentrate on firms that contributeto job creation by hiring employees. This is done by focusing on employers insteadof self-employed individuals.Business owners are identified as individuals present in the schedule 50 filesfrom the T2 that have employees. Wage workers are identified as those who arenot entrepreneurs and report a positive employment income on their T4. I use theinformation in the T1 files to control for characteristics such as gender, age andmarital status. For more information on the data see the Data Appendix.The linkage between each firm and its corresponding owner is only availablefor privately owned incorporated firms. Incorporated firms have two key charac-teristics which correspond closely to how economists typically think about firms: limited liability and separate legal identity. Furthermore, there is a growing lit-erature showing that incorporated firms tend to be larger and that they are morelikely to contribute to aggregate employment.21 There is also evidence that there islittle transition from unincorporated to incorporated status.22 These facts, highlight19According to Canadian law, each employer must file a T4 file for each of her employees. Theequivalent in the US is the W-2, Wage and Tax Statement. In this form, the employer identifiesherself, identifies the employee and reports the labour earnings of the employee.20T2 forms are the Canadian Corporate Income Tax forms. In the T2 files there is the schedule50 in which each corporation must list all owners with at least 10% of ownership. This allows meto link each firm to individual entrepreneurs. The equivalent in the US to the schedule 50 of the T2form is the schedule G of 1120 form (Corporate Income Tax Form in the US)21 Glover and Short [2010] document that incorporated entrepreneurs operate larger businesses,accumulate more wealth, and are on average more productive than unincorporated entrepreneurs.Chandler [1977] and Harris [2000] argue that over time the incorporated business structure wascreated with the explicit goal of fostering investment in large, long gestation, innovative and riskyactivities.22 Levine and Rubinstein [2017] show that there is little transition from unincorporated to incor-porated status. They also show that the observed earnings increase for incorporated business ownersdoes not take place before opening the business, indicating that incorporation is not just a result of20how incorporated firms with employees are the most appropriate measure of firmsto consider if we are interested in the interplay between entrepreneurship and theaggregate economy.23For the remainder of the paper, the empirical definition of an entrepreneur is anowner and founder of a privately owned incorporated firm with employees.1.3.2 IdentificationExogeneity in the State of UnemploymentTo identify differences in firms exclusively due to differences in outside options, weneed to focus on episodes of random assignment of an individual to unemployment.The question then is how to identify these involuntary transitions to unemploymentin the data. One possibility is to identify those unemployed based on whether theyreceived any unemployment insurance during the year. However, such an approachfaces endogeneity issues since those who do not expect to be unemployed for longwill not take up the benefits. An alternative would be to consider individuals thatdid not work for the entire year, but that would restrict the analysis to individualswith low labour market attachment.Instead, I follow an approach inspired in the literature on the effect on employ-ment and earnings of mass layoffs and plant closures.24 In particular, I identifylaid-off individuals as those that lose their job due to a firm closure. Namely, Iconsider individuals who worked for a firm last year that does not exist this year. Icompare this group to the benchmark group of individuals that worked for a firmhigher earnings, rather, people choose the firm structure based on their planned business activity. Theauthors demonstrate how the often cited puzzle, that entrepreneurs earn less than they would haveas salaried workers, is no longer true once we consider incorporated business owners. Together withother patterns of income dynamics and observable characteristics of owners, the authors highlighthow incorporated businesses are closer to firms in traditional macro models.23Another reason to focus on incorporated firms with employees is Canadian corporte law. InCanada there are significant tax advantages for incorporating as a higher earner. So to excludefrom my analysis high-earning workers that incorporate exclusively due to tax purposes, I focuson incorporated firms with employees.24In the seminal papers of Jacobson et al. [1993] and Couch and Placzek [2010], the authors doc-ument significant drops in earnings for displaced workers. Farber [2017] and Song and von Wachter[2014] complement these results by further documenting the drop in employment probability afterdisplacement.21last year that is still operating this year. These displaced individuals are almostcertainly involuntarily in that state. Focusing on the involuntarily out of work isan added benefit. Even if I could see all the unemployed in the data, I would beworried about using them since some are people who quit their job in order to be-gin the steps of opening their firm. For the remainder of the paper I refer to theindividuals, for which their employer shut down, as displaced/laid off workers andthose that did not have their employer shut down, as employed workers. 25Note that among the individuals that were employed by a firm that still existsthis year, we have both individuals that remained employed since last year as wellas individuals that had spells of unemployment of less than a year. In other words,the employed workers group is contaminated by individuals that were fired andhad unemployment spells of less than a year. These individuals are likely to benegatively selected in overall ability relative to displaced individuals. To resolvethis issue, I use within-individual variation when testing the model predictions.This is done by estimating fixed effects regressions.26This implies that I will be comparing between moments when the individualwas displaced to moments when the individual remained employed. This is a validsource of variation if displacement shocks due to firm closure are random over thelife cycle.27 We might be worried that individuals are laid off when they werealready in a downward trend in total income or earnings.28 To verify this is not aconcern, I consider individual fixed effect specifications with the pre-displacementshock income/earnings on the left hand side and the displacement shock on theright hand side :ln(wi,t− j) = 1{Prev U}i,t +ui+ vi,t (1.36)ln(yi,t− j) = 1{Prev U}i,t +κi+ εi,t (1.37)where ln(wi,t− j) is log of total annual earnings at year t− j, ln(yi,t− j) is total tax-25This choice of identifying displaced workers is also a result of having only annual frequencydata. Since I cannot observe spells smaller than 1 year of unemployment, I adopt the strategy ofusing firm closures to proxy for individuals that are unemployed for exogenous reasons.26Readers interested in the results without fixed effects can refer to section A.3.1 of the Appendix.27This is equivalent to the parallel trend restriction for validity of difference in difference estima-tors.28This issue would arise if worker-specific productivity is time varying and firms shut down be-cause many of their workers got hit by a low worker-specific productivity shock.22able income at year t− j and 1{Prev U}i,t is a dummy taking value 1 if the individ-ual was laid off at t and 0 if remained working (with j∈{2,3,4}).29 The intuition isthat if displacement shocks happen randomly in an individual’s life cycle, it shouldbe uncorrelated to pre-shock observables.Table 1.1: Tests for Randomness of displacement shockln(wi,t−2) ln(wi,t−3) ln(wi,t−4) ln(yi,t−2) ln(yi,t−3) ln(yi,t−4)1{Prev U}i,t -0.0174 -0.01047 -0.0014 -0.0199 -0.0198 -0.0024(0.0021) (0.0031) (0.0035) (0.0018) (0.0026) (0.0029)Fixed Effects Yes Yes Yes Yes Yes YesObservations 13187561 11265230 9500351 13584834 11739333 9969862Notes: Fixed effects regressions to check randommess of displacement shock. Column (1) regresses an-nual labor income from 2 periods ago (wi,t−2) on whether recevied displacement shock in current period(1{Prev U}i,t ). Column (2) regresses annual labor income from 3 periods ago (wi,t−3) on whether recevieddisplacement shock in current period (t). Column (3) regresses annual labor income from 4 periods ago(wi,t−4) on whether recevied displacement shock in current period (t). Only includes men 25 to 54 yearsold. Standard errors are clustered at the individual level. Columns (4), (5) and (6) reports results for similarregressions but with dependant variables yi,t−2, yi,t−3 and yi,t−4, respectively.In the first Column we see that displacement shocks due to firm closure are as-sociated to a 1.74% smaller annual labor earnings two periods before. In Column2 we see that these shocks are associated to a 1.05% smaller annual labor earningsthree periods before. These differences are small indicating that these shocks arenot associated to particular moments in the life cycle with unusually high or lowearnings. It is worth noting that significance is likely coming from the large samplesize which makes even such small coefficients significant. Finally, once we lookat Column 3 we see that these displacement shocks are not associated to any dif-ference in annual labor earnings 4 periods ago. Columns 4,5 and 6 show a similarpattern for past annual income.3029I do not consider j = 1 because in the data the shock happens somewhere in the interval [t−1, t].In particular, if we see a firm in t−1 and that firm no longer present at t, it is unclear if the firm diedat t−1 or at t. For that reason we might expect to see lower t−1 income and t−1 earnings for thedisplaced, since for certain cases individuals will have been displaced at t−1.30I have also verified that a similar pattern holds for lagged values of other observables such as231.3.3 Descriptive StatisticsTable 1.2 gives the summary statistics for firms operated by the entrepreneurs inthe data. Each observation is an entrepreneur operating an incorporated firm withemployees in a given period of time. Looking at the first row, we see that the firmsused in our analysis are on average young (≈ 2 years old). This is due to the factthat firms used in our analysis must be observable in their first year of operation.Then, looking at the second column, it is clear that the firms used in the analysisare on average small (≈ 6 employees). However, the average hides variation infirm size as seen by the standard deviation of 19. As is common in firm datasets,the firm distribution is such that the majority of firms are small but there are a fewextremely large firms that account for most of employment.Table 1.2: Summary Statistics FirmsMean Std Dev Number obsFirm Age (in years) 2.0753 1.9777 450,502Number of Employees 5.8736 19.4214 450,502Notes: Summary statistics for privately owned incorporated firms with employeesfor which first year of operation is observable in the sample. Each observation is anentrepreneur with a firm in a given year. Includes only male entrepreneurs between25 to 54 years of age.In Table 1.3, I report summary statistics for individuals that last year workedfor an employer that no longer operates in the current year (laid-off workers) andthose who remain employed (not laid-off). Each observation is an individual in agiven year. The first two rows report statistics for age (38.48 versus 37.23) andmarriage rates (0.58 versus 0.51). In the third row, I report the average size of thelast year employer for these individuals (laid-off, 233 versus not laid-off, 301). Theaverages for both groups indicate that most individuals in the dataset are employedby large firms despite the fact that the majority of firms are small (See Table 1.2).age and marital status. When I do so, I find a coefficient on 1{Prev U}i,t of −0.008 for age att− 2, indicating a difference of less than a month between moments where individuals receive thedisplacement shocks and moments they don’t. For marital status at t − 2, I find a coefficient of−0.0075, indicating the difference in the likelihood of being married is less than 1%.24Table 1.3: Summary Statistics IndividualsNot laid off Laid offMean Std Dev # obs Mean Std Dev # obsAge 38.48 8.55 15,651,346 37.23 8.51 284,807Marital Status 0.58 0.49 15,651,346 0.51 0.5 284,807Size employer 233.94 875.86 15,651,346 301.19 868.93 284,807Notes: Summary statistics for individuals that last year worked for a privately owned incorporatedfirm that this year shut down (laid off) and this year did not (not laid off). Includes only men be-tween 25 to 54 years of age. Age is the age of the individual, marital status is a dummy taking value1 if the individual is married and 0 otherwise. The size of employer is the number of employees ofthe employer of the individual.1.3.4 Main Empirical ResultsIn this section I verify that the differences in performance of businesses created bylaid-off versus employed workers are consistent with the predictions of the theory.The analysis focuses on men between 25 and 54 years of age. Consistent with themodel, my two measures of performance are firm number of employees (hereafter,firm size) and the exit rate for entrepreneurs.31The first outcome of interest is the number of employees hired by firms cre-ated by employed workers compared to those that were displaced. To account forobservable characteristics, I control for the business owner’s age, marital status,industry, province of residence, the year the business started and a quadratic in theage of the business. To control for the possibility of learning from the previousemployer, I control for the number of employees and the industry of the previousemployer.3231This choice of sampling restrictions is made to narrow my focus on individuals with relativelyhigh labour force attachment. All results in this section are robust to using both men and womenaged 18 to 65 years old.32If firms created by the employed are better than those created by the unemployed, as employees25Denote by yi,t the number of employees of a firm owned by individual i inperiod t. This variable can be expressed as a function of firm characteristics, ob-servable characteristics of the owner, including whether the owner was laid offwhen the firm was started, and unobservable factors. Consider the following spec-ification:log(yi,t) = β1,1+Mi,tγ1,1+Xi,tγ1,2+Li,tγ1,3+β1,21{Prev U}i,s+Ttγ1,4+ui+ εi,t(1.38)where Mi,t are characteristics of the firm (firm age, start year and industry), Xi,t is amatrix containing all observable characteristics of the owner (age group dummies,gender, marital status and province of residence), Li,t are characteristics of the in-dividual’s last employer (industry and number of employees), Tt are year dummies,ui is the set of unobservable individual characteristics affecting firm performancesuch as innate ability and 1{Prev U}i,s is a dummy indicating if the individual waslaid off when the business was started. This equation is estimated using a linearfixed effects model. β1,2 gives us the estimated difference in number of employ-ees between firms created by laid-off individuals versus those created by employedworkers. The prediction of the model is that β1,2 < 0.learn from their previous employer, we should expect a close relationship between firm size andindustry of the previous employer and the size and industry of the current firm of the entrepreneur.26Table 1.4: Log number of employeesBaseline Control GE shocks1{Prev U}i,s -0.257∗∗∗ -0.256∗∗∗(0.042) (0.042)Fixed Effects Yes YesInteraction of region year dummies No YesObservations 450,502 450,502Notes: Fixed effects regressions of log number of employees in the firm on a dummy indicating ifthe business was started by an individual who was laid off (1{Prev U}i,s). Other controls includeage-group dummies, and dummies for marital status, province of residence, start year of business,current year, 2-digit industry, 2-digit industry of prior employer, as well as the log number ofemployees working for the previous employer. Includes men aged 25 to 54 years old. Column (1)presents the results for the baseline specification. Column (2) presents the results once controllingfor local labor market shocks.Table 1.4 shows that firms created by individuals when they have been dis-placed (1{Prev U}i,s = 1) tend to be around 25% smaller relative to firms createdby the same individuals when they are working. Column 1 shows results for thebaseline specification and Column 2 shows results when controlling for each eco-nomic region and year pair.The second measure of differences in firm performance is business survival.Let zi,t denote the choice of an entrepreneur which takes value 1 if the individualchooses to exit firm ownership and 0 otherwise. Using a fixed-effects linear prob-ability model, the choice of an entrepreneur to exit entrepreneurship is a functionof owner demographic characteristics, Xi,t , characteristics of the firm, Mi,t , char-acteristics of the previous employer, Li,t , current year, Tt , whether the owner wasdisplaced or not prior to entering entrepreneurship, 1{Prev U}i,s and unobservedcharacteristics ζi : 33zi,t = β2,1+Mi,tγ2,1+Xi,tγ2,2+Li,tγ2,3+β2,21{Prev U}i,s+Ttγ2,4+ζi+υi,t .(1.39)33The definition of matrices Xi,t , Mi,t , Li,t and Ti,t are the same as in the previous regression.27β2,2 in the equation above represents the difference in the probability of exitingentrepreneurship for business owners that were displaced by firm closure whenthey started their business. The prediction of the model is that β2,2 > 0.Table 1.5: Exit ProbabilityBaseline Control GE shocks1{Prev U}i,s 0.017∗∗ 0.017∗∗(0.007) (0.0065)Ratio of probabilities 1.3 1.3Fixed Effects Yes YesInteraction of region year dummies No YesBaseline Exit Probability 0.055 0.055Observations 341,214 341,214Notes: Fixed effects regressions of the indicator for entrepreneurship exit on a dummy indicatingif current business was started by the individual when laid off (1{Prev U}i,s). Other controlsinclude age-group dummies, and dummies for marital status, province of residence, start yearof business, current year, 2-digit industry, 2-digit industry of prior employer, as well as the lognumber of employees working for the previous employer. Includes men aged 25 to 54 years old.Column (1) presents the results for the baseline specification. Column (2) presents the resultsonce controlling for local labor market shocks.Table 1.5 shows that firm ownership spells end sooner when an individualstarts a firm after displacement (1{Prev U}i,s = 1) relative to firm ownership spellsstarted when employed (1{Prev U}i,s = 0). 34 In particular, it implies that the exitrate out of entrepreneurship for individuals that were displaced when they startedthe business is 30% larger relative to the exit rate for the same individuals who34The number of observations is smaller for the regression of the exit of entrepreneurs because inthat case I need at least two lags of the current observation to include it in the regressions. Considerthe example of a firm that exited after its first year. To include the owner i of the firm in year t, wemust see him for the current period t, the period prior, t− 1, to determine he was an entrepreneurbefore and the period before that, t−2, to see if he started his business after involuntary loss of workor not. For the firm size regression, on the other hand, all that is required is to observe the individualin the current period t and in the previous period, t− 1, to see if the firm was started following anepisode of firm closure.28were working when they started their firm.35 Column 1 shows the results for thebaseline specification and column 2 shows the results when we add controls foreach pair of economic region and year to control for aggregate shocks at the locallabor market level.Next, I verify whether there are significant differences in the likelihood ofopening a firm when an individual is laid off (via firm closure) relative to whenworking. Let di,t denote the choice of an individual who does not own a firm, thisvariable takes value 1 if the individual chooses to open a firm, and 0 otherwise.Using a fixed-effects linear probability specification, the probability of an individ-ual choosing to open a firm is a function of owner demographic characteristics Xi,t ,characteristics of the previous employer, Li,t , the current year, Tt , whether the in-dividual was displaced or not prior to entering entrepreneurship, 1{Prev U}i,t , andunobserved characteristics ηi :di,t = β3,1+Xi,tγ3,1+Li,tγ3,2+β3,21{Prev U}i,t +Ttγ3,4+ηi+νi,t . (1.40)β3,2 in the equation above represents the difference in the probability of enter-ing entrepreneurship for displaced versus working individuals. The prediction ofthe model is that β3,2 > 0. Table 1.6 shows that when individuals are displaced(1{Prev U}i,t = 1), they are 93% more likely to start a firm.36 In particular theresults imply that the entry probability into firm ownership doubles when an indi-vidual is displaced via firm closure.37 Column 1 shows the results for the baselinespecification, Column 2 and Column 3 show the results are robust to excludingindividuals that in the prior year were already incorporated without employees andindividuals that in the prior year had some unincorporated self-employment in-come.3530% comes from 0.017/0.055.36These results are consistent with the findings of Evans and Leighton [1989], which state that theunemployed are more likely to become self-employed.37The number of observations in the entry regression is not the same as in Table 1.3 of summarystatistics for individuals, because I exclude individuals that started a firm by buying a share in analready existing firm.29Table 1.6: Entry ProbabilityBaseline Robust 1 Robust 21{Prev U}i,t 0.0054∗∗∗ 0.0054∗∗∗ 0.005∗∗∗(0.0002) (0.0003) (0.0002)Fixed Effects Yes Yes YesExclude if prior year already incorporated No Yes NoExclude if prior year self-emp income> 0 No No YesRatio of probabilities 1.93 1.93 1.93Baseline Entry Probability 0.0058 0.0058 0.0058Observations 15,928,932 15,873,979 15,658,403Notes: Fixed effects regressions of the indicator for entry into firm ownership on the dummy indicatingif the individual was laid off (1{Prev U}i,t ). Other controls include age-group dummies, and dummiesfor marital status, province of residence, current year, 2-digit industry of prior employer, as well as thelog number of employees working for the previous employer. Includes men aged 25 to 54 years old.Column (1) presents the results for the baseline specification. Column (2) presents the results we excludeindividuals that in the prior year were already incorporated. Column (3) presents the results once weexclude individuals that in the prior year already some positive self-employment income.The patterns documented in the data are consistent with the predictions of themodel in the previous section.38• When laid off, conditional on opening a firm, an individual hires 25.7%fewer workers relative to when opening a firm while employed.• When laid off, conditional on opening a firm, an individual is 30% morelikely to exit firm ownership, relative to when opening a firm while em-ployed.• Being laid off doubles the probability of opening a firm for an individual.38Note that the regressions in this section all make use of fixed effects, hence, I am comparingobservably identical individuals, who appear in different states, as are considered in the theoreticalsection.30One concern is that, if firms created after a lay-off tend to be the first firms anindividual creates, the results might be capturing learning-by-doing. In particular,individuals might be learning how to be an entrepreneur when they start a firmafter a lay-off, subsequently, upon entering from employment they create moreproductive firms. In Section A.1.2 of the Appendix, I show that the differencesin size and exit rate persist once I control for an individual’s total years in thesample as a business owner before the current entrepreneur spell.39 These resultsare evidence that learning-by-doing cannot explain the differences in firms createdby an individual when laid off, relative to when working for somebody else.401.4 Additional Model ImplicationIn this section I present an additional implication of my theoretical model. It isformally derived from an extension of the baseline model to a multi-sector econ-omy.41 Details of this extension are provided in the Appendix. This implication isclosely linked to the differential selection between unemployed and wage workers.Proposition 5. An increase in the wage decreases the entry rate into entrepreneur-ship among the wage workers by more than that of the unemployed.42To understand the different channels through which wages affect the selectioninto entrepreneurship, let us consider two economies, one with larger wages rela-tive to the other. A higher economy-wide wage w increases the cost of hiring otherworkers, decreasing the incentives to open a firm for both working and laid off-individuals. This translates into higher selection among both laid-off and workingindividuals. But for a worker, a higher wage also represents a higher opportunitycost of entrepreneurship.43 As a result, the worker’s response to the higher wage is39The exact controls I use are discussed in the Appendix.40This is not to say that learning-by-doing does not play a role in a firm’s outcomes. This onlyhighlights that it cannot explain the differences in firms created by individuals after a lay-off versuswhile working for somebody else.41This additional testable implication can also be derived using the baseline model without mul-tiple sectors and is available upon request from the author. The main added value of the multiplesector framework is to derive a valid instrument for wages to test the prediction.42See Section A.1.3 of Appendix for proof of Proposition.43This effect of the wage is also present for the unemployed due to the non-zero probability oftransitioning to wage work. But this effect for the unemployed is discounted and so, is weaker.31larger than that of a laid-off individual. This differential selection response trans-lates into a differential in entry rate responses to wage changes.In the Appendix, I show that from the model extension with multiple sectors Ican derive the following expression for the entry rate into entrepreneurship in aneconomy c for wage workers w and the unemployed u.Corollary 5.1. The average entry rate for wage workers in an economy c, ERc,wand that of unemployed individuals ERc,u can be expressed asERc,w = β0,w+β1,wlog(wc)+υc,w for wage workers (1.41)ERc,u = β0,u+β1,ulog(wc)+υc,u for unemployed individuals (1.42)Combining both into one specification givesERc,n,t = α0+β1log(wc,t)+β21{Prev U}c,t,nlog(wc,t)+α21{Prev U}c,t,n+µc,t(1.43)where n= 1 if the individual is laid off and n= 0 if he is working and 1{Prev U}c,t,nis an indicator for n = 1 or n = 0. I have added the time subscripts since the data isover different years. The prediction of the theory is that β1 < 0 and β2 > 0.1.4.1 IdentificationFor my identification strategy, I use variation across different local labour marketswithin the national economy. Individuals belong to a local labour market based ontheir economic regions of residence.44 The strategy is to then verify if the entryrate into entrepreneurship in a particular region c, in year t responds differently towages for unemployed versus employed individuals.45In practice, there might be reasons to believe that certain regions have a more pro-business attitude across all years. As a result, the entry rate in these regions shouldbe higher for all years, pushing up labour demand and raising wages. This region44Economic regions in Canada correspond closely to commuting zones in the US : there are 76 intotal.45Cells for which the number of displaced or employed workers of privately incorporated firms ina given economic region year pair is smaller than 20 observations are excluded from the analysis.32specific time-invariant component would create a positive correlation between theentry rate and wages. To address this concern I include region dummies, 1{c}.Similarly, there might be years in which the Canadian economy was doing well andentry into entrepreneurship was high, pushing wages higher, which would againbias our results. To address these concerns I include year dummies, 1{t}. Andfinally, there might be years in which, due to government policy, it was particularlymore advantageous to start a firm as a worker than as a laid-off individual. Thiswould bias the difference in responses between the two groups to a similar wagemovement. To control for that variation, I include year dummies interacted withthe dummy 1{Prev U}c,t,n, indicating whether or not referring to laid off or wageworkers. My final specification isERc,t,n = ξ0+ξ1log(wc,t)+ξ2log(wc,t)1{Prev U}c,t,n+ξ31{Prev U}i,t +1{c}ξ4+1{t}ξ5+1{t} ·1{Prev U}c,t,nξ6+ εc,t,n (1.44)where 1{c} are dummies for regions and 1{t} are dummies for years. The theorypredicts that ξ1 < 0 and ξ2 > 0.Using the Frisch-Waugh-Lovell Theorem, we know that the estimates of ξ1 andξ2 are the same as those obtained from the specificationÊRc,t,n = ξ0+ξ1 ̂log(wc,t)+ξ2 ̂log(wc,t)1{Prev U}c,t,n+nuc,t (1.45)where x̂ = x− (ξˆ31{Prev U}c,t,n+1{Prev U}c,t,n ·1{t}ξˆ4+1{c}ξˆ5+1{t}ξˆ6) and(ξˆ3,ξˆ4, ξˆ5,ξˆ6) are obtained by regressing x on 1{Prev U}c,t,n, 1{Prev U}c,t,n ·1{t},1{c} and 1{t}. For region level wages, it amounts to correcting for region andyear specific averages :ŵc,t = wc,t −T∑twc,t −C∑cwc,t . (1.46)This result highlights how identification comes from comparing wage growth acrossregions.331.4.2 ExogeneityDespite the use of these additional dummies in regions and years to clean up thevariation being used, there is still reason to expect that Ordinary Least Squares(OLS) estimates are biased. This is due to the presence of region-year specificdemand shocks in the error term. We expect an OLS specification to be biased by apositive relationship between wages and the entry rate into entrepreneurship.46To address this problem, I use an instrumental variable strategy that exploitsthe variation in wages due to differences in industrial composition across cities.The instrument I used was first proposed by Beaudry et al. [2012].47 In particular,the instrument for log(wc,t) isIVc,t =∑∀iκc,i,1log(wNi,t) (1.47)where i stands for industry, κc,i,1 is the first sample year employment share ofindustry i in region c and log(wNi,t) is the wage for industry i at the national levelat year t. This term is correlated to wc,t due to across city variation in industrialcomposition.48 The intuition is that regions with a higher concentration of high-paying industries in the past have larger region-wide wages.49The instrument relies on the traditional assumptions used for Bartik instru-ments. It requires region-wide demand shocks to be uncorrelated with the indus-trial composition of the region in the first year of the sample.50 One concern isallowing for mobility of individuals across regions. Section A.1.4 of the Appendixshows how allowing for imperfect mobility across regions does not change ourempirical specification.46Demand shocks are understood here as any shocks that induce more job creation by firms. Oneexample is a TFP shock.47The authors derive the instrument from a model in which industry spillovers arise from Nashbargaining over wages.48Variation in the vector of κc,i,1.49See Section A.1.5 of the Appendix for full details on how this instrument and the main explana-tory variable of interest, wc,t , are constructed in the data.50See Section A.1.3 of Appendix for formal conditions on the model structure to guarantee validityof the instrument.341.4.3 ResultsColumn 1 of Table 1.7 indicates that when we ignore endogeneity, we get a positiverelationship between wages and the entry rate for both employed (0.002) and laid-off individuals (0.002+ 0.016) as predicted by the theory. This is consistent withthe intuition that the endogeneity is being caused by demand shocks. Looking at theIV results in column 2 of Table 1.7, we see that the positive relationship betweenwages and the entry rate into entrepreneurship goes from positive to negative forwage workers (0.002 to -0.032) and from positive to zero for laid-off individuals(0.018 to -0.032+0.032).The results in column 2 indicate that, consistent with the model, the entry rateinto entrepreneurship of wage workers is more responsive to wages than the entryrate into entrepreneurship of laid-off individuals. In particular, a 1% drop in wagesincreases by 3.2 percentage points the entry rate into entrepreneurship of wageworkers and has no impact on laid-off individuals. This differential is due to therole of wages as an opportunity cost to entrepreneurship for wage workers. Finally,note that the first stage is strong as indicated by the F-statistic in column 2, row 6.35Table 1.7: Additional Implication ResultsOLS IVlog(wc,t) 0.002 −0.032∗∗(0.0077) (0.016)log(wc,t) ·1{Prev U}c,t,n 0.016∗∗∗ 0.032∗∗∗(0.0044) (0.005)City Dummies Yes YesYear Dummies Yes YesYear Dummies X 1{Prev U}c,t,n Yes YesKleibergen-Paap rk Wald F Statistic 100.92Observations 1357 1357Notes: Linear regression with ERc,n,t , the entry rate into firm ownership, as de-pendent variable. The main explanatory variables are log(wc,t), log of wages atthe city c and year t level, and log(wc,t) ·1{Prev U}c,t,n, the interaction betweenlog(wc,t) and 1{Prev U}c,t,n, an indicator taking value 1 if referring to the laid offand 0 if referring to employed individuals.1.5 Policy CounterfactualsIn this section I evaluate the impact on job creation of transferring a share of totalunemployment insurance income in the economy to unemployed individuals thatstart businesses.The theoretical framework does not model explicit frictions that rationalizepolicies promoting entrepreneurship. One way of generating welfare gains fromthese policies is to introduce liquidity constraints associated with startup costs.Such an addition would limit the tractability of the model, without adding to themain message of the paper, that policies subsidizing the unemployed affect theallocation of resources across firms. For this reason, I leave such an extension forfuture work and take as given that governments implement these policies. I focuson the impact that these policies have on the selection margins of the unemployedand wage worker as well as the resulting effect on the firm productivity distribution36and on job creation.Until now, the model has disregarded the general equilibrium effects of the en-trepreneurship margin on the job finding rate, which has been assumed exogenousand equal to f . Yet, to understand the impact of a policy on the unemploymentrate, it is crucial to allow the job finding rate to be an equilibrium object. For thisreason, I propose a simple extension of the benchmark model presented in Section2 which allows for the entrepreneurship margin to affect the job finding probabilityvia general equilibrium.51A tractable way to do that is to assume that firms managed by an entrepreneurdo not directly hire labour. Instead, they buy an intermediate good y. This inter-mediate good is produced with labour in a one-to-one fashion.52 The entrepreneurtakes the price of the intermediate good ρ as given and proceeds as before, decidinghow many intermediate goods to use (static problem) and when to stop producing(dynamic problem). The only difference is that entrepreneurs, instead of hiringlabour directly, buy intermediate goods y from intermediate goods producers thatface search frictions. 53I assume the existence of a large set of intermediate goods producers, each ofwhich can decide to post a vacancy at any point in time.54 The flow cost of postinga vacancy for intermediate goods producers is a fraction c of the equilibrium wagew. When an intermediate goods producer finds a worker, it begins productionand obtains a flow return of ρ−w. Job vacancies and unemployed workers matchaccording to a constant returns to scale matching function given by Kvγu1−γ , whereu is the measure of unemployed and v the measure of vacancies. The rate at whichthe unemployed find jobs is given by p(θ) where θ ≡ vu . The value function of theunemployed, U , is now defined byrU = bw+ p(θ)(W −U)+ψ∫zu(J(z)−U)dF(z). (1.48)51In addition, the presence of congestion externalities makes wages less flexible and is importantin determining the magnitude of the impact of the policy.52One can think of that as an intermediate sector that must transform workers so they can beemployed by the entrepreneurs. The intermediate good is then just ”transformed labour”.53This way of introducing search frictions follows closely Beaudry et al. [2014], who also includesearch frictions in a model of entrepreneurship using an intermediate goods sector.54This means that for the intermediate goods sector, firms do not come from the same pool asworkers, the unemployed and entrepreneurs.37Let s be the rate at which matches exogenously break up, then the value functionof the worker, W , is as before. Wages are determined by Nash Bargaining,φ(W −U) = (1−φ)(F−V ) (1.49)where F is the value of a filled vacancy and V of an unfilled vacancy in the interme-diate sector. The price of intermediate goods ρ is determined by market clearing(1−u−η) =∫zˆn(z,ρ)Λ(z)dz (1.50)where η is the measure of entrepreneurs, n(z,ρ) the optimal number of intermedi-ate goods to hire for a firm of productivity z facing price ρ , and Λ(z) is the measureof firms of productivity z. The full solution of this extension is in SupplementalAppendix II.1.5.1 CalibrationI calibrate the model to the aggregate economy using my full population data. Iconsider an annual frequency. r is set to 4.5%. α , the curvature of the productionfunction of the entrepreneur, is equal to the aggregate labour share, and, as such,is set to 23 . Remember the matching function is of the form m(u,v) = Kuγv1−γ . Ifollow Shimer [2005] in setting γ equal to 0.72. Still following Shimer [2005], I setφ , the Nash Bargaining parameter, equal to γ . The rate at which workers transitionto unemployment s is taken from Hobijn and S¸ahin [2009].55 For the cost of postinga vacancy, I note that as in Shimer [2005], the model allows a normalization. Fromthe free entry condition and the expressions for the value of an unfilled and a filledvacancy I arrive at56 :cwq(θ)=ρ−wr+ s⇒ θ = (cw(r+ s)(ρ−w)k )− 1γ (1.51)Equation 1.51 implies that doubling c and multiplying k by a factor of 21−γ dividesθ by half and doubles the rate at which intermediate good firms contact workers,55The authors estimate the rate at which employed individuals transition to non-work for twenty-seven OECD countries, including Canada.56(See Supplemental Appendix II for expressions)38q(θ), but does not affect the rate at which workers find jobs, p(θ). It follows thatwe can normalize θ . I follow Shimer [2005] and choose c so as to normalize θ to1. Section A.3 of the Appendix contains the results for an alternative calibrationin which I follow Hagedorn and Manovskii [2008] in setting the cost of posting avacancy to 4.5% of the equilibrium wage, c = 0.045. The results are robust to thisalternative calibration. The replacement rate for the unemployed, b is set to 0.6.For µ and σ , the parameters governing the evolution of productivity of en-trepreneur owned firms, I use the average growth rate in firm size conditional onpositive growth and the tail parameter of the ergodic distribution. In Section A.1.6of the Appendix I state and prove the formal theorem relating these moments.Finally, to make the model consistent with the patterns in the data, I choose β ,the shape parameter of the exogenous distribution business opportunities are drawnfrom, χ , the cost of shutting down and K, the scale parameter of the matchingfunction, to match the differences in the entry rate between the unemployed andworkers and the differences in size and exit between the firms created by bothgroups.The value of χ in the calibration, 0.268, represents a cost equivalent to 6%of average firm revenue. This is consistent with World Bank data (Ease of DoingBusiness Statistics) for which the cost of resolving firm insolvency for Canadais estimated at 7% of the debtor’s estate. Finally, ψ is shown to not matter inthe impact for the policy in the economy. In Table A.3.1 of section A.3 of theAppendix I show that the results are robust to changing the values for ψ . In thebaseline calibration I choose ψ = 24, corresponding to an average arrival time forbusiness projects of 12 a month. See Table A.2.1 in the Appendix for a completelist of parameter and sources/targets used. The model is highly tractable with clearintuition this comes at a cost of making it inadequate for tests of external fit ofthe model. Consistent with this, I focus on internal fit of the model for which allmoments are shown to be matched in Table A.2.1 of the Appendix.1.5.2 Policy AnalysisIn this section I use a calibrated version of the model with search frictions and aversion of the baseline model to evaluate the impact of a policy that subsidizes39entry into entrepreneurship among the unemployed. The calibration for the base-line model follows the calibration described for the model extension with the onlyadditional caveat that the rate at which the unemployed become workers ( f ) is setto match the job finding rate in the model extension and is kept at that same valueonce I evaluate the impact of policy.I consider a policy that takes 5% of total unemployment insurance (UI) incomeand redistributes it to any unemployed individual that makes the decision to start afirm. The entrepreneurship subsidy policy corresponds to entrepreneurs that wereunemployed when starting their firm receiving 30% of their previously receivedUI benefits during their first year of business. This is less than, but comparablein magnitude to, the subsidy program in British Columbia in which entrepreneursentering from unemployment remain eligible to their full UI benefits for the first38 weeks of operating the business.57The main metric for measuring the success of the policy is taken as its effecton job creation. The reason being that this is the most common argument for theuse of such policies. The question asked here is to what extent can this policygenerate higher job creation and what is the associated cost, in the form of lowerproductivity.In Table 1.8 Column 1, we see that the effect of the policy in the benchmarkmodel is a drop in average firm productivity , E(z) (-3%)), a small drop in theunemployment rate (-1%) and an increase in wages (1.29%). Despite the relativelack of movement in the unemployment rate, there is an important change in thecomposition of firms. This reallocation can be seen with the change in the numberof jobs created by wage workers, (-6.39%), and of jobs in firms started by theunemployed, (14.49%). The new equilibrium is one in which more resources arebeing used by firms created by the unemployed (low productivity) at the expense ofless being used by firms created by wage workers (high productivity). Consistentwith this, average firm exit rate increases.The subsidy policy makes entrepreneurship relatively more attractive to the57For the year 2016, given an average unemployment rate below 8%, residents of the provincewere entitled to a maximum of 40 weeks of employment insurance. This means that an unemployedthat applied to receive the subsidy is entitled to virtually the entirety of the benefits he was alreadyin British Columbia, Canada.40unemployed. Hence, their level of selectivity decreases, prompting a rise in themass of firms in the economy (via more low productivity firms). The increase inlow productivity firms decreases average firm productivity. The rise in the numberof firms increases labour demand which in turns puts upward pressure on wages.The rise in wages decreases the value of being an entrepreneur and increases thevalue of being a wage worker. As a result of these two forces, the wage workerbecomes more selective on which business projects to implement.58 This furtherincreases the share of firms created by the unemployed.58Note that for the wage worker all that has changed in the world with the policy is that wages arehigher. In the new equilibrium with the policy the value of being an entrepreneur is higher for theunemployed and lower for the wage worker.41Table 1.8: Policy outcomesBenchmark Model Model Extension(1) (2)∆E[z] -3% -2.14%∆ Unemployment Rate (% change) -1% -1.11%∆ Wage 1.29% 0.65%∆ Labor Market Tightness (θ ) − 2.35%∆ Jobs by Firms created by Unemployed 14.49% 7.12%∆ Jobs by Firms created by Workers -6.39% -7.1%∆ Average Firm Exit Rate (% change) 55.42% 36.37%Notes: Outcome of policies that make a share of total UI benefits income conditional on the unemployedopening a firm. ∆E[z] is the percentage change in the average firm productivity, ∆ Jobs by firms createdby workers is the percentage change in the measure of jobs associated to firms created by wage workers,∆ Unemployment is the percentage change in the unemployment rate. The policy takes 5% of totalunemployment insurance (UI) income and redistributes it to any unemployed individual that makes thedecision to start a firm. The entrepreneurship subsidy policy corresponds to entrepreneurs that wereunemployed when starting their firm receiving 30% of their previously received UI benefits during theirfirst year of business.In Table 1.8 Column 2 we see that the effect of the policy in the model extensionis almost identical for average firm productivity, E(z) (-2.14%) and unemployment(-1.11%). The key difference in the mechanism lies in the response of wages to theshock (1.29% versus 0.65%) and its contribution to the general equilibrium effect.After the drop in selectivity among the unemployed and the correspondingincrease in the number of firms, the price of intermediate good increases. Thisprompts more intermediate good firms to post vacancies, which in turn increaseslabor market tightness.The increase in labor market tightness has a direct and indirect general equi-librium effect. The direct effect is to increase the job finding rate, making wage42work more attractive relative to entrepreneurship. Together with the increase in theprice of intermediate goods, it increases workers’ selectivity. The indirect effect isthe rise in the worker’s threat point during wage bargaining. As a result, workersbargain higher wages, further increasing the value of wage work relative to en-trepreneurship. The indirect effect complements the direct effect further increasingworker selectivity.Since wages are determined via Nash Bargaining rather than supply and de-mand the responsiveness of wages is smaller in the model extension with searchfrictions. But the total effect on aggregates ends up being similar because withsearch frictions the model gets one more margin of adjustment, labor market tight-ness. In contrast, for the benchmark model, all of the general equilibrium adjust-ment can only happen via prices. The implication is a much smaller wage increasein the model with search frictions.Note that, despite the increase in job finding rate in the model extension and itsabsence in the benchmark, both models deliver a same change in the unemploymentrate. This is achieved by a larger inflow into the pool of unemployed in the modelextension relative to the benchmark model. This happens via a larger increase inthe firm failure rate in the model extension (55.42%) relative to the benchmarkmodel (36.37%).I conclude that, in the context of my model, the policy has close to no impacton the unemployment rate while decreasing average firm productivity and reallo-cating resources from high to low productivity firms. The results also highlightthe importance of general equilibrium effects. In particular, the channel of thesegeneral equilibrium effects will depend on the labor market structure. Note that,although I abstract from negative selection into unemployment on worker ability,adding this margin would only strengthen the results presented here. 591.6 ConclusionI study the differences between firms created by unemployed individuals relativeto otherwise identical employed individuals. I show that these differences are im-portant for our understanding of policies that promote entrepreneurship among the59This is conditional on worker and entrepreneurial ability being positively correlated.43unemployed to fight unemployment.I develop a general equilibrium model of endogenous business ownership. Inthis framework, the only difference between unemployed and employed individ-uals is their outside option. In equilibrium, due to poorer outside options, theunemployed are more likely to open a firm, but conditional on doing so, generatesmaller firms that shut down sooner. I test these implications using a novel con-fidential dataset with the universe of Canadian tax filers. I use firm closures toidentify random assignments of an individual to unemployment. I find that unem-ployment induces a doubling of the probability to start a business, and conditionalon doing so, an individual hires 26% fewer workers and is 30% more likely to exitentrepreneurship. Finally, I use the data facts to discipline a numerical version ofthe model. I evaluate the impact of a policy that subsidizes entry into entrepreneur-ship among the unemployed. The result is a drop in average productivity despitelittle movement in the unemployment rate. Furthermore, the policy induces thecreation of low productivity firms that crowd out resources from high productivityfirms.44Chapter 2Entrepreneurship, Outsideoptions and ConstrainedEfficiency2.1 IntroductionUnderstanding the process and choices that drive the creation of new firms andhence spur employment is crucial to a complete understanding of employment,productivity growth, wages, vacancy creation and a host of other labor market vari-ables. The focus of this contribution is on the entrepreneurship margin. We makea theoretical contribution to the literature on firm creation by placing the decisionof individuals to create a firm inside the search and matching framework. Jobs arecreated by ex-ante identical individuals who face a choice between entrepreneur-ship and wage work. By modelling the start-up decision as an endogenous choicein this manner we forgo the inclusion of the typical free entry condition to closethe model as in Mortensen and Pissarides [1994]. Instead the model is closed bya condition whereby entrepreneurs are indifferent between remaining unemployed45or creating a business, conditional on their productivity draw.Modelling firm creation in this manner implies an interesting distinction be-tween our framework and the baseline search model. For instance, in the standardsearch framework wages are unambiguously increasing in the value of unemploy-ment. In contrast, the direction, and not just the magnitude of this relationshipis dependent on the Nash bargaining parameter in our framework. For thresholdvalues of the bargaining parameter the slope of the wage can become negative, orindeed flat. The intuition underlying this result is that firms are created by individ-uals whose outside option is to search for wage work through rejoining the poolof unemployed workers. Due to this, the outside option value for both firms andworkers in this model is the value of unemployment. This contrasts with exogenousmodels of firm creation where the outside option value for the firm is the value ofan unfilled vacancy. As a result the equilibrium wage equation in our frameworkincludes an additional term coming from the firm side. This relationship also ap-pears counter-intuitive: for high values of workers bargaining power wages arenegatively related to the value of unemployment.Additionally, the inclusion of endogenous firm creation here implies the exis-tence of an additional externality in the model, in addition to the standard conges-tion and thick margin externalities, which we refer to as the ‘job-creation margin’.This margin arises from the endogeneous choice to search for a business idea ora job. If the labor market is tight then individuals will prefer to search for wagework and hence entrepreneurs will be more selective on which business ideas theyimplement. However, those deciding between searching for a job or a businessventure do not take into account the effect of their choice on the search processof other potential entrepreneurs or other job seekers. Their choices also affect the46choices of entrepreneurs currently operating in the market. This effect again oper-ates through changes in the entrepreneurs outside-option term, which is the valueof unemployment.Given the inclusion of this additional externality and the distinct difference inthe wage function, it is not ex-ante clear what form the efficient solution to themodel will take. In solving for the planners problem we find that the solution isidentical to that of the Hosios condition for the standard search framework: exter-nalities are balanced when agents bargaining power is equated to the elasticity ofthe matching function. However, this socially efficient solution does not pin downa clear direction for the wage, and hence a clear direction of adjustment to equilib-rium. The dynamics of the model following a shock remain sensitive to the size ofthe elasticity parameter. In particular, wages do not necessarily exert a dampeningeffect in response to exogenous shocks.This paper contributes to the theoretical literature evaluating constrained effi-ciency in search theoretic models of the labor market. The Hosios rule [Hosios,1990] states that a standard search model a la` Pissarides [2000] is constrained effi-cient when the Nash bargaining parameter is equal to the elasticity of the matchingfunction. Literature in this area has sought to examine the set of conditions un-der which the Hosios rule gives the socially efficient outcome1 or generalizes theHosios rule to alternative environments2.This paper also relates to the literature on the individual choice between work-ing and opening a business. The empirical literature is vast as exemplified by theseminal papers of Hamilton [2000] and Quadrini [2000] as well as more recent re-1see Albrecht et al. [2010], Gavrel [2011]2see Acemoglu and Shimer [1999], Julien et al. [2016]47search such as that of Humphries [2016] and Poschke [2013]. Finally entrepreneur-ship is important to the extent that the extensive margin of firm creation is importantfor the macroeconomy. In that respect there is evidence on the importance of thefirm creation process for persistence in firm outcomes (Sedla´cˇek and Sterk [2017],Moreira [2015]), wealth inequality (Quadrini [2000] and Cagetti et al. [2006]) andthe importance of young firms for job creation (Haltiwanger et al. [2013]). Thispaper contributes with a richer theoretical framework to investigate these decisionsof individuals to open a business.The remainder of this paper is structured as follows: In section 2 we present ourtheoretical model, the dynamics of which are discussed in section 3. In section 4we discuss the Hosios condition for efficiency and we present concluding remarksin section 5.2.2 ModelAt a given point in time an individual can be one of four types; a worker, an en-trepreneur, a searcher for paid work, or a searcher for a business idea. Individualssearch for a ‘business idea’ while unemployed only. Each business idea repre-sents the productivity level of the firm and is modelled as an exogenous produc-tivity draw, ε . To maintain tractability we assume there is no direct entry into en-trepreneurship from wage work3, and that there is no recall of productivity draws.Labor market tightness, defined in the standard manner, includes as the unem-ployed only those seeking wage work. It is worth noting however that this does not3This would require a separate threshold rule for each realized wage. The comparative staticsof the model in that case becomes more complex. For every shock that increases the selection onbusiness projects among unemployed, there would be a corresponding decrease in selection amongthe workers.48mean that entrepreneurship only affects market tightness on the vacancy side. Thesize of the unemployed pool is in part the result of the endogenous choice betweensearching for a job or an idea.A choice is made by all unemployed workers to either accept a job, or imple-ment a business idea. If the unemployed chooses to search for business idea, heor she receives one at rate ψ from distribution F(ε), which he or she then chooseswhether to implement or not. Individuals finding sufficiently productive businessideas post a vacancy next period, in which case they receive the value of a unfilledvacancy of productivity ε , V (ε) and lose the value of being a searcher U . If theunemployed decide to search for a job, they receive one at rate p(θ), in which casethey draw a job from the endogenous firm productivity distribution µ(ε).4 Uponfinding an employer of productivity ε , the worker receives the value of being aworker in a firm of productivity ε , W (ε). From the assumptions above it followsthat the value function of a searcher U is given byrU = b+max(p(θ)∫(W (ε∗)−U)µ(ε∗)dε∗,ψ∫ε(V (ε∗)−U)dF(ε∗)) (2.1)As all individuals are ex-ante identical, in equilibrium individuals will be indiffer-ent between searching for a job or for a business idea.The productivity threshold, below which no entrepreneurs will implement theirbusiness idea is characterized by:V (ε) =U (2.2)4This distribution is a equilibrium object that depends on which business opportunities individualschoose to implement.49The cost of posting a vacancy is given by c, q(θ) defines the firm match prob-ability. Let J(ε) denote the value of a filled vacancy of productivity ε . The valuefunctions for a vacant job (V (ε)) is standard and given byrV (ε) =−c+q(θ)(J(ε)−V (ε)). (2.3)When working for an employer of productivity ε the worker receives wage w(ε).Firms experience exogenous destruction shocks at rate λ . The value of being aworker, W (ε), is given byrW (ε) = w(ε)+λ (U−W (ε)). (2.4)The value of a filled job (J(ε)) takes into account that at exogenous rate λ the firmis destroyed and the entrepreneur transitions back to unemploymentrJ(ε) = ε−w(ε)+λ (U− J(ε)). (2.5)Wages are formed through Nash bargaining. The threat point in the bargainingprocess for both workers and entrepreneurs is the value of unemployment, U . Ifeither party chooses to walk away from the match then the firm will shut down.Equilibrium in this model is characterized by the set of equations1. V (ε) =U2. β (W (ε)−U) = (1−β )(J(ε)−U)3. W (ε)>U ∀ε > ε4. p(θ)∫(W (ε∗)−U)µ(ε∗)dε∗ = ψ ∫ε(V (ε∗)−U)dF(ε∗)50where the last equation ensures individuals are indifferent between searching for ajob or a business idea.The remainder of our analysis considers the economy in steady state. Fromsteady state equations we derive a tight, negative relationship between the thresholdproductivity and market tightness which we refer to as the Job Creation Curve,p(θ) = ψ(1−F(ε)) (2.6)Furthermore, using the entrepreneur’s value functions combined with the derivedendogenous productivity distribution we derive a second curve showing a positiverelationship between tightness and threshold productivity, which we refer to as theEntrepreneurship curve.Theorem 6. The indifference condition determining ε implies the following posi-tive relationship between ε and θ .b(r+λ )+βψ∫ε(ε∗)dF(ε∗)r(r+λ +2ψβ (1−F(ε))) =−c(r+λ )+q(θ)[(ε)(1−β )]r(r+λ +2(1−β )q(θ)) (2.7)The intuition underlying this curve is that a tighter labor market implies agreater benefit to seeking wage work. To remain indifferent, the benefits to en-trepreneurship must be high for potential entrants, which translates into a higherthreshold productivity, ε . The interaction of the Entrepreneurship curve and theJob Creation curve pins down an equilibrium pair of (θ ,ε).Finally, wages in equilibrium are given byw(ε) = βε+(1−2β )rU, (2.8)51which differs from the traditional search and matching model due to the inclu-sion of an additional −β rU term coming from the outside option term of the en-trepreneur. The direction of fluctuations in the wage due to movements in the valueof unemployment are determined by the size of the bargaining parameter. Wagesare increasing in the value of unemployment, U , for β < 12 and decreasing forβ > 12 .2.3 Model ExplorationIn this section we present some comparative statics outlining the underlying mech-anisms present in the model. From equation (2.8) it is quite clear that the directionof wage movements is dependent upon the value of the bargaining parameter. In-tuitively two effects are operating here. Firstly, an increase in U pushes wagesupward as the threat point of job seekers has increased. Secondly, failure becomesless costly to the entrepreneur as the outside option to firm closure is higher. As aresult, wages are negatively related to U when workers have a greater share of bar-gaining power. The intuition behind this seemingly counter-intuitive result is thatwhen β is high a greater weight is placed upon the decline in the cost of failureto the entrepreneur than on the cost of job loss to the worker. The reverse is trueif β < 12 . However, even when the direction of wage movements are unknown thefollowing result holds true:Theorem 7. An increase in the value of unemployment income, b leads to a highervalue of threshold productivity, ε , and a lower value of market tightness, θ , inequilibrium, implying an increase in average firm productivity.This means that even if wages fall in response to an increase in the flow value52of unemployment, net job creation will still fall. The intuition for this result issimply that a higher b provides greater insurance to potential entrepreneurs andas a result those searching for ideas become more selective on the business ideasthey implement. This raises average productivity and decreases net job creationas captured by an increase in the threshold productivity ε . Furthermore regardlessof how wages are affected there will be a decline in market tightness. This resultsfrom lower net vacancy creation. The implication of our model therefore, is thatthere is a trade-off between entrepreneur quality and quantity. If a greater socialsafety net is provided for entrepreneurs then there will be a fall in the rate of en-trepreneurship but an increase in the average quality of entrepreneurs. Furthermoreit is interesting to note that this relationship holds regardless of how wages adjust.In particular it is possible to have an increase in aggregate productivity with flator even decreasing wages. This contrasts with Mortensen and Pissarides [1994]where wages are the key channel through which the flow value of unemploymentaffects vacancy creation.Similarly, without knowing the direction of wage movements it is possible topinpoint a relationship between the other endogenous variables and the flow costof posting a vacancy.Theorem 8. An increase in the cost of posting a vacancy, c, leads to a higher valueof threshold productivity, ε , and a lower value of market tightness θ in equilibrium,implying an increase in average firm productivity.An increase to the flow cost c leads to a shift in the entrepreneurship curve,while the job creation curve remains unchanged. In a model with exogenous firmsand a free entry condition, the value of unemployment is affected only indirectly53through a change in the firm productivity distribution. In our framework there is anadditional effect whereby the value of a vacancy enters the value of unemploymentthrough the agents choice to become an entrepreneur. In both models the value ofunemployment falls as a result. The wage effect serves to dampen the employmentresponse in the case of exogenous firms, but in our model the employment responseis exacerbated if wages are negatively related to the value of unemployment.542.4 The Constrained Efficient Solution: Deriving theHosios ConditionWe solve the planners problem for the model to derive the constrained efficientsolution which is summarised by the following theorem:Theorem 9. The competitive equilibrium allocation is constrained efficient whenβ = 1−α .The condition under which the model is at a social optimum, is the same as theoriginal Hosios condition [Hosios, 1990], whereby externalities are fully balancedwhen the bargaining parameter is equal to the elasticity of the matching function.Given the unique relationship the bargaining parameter plays in our model in de-termining the direction of the wage response to changes in the value of unemploy-ment, it is worth exploring this result somewhat.In particular, the constrained efficient wage equation now takes the form:w(ε) = (1−α)ε+(2α−1)rU (2.9)Wages are declining in the value of unemployment for values of α lower than 12and strictly non-negative otherwise. A high value of α implies that workers matchprobability is sensitive to market tightness, relative to that of firms.Consider the case in which α > 12 . Holding wages constant, an increase in mar-ket tightness (θ ) has three effects. First, the value of job search increases due to arise in p(θ) holding constant the value of unemployment (U) and the threshold pro-ductivity (ε). We refer to this as the job search effect. Secondly, for entrepreneurs,the likelihood of matching with a worker falls (q(θ)) but by a lesser amount thanthe increase in p(θ), again fixing U and ε . This we call the worker finding effect.55Thirdly, the outside option effect comes from fluctuations in the value of unemploy-ment (U) which affects entrepreneurs via the outside option channel. Note that viathe outside option channel (changes in U), entrepreneurs are affected by changes inp(θ), holding changes in q(θ) constant. This contrasts with more standard searchmodels where changes in U and p(θ) affect firms only indirectly via wages oncewe hold q(θ) constant.This channel, where the decision to enter entrepreneurship is dependent on thevalue of unemployment and the value of wage work introduces novel externalities.The first being that when agents choose to search for a business idea they do nottake into account the impact of this decision on the choice between job creationand wage work for other individuals. Secondly, they do not take into account howtheir choice affects the outside-option value of entrepreneurs currently operating inthe market. These externalities arise from the presence of the job search effect andthe outside option effect, respectively, both not present in a model with exogenousfirms and free entry.In the absence of wage effects, the value of unemployment will rise, and dueto the indifference condition on entry (equation 2.2), the value of ε increases. Arise in ε decreases firm creation and increases average firm productivity. Under theconstrained efficient allocation (β = 1−α), as from equation (2.8), a larger shareof productivity accrues to the firm, and hence a smaller increase in ε maintainsthe equality. However, assuming that α > 12 , wages are increasing in the value ofunemployment, which further increases the gains to job search, exacerbating therise in ε required to make the individual indifferent. As a result, the constrainedefficient allocation generates less firm creation (higher ε) relative to the allocationwhere wages do not adjust. In other words, compared to the socially efficient56allocation, there is excessive firm entry coming from an increase in the value ofunemployment, despite the rise in q(θ).The intuition is that with α > 12 , p(θ) is more responsive to changes in θrelative to q(θ). As a result, for a rise in θ , the job search and the outside optioneffects are quite large while the worker finding effect is small. Since the job searchand the outside option effect pull ε in opposite directions the overall result is a smallresponse of ε to a rise in θ . Therefore, to attain the constrained efficient allocationprices have to move so as to generate more selection than would happen otherwise.This is achieved through wage adjustment where the bargaining parameter is suchthat wages are increasing in the value of unemployment.If we consider the opposing case where α is less than one half a similar logicapplies. An increase in tightness, θ , generates a large response of q(θ) and a smallresponse of p(θ). As a result, the job search and outside option effects are smallwhile the worker finding effect is large. The overall response of ε to the change inθ is larger than would be induced in a constrained efficient allocation. Therefore,to attain efficiency, prices must adjust to reduce selection on productivity. This isachieved when wages are decreasing in the value of unemployment. The same istrue if we consider a fall in θ . The wage response will mitigate the increased entryto entrepreneurship when α < 12 and exacerbate entry when α >12 . If the slope ofthe wage equation with respect to U was α rather than 1−2α then this mitigatingeffect on ε would not operate when α < 12 .Therefore, this model includes a range of values over which the unemploymentresponse to a shock is more severe, and a region where it is lessened. This is drivenby the ambiguity in the direction of the wage response arising from entrepreneursand workers sharing a threat point in the bargaining process. In a search model with57exogenous firm creation and a free entry condition a shock that increases tightness,θ , always feeds into a larger wage, w, via a increase in the value of unemployment,U , which partially offsets the increase in θ by decreasing the incentives for firmsto hire. The wage response here has a mitigation effect like in standard modelswithout entrepreneurs and with a free entry condition when α > 12 but has a ampli-fication effect when α < 12 . The constrained efficient solution therefore balancestraditional search externalities with additional externalities arising from the depen-dency of the gains to firm creation on the value of unemployment. In particular thesocial planner weighs the additional effects on currently operating entrepreneursand those deciding between entrepreneurship or wage work, of the endogenouschoice of agents to search for a job or an entrepreneurial venture.582.5 ConclusionWe forgo of the traditional free entry condition by proposing a more realistic frame-work in which individuals are constantly making the decision whether or not toopen a firm. We endogenize firm entry as a dynamic entry process where bothworkers and business owners are drawn from the same population. We do so byallowing ex-ante individuals to search for either a job or an idea. In the stylizedframework considered here the threat point of the entrepreneur and the worker be-come one and the same. This generates a novel interplay between the bargainingparameter and the direction of wage changes to any feasible shock.In deriving the planners solution to the model we find that unemployment ef-fects are either muted or intensified in response to a shock at the social optimum.This mechanism operates through wages and contrasts with the standard searchframework where wages serve to only dampen unemployment fluctuations. Thisresult is particularly interesting given that the Hosios condition takes the sameform.59Chapter 3Match Quality, ContractualSorting and Wage Cyclicality3.1 IntroductionCompensation arrangements influence the evolution of workers’ wages. In thischapter we examine how profit maximizing firms choose pay arrangements de-pending on worker-firm match quality, and provide evidence that such arrange-ments help shape both wage dynamics and employment durations.We begin by developing a simple model of worker pay based on match qual-ity and worker retention considerations. Our main theoretical result is that firmsretain workers in high quality matches by offering compensation that is linked tothe performance (production outcome) of the match. Moreover, as production isinfluenced by an aggregate cyclical component, the model implies that the wage ofworkers in performance-pay jobs should be more sensitive to cyclical fluctuations.In the second part of the chapter we bring these theoretical predictions to the60data. We use detailed information from the NLSY79 to characterize work histo-ries, and resort to specific questions regarding the form of compensation to distin-guish between jobs with and without performance pay components. We constructmeasures of match quality and, following an established literature, we use the un-employment rate as a proxy for business cycle conditions. Our results provideempirical support for the three main theoretical predictions of the model. First,there is a clear positive relationship between match quality and the prevalence ofjobs with performance pay. Second, match quality has a direct effect on wages, af-ter controlling for the adoption of performance pay. Third, wages in performancepay jobs exhibit significant sensitivity to cyclical conditions, while wages in jobswith no performance pay components do not. Given our focus on worker retentionmotives, we also provide evidence that job durations are significantly higher whenperformance-based pay is adopted.We relate our results to the growing literature on occupation heterogeneity andshow that variation in the way workers are compensated in different occupations isintimately linked to match quality. In fact, we argue that this simple observationcan go a long way towards understanding some of the observed differences in thecyclicality of wages, match-specific productivity and job durations across occupa-tions. To this purpose we show that jobs in “cognitive” occupations exhibit highermatch quality, are more likely to include performance pay components, have morecyclical wages and last longer.Our study naturally brings together two branches of the literature on pay ar-rangements and wage dynamics. The first looks at the choice of compensationmechanisms and their effects on wages.1 Our theoretical analysis is especially re-1A detailed overview of the vast, and growing, literature on personnel and human resource man-61lated to the work of Oyer (2004), who was the first to argue that firms may tieemployees’ pay to firm performance in order to closely match employees’ com-pensation to their outside options. Our theoretical analysis shows that this retentionmotive becomes extremely salient in the presence of match-specific heterogeneity,leading to interesting patterns of contractual sorting and wage dynamics.Some of our empirical findings confirm those by Lemieux et al. (2009, 2012),and Makridis [2014]. These studies show that performance pay jobs are concen-trated at the upper end of the wage distribution, where most jobs entail relativelyhigh skills and labor returns.2Finally, our results on the cyclicality of wages directly relate to the empiricalliterature going back to the work of Bils [1985] on the effect of aggregate labormarket conditions on employees’ wages. This line of research uses the unemploy-ment rate as a proxy for business cycle conditions. One of the most recent contribu-tions in this broad area (Hagedorn and Manovskii, 2013) proposes a theory-basedapproach to the measurement of match quality, and we adopt this method to gener-ate empirical proxies for match quality.Our findings highlight the role of aggregate labor market conditions for wages.The idea that contracts play a role in determining the cyclicality of wages is nota new one (see for example the original contribution by (Beaudry and DiNardo,1991). Unlike previous research, however, we focus on the theoretical and em-pirical linkages between match-specific productivity, pay arrangements and wagecyclicality. By explicitly studying the contract choice of a firm in the presence ofheterogeneous match qualities, we closely follow the approach used in organiza-agement is presented in Lazear and Oyer [2012].2These studies do not explicitly incorporate match quality in the analysis.62tion and personnel economics. In this way we provide novel evidence supportingthe view that firms use profit-sharing to retain well-matched workers, and this re-tention motive helps shape both wage dynamics and job durations.The remainder of the chapter is organized as follows. The model and the the-oretical predictions are discussed in Section 2. Section 3 describes the empiricalspecification and its relation to the model, as well as the measurement of matchquality and performance pay. Empirical results and various robustness checks areoverviewed in Section 4. Section 5 concludes.3.2 A Simple Model of Worker PayIn what follows we study the problem of a firm that has to decide how to compen-sate workers, given (i) time-varying aggregate conditions and (ii) match-specificproductivity. To simplify the analysis we consider a stylized model with ex-anteidentical risk neutral firms and workers. The model highlights the importance ofworker retention considerations, as in Weitzman [1984] and Oyer [2004].Production. A firm-worker pair produces output using production technologyy = Pm, m ∈ [mmin,mmax] (3.1)where P is an aggregate (economy-wide) state variable, while m is a match-specificproductivity component, assuming values between mmin > 0 and mmax < ∞. Theaggregate state is either high (PH), or low (PL), where PH > PL. The match-specificproductivity component is drawn once and persists throughout the life of the match.Timing. We assume that, for all new matches, the first production period is used63to learn about match quality. Only at the end of this initial period, after productiontakes place, match quality m is revealed to the firm and the worker.To attract a new worker the firm commits to pay some given wage in the initial(learning) period even though match quality is unknown ex-ante. We assume thatthis wage is a function of the aggregate state P and of the idiosyncratic matchquality m in the worker’s previous job. Specifically, we assume that the wage paidduring the learning period is equal to a(P)m and posit that (i) it is increasing in theaggregate state (a′(P)> 0); and (ii) that workers compensation is strictly boundedfrom above by the total value of output in the current match (a(P) < P). In thecontext of our model the firm’s commitment to pay a(P)m clearly defines the valueof each worker’s outside option.3 The assumptions we make about a(P) implythat workers have better outside options during high productivity periods, whenthe aggregate state is P = PH .At the end of the initial period the new match specific productivity is revealedand the firm offers an employment contract to workers.4 A surviving match lastsfor up to two more periods, denoted as 1 and 2. We assume that P1 = PH withcertainty, while P2 = PH with probability q and P2 = PL with probability (1−q).5Some workers might separate from the firm after the initial learning period.This happens when a sufficiently low match quality is revealed. The ex-ante par-ticipation constraint of a worker at the start of the period after learning about matchquality is3For simplicity we consider the unemployed state as a job with a latent non-zero m value.4Profits or losses incurred during the initial learning period are sunk and the firm does not takethem into account when making a new contract offer. This means that the realization of the aggregatestate during the learning period has no effect on the contract offer.5In Appendix Section A.6 we show that the same qualitative results hold if the state in the initialperiod is low (P1 = PL).64w1(m|PH)+E(w2(m))≥ a(PH)m+[qa(PH)+(1−q)a(PL)]E(m),where w1 and w2 are the wages in period 1 and 2, respectively, and E(m) is theexpected match quality for a worker who decides to leave at the end of the learningperiod. We show in Appendix A.5.2 that this participation constraint is satisfiedfor workers who draw match quality m larger than E(m). If m is below E(m) theconstraint may be violated. If so, a separation occurs and the worker moves to adifferent employer, starting a new learning period.Contractual arrangements. After the learning period, and conditional on matchquality, the firm chooses an arrangement to maximize expected profits over the re-maining two periods. In what follows we characterize the optimal contract offeredby the firm to the workers who did not quit after the learning period. By choos-ing to remain in the match these workers commit to remain with the same firm inperiod 1. However they still have the opportunity to find a new job that will paya(P)m in the following period.At the beginning of period 1 the firm offers a contract that specifies a wagefor period 1 and a state-contingent compensation for period 2 that guarantees theworker’s continuous employment (that is, it satisfies the participation constraints).We posit that the firm can offer one of three alternative pay arrangements to theworker. The three arrangements represent very diverse allocations of cyclical riskbetween worker and firm, encompassing the extreme cases in which either the firmor the worker carry all cyclical risk. The possible pay arrangements are:1. A fixed wage contract that guarantees the worker’s participation (continuous65employment within the firm). To retain the worker under this contract thefirm must offer a fixed wage that equals the highest possible outside optionconditional on x,w(m) = a(PH)m, ∀P. (3.2)This arrangement guarantees worker retention in both periods. The firm sub-sidizes the worker in bad aggregate states and carries all the production risk.2. A wage equal to the the worker’s outside option, which we call the “spotmarket” wage. This is a rolling period-by-period arrangement that stipulatesthat the wage is changed to match the start-of-period outside option of theworker as follows,w(m) =a(PH)m if P = PHa(PL)m if P = PL.(3.3)If the wage is changed between the two periods, there is a fixed (adjustment)cost T > 0 paid by the firm.3. A performance pay arrangement that stipulates that the worker compensationis a combination of a fixed wage wˆ(m) and a fraction b 6 of the match surplusPm:w(m) =wˆ(m)+bPHm if P = PH ,wˆ(m)+bPLm if P = PL.(3.4)6We impose b≤ 1. Otherwise, the worker would be able to leverage production risk.66We assume that the firm has to pay a variable cost K(m) = κ(mmax−m)≥ 0to implement performance pay. The cost K(m) is lower when quality m ishigher, indicating that workers in better matches are easier to monitor. InAppendix A.5.3 we derive additional results under the assumption of fixedcosts of implementing performance pay contracts.73.2.1 Participation Constraints and Performance Pay ContractsTo guarantee worker retention each of these contracts must satisfy the workers’participation constraints in period 2, requiring that wage w during that period is atleast as high as the available outside option. When aggregate productivity is highthe constraint isa(PH)m≤ w(m). (3.5)Similarly, the constraint for low productivity periods isa(PL)m≤ w(m). (3.6)Both the period-by-period and the fixed wage contractual arrangements triv-ially satisfy these constraints. For performance pay contracts, however, the firm’soffered wage schedule must exhibit parameter values wˆ(m) and b such that the con-tract maximizes expected profits when either one (good times) or both (good andbad times) participation constraints bind. As in Oyer [2004], we consider thesecases separately.7As we show below, two types of performance pay contract are possible, depending on parametervalues. One type of contract entails a single binding participation constraint (SPC), the other fea-tures a double participation constraint (DPC). For SPC contracts to be implemented by the firm, oneneeds the additional requirement that κ > (1−q)[(a(PH)−a(PL))− (PH −PL)]. However, no suchrequirement is necessary for DPC contracts.67Case 1: A single binding constraint. If the retention constraint is only binding ingood times (SPC, ‘single participation constraint’) we have,E[piSPC] = maxb(1+q)(PHm− wˆ(m)−bPHm)+(1−q)(PLm− wˆ(m)−bPLm)−κ(mmax−m)s.t.: a(PH)m = wˆ(m)+bPHm(3.7)After rearranging the constraint, substituting wˆ(m) in the objective and derivingthe first order condition with respect to b, one obtains∂E[piSPC]∂b= (1−q)(PH −PL)m > 0 (3.8)Since, by assumption, match quality is not negative, the optimal contract is at acorner solution,8b = 1wˆ(m) = (a(PH)−PH)m.(3.9)Given the maintained assumption that a(PH)<PH , it follows that wˆ(m)< 0. There-fore, in the case of a single binding constraint, one can interpret the pay contract asan arrangement in which the worker effectively pays upfront to “buy” the job fromthe firm. The wage is:w(m) = (a(PH)−PH)m+Pm. (3.10)8We also posit that the worker cannot leverage production risk. That is, b is bounded from aboveat 1.68Under the SPC contract participation is guaranteed in the bad state if PH −PL ≤a(PH)− a(PL). One can show that, in this case, the “L” constraint holds (eventhough it does not necessarily bind), implying that firms are able to retain workersin both high and low productivity periods.9Case 2: Two binding constraints. If the participation constraint is binding inboth good and bad times (DPC, ‘double participation constraint’), it must be thecase thata(PH)m = wˆ(m)+bPHma(PL)m = wˆ(m)+bPLm.The solution for b is derived by subtracting the “L” constraint from the “H”constraint and rearranging, which results inb =a(PH)−a(PL)PH −PL (3.11)andwˆ(m) =[a(PH)−PH a(PH)−a(PL)PH −PL]m. (3.12)Performance Pay Contracts: DPC or SPC? The discussion above suggests thatthe set of feasible performance pay contracts crucially depends on the ratio ∆a(P)∆P ,which relates the cyclical gap in outside offers (numerator) to changes in cyclicalproductivity (denominator).9To see this, substitute the optimal contract into the “L” constraint to obtain:a(PL)m < (a(PH)−PH)m+PLm.69Specifically, if [a(PH)−(a(PL)] = [PH−PL] then the two contracts are identicaland feature b= 1, with both participation constraints binding. If [a(PH)−(a(PL)]>[PH −PL] it is feasible to have a performance pay contract entailing only one bind-ing participation constraint (SPC), where the other constraint holds but does notbind. Under this contractual arrangement the worker carries all production risk.Finally, if [a(PH)− (a(PL)]< [PH−PL], the performance pay contract must featuretwo binding participation constraints (DPC) and cyclical production risk is carriedby both worker and firm.10In what follows we show that a firm will offer performance pay contracts toworkers when match quality is sufficiently high (high m). This is true whether theratio ∆a(P)∆P is greater or less than one.3.2.2 Contract Choice and Wage CyclicalityThe behavior of wages, both cross-sectionally and over time, is intimately relatedto the type of contractual arrangement offered by the firm. Moreover, as we makeclear in the following section, match quality plays a key role in determining whichcontract is offered to workers. This ‘contractual sorting’ based on match quality hasimportant consequences for wage dynamics, as different contractual arrangementsexhibit different cyclical properties.Which Contract is Offered by the Firm?Given high aggregate productivity in period 1, we compare the expected profitsthat firms achieve (over period 1 and 2) by offering each of the three contractual10To see this note that [a(PH)−a(PL)]< [PH −PL] implies that b < 1 under a DPC contract. Notethat, as we do for SPC contracts, we do not allow for DPC contracts with b > 1, as this would implythat workers can leverage the production risk.70arrangements: fixed wage, spot, or a performance pay contract. We first considerthe case of ∆a(P)∆P < 1, in which the feasible performance pay contract is DPC;then we examine the case of ∆a(P)∆P > 1, when SPC is the feasible performance paycontract. We conduct pairwise comparisons between any two contracts and showthat a simple threshold rule, based on match quality m, determines the contractoffered by the firm. Finally, we rank these thresholds and show that performancepay contracts are consistently preferred for sufficiently high levels of match qualitym.Match-quality thresholds with DPC performance pay contracts. In what fol-lows we derive the match-quality thresholds that identify which contract is pre-ferred in pairwise comparisons. Substituting the wage functions for the three pos-sible contracts (DPC performance pay, spot, fixed wage) we can write firms’ ex-pected profits as,DPC: E[piDPC]= (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m−κ(mmax−m)SPOT: E[piSPOT]= (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m− (1−q)TFW: E[piFW]= (1+q)PHm+(1−q)PLm−2a(PH)m.By pairwise comparison of expected profits, one can characterize the thresholdconditions that describe the contractual choice of the firm. We do this in Proposi-tion (10).11Proposition 10. If ∆a(P)∆P < 1, the contract choice of the firm is described by thefollowing threshold rule.11In Appendix A.5.3 we show that a modified version of Proposition (10) holds also when K(m) =K, ∀m.711. The firm prefers a performance pay contract over a spot market contract ifm≥ κmmax−T (1−q)κ≡ m1. (3.13)2. The firm prefers a performance pay contract over a fixed wage contract ifm≥ κmmaxκ+(1−q)(a(PH)−a(PL)) ≡ m2. (3.14)3. The firm prefers a spot contract over a fixed wage contract ifm≥ Ta(PH)−a(PL) ≡ m3. (3.15)Proofs are in Appendix Section A.5.2.The firm’s contract choice outlined in Proposition 10 has a simple interpre-tation. The threshold m3 is a function of adjustment costs in period 2. Underfixed wages there are no adjustment costs, but the firm subsidizes (‘overpays’) theworker relative to a spot contract if aggregate productivity is lower in period 2. Onthe other hand, under the spot contract, lowering the wage in period 2 entails afixed cost T . This cost-benefit tradeoff varies with match quality, and is reflectedin different contract choices for different match qualities. A similar intuition ap-plies to threshold m2: a fixed wage contract features a subsidy to the worker in badtimes, but implementing a performance pay contract entails a cost K(m).12Crucially, these thresholds can be ordered, as outlined in Corollary 10.1.12We note that performance pay and spot contracts exhibit the same wages; only differences in theimplementation costs differentiate the profits that accrue to the firm from each of these contracts.72Corollary 10.1. If the adjustment cost T is sufficiently small, then m1 ≥ m2 ≥ m3and the following holds:• ∀m≥ m1, the firm offers a performance pay contract;• ∀m ∈ [m3,m1[, the firm offers a spot contract;• ∀m < m3, the firm offers a fixed wage contract.Otherwise, if T is not small enough, m3 > m2 > m1 and the contractual choice ofthe firm is:• ∀m≥ m2, the firm offers a performance pay contract;• ∀m < m2, the firm offers a fixed wage contract.These results suggest that profits grow relatively faster with match quality iffirms offer performance pay contracts. It follows that there exists a match qual-ity above which performance pay contracts deliver higher profits than other con-tracts.13 By the same logic, for sufficiently low match quality, revenues do notcover the implementation costs of performance pay and spot contracts. As a result,fixed wages become the most profitable pay arrangement in lower productivitymatches.14 Finally, whether or not spot contracts are ever implemented, dependson whether the cost of implementing the contract, T , is sufficiently low. An imme-diate implication of these findings is that matches with relatively high productivityshould adopt a performance pay contract. On the other hand, jobs with low matchquality are more likely to adopt a fixed wage arrangement. Wage cyclicality is13We posit that match quality can take values high enough for this to happen.14This result is conditional on the subsidy given to the worker in a fixed wage contract, ∆a, notbeing too big. To see this, note that if ∆a→∞, then m2→ 0 and m3→ 0, which implies fixed wagesare never implemented.73affected by the contract choice in an obvious way as spot and performance payarrangements imply pro-cyclical wages while fixed pay contracts do not. As a re-sult of contract choice, there exists a relationship between match quality and wagecyclicality.Next, we turn to the case in which ∆a(P)∆P > 1 and SPC contracts are feasible,and we show that the same qualitative conclusions can be drawn.Match-quality thresholds with SPC performance pay contracts. Substitutingthe wage functions for the three possible contracts (SPC performance pay, spot,fixed wage) we can write the firm’s expected profits as,SPC: E[piSPC]= 2(PH −a(PH))m−κ(mmax−m).SPOT: E[piSPOT]= (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m− (1−q)TFW: E[piFW]= (1+q)PHm+(1−q)PLm−2a(PH)m.Proceeding as before, we show that the firm’s contract choice follows a simplethreshold rule.Proposition 11. If ∆a(P)∆P > 1, the contract choice of the firm is described by thefollowing threshold rule.1. The firm prefers a performance pay contract over a spot market contract ifm≥ κmmax−T (1−q)κ− (1−q)[(a(PH)−a(PL))− (PH −PL)] ≡ m4. (3.16)2. The firm prefers a performance pay contract over a fixed wage contract ifm≥ κmmaxκ+(1−q)(PH −PL) ≡ m5. (3.17)743. The firm prefers a spot contract over a fixed wage contract ifm≥ Ta(PH)−a(PL) ≡ m6. (3.18)The intuition for the results in Proposition 11 also relates to the varying costsand benefits for different match-specific productivities. The threshold m6 is ex-actly the same as m3 in the DPC case and has the same interpretation. Similarly,the intuition for m5 is the same as the one we discussed for m2: a fixed wagecontract ‘overpays’ workers in bad states of the world but has no implementationcosts. In contrast, a performance pay contract entails a cost K(m) but does notsubsidize workers. Finally, performance pay is preferred to spot contracts for highenough match quality m because profits grow faster with m under performance payarrangements, which explains Corollary 11.1.Corollary 11.1. If the adjustment cost T is sufficiently small, then m4≥m5≥m6 >and the following holds:• ∀m≥ m4, the firm offers a performance pay contract;• ∀m ∈ [m6,m4[, the firm offers a spot contract;• ∀m < m6, the firm offers a fixed wage contract.Otherwise, if T is not small enough, m6 > m5 > m4 and the contractual choice ofthe firm is:• ∀m≥ m5, firms offer a performance pay contract• ∀m < m5, firms offers a fixed wage contract75Brief discussion and empirical implications. Propositions 10 and 11, and theircorollaries, suggest that high productivity matches are more likely to adopt perfor-mance pay contracts, exhibit higher pay and have more cyclical wages.Our stylized model describes the firm’s retention problem over a fictitiousthree-periods interval, while real work relationships often extend over long hori-zons. Given enough time, new information may accrue and perturb the originalarrangements, possibly leading to renegotiations and separations, about which themodel is silent. However, if the contractual sorting implied by heterogeneousmatch quality is in fact due to retention motives, one might expect that differentcontracts have different implications for job durations. We explicitly examine thishypothesis in the empirical analysis.3.3 Data and MeasurementOur model of pay highlights the relationship between match quality and contractchoice. Empirically linking contractual sorting, wage cyclicality and match qualityposes several measurement issues. To identify the effects of match-specific hetero-geneity on contractual arrangements and wage dynamics one needs to: (i) establishan empirical counterpart of the wage process and control for possible confoundingeffects; (ii) outline a procedure to approximate match quality using data; (iii) iden-tify jobs in which pay is linked to output through some form of performance-relatedarrangement.In this section we describe the key features of our empirical approach. Weproceed sequentially. First, we outline the empirical counterpart of the theoreticalwage processes. Second, we show how match quality proxies can be constructedusing information about labor market tightness. Third, we describe data sources76and highlight how theory guides the data organization. Finally, we discuss how wecan identify jobs featuring performance-related pay.3.3.1 Empirical Wage ProcessesOne can show that the empirical counterparts of the different pay arrangementsexamined above can all be nested within one general wage representation. Thiswage representation is obtained through simple log-linear approximations. We be-gin by noting that, in addition to the specific mechanism outlined in the theoreticalsection, wages obviously are affected by other individual and job characteristics.Hence, allowing for an additively separable vector of characteristics X , the follow-ing proposition holds.Proposition 12. Let workers be paid according to one of the four possible contrac-tual arrangements (DPC, SPC, FW, or Spot). Assume that: (a) Xt is a log additivecomponent to the wage that captures observable worker characteristics; (b) zi jt isan approximation error. Then the conditional expectation of the wage, under anyof the contracts, can be generally represented asE[log(wi jt)|Pt ,mi j,Xt ] = β0+β1 log(mi j)+β2 log(Pt)+β3 log(Xt)+E[zi jt ](3.19)where i identifies a worker, j identifies a job, t denotes the time period and E[zi jt ] isthe expectation of the unobserved residual implied by the approximation error. Inthe case of a fixed wage contract β2 = 0, while β2 > 0 for other contracts. Underall contracts β1 > 0.The proof is obtained by log-linearization of the various wage functions. De-tails are in Appendix A.7.77We consider a simple representation of the unobserved residual productivityzi jt . Specifically, we assume that zi jt consists of an individual fixed effect ai andan i.i.d. shock ηi jt . In our empirical specification we explicitly account for observ-able heterogeneity, for time effects and for worker fixed effects. As a result, theempirical specification for the wage processes islog(wi jt) = β0+β1log(mi j)+β2log(Pt)+β3log(Vi jt)+ zi jt , (3.20)with β2 = 0 in the case of a fixed wage contract.Following Bils [1985], and a large subsequent literature, we focus on the sen-sitivity of wages to fluctuations in aggregate unemployment to capture wage cycli-cality.The theoretical analysis suggests that match quality plays a key role for thecross-sectional distribution of wages and their cyclicality. Match quality influ-ences wages directly and through contractual sorting effects. In particular, wagesensitivity to contemporaneous aggregate conditions depends on the type of pay ar-rangement in place and, therefore, on match quality. In the next section we describehow we approximate match-specific quality.3.3.2 Measuring Match QualityThe match quality proxies are constructed following the approach of Hagedornand Manovskii [2013] and build on the idea that changes in labor market tightnesshave a direct bearing on the match quality distribution. The two proxies (respec-tively denoted as qeh and qhm) rely on the assumption that the number of offers aworker receives is positively correlated with match quality. If an employed worker78receives a job offer and accepts it, then it must be the case that match quality hasa good chance of being weakly improved. Similarly, if a worker receives a joboffer and rejects it, then current match quality is more likely to be preferable tothe alternative. Hence a worker who receives many offers has, on average, bettermatch quality, whether these offers were accepted or rejected. The basic empiricalchallenge is how to measure the number of offers a worker receives. The rea-soning above suggests that labor market tightness, measured before and during aparticular job, conveys information about the number of offers. As an exampleconsider a worker i employed in the same job between periods Tbegin and Tend , withTend > Tbegin. If the sum of labor market tightness between Tbegin and Tend is high,and we observe i staying at her job, then i received and rejected relatively manyjob offers. Therefore i’s job must have high match quality. Following this logic,the variable qhmi, j is defined asqhm =Tend∑t=Tbegin(VtUt), (3.21)where Vt is an index of vacancies and Ut is the unemployment rate in period t.The same line of reasoning implies that match quality in the current job is alsosensitive to market tightness during employment periods preceding the current job.In the example above suppose that worker i had a different job prior to the currentone. Moreover, while working on the previous job the labor market was tight andshe received many offers. The fact that she received many offers before acceptingthe current job suggests that the quality of the current match is likely to be relativelyhigh. Hence past labor market tightness conveys information about current matchquality. The variable qehi, j is meant to capture past labor market conditions and is79defined as,qeh =Tbegin∑t=T1(VtUt), (3.22)where T1 < Tbegin denotes the first period of the employment cycle, that is, the firstperiod of work after involuntary unemployment.153.3.3 Data on Work HistoriesThe data source for wages is the National Longitudinal Survey of Youth (NLSY79).We construct the (weekly) job history for each worker and identify an observationas the wage of a worker at the current job.16 We construct the current unemploy-ment rate using the seasonally adjusted unemployment series from the Current Pop-ulation Survey (CPS). We use the Composite Help Wanted Index constructed byBarnichon [2010] as a measure of vacancies. Details about data are in AppendixA.5.1. All of the analysis focuses on men between 25 to 55 years old.Key to the analysis is the concept of employment cycles. An employment cycleis defined as a continuous spell of employment, possibly entailing a sequence ofjobs and employers. The cycle begins in the period when the worker transitionsfrom non-employment to employment, and ends when the worker transitions backto involuntary non-employment.17To measure individual employment cycles, and job spells within each cycle, wefollow Wolpin [1992], Barlevy [2008], and Hagedorn and Manovskii [2013]. At15The interval between T1 and Tend must not be interrupted by involuntary unemployment spells,as this would make it hard to argue for sequential on-the-job renegotiations.16For each week we define the ‘main job’ as the one with the highest mode of reported hoursworked. Past research focuses on male workers. For comparability we follow this convention.17As in Barlevy [2008] and Hagedorn and Manovskii [2013] a separation is considered voluntaryif (i) the worker reports a quit, rather than a layoff; and (ii) the interval between the end of theprevious job and the beginning of the next is shorter than 8 weeks. Employment cycles may includeshort periods of non-employment.80each interview date the NLSY provides a complete description of jobs held sincethe last interview, including start and stop dates (week), wage, hours worked, andoccupation. In addition one can link employers across interviews and identify a jobas a worker’s spell with a given employer.In the NLSY79 the information related to a specific job is only recorded onceper interview. Therefore wage changes within a job are recorded only if an individ-ual works at the same job for a period covered by two or more interviews, implyingthat within-job wage variation is identified using jobs that extend over at least twoNLSY interview dates. If a job appeared for the first time in the year T interview,and again in the year T + 1 interview, then this job counts as two observationswithin the same employment cycle. Each observation is a wage-job pair. The wagerefers to a job that was active at any time between the current and the previous in-terview date. Thus we view an observation (a wage-job pair) as the wage prevailingover the period between two successive interviews while employed at a particularjob, or in any subset of that period during which the job was active.For illustration consider the example in Figure 3.1. A worker is interviewedat date T − 2, begins to work for a specific employer between T − 2 and T − 1,is interviewed again at T − 1, T , and T + 1, but eventually stops working for thisemployer at some point between T and T + 1. Given this sequence of events, weuse the wage wT−1, recorded during the first interview, as the wage applying to theperiod between the start of the job and T − 1. Similarly, we use the wage wT forthe period between T −1 and T , and the wage wT+1 for the period between T andthe end of the job.Partitioning the data into employment cycles and job spells allows us to con-struct the match quality proxies described in Section 3.3.2. We use data on aggre-81Figure 3.1: Employment Cycles: an Example.Non-interviewJob StartInterviewwT−1Observation T −1InterviewwTObservation TNon-InterviewJob EndObservation T +1InterviewwT+1UT−1 UT UT+1qehqhmgate vacancies and unemployment to calculate tightness ratios VtUt and define: (i) qehas the sum of tightness ratios from the beginning of the employment cycle to theperiod preceding the start of the current job; (ii) qhm as the sum of market tightnessratios during a job spell. The latter captures past, current and future tightness overthe current job spell and reflects the expected match quality of that particular job.Next, we assign to each observation a contemporaneous unemployment rate,measured as the average unemployment recorded over the period in which a job isactive between consecutive interview dates. Figure 3.1 illustrates how match qual-ity proxies and unemployment rates are assigned to different observations wT−1,wT and wT+1: qeh is the sum of labor market tightness from the start of the em-ployment cycle until the start of the current job; qhm is the sum of labor markettightness from the start to the end of the current job. A different contemporaneousunemployment rate applies to each relevant time interval.823.3.4 Performance Pay in the NLSY79The NLSY79 reports partial information about performance pay for the years 1988to 1990, 1996, 1998 and 2000. For years 1988− 1990 individuals were askedwhether, in their most current job, earnings were partly based on performance.For years 1996,1998,2000, individuals were asked for each of their jobs if earn-ings featured any of the following types of compensation: piece rate, commission,bonuses, stock options and/or tips. Therefore in 1996,1998,2000, for each job-individual pair we generate a binary variable indicating if that particular type ofcompensation was used in determining the pay received for that job. A perfor-mance pay observation is then a job-year-individual triplet for which one of fol-lowing conditions is satisfied:• The year is 1988,1989 or 1990, and the individual reports being paid basedon performance;• The year is 1996,1998 or 2000 and the individual reports having earningsbased on at least one among tips, commission, bonuses or piece rate.• It is a job-year-individual triplet pertaining to a job/individual pair that satis-fies one of the above two conditions for at least one of the interviews. Thisimposes the restriction that the performance pay status is constant within ajob, adding observations for the years in which the performance pay vari-ables are not available.3.4 Empirical ResultsIn this section we report our main empirical findings. Specifically, we presentresults documenting that (i) a significant relationship exists between match qual-83ity and contractual arrangements; (ii) contractual arrangements play a key role indetermining wage cyclicality; (iii) employment durations vary with contractual ar-rangements (and match quality) as predicted by theory; (iv) occupations that ex-hibit higher average match quality tend to adopt performance-pay more frequently;wages in such occupations appear to be more cyclical, as predicted by our model.Finally, we discuss some extensions and robustness checks.3.4.1 Match Quality and Performance Pay AdoptionAn immediate implication of our theoretical analysis is that firms offer differentpay arrangements depending on match quality. Corollaries (10.1) and (11.1)) implythat high quality matches should exhibit a higher adoption of performance-relatedpay schemes.Given the information available in our sample, we can directly estimate theempirical relationship linking each job’s PPJ status to its match quality proxies.We do this by using a set of Logit models. The unit of observation for this analysisis the job-worker pair, with the dependent variable being a binary indicator forwhether the job uses any performance related compensation and the key right-hand side variables being measures of match quality. We estimate a fixed effectspecification to control for worker unobserved heterogeneity and restrict the sampleto men between ages 25 and 55.18 We also control for a variety of observable job-worker characteristics.19In Table 3.1 we report the results of this analysis for three alternative specifica-18The sampling restrictions implicit in the fixed-effect Logit estimator imply that our sample onlyincludes workers who are observed at least once in both PPJ and non-PPJ, at different points in time.19We include controls for year, geographic and SMSA region, job tenure with current employer,work experience, industry, marital status, education, age (maximum in the employment spell), unionstatus.84tions in which we control for each measure of match quality, both separately andtogether.Table 3.1: Performance Pay and Match Quality: Fixed Effects LogitsSpecificationVariables (1) (2) (3)log(qeh) 18.4*** - 19.9***[7.68] - [7.73]log(qhm) - 52.9*** 54.6***- [1.84] [1.85]Observations 2,028 2,058 2,028Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of markettightnessNote b. Estimated coefficients and associated standard errors are multiplied by 100. All standarderrors are clustered by observation start-date and end-date. Results are robust to clusteringby individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes male workers between age 25 and 55. We include controls for year,job tenure with current employer, work experience, geographic and SMSA region, industry,marital status, education, age (maximum in the employment spell), union status.The results clearly indicate the presence of a significant, and sizeable, relation-ship between match quality and performance pay adoption. Both proxies of matchquality are highly significant, and the magnitudes of their effects remain unchangedwhen they are both included.To gauge the magnitude of the match quality effects we compute the change inthe probability of being PPJ implied by a one standard deviation increase in matchquality. To this purpose, we generate a random subsample of worker-job pairs suchthat each worker is sampled only once, and use it to measure the baseline proba-bility that an individual-job pair exhibits performance pay. This exercise returnsan average probability of 38.7%. Then, we perturb each individual match qualityand make it larger by one standard deviation. This results in an average likelihood85of PPJ equal to 54.6%. Hence, our results suggest that a one-standard-deviationchange in match quality is associated to an increase of over 40% in the probabilityof being in a performance pay job. Replicating this analysis for the median proba-bility of PPJ suggests an increase from a baseline value of 26.4% to 44.5%. Theseare large effects, and clearly indicate that match quality and performance pay arestrongly associated. We confirm the robustness of this association in Section 3.4.5.As we discuss below, this strong association between match quality and con-tractual choice has important implications for wage cyclicality and job durations.3.4.2 Match Quality and Wage CyclicalityA second, crucial implication of our theoretical analysis is that selection into dif-ferent contractual arrangements has an indirect effect on the cyclicality of wages.As mentioned above, we follow an extensive literature and measure the cyclicalityof wages with respect to labor market conditions by gauging wage responses toaggregate unemployment.We use the baseline (log-linearized) approximation derived in Section 3.3.1 toestimate how the sensitivity of log wages depends on the current unemploymentrate, and on both match quality proxies. The unit of observation for this analysisis the wage observed for a job-worker pair at a point in time. We use a fixed effectspecification and, as before, also control for a full set of observable job and workercharacteristics.20 The model suggests that there should be a direct effect of matchquality proxies on wages. Moreover, as shown above, match quality also has astrong, indirect effect on wages by determining the contractual arrangement in thejob-worker relationship. This contractual selection effect has a variety of testable20We control for all variables used in the linear probability model. For workers we use currentage, rather than maximum age, to allow for within job age profiles.86implications. Namely, we use our general empirical specification (equation 3.20,derived in Section 3.3.1) to test the following theoretical predictions:(i) Do performance pay jobs (PPJ) exhibit positive cyclicality?(ii) Is any cyclicality detected among non-PPJ?21(iii) Does match-quality have a direct effect on wages after controlling for PPJstatus?We begin by documenting the properties of the pooled sample of jobs (bothPPJ and non-PPJ). Table (3.2) reports results from the analysis of such pooleddata. The first column reports results for a specification in which wages depend onunemployment, without controlling for match quality (this is the kind of regressionoriginally suggested by Bils, 1985). In the second column we add controls formatch quality as well as cyclical responses to the unemployment rate. In the thirdcolumn we extend the model by allowing for different cyclical responses dependingon PPJ status.Results suggest that match quality has a direct effect (level shift) on wages, aspredicted by the model and illustrated in Section 3.3.1. The sensitivity of wages tocyclical unemployment is however similar with or without quality controls, with agradient of roughly 1.6%. Yet, our results also indicate that all the cyclical sensitiv-ity of wages is due to PPJ status: column 3 shows that only wages in performance-pay jobs exhibit cyclical responses to the unemployment rate. Moreover, theseresponses are much stronger than in the pooled sample. A 1% increase in the un-employment rate is associated to a 3% decrease in average wages for PPJ, and tono significant wage change in non-PPJ.21Such cyclicality could occur if the cost T of implementing spot contracts is sufficiently smallthat firms offer them to a large enough share of workers.87Table 3.2: Pooled wage regressionDependent Variable: Log WageVariables (1) (2) (3)(Bils specification) (add match quality) (add match quality)U -0.0164*** -0.0167*** -0.004[0.0043] [0.0042] [0.005]log(qeh) - 7.59*** 7.47***- [0.66] [0.66]log(qhm) - 6.81*** 6.70***- [0.66] [0.68]U ·PPJ - - -0.0298***- - [0.0064]Observations 17.995 17,434 17,434R-squared 0.642 0.646 0.646Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of markettightness. The explanatory variable U ·PPJ is the interaction between current unemploymentrate and an indicator function taking value equal to one if the job includes performance-related compensation.Note b. Estimated coefficients for lnqeh and lnqhm, and associated standard errors, are multiplied by100. All standard errors are clustered by observation start-date and end-date. Results arerobust to clustering by individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes male workers between age 25 and 55. We include controls for year,job tenure with current employer, work experience, geographic and SMSA region, industry,marital status, education, age and union status.Taken together, these results are consistent with the view that match qualityhas a strong indirect effect on pay by selecting workers into different contractualarrangements, indirectly affecting wage cyclicality. To explicitly test this hypothe-sis, we perform the same analysis separately on PPJ and non-PPJ jobs. This allowsto flexibly control for observables in the two groups. Table (3.3) reports estimationresults for different PPJ status.The findings confirm that strong and significant wage cyclicality is present injobs where performance-related pay is used. In fact, the magnitudes of the cyclicalresponse of PPJ wages is almost identical to the one estimated from the pooled88Table 3.3: Wage regressions: PPJ vs non-PPJ.(1) (2) (3) (4)Variables PPJ = 1 PPJ = 0 PPJ = 1 PPJ = 0(Bils specification) (Bils specification) (add match quality) (add match quality)U -0.0283*** -0.0089 -0.0282*** -0.0096[0.0056] [0.0063] [0.0056] [0.0064]lnqeh - - 9.88*** 6.12***[1.43] [0.974]lnqhm - - 8.79*** 5.94***[1.50] [0.892]Observations 7,280 10,715 7,065 10,369R-squared 0.719 0.613 0.723 0.614Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of labourmarket tightnessNote b. Estimated coefficients for lnqeh and lnqhm, and associated standard errors, are multiplied by100 for lnqx. All standard errors are clustered by observation start-date and end-date. Resultsare robust to clustering by individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes male workers between age 25 and 55. We include controls for year,geographic and SMSA region, industry, marital status, education, age and union status.sample (-.0282 vs -0.0298 in column 3 of Table 3.2). As before, wages seemnot to respond to cyclical unemployment in jobs with no performance related pay.When we test for the significance of the difference between the cyclical gradientof PPJ and non-PPJ we reject the null hypothesis of equal coefficients at the 5%confidence level.These results document that match quality has a direct effect on wages evenafter we control for contractual arrangements (PPJ status). The match quality effectis positive as expected in all cases. Hence, higher match quality is associated tohigher wages and, on average, to stronger cyclical sensitivity.893.4.3 Evidence from Occupation GroupsAs highlighted in our discussion of match quality, we expect tighter labour mar-kets to be associated to a higher frequency of job offers to workers, which in turntranslates into higher average match quality.This line of reasoning has an interesting implication: the adoption of perfor-mance pay should be more widespread in occupations which are in high demand.The reason for this is that retention considerations (participation constraints) in-duce firms to use variable compensation as a way to keep workers when they aremost in demand. This argument suggests that employee profit-sharing or otherforms of performance-related pay should be relatively more attractive in occupa-tions which are in strong demand. This is clearly the case of cognitive and non-routine jobs over the past few decades, as documented for example by Autor andDorn [2013] and Cortes et al. [2015].In this section we document that occupations that are in higher demand exhibitlarger frequency of performance pay jobs and better match quality.Table 3.4 reports two important dimensions of heterogeneity across occupationgroups: (i) the relative frequency of PPJ; (ii) the relative share of above-medianmatch qualities. Cognitive occupations have a considerably higher occurrence ofboth PPJ and of above-median match quality, when compared to manual occupa-tions. A similar, but less marked difference, is present when comparing non-routineand routine occupations.These differences are highly significant and lend direct support to the viewthat, especially in cognitive occupations, stronger demand is associated to rela-tively higher match qualities and more frequent recourse to performance pay. Of90Table 3.4: Occupation heterogeneity: share of jobs with (i) above medianmatch quality and (ii) performance pay, by occupation group.Occupation GroupsCOG MAN NR RShare PPJ 40.7% 23.91% 33.15% 29.21%(49.13%) (42.66%) (47.09%) (45.48%)qeh above median 54.54% 46.82% 51.93% 48.67%(49.8%) (49.9%) (50%) (50%)qhm above median 57.67% 43.57% 55.41% 45.21%(49.42%) (49.59%) (49.72%) (49.78%)Observations 2,433 3,475 2,413 3,495Note a. Top panel: share of jobs with performance pay arrangements (Share PPJ) for coarse occu-pation groups: cognitive vs manual jobs (COG vs MAN); routine vs non-routine jobs (R vsNR). Standard deviations in parentheses (also as shares).Note b. Bottom panel: share of jobs with match quality above the unconditional median for coarseoccupation groups: cognitive vs manual jobs (COG vs MAN); routine vs non-routine jobs (Rvs NR). First line based on qeh match quality proxy; second line based on qhm match qualityproxy.course, contractual sorting across occupation might have direct effects on the cycli-cality of wages in different occupations, an implication that we investigate in thenext section.Wage Cyclicality across OccupationsOur theory suggests that compensation arrangements are key for the sensitivity ofwages to current unemployment. For this reason we re-estimate the general wagespecification (equation 3.20) for different occupation groups. To retain reasonablylarge, and comparable, sample sizes we focus on broad occupation categories (cog-nitive vs manual jobs; non-routine vs routine jobs).Columns (1) and (2) in Table 3.5 report results obtained for, respectively, thesamples of cognitive (Cog) and manual (Man) occupations. While we detect pos-itive, strong and significant responses of wages to current unemployment in cog-91Table 3.5: Wage Regressions: Cyclicality by Occupation Group.Dependent Variable: Log Wage(1) (2) (3) (4)Variables COG MAN NR RU -0.0245** -0.0041 -0.0204* -0.0098[0.0110] [0.0059] [0.0118] [0.0066]lnqeh 5.43*** 6.51*** 4.49*** 5.57***[1.34] [1.0] [1.50] [0.943]lnqhm 6.68*** 8.16*** 7.44*** 6.60***[1.23] [0.842] [1.34] [0.860]Observations 7,495 6,123 6,978 6,640R-squared 0.611 0.705 0.650 0.709Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of labourmarket tightnessNote b. Estimated coefficients and associated standard errors are multiplied by 100 for lnqx. Allstandard errors are clustered by observation start-date and end-date. Results are robust toclustering by individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes male workers between age 25 and 55. We include controls for year,geographic and SMSA region, industry, marital status, education, age and union status.nitive occupations, no significant effect can be detected for manual jobs. Columns(3) and (4) in Table 3.5 report results of the same regressions for an alternativeoccupation grouping in which jobs are split between non-routine (NR) and routineoccupations (R). For non-routine jobs we find weaker evidence (at the 10% confi-dence level) of wage cyclicality. Results for routine jobs indicate that current labormarket conditions have no detectable effect on wages.Taking stock of all these results, we conclude that there are visible discrepan-cies in the wage-unemployment relationship across occupation groups. In manualand routine jobs the current labor market conditions (as captured by the currentunemployment rate) have no gradient on wages. However we find evidence thatwages in cognitive occupations are strongly cyclical, while non-routine jobs exhibita somewhat weaker and less significant cyclicality. To the extent that match quality92is higher, and performance pay more widespread, among cognitive and non-routineoccupations, these results offer further evidence that contractual sorting may havean important role in determining the cyclical behavior of wages.3.4.4 Performance Pay and Job DurationsOur model highlights the role of worker retention for the adoption of performancepay. However, given its stylized nature, it has no direct implications for the du-ration of jobs, as all pay arrangements satisfy the participation constraints whena contract is offered. Nonetheless, if the retention motive is, in fact, one of themain reasons for introducing performance-related pay, one might suppose that arelationship exists between PPJ and job durations. We examine this possibilityby checking whether: (i) job durations are higher in PPJ than in non-PPJ; (ii) jobdurations are higher in occupations in higher demand.These relationships are fairly easy to test using job histories from the NLSY79,as we can construct the duration of each worker’s tenure with a given employer. InTable (3.6) we report the mean and standard deviation of job durations for differentgroups in our NLSY79 sample. We find that all duration differences are well aboveone year (five quarters or more).22 All differences (PPJ vs. non PPJ, cognitive vs.manual, routine vs. non-routine) are extremely significant at levels well below 1%.These findings confirm that PPJ jobs, or occupations in higher demand (inwhich PPJ is more prevalent), exhibit higher job durations. Hence they providedirect evidence that the adoption of alternative contractual arrangements is closelylinked to retention outcomes.22Durations in Table (3.6) refer to a sample of workers with relatively strong labor market attach-ment and are higher than durations for the overall population.93Table 3.6: Summary statistics of job durations in different occupation groups.Mean S.D. ObservationsPPJ=1 26.4 27.7 2,738PPJ=0 18.4 23.3 5,823COG 22.8 24.3 2,492MAN 17.4 21.8 3,570NR 22.3 24.3 2,460R 17.8 21.9 3,602Job durations are measured in quarters. Cog = cognitive, MAN = manual, NR = non-routine,R = routine. Unit of observation is a job/year pair.3.4.5 Extensions and RobustnessIn what follows we replicate the analysis for some alternative specifications togauge the robustness of our findings. First, we verify that the key predictions ofthe model, and baseline empirical results, are robust to the inclusion of workingwomen in our samples. Second, we estimate a simple linear probability modellinking PPJ status to match quality proxies, and show that a positive relationshipcontinues to hold. Third, we document that the main result about wage cyclicalityremains intact even when we use GDP variation, rather than unemployment, toproxy for cyclical conditions. Finally, we split workers into different educationgroups to assess whether the cyclicality of wages across education groups lines upwith the relative frequency of PPJ across these groups.Extending the sample to include women. Our baseline results are based on asample of male workers. This restriction was introduced to facilitate comparisonsto previous work on the cyclicality of wages. In what follows we extend the sampleby adding women. We maintain all the sampling restrictions described in Section3.3.3 and Appendix A.5.1, which guarantee a sample with fairly strong labor mar-ket attachment.94We begin by replicating the Logit analysis linking PPJ status to match qualityproxies. Table (3.7) shows that also in the expanded sample there exists a strong,positive and significant relationship between probability of being in a performancepay job and match quality. Both men and women exhibit an increased likelihoodof performance-related pay when match quality is higher. Magnitudes are broadlycomparable to the ones estimated for the sample on male workers and reported inTable (3.1).Table 3.7: Performance Pay and Match Quality: Fixed Effects Logits (menand women)SpecificationVariables (1) (2) (3)log(qeh) 14.6*** - 15.7***[5.55] - [5.59]log(qhm) - 67.3*** 66.0***- [1.36] [1.37]Observations 3,635 3,691 3,635Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of markettightnessNote b. Estimated coefficients and associated standard errors are multiplied by 100. All standarderrors are clustered by observation start-date and end-date. Results are robust to clusteringby individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes female and male workers between age 25 and 55. We include controlsfor year, geographic and SMSA region, industry, marital status, education, age and unionstatus.95Next, having verified the significance of this positive relationship, we moveon to replicate the wage cyclicality analysis presented in Tables (3.2-3.3) usingthe extended sample. Table (3.8) reports the regression results for a fixed effectspecification based on the pooled sample of all jobs, whether PPJ or not. Then,Table (3.9) shows the estimation results when the estimator is run separately inPPJ and non-PPJ jobs.96Table 3.8: Pooled wage regression (men and women)Dependent Variable: Log WageVariables (1) (2) (3)(Bils specification) (add match quality) (add match quality)U -0.0120*** -0.0121*** -0.0026[0.0045] [0.0044] [0.0051]log(qeh) - 6.15*** 6.06***- [0.56] [0.509]log(qhm) - 6.62*** 6.44***- [0.47] [0.483]U ·PPJ - - -0.0298***- - [0.0064]Observations 34,050 33,043 33,043R-squared 0.625 0.627 0.627Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of markettightness. The explanatory variable U ·PPJ is the interaction between current unemploymentrate and an indicator function taking value equal to one if the job includes performance-related compensation.Note b. Estimated coefficients for lnqeh and lnqhm, and associated standard errors, are multiplied by100. All standard errors are clustered by observation start-date and end-date. Results arerobust to clustering by individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes female and male workers between age 25 and 55. We include controlsfor year, job tenure with current employer, work experience, geographic and SMSA region,industry, marital status, education, age and union status.While cyclicality is slightly less pronounced, all these robustness checks con-97firm the baseline findings. The cyclical responses of wages in PPJ are highly sig-nificant, whether we pool all observations or split them by PPJ status. In contrast,no evidence of cyclicality is detected for non-PPJ. These findings provide furthersupport to the theoretical model’s predictions.Table 3.9: Wage regressions: PPJ vs non-PPJ (men and women)(1) (2) (3) (4)Variables PPJ = 1 PPJ = 0 PPJ = 1 PPJ = 0(Bils specification) (Bils specification) (add match quality) (add match quality)U -0.0187*** -0.0093 -0.0201*** -0.0092[0.0044] [0.0065] [0.0043] [0.0066]lnqeh - - 8.82*** 4.54***[1.18] [0.734]lnqhm - - 9.04*** 5.47***[1.25] [0.59]Observations 12,002 22,048 11,588 21,455R-squared 0.72 0.593 0.723 0.592Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of labourmarket tightnessNote b. Estimated coefficients for lnqeh and lnqhm, and associated standard errors, are multiplied by100 for lnqx. All standard errors are clustered by observation start-date and end-date. Resultsare robust to clustering by individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes female and male workers between age 25 and 55. We include controlsfor year, geographic and SMSA region, industry, marital status, education, age and unionstatus.98Performance pay and match quality: a linear probability model. The linearprobability specification provides a simple and relatively unrestrcited test of thestatistical relationship between PPJ and match quality proxies. As for the Logitanalysis, we estimate a fixed effect specification to control for additively separableheterogeneity and control for a variety of observable characteristics.The findings confirm that match quality and PPJ are positively and significantlylinked. A ten percent increase in the qeh match quality proxy is associated to anaverage thirty percent increase in the prevalence of performance-related pay. Theeffect is even stronger for the qhm measure of match quality: in this case a tenpercent increase in match quality is associated to a sixty percent change in theprevalence of performance pay. Interestingly, including both measures of matchquality in the right-hand side of the linear probability model does not change theirgradient or significance, suggesting that both measures capture relevant and inde-pendent aspects of match quality. When both measures are included, a ten percent-age points change in match quality is associated to a doubling of the probabilitythat performance pay is adopted.99Table 3.10: Performance Pay and Match Quality: Linear Probability Regres-sionsDependent Variable: Performance Pay IndicatorVariables (1) (2) (3)log(qeh) 2.89** - 3.09***[1.13] - [1.13]log(qhm) - 6.00*** 6.33***- [2.04] [2.03]Observations 4,704 4,810 4,704R-squared 0.630 0.632 0.631Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of markettightnessNote b. Estimated coefficients and associated standard errors are multiplied by 100. All standarderrors are clustered by observation start-date and end-date. Results are robust to clusteringby individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes male workers between age 25 and 55. We include controls for year,job tenure with current employer, work experience, geographic and SMSA region, industry,marital status, education, age (maximum in the employment spell), union status.Using GDP to gauge cyclicality. In our baseline specification we follow the litera-ture and estimate the cyclical responsiveness of wages to unemployment. Here weverify the robustness of our results to using GDP as an alternative measure of cycli-cality. Specifically, we approximate cyclical fluctuations using the log deviationsof quarterly GDP from its linear trend.Our findings suggest that the key results about wage cyclicality and performance-100related pay remain intact. Column (1) of Table (3.11) shows that the GDP gradientis positive and significant only when interacted with the PPJ dummy, indicatingthat only wages for PPJ=1 exhibit cyclical fluctuations. In columns (2) and (3) wereplicate the analysis separately for PPJ = 1 and PPJ = 0. We find that only per-formance pay jobs exhibit cyclical responses to GDP fluctuations, just as we didwhen using unemployment rate to approximate for cyclical labor market condi-tions. A 1% upward deviation of GDP from trend is associated to a 1.3% increasein wages.2323The magnitude of the cyclical wage responses in performance-pay jobs is in fact comparable tothe one estimated using the unemployment rate. Assuming that an extra 1% of GDP is associatedwith a decline in the aggregate unemployment rate of between 0.3% and 0.5%, a back of the envelopecalculation (and our estimates in Table 3.3) suggest that a 1% deviation of GDP from trend shouldbe associated to a wage change between 0.85% and 1.4%.101Table 3.11: Wage regressions using GDP as a cyclical proxy.Dependent Variable: Log Wage(1) (2) (3)Variables All PPJ = 1 PPJ = 0GDP 0.158 1.33*** -0.00514[0.253] [0.279] [0.298]GDP ·PPJ 0.797** - -[0.348] - -log(qeh) 6.61** 8.67*** 5.90***[0.678] [1.50] [0.893]log(qhm) 7.53*** 9.81*** 6.16***[0.667] [1.43] [0.972]Observations 17,434 7,065 10,369R-squared 0.646 0.723 0.614Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of markettightnessNote b. Estimated coefficients and associated standard errors are multiplied by 100. All standarderrors are clustered by observation start-date and end-date. Results are robust to clusteringby individual. Significance: *** 1%, ** 5%, * 10%.Note c. The sample includes male workers between age 25 and 55. We include controls for year,job tenure with current employer, work experience, geographic and SMSA region, industry,marital status, education, age (maximum in the employment spell), union status.Evidence from Education Groups. Next, we split workers into three groups(high school dropouts, high school graduates including those with some college,102and college graduates) and document significant differences in the prevalence ofperformance pay across different education groups. As shown in Table (3.12) theprevalence of performance-related pay is higher among more educated workers.Table 3.12: Proportion of performance pay jobs (PPJ) by education group.COL HSG HSDShare PPJ 43.56% 30.66% 25.04%(49.6%) (46.11%) (43.33%)qeh above median 39.43% 35.46% 31.28%(48.88%) (47.85%) (46.37%)qhm above median 41.47% 34.24% 30.07%(49.27%) (47.46%) (45.86%)Observations 2,011 3,832 2,564Note a. Top panel: share of jobs with performance pay arrangements (Share PPJ) for coarse educationgroups: college versus high school graduates versus high school dropouts (COL vs HSG vsHSD). Standard deviations in parentheses (also as shares).Note b. Bottom panel: share of jobs with match quality above the unconditional median for coarseeducation groups: college versus high school graduates versus high school dropouts (COL vsHSG vs HSD). First line based on qeh match quality proxy; second line based on qhm matchquality proxy.103Table 3.13: Wage Regressions: Cyclicality by Education Group.Dependent Variable: Log Wage(1) (2) (3)Variables HSD HSG CGU 0.001 -0.0084 -0.0266***[0.0125] [0.0055] [0.0103]lnqeh 5.55*** 7.01*** 6.57***[1.74] [0.792] [1.34]lnqhm 8.88*** 6.75*** 5.84***[1.91] [0.80] [1.25]Observations 1,884 9,367 6,183R-squared 0.666 0.652 0.572Note a. The notation lnqx, with x = {hm,eh}, denotes the natural logarithm of the sum of labourmarket tightnessNote b. Estimated coefficients and associated standard errors are multiplied by 100 for lnqx. Allstandard errors are clustered by observation start-date and end-date. Results are robust toclustering by individual. Significance: *** 1%, ** 5%, * 10%.Note c. We exclude women and individuals with less than 25 years old.When we re-estimate our wage specification for different education groups,results (in Table 3.13) suggest that patterns by education mirror those found foroccupations. While wages of workers with no college degrees appear to be in-sensitive to aggregate labor market fluctuations, those for college grads respondstrongly and significantly. In fact, both the sign and magnitude of the responses forcollege-graduates are similar to those estimated for workers in cognitive occupa-tions or in performance pay jobs.1043.5 ConclusionsHeterogeneity in match-specific productivity has been the object of much attentionin recent theoretical and applied studies of labor markets. This chapter investigatesthe implications of match quality heterogeneity for the choice of pay arrangements,and examines how differences in these arrangements influence wage dynamics andworkers’ retention.Several interesting and empirically relevant implications become apparent whenone explicitly considers the heterogeneity of contractual arrangements. Our theo-retical and empirical results clearly point towards a strong association betweenmatch-specific productivity, pay arrangements, and wage cyclicality. We provideevidence that employers tend to adopt performance-based pay when match qualityis higher. In turn, this is associated to better retention and longer job durations.We also find that this type of contractual sorting has implications for wagecyclicality: wages in jobs with higher match quality exhibit significant and sizeableresponses to aggregate cyclical conditions whereas lower match quality jobs exhibitno such cyclicality.These findings have implications for the behavior of wages across occupations.Retention considerations should induce firms to use variable compensation as away to retain workers whenever they are most in demand. Hence, employee profit-sharing (or other forms of performance-related pay) should be relatively more at-tractive in occupations which are in high demand. We are able to document thatjobs in cognitive occupations exhibit strong wage cyclicality and longer durations,while routine and non-cognitive jobs do not. These features are consistent withbetter average match quality and higher prevalence of performance pay jobs, ob-105servations that we are able to confirm using micro data.106ConclusionIn this thesis, I have studied the sources and consequences of heterogeneity in firmsoutcomes.In Chapter 1, I study the differences in firm outcomes between firms created byunemployed, versus employed, individuals. I start by developing a general equi-librium model of entrepreneurship in which both unemployed and wage workersmake the endogenous decision to start or not a firm. With this rich yet tractableframework, I derive key predictions which I test in the data. In particular, I usefirm closures to identify random assingment of an individual to unemployment.I find unemployment doubles the probability of an individual to start a firm, andconditional on starting, the individual hires 26% fewer workers and is 30% morelikely to exit firm ownership. These patterns are completely consistent with thepredictions of the model.This is the first general equilibrium model with both unemployed and wageworkers making the endogenous decision to start a firm or not. This is also thefirst research to evaluate the casual effect of unemployment on firm ownershipdecisions and firm performance. This is possible thanks to the novel data beingused. It is composed of the entire universe of tax filers linked to privately owned105incorporated firms in Canada. It improves on employer-employee datasets by alsohaving the link between each firm and their corresponding owner.With an extension of the theory to a multi sector environment I derive the addi-tional implication that higher wages decrease the entry rate into entrepreneurshipof wage workers by more than that of unemployed. Using city wage variation and aBartik style IV strategy for wages, I show that a 1% drop in wages increases by 3.2percentage points the entry rate into entrepreneurship for wage workers and has noimpact for laid off individuals. Such heterogeneity in entry into entrepreneurshiphas never been documented before.Finally, I use a numerical version of my general equilibrium model, disci-plined by the data, to evaluate the impact of policies that subsidize entrepreneurshipamong the unemployed. I find that the effect of these policies is to decrease averagefirm productivity and reallocate ressources to low productivity firms.In the second chapter, we analyze an extension of the standard search andmatching framework in which individuals make the endogenous decision to ei-ther look for a business project or a job. I find that the direction of wage responsesto aggregate shocks becomes dependant on which party has the most bargainingpower (the entrepreneur or the worker). 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Journal of LaborEconomics, 30(1):1–53, 2012. → page 179113Appendix ASupporting MaterialsA.1 Appendix to Chapter 1A.1.1 Proofs Benchmark ModelFor proofs and characterization of model with multiple sectors see SupplementalAppendix to the paper.Proof of Proposition 1.We know that J(z) is equal to U, ∀z≤ zˆ. We need to find the value of J(z) forz≥ zˆ.DefineB≡ (1−α)(αw)α1−α (A.1)Guess that J(z) will be of the form Cez1−α +Ge−az for z ≥ zˆ. Imposing theJ′(zˆ) = 0 condition114aGe−azˆi =C(11−α )e11−α zˆi (A.2)G =Ca(1−α)ezˆi( 11−α+a) (A.3)ThenrCez1−α +rGe−az =Bez1−α +µ1−αCez1−α −µGae−az+ σ22(11−α )2Cez1−α +σ22Ga2e−az(A.4)Then solving gives C defined byrC = B+µ1−αC+σ22(11−α )2C (A.5)C =Br− µ1−α − σ221(1−α)2(A.6)and a defined by (condition to guarantee rG =−µGa+ σ22 Ga2)r =−µa+ σ22a2 (A.7)115Choosing the positive root1a =µ+√µ2+2rσ2σ2> 0 (A.11)Which then impliesJ(z) =C(ez1−α +1a(1−α)e−a(z−zˆ)+ zˆ1−α ) (A.12)J(z) =Br− µ1−α − σ22 (11−α )2(ez1−α +1(1−α)e−a(z−zˆ)+θ zˆ) (A.13)Proof of Proposition 2.Solving generic KFE. The solution below is the same for both types of busi-ness owners (i.e., i = u,w)Let zˆ be the point at which firms exit and zi the point in which firms enter,with zi > zˆ. Let Λ(z) denote the endogenous pdf and M the measure of entrants.For type u (i = u), M is equal to ψue−β zu and for type w (i = w) M is equal toψ(1−u−η)e−β zw1 Choosing the positive root makes sense, or else for parameters values that satisfy |a|> 11−αlimz→∞J(z) =−∞ (A.8)to see this first note that∂J(z)∂ z=C(11−α )(ez1−α − e−a(z−zˆ)+ zˆ1−α ) (A.9)It follows that if a < 0 and |a|> 11−α , ∃zo, s.t.: ∀z > zo∂J(z)∂ z< 0 ∀z > zo (A.10)116Finally, let for [zi,∞[Λi(z) = Λi2(z) (A.14)and for ]zˆ,zi]Λi(z) = Λi1(z) (A.15)Then for [zi,∞[∂Λi2(z)∂ t=−µ ∂Λi2(z)∂ z+σ22∂ 2Λi2(z)∂ z2+Miβe−β ze−β zi= 0 (A.16)for ]zˆ,zi]∂Λi1(z)∂ t=−µ ∂Λi1(z)∂ z+σ22∂ 2Λi1(z)∂ z2= 0 (A.17)The four boundary conditions are1.∫ ∞ziΛi(z)dz < ∞2. Λi1(zi) = Λi2(zi)3. ∂Λi1(zi)∂ z =∂Λi2(zi)∂ z4. Λi1(zˆ) = 0GuessΛi1(z) = k11 + k12e2µσ2z (A.18)andΛi2(z) = k21 + k22e2µσ2z− Mie−β ze−β zi(µ+ σ22 β )(A.19)117From∫ ∞ziΛi(z)dz < ∞ we getk21 = 0 (A.20)From Λi1(zi) = Λi2(zi) we getk22 =Miµ+ σ22 βe−2µσ2zi + k11e−2µσ2zi + k12 (A.21)From ∂Λi1(zi)∂ z =∂Λi2(zi)∂ z we getk22 = k12−βMi σ22µ e−2µσ2zi(µ+ σ2β2 )(A.22)Equating equations (A.21) and (A.22)k11 =−Miµ(A.23)This impliesΛi1(z) =Mi−µ + k12e2µσ2z (A.24)Now using Λi1(zˆ) = 0 we getk12 =Miµe−2µσ2zˆ (A.25)It followsΛi1(z) =Mi−µ (1− e2µσ2(z−zˆ)) (A.26)andk22 =Miµe−2µσ2zˆ−βMi σ22µ e−2µσ2zi(µ+ σ22 β )(A.27)118which impliesΛi2(z) =βMi σ2−2µ e2µσ2(z−zi)(µ+ σ2β2 )− Mi−µ e2µσ2(z−zˆ)− Mie−β ze−β zi(µ+ σ22 β )(A.28)Proof of Corollary 2.1.It then followsη i =∫ zizˆΛi1(z)dz+∫ ∞ziΛi2(z)dz (A.29)Note that∫ziΛi2(z)dz =−Miσ22µ2e2µσ2(zi−zˆ)+βMi(σ22µ )2µ+ σ22 β− Miµβ + σ22 β 2(A.30)and ∫ zizˆΛi1(z)dz =Mi−µ [zi− zˆ+σ2−2µ (e2µσ2(zi−zˆ)−1)] (A.31)Which then impliesη i =Miµ+ σ2β2[β (σ22µ)2− 1β]+Mi−µ (zi− zˆ)−Mσ22µ2(A.32)η i =Miµ+ σ22 β[β (σ22µ)2− 1β− σ22µ2(µ+σ22β )]+Mi−µ (zi− zˆ) (A.33)η i =Miµ+ σ22 β[βσ44µ2− 1β− σ22µ− σ4β4µ2]+Mi−µ (zi− zˆ) (A.34)119η i =Miµ+ σ22 β[−µ+σ22 βµβ]+Mi−µ (zi− zˆ) (A.35)η i =Mi−µβ +Mi−µ (zi− zˆ) =Mi−µ [1+β (zi− zˆ)β] (A.36)Now using the fact that Mu = ψue−β zu and Mw = ψ(1−u−η)e−β zw we getηu = Auψue−β zu (A.37)andηw = Awψ(1−u−η)e−β zw (A.38)which impliesη = Auψue−β zu +Awψ(1−u−η)e−β zw (A.39)Now using u = (s+ψ(1−F(zw)))(1−η)s+ f+ψ(1−F(zw)) and 1−u−η =f (1−η)s+ f+ψ(1−F(zw))η =ψ(1−η)s+ f +ψe−β zw[Au(s+ψe−β zw)e−β zu +Aw f e−β zw ] (A.40)η =ψ[Au(s+ψe−β zw)e−β zu +Aw f e−β zw ]s+ f +ψe−β zw +ψ[Au(s+ψe−β zw)e−β zu +Aw f e−β zw ](A.41)It follows1−η = s+ f +ψe−β zws+ f +ψe−β zw +ψ[Au(s+ψe−β zw)e−β zu +Aw f e−β zw ](A.42)120which impliesηu =Au(s+ψe−β zw)ψe−β zus+ f +ψe−β zw +ψ[Au(s+ψe−β zw)e−β zu +Aw f e−β zw ](A.43)ηuη=Au(s+ψe−β zw)e−β zuAu(s+ψe−β zw)e−β zu +Aw f e−β zw(A.44)Proof of Proposition 4.In equilibrium W >U , otherwise all wage workers would exit wage work to goto the unemployment island and markets would not clear in the Walrasian market.Here I present a formal proof showing that if b < 1⇔W >U . Note that rW andrU can be rewritten asrW = w+ f (W −U)+ψ∫(max(J(z),W )−W )dF(z) (A.45)rU = bw+ s(U−W )+ψ∫(max(J(z),U)−U)dF(z) (A.46)This implies(r+ψ+ f +s)(W−U)=w(1−b)+ψ∫max(J(z),W )dF(z)−ψ∫max(J(z),U)dF(z)(A.47)121First prove b < 1⇒W >U . Using the equation A.47 above :w(1−b) =ψ(W−U)+(r+ f +s)(W−U)−(ψ∫zwJ(z)dF(z)+ψ∫ zwWdF(z)−ψ∫zuJ(z)dF(z)−ψ∫ zuUdF(z))+ψ∫ zuWdF(z)−ψ∫ zuWdF(z) (A.48)0<w(1−b)=ψ(W−U)+(r+ f +s)(W−U)+ψ∫ zwzu(J(z)−W )dF(z)−ψ∫ zu(W−U)dF(z)< (r+ f + s)(W −U)+ψ(W −U)−ψ(W −U)F(zu) (A.49)where the last inequality follows from the fact that J(z) < W for zu < z < zw. Itfollows that b < 1⇒W >U .Now to prove that W >U ⇒ b < 1 start byw(1−b)=ψ(W−U)+(r+ f +s)(W−U)+ψ∫ zwzu(J(z)−W )dF(z)−ψ∫ zu(W−U)dF(z)+ψ∫ zwzuUdF(z)−ψ∫ zwzuUdF(z) (A.50)w(1−b)=ψ(W−U)+(r+ f +s)(W−U)+ψ∫ zwzu(J(z)−U)dF(z)−ψ∫ zu(W−U)dF(z)−∫ zwzu(W −U) (A.51)122w(1−b)=ψ(W−U)+(r+ f +s)(W−U)+ψ∫ zwzu(J(z)−U)dF(z)−ψ∫ zw(W−U)dF(z)(A.52)w(1−b) = ψ(W −U)(1−F(zw))+(r+ f + s)(W −U)+ψ∫ zwzu(J(z)−U)dF(z)(A.53)Note that J(z)>U for zu < z < zw, which implies W >U ⇒ b < 1. It follows thatb < 1⇔W >U .The result that zw > zu then just follows.Proof of Corollary 4.1.Note that in steady state the flow of exiting firms of each type is equal to Mi.2Letting ERi denote Exit Rate for type i, we have(ERi)−1 = [1+β (zi− zˆ)−µβ ] (A.54)(ERw)−1 > (ERu)−1⇒ ERu > ERw (A.55)where the first inequality follows from zw > zuIt follows that in the steady state equilibrium the exit rate is higher for firms of typeu.Proof of Corollary 4.2.The expression for optimal firm size is given byn(z,w) = (αw)11−α ez1−α (A.56)2In steady state, the flow of firms exiting a group has to be equal to the flow entering.123It follows average size for type i, where i ∈ {u,w}∫zˆn(z,w)Λi(z)η idz = (αw)11−αMiη i∫zˆez1−αΛi(z)Midz (A.57)Note thatΛi(z)Midoes not depend on Mi (A.58)Now concentrate on the term∫zˆez1−αΛi(z)Midz =∫ zzˆez1−αΛi1(z)Midz+∫zez1−αΛi2(z)Midz (A.59)Taking derivative with respect to zi gives∂∫zˆ ez1−α Λi(z)Mi dz∂ zi=ezi1−αMi(Λi1(zi)−Λi2(zi))+∫ zizˆez1−αMi∂Λi1(z)∂ zidz+∫ziez1−αMi∂Λi2(z)∂ zidz(A.60)Using the expressions for Λi1(z) and Λi2(z) note that(Λi1(zi)−Λi2(zi)) = [1−µ +−β σ2−2µ +1µ+ σ22 β] = [1−µ −(µ+ σ22 β )−µ(µ+ σ22 β )] = 0 (A.61)and that∂Λi1(z)∂ z= 0 (A.62)Replacing this back in equation (A.60)∂∫zˆ ez1−α Λi(z)Mi dz∂ zi=∫ziez1−αMi∂Λi2(z)∂ zidz =∫ziez1−αβ [e2µσ2(z−zi)− e−β (z−zi)]µ+ σ22 βdz (A.63)124=β (1−α)µ+ σ22 β((−σ2(1−α)2µ(1−α)+σ2 )−(1−α)β (1−α)−1)ezi1−α (A.64)=β (1−α)µ+ σ2β2[−2(1−α)2[µ+ σ2β2 ](2µ(1−α)+σ2)(β (1−α)−1) ]ezi1−α (A.65)=2β (1−α)3(−(2µ(1−α)+σ2))(β (1−α)−1)ezi1−α > 0 (A.66)The positive sign follows from the assumption that −µ > σ22(1−α)Finally, to complete the proof note thatMiη i= (ER)−1 where ER stands for Exit Rate (A.67)With the proof that the Exit Rate is higher for type I individuals than type II, itfollows thatMwηw>Muηu(A.68)Then letting E[n]i denote average size for type i. With abuse of notation let Λi(z,z j)represent the function Λi(z) replacing zi by z j, similarly for the measure ηi(z j).Then using zw > zu,E[n]w =∫zˆn(z,w)Λw(z,zw)ηw(zw)dz >∫zˆn(z,w)Λw(z,zu)ηw(zu)dz= (αw)11−αMwηw(zu)∫zˆeρz1−ρΛw(z,zu)Mwdz >∫zˆn(z,w)Λu(z,zu)ηu(zu)dz = E[n]u (A.69)where the first inequality follows from∂∫zˆ eρz1−ρ Λi(z)Mi dz∂ zi> 0 (A.70)125and the second fromMwηw>Muηu(A.71)Now to see the result for profits note thatE[pi]i = (1−α)(wα )E[n]i (A.72)Proof of Corollary 4.3.zw > zu⇒ ψ(1−F(zu))> ψ(1−F(zw)).A.1.2 Controlling for learning by doing mechanismIn this section, I show that the differences in size and exit rate between firms createdby an individual when laid off relative to working for somebody else cannot beexplained by a learning by doing story. In particular, one concern is that thesedifferences might be driven by individuals first starting a firm when laid off, duringwhich they acquire entrepreneurial skills. After that experience, upon enteringduring wage work, individuals would generate more productive firms due to theiraccumulated experience as an entrepreneur. To show that such mechanism cannotrationalize the differences in size and exit rate, I rerun the benchmark regressionswith additional controls for the total experience an individual had accumulated asa business owner upon starting the current firm. The control I use is a quadratic intotal years I observe the individual as an entrepreneur prior to this current firm spellinteracted with dummies for current year. The interaction with years is to controlfor the fact that the value of entrepreneurial skills might vary with the businesscycle.126Table A.1.1: Log number of employeesDependant variable Log # employees Dummy for exit1{Prev U}i,s -0.2894∗∗∗ 0.013∗(0.0419) (0.0069)Fixed Effects Yes YesControls for entrepreneurial experience Yes YesRatio of probabilities N/A 1.24Baseline Exit Probability 0.055 0.055Observations 450,502 341,241Notes: Column (1) reports results for fixed effects regression of log number of employees of currentbusiness on dummy indicating if the current business was started by the individual when laid off(1{Prev U}i,s). Column (2) reports results for fixed effect regression of exit dummy (taking value 1 ifindividual exits firm ownership and 0 otherwise) on (1{Prev U}i,s). Other controls include dummiesin age groups, marital status, province of residence, year business started, current year, 2 digit NAICSindustry code for current business, 2 digit NAICS industry code for the last employer, log numberof employees for the last employer and total years individuals observed as a business owner prior tocurrent entrepreneur spell interacted with current year. Only includes men 25 to 54 years old.A.1.3 Model with multiple sectors and testable predictionModel descriptionThe baseline theoretical framework is useful in its clarity to understand exactlyhow the selection mechanism operates. But in reality an economy is composed127of different sectors each with a different labour productivity and wage. Since foreach sector the opportunity cost of entering entrepreneurship is different, this hasimplications for individual decisions to open a business. Furthermore, the modelwith multiple sectors is useful in motivating the instrument I choose when I test theadditional prediction of the theory.With this in mind I consider a small extension of the previous framework, inwhich now there are C economies each with I industries an individual can workon. What characterizes an industry is the amount of efficiency units a worker isendowed with. All workers in each economy c have the same endowment of ef-ficiency units across industries. Entrepreneurs in this scenario choose the optimalamount of efficiency units to hire and pay a same wage per efficiency unit acrossindustries. Conditional on transitioning to the working island as a worker, the un-employed transition to work at industry i at rate Ωi. It follows the problem of theunemployed individual can be summarized byrUc = bwcζc+ f (∑∀iΩiW ci −Uc)+ψ∫zcu(∑∀iΩiJc(z)−Uc)dF(z) (A.73)where wc is the unique equilibrium wage, ζc is an economy-wide efficiency unit forworkers in economy c, bwcζc is the income of the unemployed individual, W ci isthe value of being a worker at industry i at economy c. Note that since the value ofunemployment Uc and the wage per efficiency unit wc are the same across indus-tries in a same economy c, then, conditional on z, every entrepreneur is indifferentover which industry to operate in. With this in mind, I consider an equilibrium inwhich the transition rate of an entrepreneur to industry i is also given by rate Ωi.128The value function for a worker in industry i ∈ I is given byrW ci = wcνc,iζc+ s(Uc−W ci )+ψ∫zcw,i(∑∀iΩiJc(z)−W ci )dF(z) (A.74)where νc,i is the relative amount of efficiency units a worker is endowed for in-dustry i at economy c and ζc is the economy-wide efficiency unit endowment forworkers in economy c, where E[log(ζ )] ≡ ∑iΩilog(ζ ) = K is time invariant. Let∑iΩilog(νc,i) = 0. Now define the economy level wage as wc and the average in-dustry, economy level wage as wc,i ≡ wcνc,i.In equilibrium,Jc(zcw,i) =Wci and Jc(zcu) =Uc (A.75)As in the previous theoretical framework we get the result of differences inperformance between firms created by employed versus unemployed individuals.3Proposition 13. In a multi-sector model of endogenous entrepreneurship, firmscreated by employed individuals have on average more employees, higher profitsand lower exit rates. Furthermore, unemployed individuals are more likely to enterentrepreneurship relative to workers of all industries.The Proposition below highlights a prediction that lies at the heart of the selec-tion mechanism.Proposition 14.log(zcw,i) = ξw0 +ξw1 log(wc,i)+ξw2 log(wc)+ξw3 log(εc.i)+ξwc4 log(ζc) (A.76)3See Supplemental Appendix I for full characterization of the model with multiple sectors.129log(zcu) = ξu0 +ξu1 log(wc)+ξu4 log(ζc) (A.77)where ξ u1 > 0,ξw1 > 0 and ξw2 > 0, furthermore, let E[zcw,i] be the average thresholdproductivity for wage workers across industries in economy c thenE(log(zcw,i)) = ξw0 +Λwlog(wc)+ξw3 log(ζc) (A.78)where Λw = ξw1 +ξw2 > ξu1The corollary below formally relates the entry rate into firm ownership of bothwage workers and laid off individuals to region-wide wages.Corollary 14.1. The average entry rate for wage workers in an economy/region c,ERc,w and that of unemployed individuals ERc,u can both be expressed asERc,w = β0,w+β1,wlog(wc)+υc,w for employed workers (A.79)where υw is linear function of log(ζ )ERc,u = β0,u+β1,ulog(wc)+υc,u for not working individuals (A.80)where υu is linear function of log(ζ ) and β1,w < β1,u ≤ 0.Now combining both into one specification we getERc,n,t = α0+β1log(wc,t)+β21{Prev U}c,t,nlog(wc,t)+α21{Prev U}c,t,n+µc,t(A.81)130where µc is a function of log(ζc), n = 1 if the individual is involuntarily unem-ployed and n = 0 if he is working and 1{Prev U}c,t,n is an indicator for whetherthe individual was involuntarily unemployed n = 1 or was working n = 0. I haveadded the time subscripts since the data is over different time periods. The predic-tion of the theory is that β1 < 0 and β2 > 0.The following theorem gives a linearized expression for past industrial compo-sition as a function of the shocks in the model that will be useful in the discussionof the validity of the instrument.Proposition 15.κc,i,1 =ΩiΓ0Γ0+Γ2K+ΩiΓ1Γ0+Γ2Klog(νc,i,1)+ΩiΓ2Γ0+Γ2Klog(ζc,1) (A.82)From the discussion on identification we concluded that the level of variationbeing used is that of changes across regions. It follows that, using the result ofProposition 15, for consistency we needplimC,I→∞1C1IC∑c=1̂log(ζc,t)∑∀ilog(wNi,t)(ΩiΓ0Γ0+Γ2K+ΩiΓ1Γ0+Γ2Klog(νc,i,1)+ΩiΓ2Γ0+Γ2Klog(ζc,1))(A.83)where c stands for region, i for industry, C for total number of cities and I totalnumber of industries.= plimI→∞1I ∑∀ilog(wNi,t)ΩiplimC→∞1CC∑c=1(Γ0Γ0+Γ2K+Γ1Γ0+Γ2Klog(νc,i,1)+Γ2Γ0+Γ2Klog(ζc,1))̂log(ζc,t). (A.84)131In other words, the validity of the instrument is guaranteed as long as1. ̂log(ζc,t) is uncorrelated with log(ζc,1).2. The distribution of log(νc,i,1) is uncorrelated with ̂log(ζc,t).The first requirement is that region-wide comparative advantage in labour effi-ciency log(ζ ) follows a process of the formlog(ζc,t) = γc+ γt +σc,t (A.85)where σc,t =t∑j=2νi, j, with νi,t iid. This amounts to having the component of region-wide comparative advantage that varies across cities and time (σc,t) to be limited inits serial correlation. It must be that eventually past shocks to σc,t no longer influ-ence its current value.4 Note that this is a much weaker restriction than imposinglog(σc,t) to be independent across time and even weaker to assuming log(ζc,t) isindependent across time.Intuitively, the second condition states that for validity of the instrument weneed the first year industry comparative advantage distribution of a region to beuncorrelated with region-wide demand shocks at the current period. In other words,the fact that a city had a comparative advantage in a particular industry initiallyshould not impact later in the future the region-wide demand shock it receives.ProofsProof of Proposition 13.See Proofs of Corollary 19.1, 19.2, 19.3 in Supplemental Appendix I.4This property is typical but not limited to moving average processes.132Proof of Proposition 14.I log linearize (zu,zw,i, zˆ,w,wi,ζ ,εi) around (log(z∗), log(z∗), log(z∗),w∗,w∗, log(1), log(1))for the expressions of the value function of the unemployed individual rU and forthe employed individual rW . Starting by rUrγ0+ rγ1log(zu)+ rγ2log(zˆ) = φu0 +φu1 log(w)+φu2 log(ζ )+f (γ1∑∀iΩilog(zw,i))− f γ1log(zu)+α0−α1log(zu)−α2log(zˆ) (A.86)Now usingra≈ 0⇒ rγ2 ≈ 0 and a+θa+β ≈ 0⇒ α2 ≈ 0 (A.87)Rearranging giveslog(zu)=φ u0 +α0(r+ f )γ1+α1+φ u1 log(w)(r+ f )γ1+α1+f γ1(r+ f )γ1+α1∑∀iΩilog(zw,i)+φ u2 log(ζ )(r+ f )γ1+α1(A.88)Doing the same procedure for rW and rearranging giveslog(zw,i) =φw0 +α0(r+ s)γ1+α1+φw1 log(wi)(r+ s)γ1+α1+sγ1log(zu)(r+ s)γ1+α1+φw3 log(ζ )(r+ s)γ1+α1(A.89)Now using equation (A.89) to sum over all log(zw,i) gives5∑∀iΩilog(zw,i) = A1+∑∀iΩiφw1 ln(wi)(r+ s)γ1+α1+sγ1log(zu)(r+ s)γ1+α1(A.90)5Remember that E[log(νc,i)]≡ ∑∀iΩilog(νc,i) = 0 and ∑∀iΩilog(ζ ) = K (constant)133Now replace this sum back in equation (A.88) to getlog(zu) =φ u0 +α0(r+ f )γ1+α1+φ u1 log(w)(r+ f )γ1+α1+f γ1φw1 ln(w)((r+ s)γ1+α1)((r+ f )γ1+α1)+f γ1sγ1((r+ s)γ1+α1)((r+ f )γ1+α1)log(zu)+A1 f γ1(r+ f )γ1+α1+φ u2 log(ζ )(r+ f )γ1+α1(A.91)Rearranging giveslog(zu) = ξu0 +(φ u1 ((r+ s)γ1+α1)+ f γ1φw1 )((r+ f + s)γ1+α1)(rγ1+α1)log(w)+ξ u2 log(ζ ) (A.92)log(zu) = ξu0 +ξu1 ln(w)+ξu2 log(ζ ) (A.93)Now replace this final expression of log(zu) into log(zw,i) to getlog(zw,i)= ξw0 +φw1 ln(wi)(r+ s)γ1+α1+sγ1(φ u1 ((r+ s)γ1+α1)+ f γ1φw1 )((r+ s)γ1+α1)[((r+ f + s)γ1+α1)(rγ1+α1)]ln(w)+sγ1ξ u2 log(ζ )(r+ s)γ1+α1+φw3 log(ζ )(r+ s)γ1+α1(A.94)log(zw,i) = ξw0 +ξw1 ln(wi)+ξw2 ln(w)+ξw3 log(ζ ) (A.95)Now taking an average over all industries gives6Ei(log(zw,i))≡∑∀iΩilog(zw,i) = ξw0 +(ξw1 +ξw2 )ln(w)+ξw3 log(ζ ) (A.96)6Using the fact that ∑∀ilog(νc,i) = 0134Finally, note thatφw1 > φu1 ⇒ (φw1 −φ u1 )(rγ1+ sγ1+α1)+ f γ1φw1 − f γ1φw1 > 0 (A.97)Passing − f γ1φw1 − φ u1 (rγ1 + sγ1 + α1) to the other side, dividing both sides by(rγ1+ f γ1+α1+ sγ1)((r+ s)γ1+α1), and using the fact that (rγ1+α1)(rγ1+α1) = 1⇒ φw1(r+ s)γ1+α1>(rγ1+α1)(φ u1 ((r+ s)γ1+α1)+ f γ1φw1 )((r+ s)γ1+α1)((r+ f + s)γ1+α1)(rγ1+α1)(A.98)Now add sγ1(φu1 ((r+s)γ1+α1)+ f γ1φw1 )((r+s)γ1+α1)[((r+ f )γ1+α1)(rγ1+α1)+sγ1(rγ1+α1)] to both sides⇒ (ξw1 +ξw2 )≡φw1(r+ s)γ1+α1+sγ1(φ u1 ((r+ s)γ1+α1)+ f γ1φw1 )((r+ s)γ1+α1)[((r+ f + s)γ1+α1)(rγ1+α1)]>φ u1 ((r+ s)γ1+α1)+ f γ1φw1((r+ f + s)γ1+α1)(rγ1+α1)≡ ξ u1 (A.99)Proof of Proposition 15.In the supplemental appendix I show that equilibrium employment at an indus-try (Ei) isEi,c,1 =fΩiuc,1ψ(1−F(zw,i,c,1))+ s, ∀i ∈ I. (A.100)Then κc,i,1 is equal toκc,i,1 ≡ Ei,c,1Ec,1 =Ωi(ψ(1−F(zw,i,c,1))+ s)−1(∑jΩ j(ψ(1−F(zw, j,c,1))+ s)−1)−1(A.101)135Now linearize (ψ(1−F(zw,i,c,1))+ s)−1 with respect to log(zw,i,c,1) to getκc,i,1 =Ωi(ρ0+ρ1log(zw,i,c,1))(∑jΩ j(ρ0+ρ1log(zw, j,c,1)))−1 (A.102)Now remember that log(zw,i,c,1) can be written as a function of log(wc,1), log(wc,i,1)and log(ζc,1). Furthermore from market clearing we can linearize both log(wc,1)and log(wc,i,1) with respect to log(ζc,1) and log(νc,i,1) around (K,0).7 Then re-placing log(zw, j,c,1) by its expression with only log(νi,c,1) and log(ζc,1) we getκc,i,1 =Ωi(Γ0+Γ1log(νc,i,1)+Γ2log(ζc,1))(∑ jΩ j(Γ0+Γ1log(νc,i,1)+Γ2log(ζc,1)))(A.103)Now using ∑ jΩ jlog(νc,i,1) = 0 and ∑ jΩ jlog(ζc,1) = K,∀t gives the result.A.1.4 Robustness of Testable Prediction to allow for Worker MobilityIn this Appendix section I discuss the implications of allowing for mobility ofunemployed individuals across local labour markets. Let µ1 represent the rate atwhich the unemployed has the opportunity to change local labour market. Whendoing so the individual chooses the city (economic region) that gives the highestutility. It follows that the problem of the unemployed at region c can be rewrittenas(r+µ1)Uc,t = bwc,t+ψ∫zc,tu(∑∀iΩiJc,t(z)−Uc,t)dF(z)+µ1 maxcUc,t+ f (∑∀iΩiW c,ti −Uc,t)(A.104)Note that the term maxcUc,t is a city invariant time effect. It follows that afterlinearizing we get the same expressions for zu and zw as a function of wages w as7Remember that ∑∀iΩilog(νc,i,1) = 0 and ∑∀iΩiζc,t = K136in Section A.1.3 of the Appendix except now with an additional constant for zu. Asa result the empirical specification for testing the model is unchanged.A.1.5 Details on Instrument and Wage MeasureIn this section I describe how I construct my economic region/year wage measurelog(wc,t) and the instrument used in the wage regression ∑∀iκc,i,1log(wNi,t). Thedefinition of local labour market is always an economic region, and the industrycategory used is always 3 digit NAICS industry classifications. Below let p denoteindividual p in the sample.For each year t I run the following regression :log(annual worker earnings)p,t =Xp,tγ4,1+∑∀yγ4,y1{year= y}+∑∀cγ4,c1{region= c}+∑∀y∑∀cγ4,c,y1{region = c∩ year = y}+ εi,twhere Xp,t are dummies in age, gender, country of birth and 3 digit NAICSindustry code. The wage measure islog(wc,t)=∑∀yγˆ4,y1{year= y}+∑∀cγˆ4,c1{region= c}+∑∀y∑∀cγˆ4,c,y1{region= c ∩ year= y}Now for constructing the instrument I first estimate the national industry pre-137mia for each industry log(wNi,t). For each year t I run the following regression :log(annual worker earnings)p,t =Zp,tγ5,1+∑∀yγ5,y1{year= y}+∑∀Iγ5,I1{industry= I}+∑∀y∑∀Iγ5,I,y1{industry = I∩ year = y}+ εi,twhere Zp,t are dummies in age, gender, country of birth and city.Then the national industry premium islog(wNi,t) =∑∀yγˆ5,y1{year = y}+∑∀Iγˆ5,I1{industry = I}+∑∀y∑∀Iγˆ5,I,y1{industry = I∩ year = y}Finally, the employment share of a particular industry i, in region c, at the firstyear of the sample, is calculated asκc,i,1 =Total employment in industry i at region c at year 2001Total employment at region c at year 2001(A.105)A.1.6 Proofs Calibration sectionIn this section I go over the formal theorem that allows me to pin down µ and σ inthe data, where µ and σ are the two parameters governing how the productivity ofan entrepreneur owned firm evolves once the firm start operating.Proposition 16. Let δ be the shape of the size distribution of the entire population138of firms, thenE[∆log(ni,t)|∆log(ni,t)> 0] = µ1−α +σ1−α λ (−µσ) and−2µσ2=δ +11−αwhere λ (.) is the Inverse Mils Ratio.E[∆log(ni,t)|∆log(ni,t)> 0] and δ are computed using firms of all ages.Proof of Proposition 16.Note that the expression for dz(t) can be approximated aszi,t = zi,t−1+µ+σεi,t (A.106)withεi,t ∼ N(0,1) (A.107)Replacing zi,t by its expression with firm size ni,tlog(ni,t) = log(ni,t−1)+µ1−α +σ1−α εi,t (A.108)It follows∆log(ni,t) =µ1−α +σ1−α εi,t (A.109)139Now let m be E[∆log(ni,t)|∆log(ni,t)> 0] it follows,8m≡ E[∆log(ni,t)|∆log(ni,t)> 0] = µ1−α +σ1−α E[ε|∆log(ni,t)> 0] (A.110)m≡ µ1−α +σ1−α E[ε|ε >−µσ] (A.111)m =µ1−α +σ1−α λ (−µσ) (A.112)where λ (.) is the Inverse Mils Ratio.Now note that for large enough z the distribution of type j, where j ∈ {u,w}will be given by9Λ j(z) = Λ j2(z) = e2µσ2zM j[(β σ22µ e−2µz jσ2µ+ σ22 β− e−2µ zˆσ2−µ )−e−(β+2µσ2)ze−β z j(µ+ σ22 β )] (A.113)Usingez = n1−αwα(A.114)Λ j(n(z,w))=Λ j2(n(z,w))= (wα)2µσ2 n(1−α)2µσ2 M j[(β σ22µ e−2µz jσ2µ+ σ22 β− e−2µ zˆσ2−µ )−n−(1−α)(β+2µσ2)(wα )(β+ 2µσ2)e−β z j(µ+ σ22 β )](A.115)8Note that taking the unconditional expectation and comparing it to the mean in the data wouldbe wrong since the observed population of firms is a selected group among those that survived,i.e., log(n) > log(n(zˆ,w)). On the other hand, note that conditional on log(ni,t−1) being observed,conditioning on log(ni,t)> log(ni,t−1) is stronger than log(ni,t)> log(n(zˆ,w)). To see this note thatlog(ni,t−1) observed means log(ni,t−1) > log(n(zˆ,w)). It follows that once I condition on positivegrowth and adjust the expectation accordingly I don’t need to adjust for selection.9More precisely, for z≥max{z1,z2}140which impliesn−(1−α)2µσ2 Λ j(n) = (wα)2µσ2 M j[(β σ22µ e−2µz jσ2µ+ σ22 β− e−2µ zˆσ2−µ )−n−(1−α)(β+2µσ2)(wα )(β+ 2µσ2)e−β z j(µ+ σ22 β )](A.116)Now summing over all jn−(1−α)2µσ2 Λ(n) = (wα)2µσ2 ∑jM j[(β σ22µ e−2µz jσ2µ+ σ22 β− e−2µ zˆσ2−µ )−n−(1−α)(β+2µσ2)(wα )(β+ 2µσ2)e−β z j(µ+ σ22 β )](A.117)Now assume β ≥−2µσ2limn→∞n− (1−α)2µσ2 Λ(n) = (wα)2µσ2 ∑jM j[(β σ22µ e−2µz jσ2µ+ σ22 β− e−2µ zˆσ2−µ )]< ∞ (A.118)It follows that for large enough n,Λ(n) decays at speed given by n2µ(1−α)σ2 ∀i. Itfollows that for a large enough firm size, the firm size distribution will be Pareto oftail parameter x,x =−2µ(1−α)σ2−1 (A.119)It follows that given x and α , µ and σ can be pinned down by the following twoequations−2µσ2=1+ x1−α (A.120)andE[∆log(ni,t)|∆log(ni,t)> 0] = µ1−α +σ1−α λ (−µσ) (A.121)141where λ (.) is the Inverse Mils Ratio. E[∆log(ni,t)|∆log(ni,t) > 0] and x are esti-mated in the CEED data.A.2 CalibrationThe following table lists the whole set of parameters and the proceedures to choseeach parameter value. For details see main body of the paper.142Table A.2.1: CalibrationParameter value at annual frequency Source/Targetβ 8.32 Entryu/Entrywµ −0.11 E[∆log(n)|∆log(n)> 0] in dataσ 0.186 Shape of size distribution of all firms in datar 4.5% -α 2/3 Average aggregate labour shareK 0.4 E[log(nw)]−E[log(nu)]s 0.214 Hobijn and S¸ahin [2009]b 0.6 Replacement rate for unemployedχ 0.268 Exitu/Exitwc 0.562 Normalize θ to 1 as in Shimer [2005]φ 0.72 Shimer [2005]γ 0.72 Shimer [2005]ψ 24 Consider robustness to different valuesNotes: Calibration Table. Entryu/Entryw is the ratio of entry rate into entrepreneurship between the un-employed and wage workers. E[log(nw)]−E[log(nu)] is the difference in average number of employeesbetween firms created by workers versus the unemployed. Exitu/Exitw is the ratio of exit rates out of en-trepreneurship between entrepreneurs that were unemployed when they started their business and those thatwere working when they started their firm.143A.3 Alternative CalibrationIn Table A.3.1 I show that the impact of the policy in the aggregate economy isrobust to changing the value of the rate at which individuals receives businessprojects, ψ .Table A.3.1: Model Extension - Different ψ valuesψ values 12 24 36E[arrival time of projects] 1 month 12 month13 month∆E[z] -2.10% -2.14% -2.16%∆ Unemployment Rate (% change) -1.11% -1.11% -1.11%∆ Wage 0.62% 0.61% 0.60%∆ Labor Market Tightness (θ ) 2.30% 2.35% 2.38%∆ Jobs by Firms created by Unemployed 7.22% 7.12% 7.06%∆ Jobs by Firms created by Workers -7.13% -7.10% -7.08%∆ Firm Exit Rate (% change) 35.27% 36.38% 37.07%Notes: Outcome of policies that make a share of total UI benefits income conditional on the unemployedopening a firm. ∆E[z] is the percentage change in the average firm productivity, ∆ Jobs by firms createdby workers is the percentage change in the measure of jobs associated to firms created by wage workers,∆ Unemployment is the percentage change in the unemployment rate. Results are shown for differentvalues of ψ . psi is the rate at which individuals receive business projects. E[arrival time of projects] isthe expected arrival time of a business project in the economy given the ψ value chosen.144Next we go over the impact of the counterfactual policies of subsidizing ortaxing unemployed starting a business with an alternative calibration strategy forthe cost of posting a vacancy c. I follow Hagedorn and Manovskii [2008] in settingthe cost of posting of a vacancy to 4.5% of the equilibrium wage (c = 0.045). Allother parameters are chosen in the same manner as in the benchmark calibration.145Table A.3.2: Policy outcomesBaseline Calibration Robustness - c(1) (2)∆E[z] -2.14% -2.14%∆ Unemployment Rate (% change) -1.11% -1.11%∆ Wage 0.61% 0.61%∆ Labor Market Tightness (θ ) 2.35% 2.35%∆ Jobs by Firms created by Unemployed 7.12% 7.12%∆ Jobs by Firms created by Workers -7.1% -7.1%∆ Average Firm Exit Rate (percent change) 36.38% 36.38%Notes: Outcome of policies that make a share of total UI benefits income conditional on the unemployedopening a firm. ∆E[z] is the percentage change in the average firm productivity, ∆ Jobs by firms createdby workers is the percentage change in the measure of jobs associated to firms created by wage workers, ∆Unemployment is the percentage change in the unemployment rate. First column presents results for baselinecalibration. Second column shows robustness to calibration of the cost of posting a vacancy, c. In particular, Ifollow Hagedorn and Manovskii [2008] in setting the cost of posting of a vacancy to 4.5% of the equilibriumwage (c = 0.045). All other parameters are chosen in the same manner as in the benchmark calibration.146A.3.1 Firms created by Laid off versus not Laid-off individuals(without Fixed Effects)Before proceeding to the results without fixed effects, recall that the baseline groupcompared to the displaced individuals are all individuals that were employed in theprevious year by a firm that in the current year continues to exist. This impliesthat the group of entrepreneurs tagged as having entered from wage work also in-cludes individuals that were employed in the prior year to opening a firm and hadan unemployment spell in between the job and the start of a firm. As a result, thisgroup includes individuals that started a firm after being fired as long as the spellof unemployment was shorter than a year. Individuals who are fired are likely tobe a negatively selected group of the population. This negative selection becomesparticularly important if individuals fired are more likely to start a firm than indi-viduals that never lost their job.The result is that, without fixed effects, we capture some of this negative selec-tion that offsets the differences between laid off and employed individuals. Con-sistent with this concern, the results in Column (1) and (2) of Table A.3.3 indicatethat once we do not control for individual fixed effects the differences in firm sizebetween laid off and not laid-off individuals disappears and the difference in exitrates decreases and flips sign.147Table A.3.3: Log number of employeesDependant variable log # employees Exit dummy(1) (2)1{Prev U}i,s 0.012 −0.0064∗∗∗(0.013) (0.007)Fixed Effects No NoBaseline Exit Probability 0.055 0.055Ratio of probabilities Not applicable 0.9Observations 450,502 341,214Notes: Column (1) reports results for regression without fixed effects of log numberof employees of the current business on a dummy indicating if the current businesswas started by an individual when laid off (1{Prev U}i,s). Column (2) reports resultsfor regression without fixed effects of dummy for exit (takes value 1 if individual exitsentrepreneurship and 0 otherwise) on (1{Prev U}i,s). Regression on Column (2) onlyincludes individuals that last year were running a business. Other controls includedummies in age groups, marital status, province of residence, year business started,current year, 2 digit industry code for current business, 2 digit industry code for thelast employer, log number of employees for the last employer. Only includes men 25to 54 years old. Without fixed effects, we do not control for the fact that the groupof not laid-off individuals includes individuals that were fired and are likely to benegatively selected in ability. This negative selection among the individuals that werefired and started a firm offsets the differences between firms created by the employedversus laid off individuals. Standard errors are clustered at the individual level.148A.3.2 Data AppendixIn this section I describe the components of the dataset being used. The construc-tion of the data was done by Statistics Canada and not by the author.The dataset is a combination of information from three types of tax forms inCanada. The first is the T1 form, which is just the individual tax return form.10From there, we get demographic information, age and marital status, total annualincome of the individual and total labour earnings of the individual. The second isthe T4 form. This is a form that every employer must file for each of its employ-ees.11 These files give us information for each individual the firms for which theyworked for and their labour earnings in that tax year. The final tax files come fromthe schedule 50 of the T2 form. According to Canadian law, incorporated firmsmust list all owners that have at least 10% ownership. These files allow me to linkeach firm to individual entrepreneurs.12 Together these files allow me to link eachindividual to a firm they are working on or to a firm they own.The last step is matching all these incorporated firms to firms present in theLongitudinal Employment Analysis Program (LEAP) Dataset. This dataset con-tains the entire universe of firms with employees in Canada, whether incorporatedor not. From this dataset, I get a measure of the number of employees for eachfirm (ALU, average labour unit). The matching with the LEAP dataset allows usto construct a time consistent firm identifier that takes into account mergers andsplitting of a same firm in multiple ones.1310The equivalent in the United States is the 1040A form.11The equivalent in the US is the W-2, Wage and Tax Statement.12The equivalent in the US to the schedule 50 of the T2 form is the schedule G of 1120 form(Corporate Income Tax Form in the US). The only difference is that under US law, a corporationonly needs to list owners that own at least 20% of the firm.13To identify a same firm the LEAP dataset uses a strategy entitled ”labour tracking”. If a firm A149A.3.3 Supplemental Appendix I : Solving for Multi-IndustryEconomy model.This section solves for the multi-sector model economy presented in the paper. Itstarts by the full characterization of the model. Solving the model then allowsthe proof of differential performance between firms created by not working versusworking individuals. (Proposition 13 in Paper)rU = bwζ + f (∑∀ j∈IΩ jWj−U)+ψ∫zu(∑∀ j∈IΩ jJ(z)−U)dF(z) (A.122)rWi = wνiζ + s(U−Wi)+ψ∫zw,i(∑∀ j∈IΩ jJ(z)−Wi)dF(z) (A.123)where νi is the relative efficiency units a worker is endowed for industry i and ζ isan economy-wide efficiency unit endowment, where E[log(ζ )]≡∑iΩilog(ζ ) =Kis time invariant. Let νi = ν iεi, where ∑iΩilog(εi) = 0, ∑iΩilog(ν i) = 0 and ν istime invariant. Now define the economy level wage as w and the average industrylevel wage as wi ≡ wν i.∑∀ j∈IΩ jJ(zu) =U (A.124)∑∀ j∈IΩ jJ(zw,i) =Wi (A.125)splits into firm B and firm C but continues to do the exact same business as before, the method marksfirms B and C with the identifier of firm A, since firm B and C together have the same industry andworkforce as A. This is important since for all purposes, nothing has changed except for the officialnaming of the company that now are two firms, even though the owners and employees are the same.For more details see the Statistics Canada website.150Firm static decision :pi∗(z) = maxnznα −wn (A.126)which impliespi∗(z) = (1−α)(αw)α1−α ez1−α (A.127)Once a business starts operating, Z follows a geometric Brownian Motion withdrift µ < 0 and variance parameter σ .dZ(t) = (µ+σ22)Z(t)dt+σZ(t)dΩ(t) (A.128)Where Ω(t) is a standard Brownian Motion. Then it followsdz(t) = µdt+σdΩ(t) (A.129)It follows entrepreneurs face the following stopping problemrJ(z) = pi∗(z)+µJ′(z)+σ22J′′(z) if z≥ zˆ (A.130)J(z) =U−χ if z≤ zˆ (A.131)J′(zˆ) = 0 (A.132)where χ is a cost of shutting down.µ is assumed to be negative otherwise there would be an accumulation of firmsthat never exit the market. The cost of shutting down g makes the algebra tractableby guaranteeing the expressions for the distributions of both types will be identicalwith the only difference coming from the difference in thresholds zu versus zw,i151and the unemployment to employment transition rate versus the employment tounemployment transition rate, i.e., f and s.Market Clearing∑∀iEiζνi =∫n(z,w)Λ(z)dz (A.133)Proposition 17. The solution to the firm’s optimal stopping problem impliesJ(z) =Br− µ1−α − σ221(1−α)2(ez1−α +1a(1−α)e−a(z−zˆ)+ zˆ1−α ) (A.134)whereB≡ (1−α)(αw)α1−α (A.135)a =µ+√µ2+2rσ2σ2> 0 (A.136)Not surprisingly, the value function of the business owner is increasing in pro-ductivity for the range of values for which the business operates z ∈ [zˆ,∞[. 14Let Λwi, j(z) denote the measure of individuals operating a firm of productiv-ity z in industry j, that were workers in industry i else prior to opening the firmand Λui (z) the measure with productivity z that entered from unemployment intoindustry i.14To see this note that∂ 2J(z)∂ z2=C(11−α )(ez1−α1−α +ae−a(z−zˆ)+ zˆ1−α )> 0 (A.137)and for z = zˆ∂J(z)∂ z= 0. (A.138)This implies for z≥ zˆ,∂J(z)∂ z≥ 0. (A.139)152Proposition 18. For all d ∈ {u,w}, the measure of business owners of productivityz will be given by,• For z ∈ [zˆ,zd,i]Λdi, j(z) = Λdi, j,1(z) =Mdi, j−µ (1− e2µσ2(z−zˆ)) (A.140)• For z ∈]zd,i,∞[Λdi, j(z) = Λdi, j,2(z) =βMdi, jσ2−2µ e2µσ2(z−zd,i)(µ+ σ2β2 )−Mdi, j−µ e2µσ2(z−zˆi)− Mdi, je−β ze−β zd,i(µ+ σ22 β )(A.141)whereMdi, j = ψΩiue−β zu if d = u (A.142)Mdi, j = ψΩ jEie−β zw,i if d = w (A.143)We are now ready to define a Stationary competitive equilibriumDefinition 2. A Stationary competitive equilibrium is defined by a set of zu,zw,i,wi,Ei,ηui ,ηwi, j,Λui (z),Λwi, j(z),u, ∀(i, j) ∈ IxI such that• Wi >U, ∀i ∈ I• ∑∀ j∈IΩ jJ(zw,i) =Wi, ∀i ∈ I• ∑∀ j∈IΩ jJ(zu) =U• J(zˆ) =U−χ, ∀i ∈ I• The expression for J(z) is given by Proposition 17153• The expression for Λui (z) and Λwi, j(z) are given by Proposition 18• Ei is given byEi =fΩiuψ(1−F(zw,i))+ s, ∀i ∈ I (A.144)• u is given byu =11+ψAue−β zu + f ∑∀i∈IsΩi[1+Aw,i(1−F(zw,i))]s+ψ(1−F(zw,i))(A.145)whereAu =1+β (zu− zˆ)−µβ (A.146)andAw,i =1+β (zw,i− zˆ)−µβ (A.147)• ηuj is given byηuj = ψAuΩ jue−β zu (A.148)• Λwi, j(z) is given byΛwi, j = ψAw,iΩ jEie−β zw,i (A.149)•w = α[(1∑∀i Eiζνi)(∑∀i∫zˆez1−αΛui (z)dz+∑∀i∑∀ j∫zˆez1−αΛwi, j(z)dz)]1−α(A.150)The first condition states that the value of being a wage worker is higher thanthe value of being unemployed. Otherwise, no individual would ever choose to154transition to wage work and markets would not clear. The second and third guar-antee that individuals’ decisions to open a business are optimal and the last justcomes from market clearing.Next we are ready to go over the main theorem that will subsequently generateall the patterns that were documented in the data. It states that in equilibriumwage workers are more selective on which business opportunities to implement.The necessary and sufficient condition for it is simply that the income received asunemployed is lower than that received as a worker. Note that were it not the casethe equilibrium would not exist as markets would not clear.Proposition 19. In equilibrium, zw,i > zu⇔ b < 1 ∀i ∈ IThe next corollaries are all a result of the difference in selection directly relat-ing to the patterns documented empirically. The first states that businesses createdby wage workers have a smaller exit rate. This comes from the combination ofall business owners exiting at a same threshold while having different levels ofselection upon entry between the two types.Corollary 19.1. In equilibrium businesses created by wage workers have a lowerexit rate than those created by unemployedThe next corollary states that firms created by wage workers have higher profitsand more employees. This is a direct consequence of the fact that both profits andfirm size are monotonically increasing in productivity.15Corollary 19.2. In equilibrium, businesses created by wage workers, on average,have higher firm size and profits.15The result that fixing aggregates, the number of employees of a firm matches one to one withproductivity is a direct consequence of the absence of frictions in the hiring and firing process offirms.155Finally, as it is often the case with selection mechanisms an increased averageproductivity is associated to a lower entry rate. It follows that in equilibrium therate at which wage workers enter will be lower than that of unemployed.Corollary 19.3. In equilibrium the entry rate into business ownership of the un-employed is higher than that of salary workers.Proof of Proposition 17.We know that it is equal to U ∀z ≤ zˆ. We need to find the value of J(z) forz≥ zˆ. The proof just follows from the proof in Proposition 1.16Proof of Proposition 18.Solving generic KFE. The solution below is the same for both types of busi-ness owners (i.e., d = u,w). Let j refer to the industry the individual entered andi the industry the individual came from. Since the income received when unem-ployed is independent of the individual’s work history, the origin of all unemployedthat become entrepreneurs is always the same.17 With abuse of notation denoteΛdi, j as the measure of firms created by d type where d indicates whether a worker(d = w) or an unemployed (d = u), that entered into industry j and, if d = w, theowner came from industry i.Let zˆ be the point at which firms exit and zd,i the point in which firms enter, withzd,i > zˆi. Let Λ(z)di, j denote the endogenous pdf and Mdi, j the measure of entrants.For type u (d = u), Mdi, j is equal to ψΩ jue−β zu and for type w (d = w) Mdi, j is equal16Conditional on a wage, the problem for the entrepreneur is exactly as in the model with just onesector.17In other words, there is only one type of unemployment an individual can be in. In contrast,there are many different types of wage work an individual can be in.156to ψEiΩ je−β zw,iFinally, let for [zd,i,∞[Λdi, j(z) = Λdi, j,2(z) (A.151)and for ]zˆ,zd,i]Λdi, j(z) = Λdi, j,1(z) (A.152)Then for [zd,i,∞[∂Λdi, j,2(z)∂ t=−µ ∂Λdi, j,2(z)∂ z+σ22∂ 2Λdi, j,2(z)∂ z2+Mdi, jβe−β ze−β zd,i= 0 (A.153)for ]zˆi,zd,i]∂Λdi, j,1(z)∂ t=−µ ∂Λdi, j,1(z)∂ z+σ22∂ 2Λdi, j,1(z)∂ z2= 0 (A.154)The four boundary conditions are1.∫ ∞zd,iΛdi, j(z)dz < ∞2. Λdi, j,1(zd,i) = Λdi, j,2(zd,i)3.∂Λdi, j,1(zd,i)∂ z =∂Λdi, j,2(zd,i)∂ z4. Λdi, j,1(zˆi) = 0Now, to avoid cumbersome notation drop the subscript (i, j).Then, the proof just follows the same steps as the proof for Proposition 2.Proof of Proposition 19.157In equilibrium W i > U otherwise, ∀i ∈ I such U > W i all workers in that in-dustry would choose unemployment over employment in that industry and thatindustry would cease to exist.Proof of Corollary 19.1.Note that in steady state the flow of exiting firms of each type is equal to Mdi, j.18Letting ERdi denote Exit Rate for type d , where d = {u,w} having entered fromindustry i if d = w we will have(ERdi )−1 = [1+β (zd,i− zˆ)−µβ ] (A.155)(ERwi )−1 > (ERu)−1⇒ ERu > ERwi ∀i ∈ I (A.156)where the first inequality follows from zw,i > zu ∀i ∈ IIt follows that in the steady state equilibrium the exit rate is higher for firms of typeu.Proof of Corollary 19.2.The expression for optimal firm size is given byn(z,w) = (αw)11−α ez1−α (A.157)It follows average size for type (d, i, j), where d ∈ {u,w}, j the industry the18This comes from the fact that, in steady state, the flow of firms exiting a group has to be equalto the flow entering.158individual entered and i representing the industry of origin when d = w∫zˆn(z,w)Λdi, j(z)ηdi, jdz = (αw)11−αMdi, jηdi, j∫zˆez1−αΛdi, j(z)Mdi, jdz (A.158)Now to avoid heavy notation drop the subscripts (i, j) but remember all of theproof is done for a particular (i, j) group. Then the rest of the proof just followsthe proof of corollary 4.2.Proof of Corollary 19.3.To see that entry is higher for the unemployed, just note thatzw,i > zu⇒ ψ(1−F(zu))> ψ(1−F(zw,i)),∀i (A.159)A.3.4 Supplemental Appendix II : Solving for model with searchfrictionsTo get search frictions assume there is an intermediate goods sector which trans-forms individuals l into labour units y used by entrepreneurs. The intermediategoods sector has free entry condition (V = 0)rV =−cw+q(θ)(F−V ) (A.160)rF = ρ−w+λ (V −F) (A.161)V = 0 (A.162)159Wage determined by Nash Bargainingφ(W −U) = (1−φ)(F−V ) (A.163)Problem of the unemployedrU = bw+ p(θ)(W −U)+ψ∫zu(J(z)−U)dF(z) (A.164)rW = w+ s(U−W )+ψ∫zw(J(z)−W )dF(z) (A.165)Problem of the entrepreneur is as before (Optimal Stopping Problem)rJ(z) = pi∗(z)+µJ′(z)+σ22J′′(z) if z≥ zˆ (A.166)J(z) =U−χ if z≤ zˆ (A.167)J′(zˆ) = 0 (A.168)and optimal quantity n of intermediate good y to purchase solvespi∗(z)≡maxneznα −ρn (A.169)where ρ is determined by(1−u−η) =∫zˆn(z, p)Λ(z)dz (A.170)Note that total production of intermediate goods is just equal to the measure ofworkers (1−u−η) and the demand is the total demand due to entrepreneurs.160To see a relationship between w and ρ use Equations (A.160), (A.161) and (A.162)to getw =ρq(θ)c(r+ s)+q(θ)(A.171)Using the Nash Bargaining condition (Equation (A.163)) and Equations (A.162)and (A.160)cwq(θ)=φ1−φ (W −U) (A.172)Now replace w by its expressioncρc(r+ s)+q(θ)=φ1−φ (W −U) (A.173)which pins down θ for a given value of W and U . Finally, ρ is given by marketclearing in the intermediate goods sector1−u−η =∫zˆn(z,ρ)Λ(z)dz (A.174)where u is the measure of unemployed, η the measure of entrepreneurs, n(z,ρ) theoptimal amount of transformed labour to hire for a given productivity z and priceρ and Λ(z) is the distribution of firm productivity.Solving for optimal profits givespi∗(z) = (1−α)(αρ)α1−α ez1−α (A.175)Replacing ρ by its expression as a function of w and θ we getpi∗(z) = (1−α)( αw(c(r+λ )+q(θ))q(θ))α1−α ez1−α (A.176)161The cost of an intermediate goods unit for entrepreneurs is a function of wagesindividuals receive and tightness in the market θ . Note that∂pi∗(z)∂θ< 0 (A.177)and∂pi∗(z)∂w< 0 (A.178)Characterizing the EquilibriumProposition 20. The solution to the firm’s optimal stopping problem impliesJ(z) =Br− µ1−α − σ221(1−α)2(ez1−α +1a(1−α)e−a(z−zˆ)+ zˆ1−α ) (A.179)whereB≡ (1−α)(αρ)α1−α (A.180)a =µ+√µ2+2rσ2σ2> 0 (A.181)Not surprisingly, the value function of the business owner J(z) is increasing inproductivity for the range of values for which the business operates z ∈ [zˆ,∞[. 1919To see this note that∂ 2J(z)∂ z2=C(11−α )(ez1−α1−α +ae−a(z−zˆ)+ zˆ1−α )> 0 (A.182)and for z = zˆ∂J(z)∂ z= 0. (A.183)This implies for z≥ zˆ,∂J(z)∂ z≥ 0. (A.184)162Let Λw(z) denote the measure of business owners operating a business projectof productivity z that were employed by somebody else when they received thecurrent business opportunity and Λu(z) the measure of business owners operatinga business project of productivity z that were not working at the moment they re-ceived the current business opportunity.20Proposition 21. For all i ∈ {u,w}, the measure of business owners running a firmof productivity z is given by,• For z ∈ [zˆ,zi]Λi(z) = Λi1(z) =Mi−µ (1− e2µσ2(z−zˆ)) (A.186)• For z ∈]zi,∞[Λi(z) = Λi2(z) =βMi σ2−2µ e2µσ2(z−zi)(µ+ σ2β2 )− Mi−µ e2µσ2(z−zˆ)− Mie−β ze−β zi(µ+ σ22 β )(A.187)whereMi = ψue−β zu if i = u (A.188)Mi = ψ(1−u−η)e−β zw if i = w (A.189)Corollary 21.1. The measure of business owners, η , and the fraction that were not20In other words, this amount to saying that Λw(z) and Λu(z) are defined such that∫zˆΛu(z)dz+∫zˆΛw(z)dz+u+ e = 1 (A.185)where e is the measure of workers.163working prior to entering entrepreneurship, ηuη , are given by :η =ψ(1−η)s+ f +ψe−β zw[Au(s+ψe−β zw)e−β zu +Aw f e−β zw ] (A.190)ηuη=Au(s+ψe−β zw)e−β zuAu(s+ψe−β zw)e−β zu +Aw f e−β zw(A.191)whereAi = [1+β (zi− zˆ)−µβ ]. (A.192)We are now ready to define a Stationary competitive equilibriumDefinition 3. A Stationary competitive equilibrium is defined by zu,zw,ρ,η ,ηu,Λu(z),Λw(z),u,θ ,wsuch that• W >U• J(zw) =W• J(zu) =U• J(zˆ) = J(zu)−g• The expression for J(z) is given by Proposition 20• The expression for Λu(z) and Λw(z) are given by Proposition 21• u is given byu =(s+ψ(1−F(zw)))(1−η)p(θ)+ s+ψ(1−F(zw))(A.193)164• η and ηu are defined by corollary 21.1•ρ = α[1(1−u−η)(∫zˆez1−αΛu(z)dz+∫zˆez1−αΛw(z)dz)]1−α (A.194)•cρc(r+ s)+q(θ)=φ1−φ (W −U) (A.195)•w =ρq(θ)c(r+ s)+q(θ)(A.196)The first condition states that the value of being a employed worker is higherthan the value of not working. Otherwise, no individual would ever choose to tran-sition to wage work and markets would not clear. The second and third guaranteethat individuals’ decisions to open a business are optimal and the last three justcome from market clearing in the final good sector, determination of tightness inthe intermediate goods sector and wage determination via Nash Bargaining. Next,I summarize that the equilibrium can be characterized by a system of 5 equationsand 5 unknowns.A Stationary equilibrium can be characterized by 5 variables (θ ,ρ, zˆ,zu,zw)and 4 equations•rJ(zu) = bw+ f (J(zw)− J(zu))+ψ∫zu(J(z)− J(zu))dF(z) (A.197)165•rJ(zw) = w+ s(J(zu)− J(zw))+ψ∫zw(J(z)− J(zw))dF(z) (A.198)•J(zˆ) = J(zu)−χ (A.199)•ρ = α[1(1−u−η)∫zˆez1−αΛu(z)dz+∫zˆez1−αΛw(z)dz]1−α (A.200)••cρc(r+ s)+q(θ)=φ1−φ (J(zw)− J(zu)) (A.201)where J(z) is given by Proposition 20 and Λu(z),Λw(z) are given by Proposition21We are ready to go over the main theorem that subsequently generates all thepatterns that were documented in the data. It states that in equilibrium wage work-ers are more selective on which business opportunities to implement. The nec-essary and sufficient condition for it is simply that the income received while notworking is lower than that received as a worker. Were it not the case the equilibriumwould not exist as markets would not clear.Proposition 22. In equilibrium, zw > zu⇔ b < 1The next corollaries are all a result of the difference in selection directly relat-ing to the patterns documented empirically.166Corollary 22.1. In equilibrium, businesses created by employed workers have alower exit rate than those created by not working individuals.Corollary 22.1 is a result of the combination of all business owners exiting atthe same threshold while having different levels of selection upon entry betweenthe two types.Corollary 22.2. In equilibrium, businesses created by employed workers, on av-erage, have higher firm size and profits relative to those created by not workingindividuals.Corollary 22.2 is a direct consequence of the fact that both profits and firm sizeare monotonically increasing in productivity.Corollary 22.3. In equilibrium, the entry rate into business ownership of not work-ing individuals is higher than that of employed workers.Finally, as it is often the case with selection mechanisms an increased averageproductivity is associated to a lower entry rate.It follows that this stylized model is capable of capturing the differences inbusinesses created by not working individuals versus employed workers in the data.The next section derives a testable prediction from the theory and tests it in the data.Proof of Proposition 20.We know that it is equal to U ∀z ≤ zˆ. We need to find the value of J(z)for z ≥ zˆ. As in the benchmark model conditional on a price for the input of the167entrepreneur (w before, and now ρ), the optimal stopping problem is the same. Itfollows, the proof just follows from the proof in Proposition 1.21Proof of Proposition 21.Solving generic KFE. The solution below is the same for both types of busi-ness owners (i.e., i = u,w)Let zˆ be the point at which firms exit and zi the point in which firms enter,with zi > zˆ. Let Λ(z) denote the endogenous pdf and M the measure of entrants.For type u (i = u), M is equal to ψue−β zu and for type w (i = w) M is equal toψ(1−u−η)e−β zwFinally, for [zi,∞[Λi(z) = Λi2(z) (A.202)and for ]zˆ,zi]Λi(z) = Λi1(z) (A.203)Then for [zi,∞[∂Λi2(z)∂ t=−µ ∂Λi2(z)∂ z+σ22∂ 2Λi2(z)∂ z2+Miβe−β ze−β zi= 0 (A.204)for ]zˆ,zi]∂Λi1(z)∂ t=−µ ∂Λi1(z)∂ z+σ22∂ 2Λi1(z)∂ z2= 0 (A.205)The four boundary conditions are1.∫ ∞ziΛi(z)dz < ∞21Conditional on a wage, the problem for the entrepreneur is exactly as in the model with just onesector.1682. Λi1(zi) = Λi2(zi)3. ∂Λi1(zi)∂ z =∂Λi2(zi)∂ z4. Λi1(zˆ) = 0The proof then just follows the same steps as the proof for Proposition 2.Proof of Corollary 21.1.The steps of this proof just follow the steps of the proof of corollary 2.1.Proof of Proposition 22.The only difference between the value functions of U and W in the frameworkwith search frictions relative to the benchmark model is that the exogenous tran-sition rate from U to W , f , is replaced by an equilibrium object p(θ). But fromthe point of view of the individual making the decision to open a firm or not, thetransition rate from W to U is taken as given.It follows that for this proof we can just follow the same steps as the proof forProposition 4, except that I replace f by p(θ).Proof of Corollary 22.1.The proof of this corollary just follows the proof of corollary 4.1.Proof of Corollary 22.2.169The expression for optimal firm size is given byn(z,w) = (αρ)11−α ez1−α (A.206)The only difference relative to the model without search frictions is that thecost of one input for the entrepreneur was w and here it is ρ . But other than thatthe expression is identical. It follows that the proof of this corollary just followsthe proof of corollary 4.2.Proof of Corollary 22.3.zw > zu⇒ ψ(1−F(zu))> ψ(1−F(zw)).170A.4 Appendix to Chapter 2Proof of Theorem 6. To get this expression first evaluate V (ε) at ε = ε and usingU =V (ε) to obtain the following expression for UU =−c(r+λ )+q(θ)(1−β )(ε)r(r+2q(θ)(1−β )+λ )Now using the condition that individuals must be indifferent between searching fora job or for an idea we know thatrU = b+ p(θ)∫(W (ε∗)−U)dµ(ε∗)Replacing W (ε∗)−U = w−rUr+λ = β (ε)−2β rUr+λ , µ(ε) = f (ε)1−F(ε) and p(θ) = ψ(1−F(ε)) givesrU = b+ψ∫εβ (ε)−2β rUr+λf (ε)dεU =b(r+λ )+βψ∫ε(ε∗) f (ε∗)dε∗r(r+λ +2βψ(1−F(ε)))Setting both expressions for U equal we get the desired expression. This expressioncan also be written as(r+λ +2ψβ (1−F(ε)))(−c(r+λ )+q(θ)(z+ ε)(1−β ))= (r+λ +2(1−β )q(θ))(b(r+λ )+βψ∫ε(ε∗)dF(ε∗))171To see the expression implies a positive relationship between θ and ε totally dif-ferentiate with respect to both getting[−βψ(r+λ ) f (ε)ε−βψ2(1−β )q(θ)ε f (ε)− f (ε)c2β (r+λ )−q(θ)(1−β )(r+λ )−2β (1−F(ε))q(θ)(1−β )+βψ2(1−β )q(θ)ε f (ε)]dε= [q′(θ)(1−β )(r+λ )[ε−2b]+2β (1−β )q′(θ)ψ∫ε(ε∗− ε)dF(ε∗)]dθNote that ε − 2b > 0 in equilibrium otherwise for the marginal entrepreneur bothparties would be better if the match separated. This would contradict with theindividuals initial decision to become an entrepreneur.It follows that both sides of the expression above are negative implying a posi-tive relationship between θ and ε .Proof of Theorem 7. To show the result, totally differentiate the Entrepreneurshipequation with respect to ε and b holding θ constant to obtain[−βψ(r+λ ) f (ε)ε− f (ε)c2β (r+λ )−q(θ)(1−β )(r+λ )−2β (1−F(ε))q(θ)(1−β )]dε=−(r+λ +2(1−β )q(θ))(r+λ )dbFrom there we see that ε will increase for all θ levels. Since the Job Creationcurve does not shift, it follows that θ will decrease and ε will increase. To see thataggregate productivity increases remember thatµ(ε) =f (ε)1−F(ε)172It follows aggregate productivity can be written as∫εε f (ε)1−F(ε)dzProof of Theorem 8. To show the result, totally differentiate the Entrepreneurshipequation with respect to ε and c holding θ constant to obtain[−βψ(r+λ ) f (ε)ε− f (ε)c2β (r+λ )−q(θ)(1−β )(r+λ )−2β (1−F(ε))q(θ)(1−β )]dε=−(r+λ +2βψ(1−F(ε)))(r+λ )dcFrom there we see that ε will increase for all θ levels. Since the Job Creationcurve does not shift, it follows that θ will decrease and ε will increase. To see thataggregate productivity increases remember thatµ(ε) =f (ε)1−F(ε)It follows aggregate productivity can be written as∫εε f (ε)1−F(ε)dzSince ε increases with c, average firm productivity will increase following theshock.173Proof of Theorem 9. The law of motion for match surplus of average productivityrS(ε)=ξεξ −1−b−((δ∫εp(θ)βS(ε)v(ε)vdε)+(1−δ )(ψ∫ε(V (ε)−U)dF(ε)))−λS(ε)+ S˙(ε)(A.207)where ξεξ−1 =∫εε f (ε)1−F(ε)dε .∫ε p(θ)βS(ε)v(ε)v dε is the private opportunity cost of it unemployed always transi-tion back to wage work from unemployment. Note that βS(ε) =W (ε)−U . Sim-ilarly,∫ε(V (ε)−U)dF(ε)) is the private opportunity cost if unemployed alwaystransition to business ownership from unemployment. δ is the fraction of unem-ployed that search for a job. In equilibrium, individuals are indifferent whetherto search for a job or a business opportunity and so we can rewrite the conditionabove asrS(ε) =ξεξ −1 −b− (∫εp(θ)βS(ε)v(ε)vdε)−λS(ε)+ S˙(ε) (A.208)Finally using the fact that S(ε) is linear in ε , we can rewrite it asrS(ε) =ξεξ −1 −b− [λ + p(θ)β ]S(ε))+ S˙(ε) (A.209)From the Job Creation Curve,using the expression for rV (ε)J(ε) =rU + cq(θ)+U (A.210)which givesc = q(θ)(1−β )S(ε)− rU (A.211)174The social planner maximizes total welfaremaxv∫ ∞0e−rt [ξε(θ)ξ −1 (1−u− v)+ub− cv]dt (A.212)s.t. : u˙ = λ (1−u− v)− ( vu2)αu (A.213)where θ ≡ vu2Setting up the hamiltonean and taking FOCs (using ε = ψ1ξ θ−αξ ) givesc=ξξ −1(−αξ)ψ1ξ θ−αξ −1 1u2(1−u−v)− ξεξ −1−µ1[λ+ p′(θ)] (optimality for v)(A.214)andrµ1− µ˙1 = −ξξ −1ε+b−λµ1− (1−α)(vu2)α (optimality for u) (A.215)Now define pi =−µ1, and rewrite both conditions asrpi =ξξ −1ε−b−pi[λ +(1−α)p(θ)]+ p˙i (A.216)andc =ξξ −1(−ε(1−u)v)+pi[λ + p′(θ)] (A.217)For a given value of pi the two equations together with the expressions for S(ε)and ε = ψ1ξ θ−αξ allow us to solve for θ and β . pi is the additional benefit ofincreasing marginally the measure of non-unemployed in the economy. Note thatin equilibrium pi = S(ε).175Then comparing equation (A.216) and equation (A.209) gives[λ + p(θ)β ] = [λ +(1−α)p(θ)] (A.218)which impliesβ = (1−α) (A.219)A.4.1 Deriving the Endogenous Productivity DistributionThe law of motion for the measure of vacancies of a particular productivity ε isv˙(ε) = ψ(1− γ)u f (ε)−q(θ)v(ε) ∀ε ≥ εv(ε) = 0 ∀ε < εSetting the expression above to zero impliesq(θ)v(ε) = ψ(1− γ)u f (ε)Integrating with respect to ε and dividing the integrated expression in the equationabove yieldsµ(ε) =v(ε)v=f (ε)1−F(ε)This equation states that the distribution of enacted ideas, or firm productivity inthe economy, is fully characterized by the underlying distribution of feasible ideasand the threshold rule for entering entrepreneurship.176A.4.2 Deriving the Job Creation CurveFor the remainder of our analysis we will consider the economy to be in steadystate. The law of motion of the measure of jobs in the economy is given byn˙ = p(θ)γu−λnThe law of motion of the measure of total entrepreneurs in this economy is givenbye˙ = ψ(1−F(ε))(1− γ)u−λnSetting these two to zero implies thatp(θ) =ψ(1−F(ε))(1− γ)γThe law of motion of the total unemployed looking for a job in this economy isu˙w = γ2λn− p(θ)γuand that for those looking for an idea isu˙v = (1− γ)2λn− (1− γ)uψ(1−F(ε))Setting these two to zero implies thatp(θ) = ψ(1−F(ε))177A.5 Appendix to Chapter 3A.5.1 DataIn this section we describe the data sources, as well as how we construct workhistories and other relevant variables.Data SourcesThe main data source is the National Longitudinal Survey of Youth (NLSY79).The NLSY79 is a nationally representative sample of individuals aged 14 to 22 in1979. The sample period is 1979 to 2010, which makes the maximum age in thesample equal to 53. The NLSY79 consists of three samples: a main representativesample, a military sample, and a supplemental sample designed to over-representminorities. We only use the main representative sample. Throughout the baselineanalysis we focus on males 25 year or older. To gauge robustness we also extendthe sample to women who satisfy the sampling restrictions.Observations for which the reported stop date of the job precedes the reportedstart date, as well as jobs that last less than 4 weeks, are dropped. FollowingHagedorn and Manovskii [2013] we impose some basic sampling restrictions: (i)all observations for which the reported hours worked are below 15 hours are ex-cluded; (ii) the education variable is forced to be non-decreasing over the life cycle.Wages are deflated using the CPI. Following Barlevy [2008] we only consider ob-servations with reported hourly wages above $0.10 and below $1,000. Only obser-vations for individuals that have completed a long-term transition to full time labormarket attachment are used in the analysis. As in Yamaguchi [2010], an individualis considered to have made this transition starting from the first employment cy-178cle that lasts 6 or more quarters. Finally, for each job we assign the mode of hoursworked as the relevant value for that job. The reorganized NLSY79 data consists of34,860 job-wage observations, for a sample of 5,712 individuals. Not all of theseobservations can be used in the estimation because some control variables may bemissing in certain years.Jobs and Employment CyclesWe define each job as one subset of an employment cycle during which the em-ployer does not change. Each wage observation in the NLSY79 is linked to a mea-sure of the current unemployment rate. To construct the current unemploymentrates, we use the seasonally adjusted unemployment series from the Current Pop-ulation Survey (CPS). We use the Composite Help Wanted Index constructed byBarnichon [2010] as a measure of vacancies.22 We use the crosswalk provided byAutor and Dorn [2013] to link Census occupation codes with Dorn’s ‘standardized’occupation codes.23 We classify occupations into four categories: non-routine cog-nitive, non-routine manual, routine cognitive, and routine manual.24 Furthermore,as in Yamaguchi [2012], if a worker reports having the same job between period tand t+2, with occupation i in year t, occupation B in year t+1, and again occupa-tion i in t +2, then we assume that occupation B is misclassified and we correct itto be A. To minimize the effects of other coding errors, we follow Neal [1998] andPavan [2006] and disregard observations that report a change in occupation withina job (during a spell with the same employer). Industry codes are aggregated upto 15 major categories to make them comparable over time. In order to reduce the22https://sites.google.com/site/regisbarnichon/research.23David Dorn’s crosswalks are available at http://www.cemfi.es/dorn/data.htm.24This classification replicates the one presented in Cortes and Gallipoli [2014], Table A.1.179effects of industry coding error, and similar to the treatment of occupations, weonly consider observations for which there are no industry changes within the job.A.5.2 ProofsProofs for Model SectionProof of Proposition 10. Derivation of m1:E[piDPC] = (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m−κ(mmax−m)≥ (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m− (1−q)T = E[pispot ]⇒−κ(mmax−m)≥−(1−q)TRearrange to have:m >κmmax−T (1−q)κ≡ m1 (A.220)Derivation of m2:E[piDPC] = (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m−κ(mmax−m)≥ (1+q)PHm+(1−q)PLm−2a(PH)m = E[piFW ]⇒2a(PH)m− (1+q)a(PH)m− (1−q)a(PL)m+κm≥ κmmaxm [(1−q)(a(PH)−a(PL))+κ]≥ κmmax180Rearrange to have:m≥ κmmaxκ+(1−q)(a(PH)−a(PL)) ≡ m2 (A.221)Derivation of m3:E[pispot ] = (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m− (1−q)T≥ (1+q)PHm+(1−q)PLm−2a(PH)m = E[piFW ]Rearrange to have m on the left hand side:m≥ Ta(PH)−a(PL) ≡ m3 (A.222)Now for the second part of the proposition :m1 ≥ m2 iffκmmax−T (1−q)κ>κmmaxκ+(1−q)(a(PH)−a(PL))181which impliesκ2mmax−κT (1−q)+(1−q)(a(PH)−a(PL))κmmax−T (1−q)2 (a(PH)−a(PL))≥ κ2mmax−κT (1−q)+(1−q)(a(PH)−a(PL))κmmax−T (1−q)2 (a(PH)−a(PL))≥ 0−κT +(a(PH)−a(PL))κmmax−T (1−q)(a(PH)−a(PL))≥ 0(a(PH)−a(PL))κmmaxκ+(1−q)(a(PH)−a(PL)) ≥ T (A.223)m2 ≥ m3, iffκmmaxκ+(1−q)(a(PH)−a(PL)) ≥Ta(PH)−a(PL)which implies(a(PH)−a(PL))κmmaxκ+(1−q)(a(PH)−a(PL)) ≥ T (A.224)It follows the above thresholds are ordered according to• If T ≤ (a(PH)−a(PL))κmmaxκ+(1−q)(a(PH)−a(PL)) , then m1 ≥ m2 ≥ m3• If T > (a(PH)−a(PL))κmmaxκ+(1−q)(a(PH)−a(PL)) , then m3 > m2 > m1.Proof of Corollary 10.1. Proposition 1 implies182(a) For sufficiently low T: If T ≤ (a(PH)−a(PL))κmmaxκ+(1−q)(a(PH)−a(PL)) then:1. If m ≥ m1 then the firm offers a performance pay contract. In this range aDPC contract is preferable over both FW and SPOT.2. If m3 ≤ m < m1 then the firm offers a SPOT contract. In this range SPOT ispreferable over both DPC and FW.3. If m < m3 then the firm offers a FW contract.(b) For sufficiently high T: If T > (a(PH)−a(PL))κmmaxκ+(1−q)(a(PH)−a(PL)) then:1. If m≥m2 then the firm offers a DPC contract. In this range DPC is preferableto FW by definition of the threshold m2 and it is also preferable to SPOTbecause m > m1.2. If m < m2 then the firm offers a FW contract. In this range FW is preferableto DPC by definition of the threshold m2, and it also preferable to SPOTbecause m < m3.Proof of Proposition 11. Derivation of m4:E[piSPC] = 2(PH −a(PH))m−κ(mmax−m)≥ (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m−T (1−q) = E[pispot ]⇒(1−q)(PH −a(PH))m− (1−q)(PL−a(PL))m+κm≥ κmmax−T (1−q)m [(1−q)(PH −PL− (a(PH)−a(PL)))+κ]≥ κmmax−T (1−q)183Rearrange to have :m >κmmax−T (1−q)κ− (1−q)[(a(PH)−a(PL))− (PH −PL)] ≡ m4 (A.225)Derivation of m5:E[piSPC] = 2(PH −a(PH))m−κ(mmax−m)≥ (1+q)PHm+(1−q)PLm−2a(PH)m = E[piFW ]2PHm−κ(mmax−m)≥ (1+q)PHm+(1−q)PLm(1−q)(PH −PL)m+κm≥ κmmaxRearrange to have :m≥ κmmax(1−q)(PH −PL)+κ ≡ m5 (A.226)Derivation of m6:E[pispot ] = (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m− (1−q)T≥ (1+q)PHm+(1−q)PLm−2a(PH)m = E[piFW ]Rearrange to have m on the left hand side:m≥ Ta(PH)−a(PL) ≡ m6 (A.227)184Now for the second part of the proposition :m4 ≥ m5 iffκmmax−T (1−q)κ− (1−q)(a(PH)−a(PL)− (PH −PL)) >κmmaxκ+(1−q)(PH −PL)which impliesκ2mmax−κT (1−q)+(1−q)(PH −PL)(κmmax−T (1−q))≥ κ2mmax− (1−q)((a(PH)−a(PL))− (PH −PL))κmmax−κT (1−q)+(1−q)(PH −PL)κmmax−T (1−q)2 (PH −PL)≥−(1−q)(a(PH)−a(PL))κmmax+(1−q)(PH −PL)κmmax−κT (1−q)−T (1−q)2 (PH −PL)≥−(1−q)(a(PH)−a(PL))κmmaxκT +T (1−q)(PH −PL)≤ (a(PH)−a(PL))κmmaxT ≤ κmmax(a(PH)−a(PL))κ+(1−q)(PH −PL) (A.228)185m5 > m6, iffκmmaxκ+(1−q)(PH −PL) >Ta(PH)−a(PL)which impliesT ≤ κmmax(a(PH)−a(PL))κ+(1−q)(PH −PL) (A.229)It follows the above thresholds are ordered according to• If T ≤ κmmax(a(PH)−a(PL))κ+(1−q)(PH−PL) , then m4 ≥ m5 ≥ m6• If T > κmmax(a(PH)−a(PL))κ+(1−q)(PH−PL) , then m6 > m5 > m4.Proof of Corollary 11.1. Proposition 2 implies(a) For sufficiently low T: If T ≤ κmmax(a(PH)−a(PL))κ+(1−q)(PH−PL) then:1. If m ≥ m4 then the firm offers a performance pay contract. In this range aSPC contract is preferable over both FW and SPOT.2. If m6 ≤ m < m4 then the firm offers a SPOT contract. In this range SPOT ispreferable over both DPC and FW.3. If m < m6 then the firm offers a FW contract.(b) For sufficiently high T: If T > κmmax(a(PH)−a(PL))κ+(1−q)(PH−PL) then:1. If m≥m5 then the firm offers a SPC contract. In this range SPC is preferableto FW by definition of the threshold m5 and it is also preferable to SPOTbecause m > m4.1862. If m < m5 then the firm offers a FW contract. In this range FW is preferableto SPC by definition of the threshold m5, and it also preferable to SPOTbecause m < m6.Period 1 participation constraint (after learning period)In the main text we explain that an ex-ante participation constraint must hold forworkers who choose to stay with their employer:w1(m|PH)+E(w2(m))≥ a(PH)m+[qa(PH)+(1−q)a(PL)]E(m)Fixed wage contract: in this case w1(m) = w2(m) = a(PH)m. Therefore:2a(PH)m≥ a(PH)m+[qa(PH)+(1−q)a(PL)]E(m)a(PH)m≥ [qa(PH)+(1−q)a(PL)]E(m)m≥ [qa(PH)+(1−q)a(PL)]a(PH)E(m)Since [qa(PH)+(1−q)a(PL)]a(PH) < 1 it implies that for any m > E(m) the match does notseparate.Spot contract: in this case w1(m) = a(PH)m and E(w2(m)) = qa(PH)m+ (1−q)a(PL)m. Therefore:a(PH)m+qa(PH)m+(1−q)a(PL)m≥ a(PH)m+[qa(PH)+(1−q)a(PL)]E(m)[qa(PH)+(1−q)a(PL)]m≥ [qa(PH)+(1−q)a(PL)]E(m)m≥ E(m)187Which trivially implies that under spot contract matches survive if m > E(m).SPC: in this case equation (12) implies that the wages are w1(m) = a(PH)m andE(w2(m)) = (a(PH)−PH)m+qPHm+(1−q)PLm. Substitute:a(PH)m+(a(PH)−PH)m+qPHm+(1−q)PLm≥ a(PH)m+[qa(PH)+(1−q)a(PL)]E(m)a(PH)m+(1−q) [PL−PH ]m≥ [qa(PH)+(1−q)a(PL)]E(m)mE(m)>qa(PH)+(1−q)a(PL)a(PH)+(1−q) [PL−PH ]Note that the last condition implies a threshold for m such that matches do notseparate. In addition, it can be shown that given the assumption that a(PH)−a(PL) ≥ PH −PL, which is required for SPC, the right hand side of this conditionis smaller than 1. Therefore, it must be that the threshold is lower than E(m) andtherefore every match with m > E(m) does not separate before period 1. To seethis, check the conditions such that the right hand side is smaller than 1:qa(PH)+(1−q)a(PL)a(PH)+(1−q) [PL−PH ] < 1qa(PH)+(1−q)a(PL)< a(PH)+(1−q) [PL−PH ]0 < (1−q) [a(PH)−a(PL)− (PH −PL)]PH −PL < a(PH)−a(PL)DPC : in this case the wages are identical as to those in a spot contract. The resultsjust follow for the results for Spot contract described above.188A.5.3 Results with K(m) = K, ∀mThe firm has the choice between the following contracts and corresponding ex-pected profits :DPC: E[piDPC]= (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m−K.SPOT: E[piSPOT]= (1+q)(PH −a(PH))m+(1−q)(PL−a(PL))m− (1−q)TFW: E[piFW]= (1+q)PHm+(1−q)PLm−2a(PH)m.After comparing expected profits, one can characterize the threshold condi-tions. We do this in Proposition (23).Proposition 23. The firm decides which contract to offer depending on observedmatch-quality.1. The firm prefers a performance pay contract over a fixed wage contract ifm≥ K(1−q)a(PH)−a(PL) ≡ m2 (A.230)2. The firm prefers a spot contract over a fixed wage contract ifm≥ Ta(PH)−a(PL) ≡ m3 (A.231)3. The firm prefers a performance pay contract over a spot market contract ifT (1−q)> K (A.232)From the above set of thresholds we can see that whether or not firms offer spotor performance pay (DPC) contracts depends crucially on the costs T and K of each189contract. These costs cannot be observed in the data. However, independent ofthese costs, we get the result that for low enough match quality m only fixed wagecontracts will be implemented.25 Hence, the conclusion from this section is thatwhile for low match quality values m only fixed wage contracts are implemented,for high enough m employers could offer either performance pay or spot contracts.Secondly, it also tells us that performance pay contracts should exhibit more wagecyclicality since jobs not paid according to performance include both spot and fixedwages. 26A.6 An alternative assumption on period 1 aggregateproductivity: P1 = PLIn what follows we consider our model and the empirical implications when thestate of the world at the t = 1 is low, P1 = PL. We follow the same steps as de-scribed as in the main text. We start by solving for the optimal choice of b, thenperform the pairwise comparisons between contracts, and rank the range of matchquality for which we should observe different types of contracts.SPCThe optimal choice of b is given bymaxb{q(PHm− wˆ(m)−bPHm)+(2−q)(PLm− wˆ(m)−bPLm)−κ(mmax−m)}(A.233)25To see this note that, independant of the values of K and T , the thresholds imply that for m ≤min(m2,m3) fixed wages are implemented by employers.26This is true given that wage cycliclality is identical between wages determined by (DPC) con-tracts and spot wages.190subject toa(PH)m = wˆ(m)+bPHm (A.234)Now using wˆ(m) = a(PH)m−bPHm and replacing it in the maximization problemgivesmaxb{q(PHm−a(PH)m+bPHm−bPHm)+(2−q)(PLm−a(PH)m+bPHm−bPLm)}−κ(mmax−m)(A.235)Taking first order condition gives(2−q)(PH −PL)m > 0 (A.236)which implies b = 1 and wˆ(m) = a(PH)m−PHm. So it follows thatE[piSPC] = q(PHm−a(PH)m)+(2−q)(−a(PH)m+PHm)−κ(mmax−m) (A.237)E[piSPC] = 2(PH −a(PH))m−κ(mmax−m) (A.238)DPCThe optimal choice of b is givena(PH)m = wˆ(m)+bPHm (A.239)a(PL)m = wˆ(m)+bPLm (A.240)191Subtracting one equation from the other givesb =a(PH)−a(PL)PH −PL (A.241)and replacing b back into the H constraint giveswˆ(m) = [a(PH)−PH a(PH)−a(PL)PH −PL ] (A.242)It follows thatE[piDPC] = q[PH −a(PH)]m+(2−q)[PL−a(PL)]m−κ(mmax−m) (A.243)SpotE[piSpot ] = q(PH −a(PH))m−T q+(2−q)(PL−a(PL))m (A.244)Fixed WagesE[piFW ] = q(PH−a(PH))m+(2−q)(PL−a(PH))m=(qPH+(2−q)PL)m−2a(PH)m(A.245)192Deriving Cutoff Conditions We start by considering the case where a(PH)−a(PL)< PH−PL. Recall this is the case for which DPC is feasible and SPC is not.Then we proceed to the case where SPC is feasible and DPC is not.1st Case : a(PH)−a(PL)< PH −PLDPC is preferred to Spot ifq(PH −a(PH))m+(2−q)(PL−a(PL))m−κ(mmax−m)> q(PH −a(PH))m+(2−q)(PL−a(PL))m−T q (A.246)which simplifies toT q > κ(mmax−m) (A.247)m >κmmax−T qκ≡ m1 (A.248)DPC is preferred to FW ifq(PH −a(PH))m+(2−q)(PL−a(PL))m−κ(mmax−m)> q(PH −a(PH))m+(2−q)(PL−a(PH))m (A.249)193which simplifies to−qa(PH)m− (2−q)a(PL)m−κ(mmax−m)>−2a(PH)m (A.250)(2−q)(a(PH)−a(PL))m > κ(mmax−m) (A.251)m >κmmax(2−q)(a(PH)−a(PL))+κ ≡ m2 (A.252)Spot is preferred to FW ifq(PH −a(PH))m+(2−q)(PL−a(PL))m−T q> q(PH −a(PH))m+(2−q)(PL−a(PH))m (A.253)which simplifies to−qa(PH)m− (2−q)a(PL)m−T q >−2a(PH)m (A.254)m >T q(2−q)(a(PH)−a(PL)) ≡ m3 (A.255)Ordering of the thresholdsWe have m1 > m2 iffκmmax−T qκ>κmmax(2−q)(a(PH)−a(PL))+κ (A.256)194which implies(2−q)(a(PH)−a(PL))κmmax > T q(κ+(2−q)(a(PH)−a(PL)) (A.257)κmmax(2−q)(a(PH)−a(PL))κ+(2−q)(a(PH)−a(PL)) > T q (A.258)and we have m2 > m3 iffκmmax(2−q)(a(PH)−a(PL))+κ >T q(2−q)(a(PH)−a(PL)) (A.259)which impliesκmmax(2−q)(a(PH)−a(PL))(2−q)(a(PH)−a(PL))+κ > T q (A.260)It follows the two possible cases are1. κmmax(2−q)(a(PH)−a(PL))(2−q)(a(PH)−a(PL))+κ > T q, which implies m1 > m2 > m32. κmmax(2−q)(a(PH)−a(PL))(2−q)(a(PH)−a(PL))+κ ≤ T q, which implies m3 > m2 > m1For κmmax(2−q)(a(PH)−a(PL))(2−q)(a(PH)−a(PL))+κ > T q, we obtain• ∀m such that m > m1, DPC is implemented• ∀m such that m ∈ [m3,m1], Spot is implemented• ∀m such that m < m3, FW is implemented.195For κmmax(2−q)(a(PH)−a(PL))(2−q)(a(PH)−a(PL))+κ < T q, we obtain• ∀m such that m > m2, DPC is implemented.• ∀m such that m≤ m2, FW is implemented.2nd Case : a(PH)−a(PL)> PH −PLSPC is preferred to Spot if2(PH −a(PH))m−κ(mmax−m)> q(PH −a(PH))m+(2−q)(PL−a(PL))m−T q(A.261)which implies2(PH −a(PH))m−κ(mmax−m)> q(PH −a(PH))m+(2−q)(PL−a(PL))−T q(A.262)T q−κ(mmax−m)> (2−q)[(a(PH)−a(PL))− (PH −PL)]m (A.263)(κ− (2−q)[(a(PH)−a(PL))− (PH −PL)])m > κmmax−T q (A.264)m >κmmax−T qκ− (2−q)[(a(PH)−a(PL))− (PH −PL)] ≡ m4 (A.265)196SPC is preferred to FW if2(PH −a(PH))m−κ(mmax−m)> q(PH −a(PH))m+(2−q)(PL−a(PH))m(A.266)which implies(2−q)(PH −PL)m+κm > κmmax (A.267)m >κmmaxκ+(2−q)(PH −PL) ≡ m5 (A.268)Ordering of the thresholdsWe have m4 > m5 iffκmmax−T qκ− (2−q)[(a(PH)−a(PL))− (PH −PL)] >κmmaxκ+(2−q)(PH −PL) (A.269)which implies−κT q−T q(2−q)(PH −PL)+κmmax(2−q)(PH −PL)>−(2−q)[(a(PH)−a(PL))− (PH −PL)]κmmax (A.270)κmmax(2−q)[(a(PH)−a(PL))− (PH −PL)+(PH −PL)]> κT q+T q(2−q)(PH −PL) (A.271)κmmax(2−q)κ+(2−q)(PH −PL) > T q (A.272)197and we have m5 > m3 iffκmmaxκ+(2−q)(PH −PL) >T q(2−q)(a(PH)−a(PL)) (A.273)which impliesκmmax(2−q)(a(PH)−a(PL))κ+(2−q)(PH −PL) > T q (A.274)It follows the two possible cases are1. κmmax(2−q)(a(PH)−a(PL))κ+(2−q)(PH−PL) > T q, which implies m4 > m5 > m32. κmmax(2−q)(a(PH)−a(PL))κ+(2−q)(PH−PL) ≤ T q, which implies m3 > m5 > m4For κmmax(2−q)(a(PH)−a(PL))κ+(2−q)(PH−PL) > T q, we obtain• ∀m such that m > m4, SPC is implemented• ∀m such that m ∈ [m3,m4], Spot is implemented• ∀m such that m < m3, FW is implemented.For κmmax(2−q)(a(PH)−a(PL))κ+(2−q)(PH−PL) ≤ T q, we obtain• ∀m such that m > m3, DPC is implemented.• ∀m such that m≤ m3, FW is implemented.198A.7 Proof for Empirical Wage Processes sectionProof of Proposition 12. Proof. Log-linearize (w,m,P,X) around (w∗,m∗,P∗,X∗)for the SPC and spot contract wage expressions and (w,m,X) around (w∗,m∗,X∗)for the fixed wage contract, whereP∗ =Ph+Pl2w∗ = E[w], m∗ = E[m], X∗ = E[X ] (A.275)Log-linearization results in:1. For SPC : w∗(log(w)−log(w∗))= (Ph+Pl2 +a(Ph)−Ph)m∗(log(m)−log(m∗))+P∗m∗(log(P)− log(P∗))+X∗γ(log(X)− log(X∗))2. For Fixed wage : w∗(log(w)− log(w∗)) = a(Ph)m∗(log(m)− log(m∗)) +X∗γ(log(X)− log(X∗))3. For Spot : w∗(log(w)− log(w∗)) = da(P)dP |P=P∗P∗m∗(log(P)− log(P∗)) +a(P∗)m∗(log(m)− log(m∗))+X∗γ(log(X)− log(X∗))4. For DPC : w∗(log(w)−log(w∗))= da(P)dP |P=P∗P∗m∗(log(P)−log(P∗))+a(P∗)m∗(log(m)−log(m∗))+X∗γ(log(X)− log(X∗))After rearranging, and keeping only log(w) on the left hand side, we obtain:1. For SPC : log(w)= −(log(X∗)−log(w∗)w∗+log(m∗)+log(P∗))w∗ +(Ph+Pl2 +a(Ph)−Ph)m∗w∗ log(m)+P∗m∗w∗ log(P)+X∗γw∗ log(X)2. For Fixed wage : log(w)= −(log(m∗)+log(X∗)−log(w∗)w∗)w∗ +a(Ph)m∗w∗ log(m)+X∗γw∗ log(X)3. For Spot : log(w)= −(log(P∗)+log(m∗)+log(X∗)−log(w∗)w∗)w∗ +a(P∗)m∗w∗ log(m)+da(P)dP |P=P∗P∗m∗w∗ log(P)+X∗γw∗ log(X)1994. For DPC : log(w)= −(log(P∗)+log(m∗)+log(X∗)−log(w∗)w∗)w∗ +a(P∗)m∗w∗ log(m)+da(P)dP |P=P∗P∗m∗w∗ log(P)+X∗γw∗ log(X)Denote the by β1 and β2 the coefficients multiplying log(m) and log(P), re-spectively. Then:1. βDPC1 > 0,βSPC1 > 0,βFW1 > 0,βSpot1 > 02. βDPC2 > 0,βSPC2 > 0,βSpot2 > 0 and βFW2 = 0In particular, to see that β SPC2 > 0, note thata(Ph)−a(Pl) > Ph−Pl⇒ a(Ph)> Ph−Pl⇒ Ph+Pl2> Pl > Ph−a(Ph)⇒ Ph+Pl2+a(Ph)−Ph > 0where a(Ph)−a(Pl)> Ph−Pl is just the necessary condition for the SPC con-tract to be feasible.200

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