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Effects of labor regulation on informal labor markets Becerra-Camargo, Oscar 2016

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Effects of Labor Regulation on InformalLabor MarketsbyOscar Becerra-CamargoB.Sc., Universidad Nacional de Colombia, 2005M.Sc., Universidad Nacional de Colombia, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Economics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2016c© Oscar Becerra-Camargo 2016AbstractThis thesis examines the effects of labor regulation on formal (regulated)labor markets in Latin America. It is divided in three chapters, in which Ianalyze the effects of pension programs on formal-sector labor supply andthe effects of payroll taxes on formal-sector labor demand.The first two chapters analyze how future pension benefits affect formal-sector labor supply. Since formal-sector jobs comply with labor regulation,including contributions to pension plans, formal-sector workers receive long-run benefits in the form of pensions. If workers account for such benefitswhen they search for formal-sector jobs, the pension system affects formal-sector labor supply before the retirement age. In Chapter 1, I estimate thecausal link between future pension benefits and formal-sector labor supplyby using a cohort-based reform undertaken in Colombia. I demonstratethat workers with higher pension gains are more willing to work in formal-sector jobs, rather than working in unregulated businesses or by themselves.The result is consistent with a life-cycle model of formal-sector labor supplypresented in Chapter 2, where pension benefits are an amenity of working inthe formal sector. The results suggest that pension reforms may have largeeffects on the labor market that should be taken into account in the designof pension programs.Chapter 3 analyzes the effect of payroll taxes on formal-sector labor de-mand in the presence of wage rigidity. In particular, I study the impact of areduction of payroll taxes on the creation of formal-sector jobs in Colombia,where about 40 percent of formal-sector workers earn the minimum wage.Using a reform that granted tax credits to firms hiring workers younger than28 years of age, I obtain estimates of the effect of payroll taxes on formal-sector employment and wages. I show that payroll tax incidence is borneiiAbstractby formal-sector employers. The reduction in payroll taxes increased formal-sector employment and had no effects on wages. Using the estimation results,I recover an estimate of the elasticity of the formal-sector labor demand of-0.44. This result implies that a 10 percent increase in the minimum wagereduces formal-sector employment by 4.4 percent.iiiPrefaceThis dissertation is original, unpublished, independent work by the author,Oscar Becerra.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Pension Incentives and Formal-Sector Labor Supply . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Institutional background . . . . . . . . . . . . . . . . . . . . 61.2.1 Labor market institutions . . . . . . . . . . . . . . . . 61.2.2 The Colombian pension system . . . . . . . . . . . . . 71.3 Pension incentives and formal-sector labor supply . . . . . . 101.3.1 Retirement and formal-sector participation decisions . 121.3.2 Model implications . . . . . . . . . . . . . . . . . . . 131.3.3 General equilibrium . . . . . . . . . . . . . . . . . . . 161.4 Data and empirical approach . . . . . . . . . . . . . . . . . . 171.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.4.2 Identification strategy . . . . . . . . . . . . . . . . . . 191.5 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . 231.5.1 Identification checks . . . . . . . . . . . . . . . . . . . 23vTable of Contents1.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 251.5.3 Elasticity of formal-sector labor supply with respect tothe net-of-tax share . . . . . . . . . . . . . . . . . . . 311.6 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 332 A Life-Cycle Model for Formal-Sector Labor Supply . . . 542.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 542.2 The environment . . . . . . . . . . . . . . . . . . . . . . . . . 562.3 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.3.1 Numerical example . . . . . . . . . . . . . . . . . . . 622.4 No savings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642.4.1 Numerical example . . . . . . . . . . . . . . . . . . . 652.5 Separation rate less than one . . . . . . . . . . . . . . . . . . 662.6 Defined-contribution pension plan . . . . . . . . . . . . . . . 682.7 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Labor Demand Responses to Payroll Taxes in an Economywith Wage Rigidity . . . . . . . . . . . . . . . . . . . . . . . . . 773.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.2 Conceptual framework . . . . . . . . . . . . . . . . . . . . . . 803.3 Institutional background . . . . . . . . . . . . . . . . . . . . 843.3.1 Colombian payroll taxes and labor market . . . . . . 843.3.2 First Job Act . . . . . . . . . . . . . . . . . . . . . . . 863.4 Empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . 873.4.1 Data and sample selection . . . . . . . . . . . . . . . 873.4.2 Identification strategy . . . . . . . . . . . . . . . . . . 903.5 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . 933.5.1 Identification checks . . . . . . . . . . . . . . . . . . . 933.5.2 Baseline results . . . . . . . . . . . . . . . . . . . . . 943.5.3 Heterogeneity analysis . . . . . . . . . . . . . . . . . . 973.6 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 100Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112viTable of ContentsAppendicesA Appendix to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . 117A.1 Model implications and robustness tests . . . . . . . . . . . . 117B Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . 127B.1 Formal-sector labor supply of the young worker . . . . . . . . 127C Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . 131C.1 Robustness test . . . . . . . . . . . . . . . . . . . . . . . . . 131viiList of Tables1.1 Labor market composition and average wages, Colombia, 2011 351.2 General Pension System characteristics . . . . . . . . . . . . . 361.3 Identification checks, 2005 . . . . . . . . . . . . . . . . . . . . 381.4 RD estimation results, 2005 and 2011 . . . . . . . . . . . . . . 391.5 RD estimation results for wages in the formal sector, 2011 . . 401.6 Estimation results for other labor market outcomes, 2005 . . 411.7 Estimation results by educational attainment – Men, 2005 . . 421.8 RD results for indicators of household characteristics, 2005 . . 431.9 RD results by household characteristics – Men, 2005 . . . . . 441.10 Estimation results by region – Men, 2005 and 2011 . . . . . . 452.1 Pros and cons of working in the formal sector . . . . . . . . . 733.1 Payroll taxes in Colombia, 2010 . . . . . . . . . . . . . . . . . 1023.2 Summary statistics, average 2010-2012 . . . . . . . . . . . . . 1033.3 Balance tests, 2010 . . . . . . . . . . . . . . . . . . . . . . . . 1043.4 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . 1053.5 Estimation results for subsamples . . . . . . . . . . . . . . . . 106A.1 Robustness test, 2005 . . . . . . . . . . . . . . . . . . . . . . 124A.2 Robustness test, 2011 . . . . . . . . . . . . . . . . . . . . . . 125A.3 Estimation results with alternative definitions of formal em-ployment,2005 . . . . . . . . . . . . . . . . . . . . . . . . . . . 126C.1 Regression Discontinuity robustness test, 2011-12 . . . . . . . 132C.2 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . 133viiiList of Figures1.1 Distribution of wages for workers with High School diplomaor less, 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461.2 Replacement rate for the defined-benefit systems by weeks ofcontributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 471.3 Distribution of workers by age and number of weeks . . . . . 481.4 Probability of working in the formal-sector at age a = 50 . . . 491.5 Rolling t-statistics for testing the manipulation in date ofbirth, 2005 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501.6 RD estimation results, 2005 and 2011 . . . . . . . . . . . . . . 511.7 Labor force participation, salaried-informal employment andself-employment rates for Men, 2005 . . . . . . . . . . . . . . 521.8 Elasticity of the formal-sector labor supply to changes in thenet-of-tax share . . . . . . . . . . . . . . . . . . . . . . . . . . 532.1 Simulation results, model with savings . . . . . . . . . . . . . 742.2 Replacement rate . . . . . . . . . . . . . . . . . . . . . . . . . 752.3 Simulation results, model with no savings . . . . . . . . . . . 763.1 Effect of a reduction of payroll taxes in an economy with aninformal sector . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.2 Formal-sector employment and wages by age, 2010–2012 . . . 1083.3 Estimated employment effects by Semester, 2010–2012 . . . . 1093.4 Estimated employment effects by Age Group . . . . . . . . . 1103.5 Fraction of workers earning the minimum wage by firm size,2010-2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111ixAcknowledgementsI would like to express my deepest gratitude to Thomas Lemieux, JoshuaGottlieb, and Florian Hoffmann for their outstanding guidance in the prepa-ration of this document. Their invaluable advice and support made thisproject possible.I would also like to thank Vancouver School of Economics’ professors PaulBeaudry, Nicole Fortin, Nancy Gallini, David Green, Kevin Milligan, MaritRehavi, Tomasz Swiecki, and Yaniv Yedid-Levi for their useful commentsand the valuable discussion in and out of the classroom. I would like togive a special acknowledgment to my fellow classmates in the UBC PublicFinance Reading Group: Alix Duhaime-Ross, Timea Laura Molnar, DanielShack, Lori Timmins, and Tzu-Ting Yang for all the hours we spent togetherdiscussing this project.Finally, I thank Carlos Prada and Luz Angela Malagón from the Colom-bian Statistics office (DANE), and Mauricio Olivera and Adriana Hernandezfrom Colpensiones for facilitating access to the Census, PILA and Colpen-siones datasets. This work represents my sole views and does not necessarilyreflect those of DANE or Colpensiones.xTo Liceth, the best teammate I could have ever asked for.xiChapter 1Pension Incentives andFormal-Sector Labor Supply1.1 IntroductionDoes the prospect of future pension benefits determine workers’ choices indeveloping economies? Workers in these economies are able to respond topublic policies by changing their search strategies for finding work betweenthe formal and informal sectors. If workers respond to the prospect of pensionbenefits by changing their search for formal-sector jobs, then the pensionsystem affects formal-sector labor supply.The informal sector encompasses the set of firms and workers that donot comply with government regulation, including the payment of mandatedcontributions (e.g., pension) and taxes (Perry, Maloney, Arias, Fajnzylber,Mason, and Saavedra-Chanduvi, 2007).1 As a result, informal-sector workersare not covered by mandated benefits and other insurance included in theregulation. About 50 percent of Latin American workers work in the infor-mal sector, which is mostly less-educated people working as a self-employedworker or as a salaried-worker in a small firm (Perry et al., 2007). Empiricalevidence suggests that many informal-sector workers are part of an inte-grated labor market in which they move between sectors depending on thebenefits in each sector and the cost of finding formal-sector jobs (Maloney,2004).1As Santa María, García, and Mujica (2009) point out, the decision of firms to operatein the informal sector is the outcome of weak enforcement by tax authorities, high reg-ulation costs for registering, and low valuation of the benefits of operating in the formalsector.11.1. IntroductionWorkers’ behavioral responses along the formal-informal margin are animportant consideration for the design of retirement policies in Latin Amer-ican countries. In Latin America, approximately 50 percent of workers donot contribute to the pension system. Since most of these workers have a lowincome, the lack of pension contributions exacerbates income inequality af-ter retirement (Frölich, Kaplan, Pagés, Rigolini, and Robalino, 2014). LatinAmerican policymakers have implemented major pension reforms in responseto concerns about low coverage and high inequality in benefits. These reformshave included new types of funding, changes in qualifying conditions for re-ceiving a pension, and the introduction of pension assistance programs.2 Yetthese reforms have a potential offsetting cost. They may reduce the workers’expected gains from retirement contributions, thereby reducing the incentiveto search for formal-sector jobs.Despite the importance of workers’ behavioral response to retirementpolicies, the empirical evidence establishing a causal link between pensionincentives and formal-sector labor supply is scarce. The main empiricalchallenge is that the observable determinants of a worker’s expected pensionbenefits are likely correlated with unobservable determinants of the worker’scurrent labor choices. In absence of non-linear patterns in the pension benefitformulas, the variation in determinants of future expected benefits does notidentify the causal link between pension-related incentives and formal-sectorlabor supply (Liebman, Luttmer, and Seif, 2009).In this paper, I estimate the causal link between pension-related incen-tives and formal sector labor supply. I overcome the identification problemusing quasi experimental variation from a cohort-based reform to the Colom-bian pension system. In 1993, the Colombian government increased thepension contribution rate and changed the minimum qualifying conditionsfor receiving a pension in the defined-benefit system. However, the reformdid not change the qualifying conditions for eligible men born before April2Ten countries in the region implemented major reforms to their pension systems: Chile(1981 and 2008), Peru (1993), Colombia (1994), Argentina (1994, 2008), Uruguay (1996),Mexico (1997), Bolivia (1997), El Salvador (1998), Costa Rica (2000), Nicaragua (2000),and Dominican Republic (2003). A detailed list and discussion of other non-contributorypension programs is in Bosch, Melguizo, and Pagés (2013).21.1. Introduction1954 and eligible women born before April 1959. Compared with youngerworkers, eligible workers could retire contributing for fewer years (20 yearsinstead of up to 25), and at an earlier age (55 years for women and 60 yearsfor men, instead of 57 and 62). In this way, the reform permanently changedthe long-run gains from a formal-sector job depending on the worker’s birthdate.The difference in qualifying conditions by date of birth provides a sourceof exogenous variation to estimate the causal link between pension-relatedincentives and formal-sector labor supply. To estimate this effect, I imple-ment a two-stage procedure. First, I use a regression discontinuity design(RD) on two new confidential datasets from 2005 and 2011. I compute thedifference between formal-sector outcomes for workers born just before andjust after the eligibility cutoffs. If there is no other economic or institutionalfactor to explain a discontinuous change in formal-sector labor supply atthe cutoff, the difference is an estimate of the causal link between pension-related incentives and formal-sector labor supply. Second, I use additionalassumptions to recover the elasticity of the formal-sector labor supply withrespect to the net-of-tax share, a measure of the efficiency costs of pensiontaxes (Feldstein and Liebman, 2002).To understand the impact of the change in qualifying conditions onformal-sector labor supply, I develop a model that characterizes workers’decisions about retirement and job search in the formal and informal sec-tors. The model builds on the framework proposed by Chetty (2006) forunemployment insurance and adapted by Gerard and Gonzaga (2014) to in-clude an informal sector. I modify the model to incorporate a defined-benefitpension system, where the worker is entitled to a pension after reaching aminimum retirement age and a minimum number of years of contributions(the vesting period). In the model, workers search for formal-sector jobsbecause these jobs increase the likelihood of getting pension benefits in thefuture. Within an age group, the long-run gains from working in the formal-sector are a nonlinear function of the years of contribution. The higher gainsconcentrate among workers who are just below the vesting period, since theyare the ones more likely to see the vesting period as binding.31.1. IntroductionThe comparative statics of the model show that the effect of an increasein the minimum qualifying conditions on labor supply is heterogeneous, andthat even its sign is ambiguous. The direction of the response depends onthe worker’s previous contributions relative to the new vesting period. Onthe one hand, workers who are a long way from satisfying the new vestingrequirement reduce their search effort for formal-sector jobs, given their lowlikelihood of ever vesting. On the other hand, workers who are close tosatisfying the new vesting requirement increase their search effort for formal-sector jobs to secure their pension benefits. The magnitude of the effectdepends on the worker’s age and opportunities to find a formal-sector job.I present four main empirical findings. First, there is a sizable and signif-icant response in formal-sector labor supply to changes in pension incentives.The effect is concentrated among men. For men, the average effect of harderqualifying conditions on salaried-formal labor supply is negative 12 percentin 2005, while it is positive 7 percent in 2011. The change is consistent withthe insights provided by the model. By 2005, many workers born beforeApril 1954 had not reached the minimum 20 years of contribution for a pen-sion, giving them more incentives to work in the formal-sector than workersborn after April 1954, who have to contribute to the system a minimum of25 years. By 2011 many workers born before April 1954 had already metthe required 20 years of contribution, thereby losing their incentive to con-tribute. In addition, I find little evidence suggesting that the changes in theformal-sector labor supply is offset by changes in wages.Second, the change in formal employment is related to a shift from self-employment to salaried-formal employment, with no response along the ex-tensive margin. The estimated effect of harder qualifying conditions on self-employment (which is mostly informal) is positive and of similar magnitudeto the negative effect on salaried-formal employment. The estimated effecton labor force participation is not significant. These results are similar tothose of Almeida and Carneiro (2012), who found that higher mandatedbenefits with no wage adjustment generate an incentive for self-employedworkers to switch to salaried-formal jobs.Third, the response of formal-sector labor supply to pension incentives41.1. Introductionis heterogeneous, and depends on the worker’s labor market opportunities.The effect is concentrated among workers for whom the minimum qualify-ing conditions are binding. I analyze the response for groups with differentpropensities to work in the formal sector (e.g., education and region). Inthe analysis by educational attainment, I find that workers with primaryand post-secondary education are less responsive to pension incentives thanworkers with secondary education. This result is consistent with the modelpredictions; workers for whom the minimum qualifying conditions are notbinding are less sensitive to changes in pension incentives. Intuitively speak-ing, increasing the likelihood of securing future pension benefits is not arelevant factor for workers with no prospect of getting a pension, or workerswho know with certainty they will get a pension. I obtain consistent resultsfor other subsamples, such as those based on regional variation and maritalstatus.Fourth, I estimate an elasticity of the formal-sector labor supply with re-spect to the net-of-tax share of 1.7. Using variation by region and education,I regress the change in formal-sector employment at the discontinuity on thechange in the predicted net-of-tax share for workers at the discontinuity.Consistent with the predictions of the model, workers with higher pensionincentives along the formal-informal margin also exhibit higher responses informal-sector labor supply. The estimate is likely a lower bound of the actualelasticity, suggesting large behavioral responses.The paper is organized as follows: Section 1.2 describes the labor marketinstitutions and the Colombian pension system. Section 1.3 presents theconceptual framework that provides insights about the expected sign andsources of heterogeneity in the results. Section 1.4 discusses the identificationstrategy and the data sources. Section 1.5 reports the estimation results, andSection 1.6 concludes.51.2. Institutional background1.2 Institutional background1.2.1 Labor market institutionsThe Colombian government mandates that employers provide benefits totheir employees, and that self-employed workers contribute to the pensionand contributory health care systems. Workers covered by mandated benefitsare considered formal-sector workers.Formal-sector jobs generate two types of gains for workers. First, formal-sector workers have access to mandated benefits. For salaried workers,formal-sector jobs provide the following: insurance from the pension andcontributory health care systems, paid vacations (two weeks per year), sever-ance payments (an additional monthly wage per year of tenure), a maximumnumber of working hours (48 per week), maternity leave (14 weeks), a 13thmonth of pay each year, access to subsidies for children’s education, andcompliance with the minimum wage. For self-employed workers, the gainfrom paying their contributions is limited to the insurance provided by thepension and the contributory health care systems.3Second, formal-sector workers earn higher wages. As La Porta andShleifer (2014) show, formal-sector firms tend to pay higher wages thaninformal-sector firms, and formal self-employed workers tend to have moreeducation. Using data from the household surveys (described in Section1.4.1), Table 1.1 presents the average wage and distribution of urban work-ers aged 20 to 65 who work at least 30 hours per week. In the table, I definea formal-sector worker as a worker making a contribution to the pensionsystem and covered by the contributory health care system.4 The averageformal-to-informal wage gap is 75 percent for salaried workers and 100 per-cent for self-employed workers. The wage gap is positive regardless of the3The minimum contributions for the pension and contributory health care systems are16 and 12 percent of the minimum wage.4The coverage of pension and contributory health care systems is a widely-used measureof formal employment (Perry et al., 2007). Because workers are not subject to penaltiesfor being without coverage, it is unlikely that they would misreport their coverage sta-tus. Moreover, the formal employment indicators are consistent with aggregate statisticsobtained from administrative data.61.2. Institutional backgroundworker’s level of education and type of employment. Nonetheless, as Figure1.1 shows, the wage for a large fraction of informal-sector workers is abovethe minimum wage.Despite the gains available from working in the formal sector, other sup-ply and demand factors may prevent workers from working in this sector. Onthe labor supply side, workers may find it optimal to work in the informalsector (Maloney, 2004). Studies show that low valuation of mandated bene-fits, social programs that substitute the mandated benefits, and preferencesfor independent work reduce the incentives to search for formal-sector jobs(Levy, 2008; Perry et al., 2007). On the labor demand side, firms may find itoptimal to operate informally in response to high regulation costs and weakenforcement, thereby reducing workers’ chances of finding a formal-sectorjob. The effect of labor market regulation is evident in Figure 1.1, as a largefraction of formal-sector workers earn the minimum wage.1.2.2 The Colombian pension systemIn 1993, the Colombian government introduced the General Pension System(GPS), a new system intended to increase coverage and equality in retirementbenefits while improving the financial viability of the system. The GPSintegrates two pension systems: a new system to cover all new entrants, menborn after March 1954, and women born after March 1959; and a transitionsystem to cover all other workers.For young workers and new entrants, the GPS allows workers to choosebetween two pension systems. All public and private sector workers mustcontribute to one system, and their choice determines their pension eligibilityand benefits.5 The first system, the social insurance system, allows workersto contribute to a defined-benefit pension plan managed by Colpensiones(the public pension fund). In the defined-benefit plan, the pension benefitsare the maximum between a fraction of the worker’s wage and the minimumwage, while eligibility is based on the worker’s age and years of contribu-tion. The second system, the individual account system, allows workers to5Workers can switch systems every five years, up to the last ten years before theminimum retirement age (62 for men and 57 for women).71.2. Institutional backgroundcontribute to a defined-contribution plan managed by private pension funds.In the defined-contribution plan, the pension fund invests the worker’s con-tributions in the capital market, and the principal and returns constitutethe worker’s savings for retirement. The worker’s benefits and eligibility arebased on the accrued capital. The defined-contribution plan also includes aguaranteed minimum pension of a monthly minimum wage. Eligibility forthe guaranteed minimum pension is based on the worker’s age and years ofcontribution.6For all other workers, the GPS is the transition system where workerscontribute to a defined-benefit plan managed by Colpensiones. Unlike thesocial insurance system, the transition system retains the pre-reform eligi-bility and benefits for eligible workers. The eligibility criteria were basedon age and contributions at the time the reform took effect (April 1, 1994).Originally, three groups of employees were eligible for the transition system:men born before April 1954 who had contributed before April 1994, womenborn before April 1959 who had contributed before April 1994, and youngerworkers who had contributed to the system for at least 750 weeks (just over14 years). A 2005 reform required eligible workers to have contributed morethan 750 weeks by July 2005 and meet the qualifying conditions by 2014.7Table 1.2 and Figure 1.2 summarize the main characteristics of the GPS.Workers in the three systems face the same contribution rate (16 percent)8but different minimum qualifying conditions. Compared with younger work-ers and new entrants, an eligible worker could retire having contributed forfewer years (20 years instead of up to 25) and at an earlier age (55 years forwomen and 60 years for men instead of 57 and 62). Although the transition6When workers do not accumulate enough time (and capital) for being entitled to apension, their contributions are refunded in a lump-sum payment. In the social insurancesystem they receive their contributions adjusted by inflation, in the individual accountsystem they receive the accrued capital plus interest.7In the rest of the paper, I focus on the eligibility criteria based on the date of birthof the worker. The criterion based on 750 weeks by 1993 has a limited effect on youngerworkers, given that the requirement implies that men younger than 40 and women youngerthan 35 would have worked by at least 14 years in the formal sector. Moreover, after the2005 reform, men born after 1954 and women born after 1959 became ineligible for thetransition system, even though they could have met the original eligibility criteria.8The contribution rate before the 1993 reform was 6 percent.81.2. Institutional backgroundsystem has a higher replacement rate than the social insurance system, theminimum pension guarantee implies that low wage workers face the sameeffective replacement rate in both systems (Figure 1.2). This is a relevantfeature of the system given that 90 percent of workers in the GPS reportearnings between one and two times the minimum wage.Relevance of the minimum qualifying conditions. The importanceof differences in the minimum qualifying conditions for a pension depends onwhether the workers take these conditions into account when making theirretirement decisions. Figure 1.3 shows that most workers claim their pen-sion benefits as soon they meet the requirements. Based on statistics fromColpensiones, Figure 1.3 displays the distribution by age and weeks of contri-bution for non-retired men and women who contributed to Colpensiones upto December 2013. I focus on workers around the minimum retirement age,60 years for men and 55 years for women. The distribution exhibits a cleardiscontinuity at the minimum retirement age when the number of weeks isabove 1,000 (the minimum for the transition system) and the discontinuitywidens as the number of weeks increases.Interactions with other programs. The introduction of the GeneralPension System generated cohort differences in the minimum qualifying con-ditions and pension benefits received by workers. However, the differencesin the conditions may have a limited effect on the workers’ behavior if therewere other cohort-based assistance programs targeted to the same popula-tion.In recent years, Colombia has expanded several non-contributory socialassistance programs. Three of the most significant programs are the non-contributory health care system, conditional cash transfers for families withchildren aged 0 to 17, and a subsidy of approximately 20 percent of theminimum wage for old-age population. The eligibility for these programsis based on a poverty score index computed by the Colombian government,and the programs’ eligibility threshold changes by program. An importantfeature of the poverty score index is that it does not depend on whether91.3. Pension incentives and formal-sector labor supplythe person has a formal-sector job, or whether the person is eligible for thetransition system. Consequently, other assistance programs do not offset thecohort differences caused by eligibility for the transition system.1.3 Pension incentives and formal-sector laborsupplyTo understand the incentives that workers consider when making their laborsupply decisions, I present a model of workers’ decisions with respect toretirement and formal-sector participation. In this model, a representativeworker chooses between retiring and searching for a job, given a defined-benefit pension plan and a labor market with an informal sector.The representative worker lives for T − a0 + 1 periods, indexed by a =a0, . . . , T . Each period, the worker chooses whether to retire and leave thelabor market permanently. If he retires and is eligible for retirement benefits,he receives a fraction b of the wage in the formal sector wf along with otherbenefits valued θr (e.g., health care). If he retires and is not eligible forretirement benefits, he gets zero income. Thus, the retiree’s earnings at agea are ea (τa−1) bwf . The variable ea (τa−1) is an indicator of the worker’spension eligibility, where τa−1 stands for the number of periods the workerhas worked in the formal sector. To be entitled to retirement benefits, theworker is required to work for at least τ∗ periods in the formal sector and beat least R periods old, and thus ea (τa−1) = 1 {τa−1 ≥ τ∗} · 1 {a ≥ R}.If the worker does not retire, he draws a random shock of searching for aformal-sector job ψa ∈ R, which follows an i.i.d distribution with cumulativedistribution G (·). ψa is measured in utility units and it is used as a catch-allvariable summarizing the relative cost of searching and workers’ preferencesfor formal-sector jobs. After drawing ψa, the worker decides between workingin the formal sector and working in the informal sector. If he chooses towork in the formal sector, he will receive a wage wf along with mandatedbenefits (valued θf ), will face the utility shock ψa, and will be liable to paythe pension tax rate tnom. Additionally, his cumulative number of periods101.3. Pension incentives and formal-sector labor supplywith a contribution to the pension system will increase by one period (soτa = τa−1 + ha, where ha is an indicator of whether the worker searches fora formal-sector job). If he chooses to work in the informal sector, he willreceive a wage wi (I assume that wi ≤ wf (1− tnom) and θr ≥ θf ). Forsimplicity, I assume that the worker loses his job at the end of the period,and that he cannot save. In Chapter 2 I show that the model implicationsare robust to more general assumptions.Since the worker does not save, so his consumption per period is equal tohis income. Let ra denote an indicator of whether the worker retires at thebeginning of period a. Given τa−1, the worker’s problem at the beginning ofperiod a isva (τa−1) = maxra∈{0,1}{vwa (τa−1) , vra (τa−1)} (1.1)wherevwa (τa−1) =E maxha∈{0,1}{u(wi)+ βva+1 (τa−1) ,u(wf (1− tnom))+ θf − ψa + βva+1 (τa−1 + 1)}vra (τa−1) =u(ea (τa−1) bwf)+ ea (τa−1) θr + βvra+1 (τa−1)and τa0−1 = 0. In the definitions above, u (c) is the worker’s utility overcurrent consumption, which I assume to be continuous, strictly increasing,concave, and state-independent; 0 < β < 1 is the discount factor, andvwT+1 (τT ) = vrT+1 (τT ) = 0.The model encompasses the two common views in the literature about theincentives for workers to work in the informal sector (Gerard and Gonzaga,2014). First, workers may choose to work in the informal sector becausethe perceived gains from formal-sector jobs are low. In the model, low gainsfrom searching are represented by a low formal-to-informal wage gap and alow valuation of the mandated benefits provided by a formal-sector job (i.e.,low θf and β). Second, workers may choose to work in the informal sectorbecause finding a formal-sector job is difficult due to labor market rigidities111.3. Pension incentives and formal-sector labor supplyand other structural characteristics (e.g., preferences for independent work).In the model, less favorable labor market opportunities are represented bya distribution of search costs with a heavier right tail. When G (ψ) has aheavy right tail, it is likely that the worker draws a large value of ψ, highenough to offset the gains from working in the formal sector. It is commonto have these two forces interact and reinforce each other. For example,workers with narrower wage gaps may also face higher search costs, furtherreducing the incentive to work in the formal sector.1.3.1 Retirement and formal-sector participation decisionsThe labor supply plan that solves the worker’s problem can be obtained bybackward induction. Given the value function, the worker’s labor supplyand retirement decisions can be obtained in a two-stage procedure. In thefirst stage, the worker finds the optimal plan for searching for a formal-sector job and the value function from working. In the second stage, theworker compares the value function from working with the value functionfrom retiring, and determines the optimal retirement decision policy.In the first stage, given a realization of the search cost ψa, the workersearches for a job in the formal sector as long as the gains from the searchare greater than the costs. Thus, the worker searches for a formal-sector job(sets ha = 1) ifu¯a (τa−1) = u˜+ β∆va+1 (τa−1 + 1) ≥ ψa. (1.2)where u˜ and ∆va+1 (τa−1 + 1) are defined asu˜ = u(wf (1− tnom))+ θf − u (wi)∆va+1 (τa−1 + 1) = va+1 (τa−1 + 1)− va+1 (τa−1) .In inequality (1.2), u¯a (τa−1) summarizes the gains from working in a formal-sector job. The first term represents the short-run gains, that is, the utilitygains determined by the differences in wages in both sectors along with themandated benefits. The second term represents the long-run gains, that is,121.3. Pension incentives and formal-sector labor supplythe gain that one additional period of working in the formal sector has onthe likelihood that the worker will receive pension benefits in the future.From inequality (1.2), the ex ante probability that a worker works in theformal sector isP (ha = 1 | τa−1) = G (u¯a (τa−1)) , (1.3)and the value function from working isvwa (τa−1) = u(wi)+ va+1 (τa−1)+G (u¯a (τa−1))E ( u¯a (τa−1)− ψa|ψa ≤ u¯a (τa−1)) .(1.4)In the second stage, the worker retires if the value function from retiringis greater than the value function from working. Thus, the worker retires(sets ra = 1) ifvra (τa−1) ≥ vwa (τa−1) . (1.5)1.3.2 Model implicationsThe model provides four useful predictions that contribute to understandthe empirical results of the paper. The first three predictions are discussedin detail in the Appendix A.1.The first prediction of the model is that, when the replacement rate equalsone, the worker retires as soon as he meets the qualifying conditions. Theretiree receives the wage in the formal sector as pension and does not have topay the search cost. Since b = 1 is the effective rate faced by Colombian low-wage workers, the result is consistent with the patterns reported in Section1.2.2, where workers retire as soon as they meet the minimum requirementsof age and years of contribution.9 Values of b lower than one may delay theretirement decision, depending on the value function conditional on working.The second prediction of the model is that the long-run gains from aformal-sector job are heterogeneous and depend on the worker’s employment9An alternative explanation is that the worker is myopic or information constrained. Ifso, he may take the requirement conditions as target values regardless of the incentive todelay his retirement. In Chapter 2 I develop a version of the model in which the minimumretirement age is exogenous, and the predictions hold.131.3. Pension incentives and formal-sector labor supplyhistory (τa−1). Equations (1.2) and (1.3) imply that the worker’s search forformal-sector jobs depends on the long-run gains from working in the formalsector. However, not all workers have the same long-run gains. Workers whocannot accumulate enough years to meet the vesting requirement will notreceive pension benefits; therefore their long-run gains from a formal-sectorjob are zero (∆va+1 (τa−1 + 1) = 0). Similarly, workers who already metthe vesting requirement do not have long-run gains from working an extraperiod in the formal sector. For the remaining workers, the long-run gainsfrom working in the formal sector are positive. Because the probability ofworking in the formal sector is an increasing function of the long-run gainsfrom a formal-sector job, the result implies that workers with positive long-run gains search more actively for formal-sector jobs. Nonetheless, someworkers with no long-run gains continue to work in the formal sector, buttheir decision is motivated by short-run gains only.The third prediction of the model is that a change in the minimum re-tirement age R or the vesting period τ∗ affects formal-sector labor supply.The effect of an increase in R on formal-sector labor supply is negative, sinceit reduces the long-run gains from working in the formal sector. In contrast,the effect of an increase in τ∗ on formal-sector labor supply is ambiguous.The increase in τ∗ shifts the long-run gains from working in the formal sec-tor to the right, generating two opposite effects depending on the worker’semployment history. On the one hand, workers who are close to meetingthe new vesting requirement increase their search efforts to reach the newthreshold. On the other hand, workers with a few existing years of contri-bution reduce their search efforts because it is unlikely that they will meetthe new requirement.Finally, the fourth prediction of the model is that the magnitude of theresponse to changes in the qualifying conditions for retirement depends onthe worker’s labor market opportunities. The response is smaller in labormarkets with low formality rates (a low value of u˜ and a search cost distribu-tion with a heavy right tail), and labor markets with high formality rates (ahigh value of u˜ and a search cost distribution with a light right tail). WhenP (ha = 1 | τa−1) → 0, workers cannot reach the vesting requirement and141.3. Pension incentives and formal-sector labor supplythe long-run gains from searching are zero. When P (ha = 1 | τa−1) → 1,workers always reach the vesting requirement and the long-run gains fromsearching for formal-sector jobs are zero. The effect of changes in the qual-ifying conditions is concentrated among workers who struggle to meet thevesting requirement but for whom reaching this threshold is still possible.Figure 1.4 shows the expected value function (va+1 (τa), top) and theprobability of searching for a formal-sector job (G (u¯a (τa−1)), bottom) byyears of contribution for two simulated cohorts aged a = 50. Both cohortsface the same labor market opportunities, but different defined-benefit pen-sion plans. One plan sets a minimum retirement age of R = 60 years, avesting period of τ∗ = 20 years, and a replacement rate of b = 1. The otherplan sets R = 62, τ∗ = 25 and b = 1.10 Since b = 1 in both plans, work-ers facing both schemes retire as soon as they meet the requirements. Forboth cohorts, the long-run gains from working one more period in the formalsector are higher in years just below the vesting period, as working in theformal sector increases more the likelihood of securing pension benefits. As aresult, the probability of working in the formal sector is higher in years justbelow the vesting period. An increase of the minimum qualifying conditionsshifts the expected value function to the right (workers have to work moretime to reach the vesting period) and reduces its level (workers receive thepension benefits for less time).The probability of working in a formal-sector job given the two pensionplans is presented in the bottom panel of Figure 1.4. The figure shows thatan increase in the minimum qualifying conditions has a heterogeneous effecton the formal-sector labor supply, depending on the years of formal-sectorexperience. Workers with a few years of experience are not sensitive todifferent qualifying conditions, as they are too far from reaching the vestingrequirements. Similarly, workers with many years of formal-sector experienceare not sensitive to different qualifying conditions, as they already securedtheir pension benefits. For the rest of workers, the increase of the minimum10In addition, I assume that workers’ work from a0 = 20 up to T = 75 years andtheir utility is linear. I also assume that wf (1− tnom) = 1.2, wi = 1, θr = θf = 0,ψi.i.d∼ U (0, 0.5), and β = 11.05.151.3. Pension incentives and formal-sector labor supplyqualifying conditions has two types of effects on formal-sector employment.On the one hand, harder qualifying conditions discourage workers with a fewperiods of formal-sector experience, given the difficulty in reaching the newvesting requirement. On the other hand, more difficult qualifying conditionsencourage workers approaching the new vesting requirement to search forformal-sector jobs, given that they are required to contribute additional yearsto reach the new vesting period. The sign of the overall effect of changes inminimum qualifying conditions on formal-sector labor supply is ambiguousand depends on the distribution of the workers’ formal-sector experience.1.3.3 General equilibriumThe model shows that future pension benefits create incentives for workersto work in the formal sector. In general equilibrium, though, changes in thelong-run gains from working in the formal sector should be offset by changesin wages. Because future pension benefits are attractive to workers, workerswould be willing to give up part of their wage in order to get the long-rungains from a formal-sector job (Summers, 1989).The previous observation implies that, in equilibrium, the wage gapshould exhibit an inverse pattern to that observed in Figure 1.4. Changesin qualifying conditions would be reflected in wages, leaving formal employ-ment unchanged. However, the result requires that the extra benefits canbe passed on to workers by way of lower wages, which are determined bythe wage-setting process (Saez, Matsaganis, and Tsakloglou, 2012). Institu-tional factors such as minimum wage laws, search based on posted earnings,unobservable employment history, and pay fairness norms may prevent firmsfrom setting differential wages among workers. If firms are not able to seta different wage scale for workers who do similar work, the response of theformal-sector labor supply changes the wage gap for all workers. As a result,the comparative statics of changes in the minimum retirement age and thevesting period exhibit similar patterns to the presented in Figure 1.4.161.4. Data and empirical approach1.4 Data and empirical approach1.4.1 DataTo measure the effects of changes in qualifying conditions on formal-sectorlabor supply, I combine two new sources of confidential data. The first sourceis the microdata from the long-form questionnaire of the Colombian Censusof 2005. This is a cross-sectional dataset including information about labormarket outcomes, pension and health care coverage, and demographic andhousehold characteristics. The second source is the PILA dataset of 2011, anadministrative dataset that collects information on all workers and earningsin the formal sector.These two datasets have limitations but are highly complementary: Iam able to analyze factors with the Census dataset that I am not able toanalyze with the PILA dataset, and vice versa. In particular, the Cen-sus dataset does not include information about workers’ earnings, while thePILA dataset does not include information about informal employment ordemographic characteristics. Moreover, using both datasets, I am able tostudy the response of the formal-sector labor supply to changes in the pen-sion incentives as the workers age.Neither the Census nor PILA datasets includes the worker’s employmenthistory. I complement the information from the Census and PILA datasetswith the distribution of years of contributions from the Colombian householdsurveys.Colombian Census (2005)The long-form questionnaire of the Colombian Census for 2005 collates in-formation from 2 million households and 9.7 million people, approximately20 percent of Colombian households. The dataset includes date of birth(in months), demographic information, type of employment, contributionsto the pension system, and health care system coverage. The informationabout date of birth is reliable since the interviews were carried out in personand the interviewer was able to verify the date of birth from the respondent’s171.4. Data and empirical approachidentification card. In the absence of an identification card, the date of birthwas either provided by the respondent or inferred on the basis of the reportedage. The birth date for 92 percent of the urban population was establishedon the basis of their identification card.The sample used in this paper is based on people living in urban areas,with a known date of birth, and born up to four years before or after the dateof eligibility for the transition system (April 1950 to April 1958 for men, andApril 1955 to April 1963 for women). The final samples sizes are 129,061 formen and 178,990 for women.PILA dataset (2011)The PILA dataset is a new dataset designed to collect information fromthe system used by firms and independent workers to pay for mandatedbenefits. Since formal-sector workers must be covered by mandated benefits,the dataset collects information for all formal-sector workers, and includesidentifiers for employer and employee, basic wage, job location, gender anddate of birth (in days) of the employee. The worker’s date of birth and genderare added by the Ministry of Health based on the employee’s identificationcard number. This dataset also includes information about firm ownership(public or private) and type of worker (independent or employee). It includesapproximately eight million employer-employee pairs per month.I select information from the entire dataset about all private-sector em-ployees between February and December 2011 (66 percent of total formalemployment). Although the dataset incorporates all formal workers, thereare some problems with the identification numbers for employers and em-ployees. To avoid false transitions in and out of the dataset, I fill in job spellsin cases where an employer-employee match is missing and where the datasetrecords the same match up to three months before and after. In addition, Idrop employees who appear only once in the dataset.The sample used in this paper is based on all workers who were born upto two years before and after the eligibility threshold (April 1952 to March1956 for men, and April 1957 to March 1961 for women). The final sample181.4. Data and empirical approachsizes are 964,558 for men (about 88,000 observations per month), and 927,961for women (about 84,000 observations per month).Household Surveys (2006-2011)The Colombian Household survey is the official source of employment statis-tics in Colombia. After a large methodological change in 2006, the datasetincludes information about an individual’s date of birth (in months), andcoverage in terms of pension and contributory health care systems. The sur-veys also contain information about a worker’s earnings and the number ofyears of contributions made (conditional on contributing). The main limi-tation of the household surveys for this study is the small sample size forthe cohort of interest. The number of observations by birth month in a yearis approximately 200 people, and only about 40 people report informationregarding years of contributions.The sample used in this paper is based on all urban workers born up tothree years before and after the eligibility threshold. The final sample sizesare 12,222 for men and 19,139 for women.1.4.2 Identification strategyTo identify the effect of pension incentives on the formal labor market out-comes, I use a two-stage approach. In the first stage, I use a regressiondiscontinuity design (RD) to estimate the effect of harder qualifying condi-tions on labor market outcomes. These estimations provide evidence on theresponse of formal-sector labor supply to pension incentives, without makingfurther assumptions about workers’ earnings and expectations. In the secondstage, I use additional assumptions to recover an estimate of the elasticityof the formal-sector labor supply with respect to the net-of-tax share.Effect of harder qualifying conditions on labor market outcomesTo identify the causal link between future pension benefits and formal-sectorlabor supply, I use a sharp regression discontinuity design. Given a cross-191.4. Data and empirical approachsectional sample of population, I run regressions of the formYi = α0 + ρ1{DOBi≥0} +K∑k=1(αk + βk1{DOBi≥0}) ·DOBki + εi (1.6)where Yi is an indicator of the formal-sector labor supply; DOBi is the nor-malized date of birth of the individual (DOBi = 0 corresponds to the cutofffor harder qualifying conditions); 1{DOBi≥0} is a treatment indicator equal toone for people born after the cutoff, who are the ones facing harder qualify-ing conditions; and∑Kk=1(αk + βk1{DOBi≥0}) ·DOBki is a control function.Based on the reported date of birth, the relevant cutoff for eligibility for thetransition system is April 1954 for men and April 1959 for women. Workersborn before those dates were eligible for retirement benefits with 1,000 weeksof contributions and at an age of 55 (women) and 60 (men), while workersborn after those dates are required to retire two years later (older), and aftercontributing up to 300 additional weeks.The identifying assumption in this setup is that unobserved determi-nants of the formal-sector labor supply evolve smoothly around the eligibilitythreshold. Under this assumption, ρ can be interpreted as the average effectof harder qualifying conditions on the formal-sector labor supply, defined asρ = limc↓0E (Yi|DOBi = c)− limc↑0E (Yi|DOBi = c) . (1.7)(Imbens and Lemieux, 2008). However, as discussed in Section 1.3, theresponse of the formal-sector labor supply to changes in minimum qualifyingconditions depends on the worker’s age (a) and years of contribution (τa−1).Therefore, ρ corresponds to the weighted average of the effect by previouscontributions, i.e.,ρ =ˆτa−1(limc↓0E(Yi|DOBi = c, τ ′)− limc↑0E(Yi|DOBi = c, τ ′))dFa(τ ′),(1.8)where Fa (τ) represents the distribution of years of contribution at age a.201.4. Data and empirical approachSince the expected change in qualifying conditions has an ambiguouseffect on the formal-sector labor supply, the sign of ρ is ambiguous. Asdiscussed in Section 1.3, the expected effect is positive for workers who area long way from reaching the new vesting threshold, while it is negative forworkers near the new vesting requirement. The sign of the average effectdepends on the specific distribution of the number of years of contributionsin the population.Although the distribution of the years of contribution is not observedin the data, the analysis in Section 1.3 provides useful insights about theexpected sign and magnitude of ρ. First, ρ should increase with the worker’sage, as the distribution of τ shifts toward higher values of τ as workers age,putting more weight on the positive effects. Second, ρ should be smaller(in absolute value) for groups of workers with a low probability of findinga formal-sector job. For them, the estimated average effect should be smallsince they have low long-run gains from searching and a right-skewed dis-tribution of previous contributions. A similar explanation would apply tothe result for workers with a high probability of finding a formal-sector job.Workers with a middle-range probability of finding formal-sector jobs are themost responsive to changes in the minimum qualifying conditions.An additional assumption is required for the estimation of the effects ofharder qualifying conditions on formal-sector labor supply for 2011. In 2011,the sample is restricted to the universe of formal-sector workers. Because ofthat, regression discontinuity estimates are based on counts of formal-sectorworkers instead of the size of the formal-sector employment relative to theentire population. The identification strategy assumes that the density ofthe population by birth date evolves smoothly around the eligibility thresh-old. If so, the estimates based on counts of formal-sector employees identifya change in formal-sector employment in response to harder qualifying con-ditions and not to a change in the population by birth date.To estimate equation (1.6), I run regressions separately by gender, as thecohorts affected by the reform are different. I cluster the standard errorsby date of birth in months to account for potential misspecification in thecontrol function (Lee and Card, 2008). I also follow the standard practice211.4. Data and empirical approachof testing the sensitivity of the results to the choice of control functions andbandwidth.Labor Supply Elasticity with Respect to the Net-of-Tax ShareI next measure the incentive effects of pension benefits on the labor supply bycalculating the elasticity of labor supply with respect to the net-of-tax shareof income (Liebman et al., 2009). This elasticity is a common measure ofthe efficiency costs of pension policies, as the deadweight loss of the pensiontax is proportional to it (Feldstein and Liebman, 2002).I estimate the elasticity with respect to the net-of-tax share, one minusthe effective pension tax rate, along the formal-informal margin, defined asσ =d lnLfad ln(1− teffa) , (1.9)where Lfa is the formal-sector labor supply for workers of age a, and teffa isthe effective pension tax rate for workers of age a,teffa = tnom − βEPWa+1 (τ + 1)− EPWa+1 (τ)w= tnom − β∆EPWa+1 (τ + 1)w.In the definition of teffa , tnom is the pension tax rate, EPWa (τ) stands forthe expected pension wealth at age a and τ years of contribution, and w isthe worker’s wage. In Section 1.5.3, I present a detailed discussion of theprocedure used to compute the net-of-tax share.The net-of-tax share measures the net gains from working in the formalsector in the current period. The share takes into account the pension taxrate paid for a worker and the change in the expected pension wealth derivedfrom working an additional period in the formal sector. Based on the resultsfrom Section 1.3, formal-sector labor supply is increasing in the long-rungains from working an additional period in the formal sector. Thus, theexpected sign of σ is positive.221.5. Estimation resultsTo estimate σ, I split the sample into groups characterized by differentpropensities to work in the formal sector (e.g., by education and region). Foreach group (denoted by X), I estimate the average change at the disconti-nuity of the formal-sector employment(∆ lnLfaX)and compute the averagechange at the discontinuity of the net-of-tax share(∆ ln(1− teffaX)). Then,I estimate σ by running the regression∆ lnLfaX = α0 + σ∆ ln(1− teffaX)+ εX . (1.10)In equation (1.10), two sources of variation identify σ: the variation inducedby the change in the minimum qualifying conditions and the variation acrossgroups with different labor market opportunities.1.5 Estimation results1.5.1 Identification checksThe identification strategy relies on the assumption that the unobserveddeterminants of formal-sector labor supply evolve smoothly around the eligi-bility threshold. This assumption could be undermined in at least two ways:First, workers who are likely to work in the formal sector could manipulatetheir date of birth in order to appear eligible for the program when theyare, in fact, not eligible (McCrary, 2008). Second, the estimated effect ofthe policy could be confounded by changes in other covariates that mightinfluence the outcome (Imbens and Lemieux, 2008). In this section, I assessthese two potential ways in which the identification could be compromised.I test the manipulation hypothesis by estimating the density of the totalpopulation by date of birth above and below the eligibility thresholds, andimplementing the test statistic proposed by McCrary (2008).11 The resultsare presented in the top panel of Table 1.3. The manipulation hypothesisimplies that the estimated difference should be negative, as younger workers11Because the census data are reported by birth month, I run the regressions groupedby date of birth in months and use a bandwidth of 48 months. In all specifications, I usea triangular kernel.231.5. Estimation resultsmight change their documentation to appear eligible for the transition sys-tem. The estimated effect for men is positive and not significant, supportingthe idea that men did not manipulate their date of birth to appear eligible forthe transition system. In contrast, the estimated effect for women is positiveand significant. Although the sign of the estimated effect for women is theopposite of the expected sign under the manipulation hypothesis, the resultsraise concerns that population characteristics may change sharply aroundthe discontinuity.To further test the potential for manipulation by women, I run the Mc-Crary density test with a placebo discontinuity ranging from March 1949to February 1960. The t-statistics for each month are presented in Figure1.5. The t-statistics exhibit two-year cyclical patterns over time, where thelargest (absolute) values occur around March and September. The cyclicalpattern occurs for both men and women, and the significant effect in March1959 also occurs in the density for men. Using the regression estimates of thechange in the density for men and women born around March 1959, I testwhether the changes at the boundary are equal for the density for men andwomen, and I fail to reject the null hypothesis (p-value 0.394). The resultssuggest that the sharp change observed in the density of population by dateof birth for women is the result of demographic trends and it is not explainedby the eligibility for the transition system. Nevertheless, the discontinuityfor women suggests to be cautious when interpreting the results for women.In addition to the manipulation tests, I look for discontinuities at theeligibility thresholds in other observable variables that might explain theworker’s labor supply choice. The variables are indicators for whether indi-viduals have a high school diploma or less, whether they report any disability,and whether they identify as members of an ethnic group (black or indige-nous). These variables are predetermined by the time the policy change tookplace and are correlated with the likelihood that an individual has a formal-sector job. Thus, significant differences in these variables would suggest thatthere are other unobservable factors that may be driving the labor supplydecisions around the discontinuity. The bottom panel of Table 1.3 indicatesthat there are no significant differences in any of these indicators for either241.5. Estimation resultsmen or women.Taken together, the results in Table 1.3 and Figure 1.5 provide evidencesupporting the assumption that other determinants of the formal-sector la-bor supply evolve smoothly around the eligibility threshold. Although thedistribution by date of birth for women is not continuous around the eli-gibility threshold, the placebo test suggests that the change is caused bytime trends other than changes in the pension eligibility. Nonetheless, theinterpretation of the results for women must take into account this caveat.1.5.2 ResultsThe results of estimating equation (1.6) are presented in Table 1.4, and thegraphical analysis is presented in Figure 1.6.The top panel of Table 1.4 presents regression discontinuity estimatesof the effect of harder qualifying conditions on salaried-formal employmentfor 2005. I use an indicator of whether the person works as salaried-formalworker as the dependent variable.12 Thus, the estimated effect is the av-erage effect of harder qualifying conditions on salaried-formal employmentrate. This specification is my preferred specification because it is more robustto changes in the population unrelated to workers’ self-selection, a particu-lar concern given the results from the identification checks for women. Themiddle and bottom panels of Table 1.4 show the regression discontinuity es-timates for the log of the number of salaried-formal workers for 2005 and2011. The two panels have the advantage of being comparable over time.In all regressions, I use a quadratic polynomial in date of birth as a controlfunction to account for potential non linearities in the formal-sector employ-ment rate, and I use a bandwidth of 48 months for 2005, and of 730 days for2011.13The results in Table 1.4 show that Colombian workers actively respondedto changes in the pension incentives. For men, the estimated effect is signif-12In 2005, I define a person as a salaried-formal worker when the person worked as asalaried employee, contributed to the pension system, and was covered by the contributoryhealth care system.13The Imbens and Kalyanaraman (2012) optimal bandwidth for the 2005 regression is55 months.251.5. Estimation resultsicant and changes over time. In 2005, the average effect of harder qualifyingconditions decreased the salaried-formal employment rate by 2.6 percentagepoints (on a base of 18 percent). The effect is confirmed by the specificationthat uses the number of salaried-formal workers for 2005 as dependent vari-able (panel B of Table 1.4). The regression discontinuity estimates show thatthe increase in the number of salaried-formal workers at the discontinuity isnegative 12 percent. In 2011, the estimated average effect on salaried-formalemployment for men is positive and significant, implying an increase of 6.8percent. The results are robust to the definition of formal worker, and tothe choice of control functions, bandwidth, estimators, and controls (TablesA.1 to A.3 in the Appendix A).The results for men are consistent with the framework presented above,in which the average effect of harder qualifying conditions depends on theworker’s age. Table 1.4 presents information about the distribution of theyears of contribution for workers born around the eligibility threshold, basedon the household surveys for 2006 and 2011.14 Since workers accumulatemore years of experience in the formal sector as they age, the distribution ofyears of contribution is more concentrated on values above 20 years in 2011than in 2005. As a result, the average effect for 2011 should be greater thanthe average effect for 2005, given that fewer eligible workers have long-runincentives to search for formal-sector jobs, as they already met the vestingrequirement.The results for women are intriguing. The 2005 estimates do not showany sizable or significant response. For 2011, however, Table A.2 showssignificant results, depending on the specification. Since the 2011 resultsare not normalized by the population by date of birth, it is not possible todisentangle the potential effect of changes in the policy from the documentedchanges in the total population around the discontinuity. One explanationfor the lack of response by women is that the transition system requiredworkers to have already contributed to the pension system by 1994. Thiscondition limited the applicability of the reform for women because of theirrelatively low labor force participation prior to this time (62 percent from14The distribution is conditional on making contributions.261.5. Estimation results1984 to 1993).15General equilibrium. To address the general equilibrium response tochanges in pension incentives, I estimate the effect of harder qualifying con-ditions on the wages of formal-sector workers in 2011. If firms are able toset different wages between workers, wages offset part of the long-run gainsfrom a formal-sector job. Therefore, the expected sign of the average effectof harder qualifying conditions on wages is the opposite to the sign of theaverage effect on employment. The estimates for the formal-sector wagesare presented in the top panel of Table 1.5. The average effect of harderqualifying conditions on formal-sector wages is about negative 3 percent formen and is not significant for women (columns (1) and (5)). Since the effecton employment is positive in 2011, the result on average wages suggests thatpart of the workers additional search effort is offset by a change in wages.To understand the sources of the aggregate results, I estimate the averageeffect of harder qualifying conditions on formal-sector wages and employmentby wage range. The results are presented in the bottom panel of Table1.5. Consistent with the analytical framework used here, low-wage menare the most responsive to changes in pension incentives. This occurs fortwo reasons. First, low-wage workers are more likely to find the minimumqualifying conditions binding. Second, the replacement rate for low-wageworkers is close to one. As a result, they do not have additional long-rungains from working in the formal sector once they meet the requirements.The response from women is not significant.The top panel of Table 1.5 presents the average effect of harder qualifyingconditions on formal-sector wages by wage range. For men, the estimatedeffects are small and not significant. The difference relative to the aggregateresults is driven by a composition effect, as the number of workers earningthe minimum wage is larger for younger workers (panel B of Table 1.5).Because the change of the minimum wage around the discontinuity is zero,the average effect on wages goes down. Thus, the results indicate that the15Between 1984 and 1993, the labor force participation rate for men around the discon-tinuity threshold was 97 percent.271.5. Estimation resultsimpact of the policy change on wages was limited.Nonetheless, the results presented in Table 1.5 do not rule out the possi-bility that changes in pension benefits are offset by changes in wages. The re-gression discontinuity estimates are intended to identify differential changesin the wages around the eligibility threshold. If the response in wages isassociated with spillover effects, the estimates presented above are a lowerbound of the actual response of the formal-sector labor supply to pensionincentives.Composition effects. I complement the analysis by testing the effect ofpension incentives on the composition of the labor force. Based on infor-mation from 2005, I run versions of equation (1.6) for indicators of whetherthe worker is self-employed, whether the worker works as a salaried-informalworker, and whether the worker is in the labor force.The estimation results are presented in Table 1.6, while the graphical evi-dence for men is presented in Figure 1.6. The reduction in the salaried-formalemployment for men is associated with increases in informal-sector employ-ment, in particular self-employment. The regression discontinuity estimatefor the self-employment indicator is of the same magnitude but oppositesign as that of the estimate for the salaried-formal employment indicator. Incontrast, the estimates using salaried-informal and labor force participationindicators as dependent variables are not significant. For women, there isno significant response in labor force participation or type of employment.Similar results have been noted in the literature concerned with the effectof mandated pension benefits on formal-sector labor supply. For instance,Almeida and Carneiro (2012) found that higher mandated benefits with nowage adjustment generate an incentive for Brazilian self-employed workersto switch to salaried-formal jobs.Heterogeneity analysis. In this section, I analyze the differential effectof harder qualifying conditions on formal-sector labor supply for differentgroups. Because not all groups exhibit the same propensity to work in theformal sector, the group analysis provides evidence on the mechanisms driv-281.5. Estimation resultsing the aggregate results.I estimate the response of the formal-sector labor supply to changes inpension incentives for subsamples. To estimate this response, I group work-ers according to three demographic characteristics: educational attainment,household composition (e.g., presence of a spouse in the household), and re-gion. In what follows, I present the results for men. The results for womenare not significant and may be affected by changes in the distribution ofpopulation by date of birth. Due to data availability, I present the resultsfor educational attainment and household characteristics for 2005, and theregional results for 2005 and 2011.The first set of results is for workers grouped according to educationalattainment. Less-educated workers are more likely to react to pension in-centives for two reasons. First, these workers face higher replacement rateswith no incentives to contribute beyond the vesting period. Second, theyface lower formal-sector employment rates, which makes the condition forminimum years of contribution binding.The estimation results show that the effect of harder qualifying conditionsis concentrated among workers with secondary education (Table 1.7).16 Forworkers with secondary education, harder qualifying conditions reduced thesalaried-formal employment rate by 9 percentage points (on a 21 percentbasis). In contrast, the estimated effects for workers with primary or post-secondary education are smaller and not significant. The third column ofTable 1.7 shows the average salaried-formal employment rate by educationalattainment. Consistent with the theoretical framework set out in this paper,workers with low or high informality rates are less responsive to changes inpension benefits.The second set of results is for workers grouped according to the compo-sition of the household. I analyze the response of workers in households withdifferent incentives to search for formal-sector jobs. The samples are defined16My implicit assumption is that workers do not change their schooling as response tothe change in the pension qualifying conditions. Since men at the eligibility cutoff were 40years old when the reform took place, this assumption seems reasonable and is consistentwith the evidence presented in the identification checks (Table 1.3).291.5. Estimation resultsaccording to the person’s marital status and whether the person is livingin a household with only one member in the labor force. Married men andmen living in a household with only one member in the labor force shouldrespond more actively to harder qualifying conditions. First, men tend toget married to younger women (the median difference is 5 years). Given thatthe survivor pension rate is 100 percent, the long-run benefits of getting apension are higher for households with married couples. Second, men livingin households with only one member in the labor force may have limitedfamily support after retirement. A concern with this part of the analysis isthat the variables used to select the samples are endogenous to the eligibil-ity for the transition system. However, I find no evidence that householdstructure changes as result of harder qualifying conditions (Table 1.8).Table 1.9 reports the results for the different subsamples. The effectof pension incentives varies systematically depending on household charac-teristics. The response is concentrated among married men, and amonghouseholds where there is only one member in the labor force.The third set of results is for workers grouped according to region. Insti-tutional factors and economic development generate differential formal-sectorpatterns by region (La Porta and Shleifer, 2014). The regional differencesprovide additional evidence on the relationship between the labor supplyresponse to pension incentives and the labor market opportunities.Table 1.10 reports the regression discontinuity estimates by region for2005 and 2011. I group workers based on their departments’ (provinces’)GDP per capita excluding oil. The developed departments are Bogota-Cundinamarca, Antioquia, and Valle, and the developing departments com-prise the rest of the country. The developed regions represent about 60percent of the total GDP and 45 percent of total population in 2005. Theaverage response to changes in the pension benefits is large and significantfor developed regions, which offer most of the formal-sector employment.In summary, the results presented in this section support the view thatthe formal-sector labor supply responds to pension incentives. The estimatedaverage responses of formal-sector labor supply to harder qualifying condi-tions are heterogeneous and depend on labor market opportunities for the301.5. Estimation resultsworker. The effect is concentrated among workers for whom the minimumqualifying conditions for retirement are binding, workers having higher ex-pected pension wealth, and workers in households with only one member inthe labor force.1.5.3 Elasticity of formal-sector labor supply with respectto the net-of-tax shareTo compute the elasticity of the formal-sector labor supply with respect tothe net-of-tax share (σ), first I compute the average change in the net-of-taxshare at the discontinuity for selected samples. Next, I recover the elasticityby regressing the estimates of average changes in formal-sector employmenton average changes in the net-of-tax share.To estimate σ, first I compute the net-of-tax share for subsamples ofworkers with different propensities to work in the formal sector. These sub-samples are defined according to region and educational attainment for 2005,and region and wage range for 2011 (12 groups).17 For each subsample (de-noted by X), I compute the average change in the net-of-tax share at thediscontinuity. To do this, I construct a grid for the expected pension wealthfor every combination of age a and years of contribution τ , EXPWa (τ). Iassume that the worker will retire as soon as he meets the conditions forretirement, and that he will enjoy the pension benefits until age 80. Theconditions and benefits that the worker receives after retirement are definedby the pension system. If the worker does not meet the retirement condi-tions by age 65, he will ask for a refund of his contributions to date. Forthe refund of contributions, I assume that the average contribution rate of aworker over his lifetime is 10 percent, as the pension contribution rate before1994 was 6.5 percent of the worker’s wage. If the worker does not retire, theworker will work an additional period in the formal sector with probability17For 2005, I grouped workers according to their place of residence (developed and devel-oping regions) and their educational attainment (primary, secondary and postsecondaryeducation) for 6 groups in total. For 2011, I grouped workers according to their place ofwork (developed and developing regions) and their wage range (1, 1-2, and 2+ times theminimum wage) for another 6 groups.311.5. Estimation resultspX (a).Next, I compute the change in the log net-of-tax share at the discontinuityas∆ ln(1− teffaτ ′X)= ln(1− tnom + β∆EXPWSIa+1 (τ′ + 1)wX)− ln(1− tnom + β∆EXPWTa+1 (τ′ + 1)wX).where the superscripts SI and T denote that the expected pension wealthis computed using the conditions of the transition and the social insurancesystems. I assume a pension tax rate of 4 percent, the contribution paidby salaried-formal workers.18 Given that the estimates of the changes inemployment are observed for men in 2005 and 2011, I compute the changein the log net-of-tax share for workers at age 51 and 57 (the age of the eligiblemen at the cutoff in 2005 and 2011). Finally, using information about thedistribution of the number of years of contribution for the group X at agea, FaX (τ), I compute the average change of the log net-of-tax share alongthe formal-informal margin as∆ ln(1− teffaX)=∑τ ′∆ ln(1− teffaτ ′X)dFaX(τ ′).In the calculation of ∆ ln(1− teffaX), I estimate pX (a) from the 2005 censusand FaX (τ) from the household surveys of 2006 and 2011. Moreover, Iassume that wX is constant over time and I set it to twice the minimumwage for skilled workers and to the minimum wage for the other groups.19For the second stage of the estimation of σ, I regress the changes in theformal-sector employment on the change of the net-of-tax share. Figure 1.818In Colombia, the pension tax rate for all workers is 16 percent of the monthly wage.Since for salaried workers the employer pays 12 percentage points, I am assuming thatthe employers cannot pass through the additional contribution to lower wages. This islikely the case for minimum wage workers. The results are not sensitive to changes in thepension tax rate.19The skilled workers are workers with post-secondary education for 2005 and workerswith wages above twice the minimum wage for 2011.321.6. Final remarksdisplays a scatterplot with the average changes in log employment (verti-cal axis) and in net-of-tax share (horizontal axis) at the discontinuity. Thegroups from 2005 and 2011 are represented by triangles and circles, respec-tively. Consistent with the predictions of the model, workers with strongerpension incentives along the formal-informal margin also exhibit strongerresponses in their formal-sector labor supply. A linear regression on thesepoints yields an estimated elasticity of σ = 1.66. The estimated elasticityis slightly larger than the values of the same regression when restricted tocross through the origin (σ = 1.60) and the median value of the elasticity bygroup (σ = 1.47). Regardless of the estimator used, the implied values of σare estimated with low precision.The implied value of σ is likely a lower bound of the actual elasticityfor at least three reasons. First, the estimates of changes in the formal-sector labor supply do not account for spillover effects, for instance, offset-ting effects of wages affecting workers born before and after the eligibilitythreshold. Second, because of the definition of the transition system, a frac-tion of the population could not take up the benefits (Section 1.2.2). Third,∆ ln(1− teffaX)may over-estimate the actual change in the net-of-tax sharealong the formal-informal margin. In particular, ∆ ln(1− teffaX)would besmaller (and σ larger) if workers have a lower discount rate β or worker’sutility function is concave (Stock and Wise, 1990).1.6 Final remarksIn this paper, I show that workers take into account their future pensionbenefits when it comes to making their labor supply decisions. Using theColombian pension system, I show that a change in future pension benefitsgenerates a large shift between the formal-sector and informal-sector laborsupply. In contrast, there is no effect on labor force participation. Theresponse is heterogeneous and depends on the worker’s age, employmenthistory, and opportunities to find formal-sector jobs. Using additional as-sumptions, I obtain an elasticity of formal-sector labor supply with respect33to the net-of-tax share of 1.7.Although the estimation results cannot be generalized to other cohortsor to other countries, the results suggest that the behavioral response topension incentives may be large. Workers’ behavioral responses should betaken into account in the design of pension programs, as such responses maycreate large efficiency costs. In particular, pension programs that reducethe value of the expected pension benefits have a negative effect on formal-sector labor supply. From a fiscal perspective, the effect of such programs istwofold. On the revenue side, these programs reduce the revenue achieved byway of contributions to the pension system, since fewer workers contribute.On the expenditure side, these programs increase the future expenditurein assistance programs, since more retirees would claim non-contributorypension benefits.Nevertheless, a comprehensive evaluation of pension programs must takeinto account other factors that may mitigate their efficiency costs. For ex-ample, the welfare gains from the insurance against consumption losses afterretirement may be significant. Additionally, the overall effect of pension pro-grams depends on which sector of the population is affected. For instance,non-contributory pension programs for workers with low opportunities offinding formal-sector jobs could be welfare enhancing. For these workers,the behavioral response is small and the extra gains from insurance may belarge.34Table 1.1: Labor market composition and average wages, Colombia, 2011Composition (percent) Average wage to min. wage ratioHighSchool orlessPostSec-ondaryTotalHighSchool orlessPostSec-ondaryTotalSalaried-employed- Formal 37.7 65.2 47.7 1.4 2.8 2.1- Informal 17.5 7.3 13.8 1.1 1.4 1.2Self-employed- Formal 5.1 11.2 7.3 1.9 3.8 3.0- Informal 39.4 16.2 31 1.3 2.3 1.5Observations 76,920 38,786 115,706 76,920 38,786 115,706Notes: The table reports the composition and average wages of urban workers aged 20 to 65 working at least 30 hours per week.To avoid the effect of outliers and misreported information in the wage distribution, I trim the top 1 percent of workers of the wagedistribution, and workers with wages below 40 percent of the minimum wage. A formal worker is defined as a worker who is makingcontributions to the pension system and is covered by the contributory health care system. Source: Colombian Household Surveys,201135Table 1.2: General Pension System characteristicsTransition Social Insurance Individual AccountManaged by Colpensiones Colpensiones Private pension fundsType of system Defined benefit Defined benefit Defined contributionEligibilityWorkers born beforeApril 1959 (women) orApril 1954 (men) with750 weeks ofcontributions by July2005.†All public and private sector workers(including self-employed††) not eligible forthe transition system.QualifyingconditionsPrivate sector workers:55 years (women), 60years (men) AND 1,000weeks of contributionsin any time.Public workers: 50 years(women), 55 years(men), AND 20 years ofservice.All workers: 55 years(women), 60 years(men) AND 1,050 to1,300††† weeks ofcontributions in anytime. Starting in 2014,minimum age increasedby two years to 57 forwomen and 62 for men.All workers: Enoughcapital to buy anannuity of 1.1 minimumwages, OR 57 years(women), 62 years(men) and 1,150 weeksof contributions in anytime for an annuity of aminimum wage.Total contribution 16% of wage – 11.5% contribution, 4.5% for administrative fees and insurance.(Salaried workers: 12% paid for the employer - 4% paid for the employee.Self-employed workers pay 16%)Continues in next page.36General Pension System characteristics (continued)Transition Social Insurance Individual AccountReplacement rateFunction of length ofcontributions. From65% to 85% (See Figure1.2)Function of length ofcontributions and wage.From 65% to 85% (SeeFigure 1.2).It depends only on theaccrued capitalPension rangeAt least 1 Minimumwage1-25 Minimum wagesAt least 1 MinimumwageSurvivor benefits 100 percent 100 percent 100 percentContributionsrefundContributions adjusted by inflation (lump-sum payment)Accrued capital +interest (lump-sumpayment)Coverage Statistics (2005) - MillionsTotal 5.67 5.951-2 Min. wage 5.22 5.08Aged 45+ 2.35 0.67Retirees 0.82 0.02Notes: † The limit of 750 weeks of contributions by July 2005 was introduced in 2005. †† Contributions for Self-employed workersbecome compulsory since January 2003. ††† Starting in 2003, the length of contributions needed to qualify for a pension increasedgradually from 1,000 weeks in 2004 up to 1,300 weeks in 2015. Coverage statistics taken from the Superintendencia Financiera website.Source: Santa María, Steiner, Botero, Martinez, Millán, Arias, and Schutt (2010), Llano, Cardona, Guevara, Casas, Arias, and Cardozo(2013) and texts of the reforms.37Table 1.3: Identification checks, 2005A: McCrary’s density testMen WomenTest Statistic 0.024 0.078(Bandwidth 48 months) [0.033] [0.025]∗∗∗Observations 126,095 175,047B: Balance tests (estimates scaled up by 100)High School or less indicator 0.68 0.25(Bandwidth 48 months) [1.21] [1.12]Disability indicator -0.21 0.48(Bandwidth 48 months) [1.03] [0.71]Ethnical minority indicator -0.13 0.99(Bandwidth 48 months) [0.74] [0.64]Observations 78,655 110,626Notes: The Table presents estimates for testing factors that affect the validity of theidentification assumptions required for the regression discontinuity design described inSection 1.4.2. The top panel presents the estimation results by gender for the test proposedby McCrary (2008), to test potential discontinuities in the density of the running variable(population by date of birth). The bottom panel presents RD estimates for observabledeterminants of formal-employment and other predetermined variables, to gather evidenceabout other potential changes that may confound the estimated effect of the policy. Eachcell reports an RD estimate based on a separate regression of a variable predeterminedby the time of the introduction of the policy as dependent variable versus a quadraticpolynomial on date of birth and its interaction with a dummy for being born after March-54(men) and March-59 (women) as independent variables (See equation (1.6)). The selectedvariables are indicator variables for whether the person’s has a high school diploma orless, whether the person reports any disability, and whether the person identifies himselfas a member of a ethnic group (black or indigenous). Regressions were computed usingthe IPUMS Colombian Census dataset. Standard errors clustered by date of birth (inmonths) in brackets. * p<0.1, ** p<0.05, *** p<0.01.38Table 1.4: RD estimation results, 2005 and 2011RD estimates Dist. of years of contribution (%)Men Women Men Women0-10 11-20 21+ 0-10 11-20 21+A: 2005 Results – Dependent variable: Salaried-formal indicatorHarder qualifying conditions -2.62 -0.18 20.2 39.8 40.0 27.6 36.7 35.7(Bandwidth 48 months) [1.28]∗∗ [1.03]Observations 129,061 178,990Mean Dep. Variable (%) 18.1 15.7B: 2005 Results – Dependent variable: Log salaried-formal workers by date of birth in monthsHarder qualifying conditions -11.9 8.53 20.2 39.8 40.0 27.6 36.7 35.7(Bandwidth 48 months) [8.65] [7.60]Observations 15,349 20,616C: 2011 Results – Dependent variable: Log salaried-formal workers by date of birth in daysHarder qualifying conditions 6.79 2.03 13.0 31.6 55.5 20.8 37.6 41.5(Bandwidth 48 months) [2.39]∗∗∗ [2.17]Observations 964,558 927,691Notes: All estimates scaled up by 100. Each cell reports an RD estimate based on a separate regression of a labor market indicator on aquadratic polynomial on date of birth and its interaction with a dummy for being born after March-54 (men) and March-59 (women) asindependent variables (See equation (1.6)). Panel A includes the total population and uses as dependent variable an indicator variableof whether the person is a salaried worker making contributions to the pension system and being covered by the contributory healthcare system – so the RD estimate is an effect on the salaried-formal employment rate. Panels B and C report the RD estimates ofregressions in which the dependent variable is the log number of salaried-formal workers for 2005 and 2011. Regressions were estimatedusing the Colombian Census long-form questionnaire dataset (2005) and the PILA dataset (2011). Standard errors clustered by dateof birth (in months) in brackets. ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01. The distribution of years of contribution is conditional on makingcontributions, and it is based on the Household Surveys data of 2006 and 2011.39Table 1.5: RD estimation results for wages in the formal sector, 2011Men WomenAll At Wm 1-2 Wm 2+ Wm All At Wm 1-2 Wm 2+ Wm(1) (2) (3) (4) (5) (6) (7) (8)A: RD Estimates for log wages (estimates scaled up by 100)Harder qualifying conditions -3.11 – -0.25 -1.51 1.14 – 0.23 1.2(Bandwidth 730 days) [0.82]∗∗∗ [0.56] [1.46] [1.51] [0.83] [1.85]Observations 964,558 416,927 287,659 259,972 927,691 365,667 321,405 240,619B: RD Estimates for log number of workers (estimates scaled up by 100)Harder qualifying conditions 6.79 10.51 7.22 0.39 2.03 0.98 1.95 4.99(Bandwidth 730 days) [2.39]∗∗∗ [3.36]∗∗∗ [2.03]∗∗∗ [3.03] [2.17] [3.41] [3.47] [3.84]Observations 964,558 416,927 287,659 259,972 927,691 365,667 321,405 240,619Notes: Each cell reports an RD estimate based on a separate regression of a labor market indicator on a quadratic polynomial on dateof birth and its interaction with a dummy for being born after March-54 (men) and March-59 (women) as independent variables (Seeequation (1.6)). Panel A includes salaried-formal workers for 2011 and reports the RD estimates using as dependent variable the logmonthly wage of formal workers. Columns (1) and (5) presents the results for the full sample, while columns (2) to (4) and (6) to (8)show the results for subsamples defined by wage range. By construction, the difference at the discontinuity for workers at the minimumwage is zero. Panel B reports the RD estimates of regressions in which the dependent variable is the log number of salaried-formalworkers for 2011 following the same sample selections than panel A. Regressions were estimated using the PILA dataset. Standarderrors clustered by date of birth (in months) in brackets. * p<0.1, ** p<0.05, *** p<0.01.40Table 1.6: Estimation results for other labor market outcomes, 2005A: RD estimates for other labor market outcomes – Men, 2005Estimates scaled up by 100Lab. Force Salaried Salaried Self-participation formal informal employedHarder qualifying conditions 1.20 -2.62 0.21 2.49(Bandwidth 48 months) [1.39] [1.28]∗∗ [1.47] [1.33]∗Observations 129,061 129,061 129,061 129,061Mean dep. variable (%) 78.3 18.1 27.3 25.7B: RD estimates for other labor market outcomes – Women, 2005Estimates scaled up by 100Lab. Force Salaried Salaried Self-participation formal informal employedHarder qualifying conditions -0.69 -0.18 -0.86 0.68(Bandwidth 48 months) [1.76] [1.03] [1.32] [0.93]Observations 178,990 178,990 178,990 178,990Mean dep. variable (%) 49.7 15.7 18.9 10.9Notes: Each cell reports an RD estimate based on a separate regression of a differentlabor market indicator on a quadratic polynomial on date of birth and its interaction witha dummy for being born after March-54 (men) and March-59 (women) as independentvariables (See equation (1.6)). The columns labeled salaried-formal present the baselineRD estimates presented in Table 1.4. The additional columns reports results of RD es-timates for labor force participation, salaried-informal employment, and self-employmentrate. Regressions were estimated using the Colombian Census long-form questionnairedataset. Standard errors clustered by date of birth (in months) in brackets. * p<0.1, **p<0.05, *** p<0.01.41Table 1.7: Estimation results by educational attainment – Men, 2005A: 2005 Results - Dependent variable: Salaried-formal employment indicator(Estimates scaled up by 100)RD Sal-formal Dist. of years of contribution (%)Estimate emp. rate 0-10 11-20 21+Primary -0.16 10.6 29.3 35.6 35.1(Bandwidth 48 months) [1.58]Secondary -9.32 21.2 26.3 40.8 33.0(Bandwidth 48 months) [3.38]***Post-Secondary -0.82 38.4 8.0 41.5 50.5(Bandwidth 48 months) [2.91]Observations 129,061Mean dep. variable (%) 18.1Notes: The first column reports RD estimates based on a separate regression of the salaried-formal employment indicator on aquadratic polynomial on date of birth and its interaction with a dummy for being born after March-54 (men) and March-59 (women)as independent variables and educational attainment. The cells report the average effect of harder qualifying conditions by educationalattainment (primary or less, secondary or at least some secondary, and post-secondary). Regressions were estimated using the ColombianCensus long-form questionnaire dataset. Standard errors clustered by date of birth (in months) in brackets. * p<0.1, ** p<0.05, ***p<0.01. The distribution of years of contribution is conditional on making contributions, and it is based on the Household Surveysdata of 2006 and 2011.42Table 1.8: RD results for indicators of household characteristics, 2005(Estimates scaled up by 100)Dependent variable Married Only workerin householdHarder qualifying conditions 0.42 -2.08(Bandwidth 48 months) [1.44] [1.49]Observations 110,174 106,811Mean dep. variable (%) 83.1 38.7Notes: Each cell reports an RD estimate based on a separate regression of the householdcomposition indicator on a quadratic polynomial on date of birth and its interaction witha dummy for being born after March-54 (men) and March-59 (women) as independentvariables (See equation (1.6)). The first column presents RD estimates using as dependentvariable an indicator variable for marital status (1 if married, 0 otherwise). The secondcolumn restricts the sample to households with at least one person in the labor force, andestimates the model using as dependent variable an indicator for being the only member ofthe household in the labor force. Regressions were estimated using the Colombian Censuslong-form questionnaire dataset. Standard errors clustered by date of birth (in months)in brackets. * p<0.1, ** p<0.05, *** p<0.01.43Table 1.9: RD results by household characteristics – Men, 2005(Estimates scaled up by 100)RD Sal-formal Dist. of years of contribution (%)Estimate emp. rate 0-10 10-20 21+A: Estimates for men with spouse in the householdNo Spouse 1.40 21.9 11.5 62.5 26.0(Bandwidth 48 months) [3.68]Spouse -3.96 18.3 21.6 36.6 41.8(Bandwidth 48 months) [1.60]∗∗Observations 110,174Mean dep. variable (%) 19.6B: Estimates for men in households with one or more members in the labor forceMore than one member in LF -0.89 16.4 21.7 36.1 42.2(Bandwidth 48 months) [1.83]Only member in labor force -6.23 20.3 15.9 50.7 33.4(Bandwidth 48 months) [1.91]∗∗∗Observations 110,174Mean dep. variable (%) 20.5Notes: The first column of the Table reports an RD estimate based on a separate regression of the salaried-formal employmentindicator on a quadratic polynomial on date of birth and its interaction with a dummy for being born after March-54 (men) andMarch-59 (women) as independent variables (See equation (1.6)). The top panel reports the results for the samples of married andunmarried men, while the bottom panel reports the results for the sample of workers who are the only member of the family in thelabor force. Regressions were estimated using the Colombian Census long-form questionnaire dataset. Standard errors clustered bydate of birth (in months) in brackets. * p<0.1, ** p<0.05, *** p<0.01. The distribution of years of contribution is conditional onmaking contributions, and it is based on the Household Surveys data of 2006 and 2011.44Table 1.10: Estimation results by region – Men, 2005 and 2011(Estimates scaled up by 100)RD Sal-formal Dist. of years of contribution (%)Estimate emp. rate 0-10 10-20 21+A: 2005 Results - Dependent variable: Salaried-formal employment indicatorDeveloping regions -0.80 13.3 16.7 38.9 44.4(Bandwidth 48 months) [1.66]Developed regions -3.99 21.3 22.4 40.3 37.3(Bandwidth 48 months) [1.66]∗∗Observations 129,061Mean dep. variable (%) 18.1B: 2011 Results - Dependent variable: log number of workersDeveloping regions 1.58 18.1 14.0 38.4 47.7(Bandwidth 730 days) [5.68]Developed regions 8.21 23.3 12.7 29.6 57.7(Bandwidth 730 days) [2.38]∗∗∗Observations 964,558Notes: The first column reports RD estimates based on a separate regression of a salaried-formal employment variable on a quadraticpolynomial on date of birth and its interaction with a dummy for being born after March-54 (men) and March-59 (women) asindependent variables by region (See equation (1.6)). The top panel presents results by region for 2005, while the bottom panel reportsthe results for 2011. I defined developed regions as the departments (provinces) with the highest GDP per capita excluding oil, namely,Bogota and Cundinamarca, Antioquia, and Valle, and less developed regions are the other provinces. Regressions were estimated usingthe Colombian Census long-form questionnaire (2005) and the PILA (2011) dataset. Standard errors clustered by date of birth (inmonths) in brackets. * p<0.1, ** p<0.05, *** p<0.01. The salaried-formal employment rate for 2011 is based on Household Surveysdata. The distribution of years of contribution is conditional on making contributions, and it is based on the Household Surveys dataof 2006 and 2011.45Figure 1.1: Distribution of wages for workers with High School diploma orless, 2011InformalFormal0123Density-1 0 1 2 3Log monthly wage relative to the minimum wageLog wage distribution, 2011Notes: The figure displays kernel estimates of the density of the log monthly wage relativeto the minimum wage for the formal (black line) and informal (grey line) sector. Theselected sample includes all urban men and women aged 20 to 65, with High Schooldiploma or less, working at least 30 hours per week. To minimize misreporting errors, Idrop the top 1 percent wages and wages below 40 percent the minimum wage. Formal-sector workers are defined as workers who contributed to the pension and are covered bythe contributory health care system.46Figure 1.2: Replacement rate for the defined-benefit systems by weeks ofcontributionsOld conditions607080901001 1.5 2 2.5 31000 weeksOld conditionsNew conditions607080901001 1.5 2 2.5 31300 weeksOld conditionsNew conditions607080901001 1.5 2 2.5 31400 weeksOld conditionsNew conditions607080901001 1.5 2 2.5 31800 weeksReplacement rate (percentage)Reference wage (relative to Wm)Notes: The figure displays the replacement rates as percentage of the reference wagefor the social insurance (gray line) and the transition (black line) systems. Each panelrepresents the particular value of the formula defining the replacement rate by weeks ofcontributions. For the insurance system the vesting period is 1,300 weeks.47Figure 1.3: Distribution of workers by age and number of weeks01234501234556 58 60 62 64 56 58 60 62 6456 58 60 62 64 56 58 60 62 64800-1000 weeks 1000-1200 weeks1200-1400 weeks 1400-1600 weeksNumber of workers (thousands)Age in August 2013, yearsMen01234501234551 53 55 57 59 51 53 55 57 5951 53 55 57 59 51 53 55 57 59800-1000 weeks 1000-1200 weeks1200-1400 weeks 1400-1600 weeksNumber of workers (thousands)Age in August 2013, yearsWomenNotes: The figure presents the distribution by age, weeks of contribution and gender fornon retired workers who have made contributions to the public pension system throughouttheir lifetime up to December 2013, based on Colpensiones administrative data. Once theworkers claim the pension benefits they are excluded from the dataset. The reference dateof birth is calculated relative to August 2013, as the expected processing time for awardingretirement benefits is four months.48Figure 1.4: Probability of working in the formal-sector at age a = 50(a) Expected value function at age 50, va+1 (τa)SamegainsHigher long-rungains for Plan 1Higher long-rungains for Plan 2Same gainsfor both plans1515.51616.51717.5Expected value function0 10 20 30Formal-Sector experience (Years of Contributions)Plan 1: R=60,τ*=20,b=1Plan 2: R=62,τ*=25,b=1(b) Probability of working in the formal sector at age 50, G (u¯a (τa−1))SamelaborsupplyHigher formal-sectorlabor supplyfor Plan 1Higher formal-sectorlabor supplyfor Plan 2Same formal-sectorlabor supplyfor both plans0.2.4.6.81Prob. of working as formal0 10 20 30Formal-Sector experience (Years of Contributions)Plan 1: R=60,τ*=20,b=1Plan 2: R=62,τ*=25,b=1Notes: The figure shows an example of the expected value function (va+1 (τa), top) andthe probability of searching for a formal-sector job (G (u¯a (τa−1)), bottom) by years ofcontribution for two simulated cohorts aged a = 50, given two defined-benefit pensionplans. For the example, I assume that workers live from a0 = 20 until T = 75 and theirutility function is linear. I also assume that wf (1− tnom) = 1.2, wi = 1, θr = θf = 0,ψi.i.d∼ U (0, 0.5), and β = 11.05. The pension plans are given by R = 60, τ∗ = 20 and b = 1(labeled Plan 1) and R = 62, τ∗ = 25 and b = 1 (Plan 2). Panel (a) shows the workers’expected value function by pension plan. Increasing the minimum qualifying conditionsreduces the workers’ expected utility and changes the long-run gains from working in theformal sector (the slope of the expected value function). Panel (b) shows the probabilityof working in the formal sector by pension plan. Harder qualifying conditions shift tothe right the long-run gains from working one more period in the formal sector, as ittakes longer to reach the vesting period. The response of formal-sector labor supply toharder qualifying conditions is heterogeneous, and depends on the workers’ formal sectorexperience.49Figure 1.5: Rolling t-statistics for testing the manipulation in date of birth,2005Mar-1959-4-2024 1950m1 1955m1 1960m1 MenMar-1959-4-2024 1950m1 1955m1 1960m1 Woment-statisticsCutoffNotes: The figure displays the t-statistics using the test proposed by McCrary (2008) fortesting discontinuities in the density of the running variable in the regression discontinuitysetup. Each panel represents the value of the t-statistics changing the cutoff point, wherethe vertical dashed lines show the relevant cutoff dates for harder qualifying conditions inColombia (April 1954 for men and April 1959 for women).50Figure 1.6: RD estimation results, 2005 and 201110152025Sal. Formal employment rate1950m4 1954m4 1958m42005: Men3.844.24.4Workers by birthdate (logs)01apr1952 01apr1954 31mar19562011: Men1214161820Sal. Formal employment rate1955m4 1959m4 1963m42005: Women3.83.944.14.24.3Workers by birthdate (logs)01apr1957 01apr1959 31mar19612011: WomenDate of BirthNotes: The figure presents the salaried-formal employment indicators by gender and dateof birth. Each point represents the 2-month average of the salaried-formal employmentrate by month in 2005 and the 47-days average of the log number of workers by age in2011. The regression estimates on the graphs are based on the estimates reported in panelsA and C of Table 1.4. Confidence bands are computed based on standard errors clusteredby date of birth (in months).51Figure 1.7: Labor force participation, salaried-informal employment and self-employment rates for Men, 2005707580851950m4 1954m4 1958m4Labor force participation101520251950m4 1954m4 1958m4Salaried-formal employment2224262830321950m4 1954m4 1958m4Salaried-informal employment2022242628301950m4 1954m4 1958m4Self-employmentPercentage of population by ageDate of BirthNotes: The figure presents the labor force participation rate, salaried-informal employmentand self-employment rate for men by date of birth. Each point represents the 2-monthaverage of the specific labor market outcome. The regression estimates on the graphs arebased on the quadratic fit of the microdata (Table 1.6) of the Colombian Census long-formquestionnaire dataset. Confidence bands are computed based on standard errors clusteredby date of birth (in months).52Figure 1.8: Elasticity of the formal-sector labor supply to changes in thenet-of-tax shareReg0 (Prim)Reg0 (Sec)Reg0 (PSec)Reg1 (Prim)Reg1 (Sec)Reg1 (PSec)Reg0 (Wm)Reg0 (1-2Wm) Reg0 (2+Wm)Reg1 (Wm)Reg1 (1-2Wm)Reg1 (2+Wm)s = 1.66-.8-.6-.4-.20.2Dlog Lf X-.1 -.05 0 .05Dlog(1-teffX)Notes: The Figure displays the average change in the log net-of-tax share (horizontalaxis), computed in Section 1.5.3, and the average change in the salaried-formal laborsupply (vertical axis), derived from the results obtained in Section 1.5.2. Each pointrepresents a combination of regions (developing and developed, denoted Reg0 and Reg1)and educational attainment (primary, secondary and post-secondary) or wage range (1,1-2, 2+ Minimum wages). The regression slope corresponds to an estimate of the elasticityof the formal-sector labor supply with respect to the net-of-tax share along the formal-informal margin.53Chapter 2A Life-Cycle Model forFormal-Sector Labor Supply2.1 IntroductionIn Chapter 1, I provide empirical evidence of the importance of pension pro-grams in a worker’s decision to participate in the formal (regulated) sector.20In this chapter, I propose a general life-cycle analysis to study the interactionbetween pension incentives and formal-sector labor supply before retirement.Using this analysis, I identify the gains from working in the formal sectorand characterize their relationship with financial and pension wealth.This chapter contributes to the literature on formal-sector labor supplyby introducing the life-cycle component into the analysis. In the model, arepresentative agent’s decision to participate in the formal sector relies onthe gains from working in the formal-sector, his preferences for formal-sectorjobs, and the labor market conditions that may prevent him from getting aformal-sector job (Gerard and Gonzaga, 2014; Meghir, Narita, and Robin,2015; Rauch, 1991). This approach is consistent with available evidence forLatin American economies, which suggests that workers are mobile acrosssectors and that many informal-sector workers exhibit high levels of satis-faction with their job (Maloney, 1999, 2004; Perry et al., 2007). Comparedwith an informal-sector job, a formal-sector job generally pays higher wages20In what follows, I define informal sector as the set of firms and workers that do notcomply with government regulation, such as the payment of mandated contributions andtaxes. A firm operating in the informal does not pay taxes (including payroll taxes), but itis subject to fines if it is inspected. Regarding workers, informal-sector workers do not paycontributions to the mandated benefit and insurance systems, but they are not coveredby mandated benefits and other insurance included in the regulation.542.1. Introductionand provides benefits in the form of insurance and future pension benefits.Nonetheless, the representative agent’s decision depends on his own prefer-ences for formal-sector jobs, his net valuation of the benefits from workingin the formal sector, and the availability of formal sector jobs.In the model setup, I explicitly account for the relative gains and costsfrom working in the formal sector. I specifically account for the gains fromworking in the formal sector by incorporating sector-specific wages and adefined-benefit pension plan that entitles the representative worker to pen-sion benefits after retirement. With respect to the costs from working inthe formal sector, I build on Gerard and Gonzaga (2014) and Eissa, Kleven,and Kreiner (2008) and introduce formal-sector participation shocks. Theseshocks are a catch-all variable that includes the worker’s preferences forformal-sector jobs, the worker’s net valuation of the benefits from workingin the formal sector, and the availability of formal sector jobs.The gains from working in the formal-sector are summarized by thethreshold u¯. This threshold represents the lifetime utility gains from work-ing one more period in the formal sector. When the representative worker’sutility gains are larger than the utility shock, he chooses to work in the for-mal sector. In this setup, u¯ is a function of the worker’s age, his potentialearnings in both sectors, his financial wealth (assets), and his future pensionbenefits.The model results are qualitatively similar in all cases, but they dependon the basic assumptions on the relationship between pension and financialwealth and the type of pension plan. When I assume that financial andpension wealth are perfect substitutes, I show that the short and long-rungains from working in the formal sector cannot be separated. Working in theformal sector increases the workers’ lifetime income, as it increases presentearnings and the future pension wealth. Then, consumption smoothing leadsworkers to increase their present and future consumption, having a positiveimpact on their utility in both the short and the long-run. In contrast,when I assume that workers cannot save, the short and long-run gains areseparated. The short-run utility gains come from an increase in presentearnings while the long-run utility gains come from an increase in the pension552.2. The environmentwealth. Finally, when I change the pension plan from a defined-benefit to adefined-contribution pension plan, I show that workers internalize the long-run gains from contributing to the pension system and reduce their financialwealth by the amount they contribute to the plan. As a result, in a defined-contribution system the gains from working in the formal sector come fromthe increase in present earnings only.A direct implication of the model is that, when the pension system is adefined-benefit pension system, the change in the pension wealth is the maindriver of the long-run gains from working in the formal sector. Nonetheless,the level of wealth determines the sensitivity of the workers to the utilitygains from working in the formal sector. In particular, I show that when theper-period utility function is concave, the threshold u¯ is a decreasing functionof the level of financial wealth. Thus, when workers have more assets, anincrease in lifetime income from working in the formal-sector has a smallerimpact on lifetime utility.The rest of the chapter is organized as follows. Section 2.2 describesworkers’ incentives to participate in the formal-sector. Sections 2.3 intro-duces the model setup, and characterizes formal-sector labor supply. Sec-tions 2.4 and 2.5 present a version of the model where workers cannot saveand a version of the model where workers lose their job with certain proba-bility. Section 2.6 presents the results of a model with savings and pensionwealth assuming a defined-contribution pension plan. Finally, Section 2.7sets out the conclusions.2.2 The environmentThe model assumes a representative agent lives for three periods (youngworker, adult worker, and retiree), indexed by a ∈ {1, 2, 3}. Every period,the agent chooses how much of his income to consume, how much to save,and whether to work in the formal or in the informal sector. The agent has aset of exogenous characteristics (e.g., education and ability), denoted by X,that will determine his wage in each sector and formal-sector participationshocks while working. I assume that the agent always finds a job in the562.2. The environmentsector he chooses, and that he loses his job by the end of the period.Because the formal sector is the only one complying with labor regula-tion, working in either the formal or the informal sector entitles the agent toa different set of benefits and costs, summarized in Table 2.1. If he works inthe formal sector, he receives a wage of wfa (X) and pays mandatory contri-butions to the pension system and other insurance programs at rates tp andtc. Mandatory contributions entitle the worker to receive non-monetary ben-efits in the short-run (e.g., health care) and increase the working experienceused to compute pension benefits in the long-run. If the agent works in theinformal sector, he receives a wage of wia (X), does not pay payroll taxes, yethe may be eligible for social assistance programs in the short and long-run(e.g. public health care and a social pension). In what follows, I assume thatthe formal-sector wage is greater or equal than the informal-sector wage (i.e.,wfa (1− tc − tp) ≥ wia), which is a common feature of informal labor mar-kets in Latin America (Albrecht, Navarro, and Vroman, 2009; Meghir et al.,2015).At the beginning of the first two periods, the agent draws an i.i.d. randomutility shock ψa ∈ R with cumulative distribution G ( ·|X). ψa encompassesthree unobservable determinants of the worker’s participation in the formalsector frequently found in the literature. First, there is evidence suggestingthat workers have a low valuation of the benefits provided by formal-sectorjobs because they have access to social programs that substitute those ben-efits (e.g., public health care) (Camacho, Conover, and Hoyos, 2013; Galianiand Weinschelbaum, 2011; Levy, 2008). Second, workers may prefer to workin the informal-sector because informal-sector jobs are in line with theirneeds for job independence and time flexibility (Maloney, 1999, 2004). Fi-nally, labor market frictions and regulations may prevent workers from find-ing formal-sector jobs (Joubert, 2015; Meghir et al., 2015; Ulyssea, 2010). Iintroduce ψa as a utility cost. In this setup, a higher value of ψa means thatthe worker has less incentives to participate in the formal sector. The modelassumes that the distribution of ψa is conditional on the agent’s characteris-tics X. For example, if college graduates find jobs in the formal-sector easierthan high-school graduates, then G (ψa|College) ≥ G (ψa|HighSchool) for572.3. The modelall ψa.The final element of the model is the pension plan. The agent retires atthe mandatory retirement age a = 3, leaving the labor force permanently.After retirement, he receives a per-period benefit of B (τ2, X), which is anon-decreasing function of the number of periods contributed to the pensionsystem while he worked, denoted by τ2. If the worker never contributed tothe pension system, he receives a social pension equal to B (0, X). Finally,the model assumes that the worker does not have any bequest motive, so heexhausts his income and savings by age a = 3. The definition of the pensionplan intends to capture the basics from a defined contribution system, whichis the most common system used in Latin American countries (Bosch et al.,2013).The interaction of sector-specific benefits from working, formal-sectorparticipation shocks, and the pension plan, provides the basis to characterizethe agent’s formal- sector labor supply.2.3 The modelEach period, a representative agent chooses consumption (denoted by ca ∈R+), assets (Aa ∈ R), and formal-sector labor supply (ha ∈ {0, 1}) to max-imize his expected lifetime utility. In what follows, I assume that lifetimeutility is time-separable, with a per-period utility function u (c) strictly con-tinuous and concave. Although the representative worker’s decisions areconditional on his characteristics X, I omit them to simplify notation.The agent’s decision variables depend on his age. When he is a worker(ages 1 and 2), he chooses a consumption and formal-sector labor supplyplan that solvesva (τa−1, Aa−1) = maxca,Aa,hau (ca)− ψaha + βEva+1 (τa, Aa) (2.1)582.3. The modelsubject toAa = (1 + r)Aa−1 + wia + ha(wfa (1− tc − tp)− wia)− ca (2.2)τa = τa−1 + ha (2.3)with Aa−1 and τa−1 given. In equations (2.1) and (2.2), r and β repre-sent the interest rate and the discount factor, respectively. Additionally,Eva+1 (τa, Aa) is the expected value function, where the expectation is alsoa function of τa and Aa. For tractability, I assume β = 11+r .Equations (2.1) to (2.3) formalize the setup discussed in Section 2.2. Ifthe agent works in the formal sector (ha = 1), he faces the utility shockψa, receives a formal-sector wage net of contributions wfa (1− tc − tp) andincreases his formal-sector experience by one more period. If he works inthe informal-sector (ha = 0), he receives a informal-sector wage wia, does notincur in the utility shock, and does not increase his formal-sector experience.When the agent retires (age 3), he chooses a consumption plan that solvesv3 (τ2, A2) = maxc3,A3u (c3) (2.4)subject toA3 = (1 + r)A2 +B (τ2)− c3 (2.5)where B (τ2) represents the retiree’s pension wealth (i.e., his income fromthe pension plan). Because the retiree does not have bequest motives, thevalue function after age 3 is equal to zero.The optimal consumption and formal-sector labor supply plan can beobtained by backward induction. To begin with, the optimal consump-tion plan for the retiree is to consume all his wealth, setting c3 (A2, τ2) =(1 + r)A2 +B (τ2). As a result, the value function for period 3 is equal tov3 (τ2, A2) = u (c3 (τ2, A2)) . (2.6)From the properties of the utility function and the pension plan, the valuefunction defined in (2.6) is an increasing function of financial wealth and592.3. The modelformal-sector experience.The definition of the value function v3 (τ2, A2) allows to characterize theoptimal consumption and formal-sector labor supply plans before retirement.Conditional on formal-sector choice, the first order conditions of the worker’sproblem implies that u′ (c2) = u′ (c3) and so c2 = c3.Let cf2 , Af2 , ci2, and Ai2 denote the optimal consumption and savings planconditional on working in the formal and informal sector. Using the conditionc2 = c3 and the budget constraint (2.2), the consumption and savings planconditional on sector choice isci2 =11 + β((1 + r)A1 + wi2 + βB (τ1))(2.7)cf2 =11 + β((1 + r)A1 + wf2 (1− tc − tp) + βB (τ1 + 1))(2.8)Ai2 =β1 + β((1 + r)A1 + wi2 −B (τ1))(2.9)Af2 =β1 + β((1 + r)A1 + wf2 (1− tc − tp)−B (τ1 + 1)), (2.10)while the value function conditional on sector choice isvi2 (τ1, A1) = (1 + β)u(ci2)= v˜i2 (τ1, A1) (2.11)vf2 (τ1, A1) = (1 + β)u(cf2)− ψ2 = v˜f2 (τ1, A1)− ψ2. (2.12)Finally, using equations (2.11) and (2.12), it is possible to characterizethe worker’s formal-sector labor supply for age 2. Because the worker facesthe utility shock only when he works in the formal sector, he chooses to workin the formal sector as long the utility gains are larger than the participationcosts. Thus, the worker sets h1 = 1 ifu¯2 (τ1, A1) = v˜f2 (τ1, A1)− v˜i2 (τ1, A1) ≥ ψ1. (2.13)The threshold u¯2 (τ1, A1) encompasses the utility gains from working in theformal sector. Working in the formal sector increases the worker’s lifetimeincome, as it increases the current income by the formal-to-informal wage602.3. The modelgap(wfa (1− tc − tp)− wia)and increases his future pension benefits. Con-sumption smoothing implies that the additional income is allocated betweenpresent and future consumption. Thus, in absence of utility shocks, theworker’s lifetime utility is higher when he works in the formal sector (i.e.,u¯2 (τ1, A1) ≥ 0). The worker’s final choice depends on his preferences forformal-sector employment, his net valuation of the mandated benefits, andthe availability of formal-sector jobs, all of them summarized by ψa.Equation (2.13) is also informative about the effect of a worker’s financialwealth and his level of formal-sector experience on the utility gains fromworking in the formal sector. This equation indicates that the long-run gainsfrom working one more period in the formal sector depend on the changeof the pension wealth. However, equation (2.13) also shows that the levelof wealth makes the worker less sensitive to long-run gains from working inthe formal sector. Intuitively, working in the formal sector increases lifetimeincome, yet this increment is relatively less important when the worker hasmore financial or pension wealth. To see this, note that the partial derivativeof u¯2 (τ1, A1) with respect to A1, the marginal change of the worker’s utilitygains to a change in financial wealth is∂u¯2 (τ1, A1)∂A1= (1 + r)(u′(cf2)− u′ (ci2)) , (2.14)which is negative as long as u′′ (c) < 0. Thus, when the worker has moreassets, the curvature of the utility function implies that the worker becomesless sensitive to the gains from working one more period in the formal sector.A second implication of the model is that the gains from working in theformal sector are a non-monotonic function of the formal-sector experience,as they depend on the curvature of the pension plan B (·) around τ1. Thepartial derivative of equation (2.13) with respect to τ1 is∂u¯2 (A1, τ1)∂τ1= β(u′(cf2)B′ (τ1 + 1)− u′(ci2)B′ (τ1)). (2.15)Thus, when B (·) is concave around τ1, then B′ (τ1 + 1) ≤ B′ (τ1) and thederivative in (2.15) is negative. When B (·) is convex around τ1, then the612.3. The modelsign for (2.15) is ambiguous and depends on the relative size of the productbetween the marginal utility of consumption and the marginal change inB (·).After characterizing the optimal consumption and formal-sector laborsupply plan of the worker, the ex-ante probability of working in the formalsector isP (h2 = 1| τ1, A1) = P (u¯2 (τ1, A1) ≥ ψ2) = G (u¯2 (τ1, A1)) (2.16)while the expected value function for age 2 isEv2 (A1, τ1) = (1 + β)u(ci2)+G (u¯2 (A1, τ1))E (u¯2 (A1, τ1)− ψ2 | ψ2 ≤ u¯2 (A1, τ1)) .(2.17)Using (2.17) it is possible to characterize the optimal consumption and laborsupply plan for the young worker (a = 1). However, the plan {c1, A1, h1} hasno analytical solution. I show in Appendix B.1 that the properties of thesolution described in this section also hold for the young worker.2.3.1 Numerical exampleTo illustrate the characteristics of the utility gains from working in the formalsector, u¯2 (τ1, A1), Figure 2.1 presents a numerical example for a hypotheticaladult worker (age 2). In this example, I assume that the worker’s utilityfunction is logarithmic, that the wages in the formal and informal sectorare wf = 1.1 and wi = 1, and that the worker does not have to contributeto the mandated benefits and pension systems (tc = tp = 0). Regarding thepension plan, I assume a replacement rate (the fraction of the formal-sectorwage the retiree receives as a pension) that is an increasing function of formal-sector experience: 0.5×(1 +(1 + e−2(τ1−1))−1). I choose a logistic functionbecause it allows me to show the results under a pension plan that is convexor concave depending on the formal-sector experience (see Figure 2.2). In thesimulation, I use small changes in the formal-sector experience to characterizein detail the shape of u¯2 (τ1, A1).622.3. The modelFigure 2.1 shows the main points presented in the model. Gains fromworking in the formal sector are non negative and they are determined bythe agent’s financial wealth (A1) and formal-sector experience (τ1). Whenworkers have low financial wealth, for instance A1 = −0.5, the gains arehigher, as working one more period in the formal sector increases substan-tially their lifetime income. In contrast, workers with high financial wealthare less sensitive to the utility gains from working in the formal sector. Forexample, assuming τ1 = 0, the increase in the lifetime income by workingone more period in the formal-sector is the wage gap only (the change inthe replacement rate is close to zero). The additional wage received fromworking in the formal sector(wf − wi = 0.1) increases consumption by 10percent for workers with no financial wealth (A1 = 0), while it increases con-sumption by 2.3 percent for workers with higher levels of financial wealth(A1 = 5).21 The additional utility gains are associated with the increase offuture consumption via an increase in savings.Moreover, the utility gains from working in the formal sector are a func-tion of the agent’s formal-sector experience, and follows closely the slope ofthe pension benefits received in age a = 3. Despite the long-run gains fromworking in the formal sector are close to zero for low and high values offormal-sector experience, the utility gains for workers with a few periods offormal-sector experience are larger. This is the result of the workers’ abil-ity to save: analogous to the example with financial wealth, workers withhigher pension wealth are less sensitive to the increase in the lifetime in-come associated with working one more period in the formal sector. Becauseworkers with a few periods of formal-sector experience have lower pensionwealth, the increase in lifetime income from working in the formal sector isrelatively more important for them.21The agents’ consumption plan conditional on sector choice and financial wealth arecf2 (τ1 = 0, A1 = 0) = 0.8585, ci2 (0, 0) = 0.7805, cf2 (0, 5) = 3.5474, and ci2 (0, 5) = 3.4695.632.4. No savings2.4 No savingsIn the previous section, I characterize the optimal consumption and laborsupply plan given the gains from working in the formal sector. The previoussetup assumed that the worker can save, and therefore he uses the increase inlifetime income from working in the formal sector to increase present and fu-ture consumption. Nonetheless, this may not be an appropriate assumptionfor workers in Latin American economies, especially the ones more likely towork in the informal sector. Empirical evidence from Latin America showsthat low income population exhibit low or negative saving rates, and theiraccess to adequate financial instruments to save is rather limited (Cavalloand Serebrisky, 2016).Due to these limitations to saving behavior, I examine a version of themodel in which the workers cannot save, and so Aa = 0 for all a. Except forthis assumption, the model setup is the same as that presented in Section 2.3.Again, the consumption and formal-sector labor supply plan can be obtainedby backward induction. In the last period, the retiree consumes all hisincome, that in this case is equivalent to his pension wealth. Therefore, thevalue function for the retiree is v3 (τ2) = u (B (τ2)).When the agent is still working, he chooses a consumption and formal-sector labor supply plan that solvesva (τa−1) = maxca,hau (ca)− ψaha + βEva+1 (τa) (2.18)subject toca = wia + ha(wfa (1− tc − tp)− wia)(2.19)τa = τa−1 + ha (2.20)with τa−1 given. Without savings, the representative worker’s optimal con-sumption plan is to consume all his income per period and, given a realizationof the utility shock ψa, the worker works in the formal sector as long as thegains from the search are greater than the costs. Thus, the worker works in642.4. No savingsthe formal-sector ifu¯a (τa−1) = u(wfa (1− tc − tp))− u (wia)+β (Eva+1 (τa + 1)− Eva+1 (τa)) ≥ ψa(2.21)and the ex-ante probability that a worker works in the formal sector is givenbyP (da = 1 | τa−1) = G (u¯a (τa−1)) . (2.22)As in the model in which the worker can save, u¯a (τa−1) summarizes thegains from working in a formal-sector job. The first term represents short-rungains, that is, utility gains that come from the wage gap. The second termrepresents long-run gains, that is, the utility gains that come from increasingthe pension benefits due to an increase in formal-sector experience.Due to the assumptions on the wage gap and the pension plan, u¯a (τa−1)is a non-negative, non-monotonic function of τa−1. For example, when a = 2,the derivative of u¯2 (τ1) with respect to τ1 is∂u¯2 (τ1)∂τ1= β(u′ (B (τ1 + 1))B′ (τ1 + 1)− u′ (B (τ1))B′ (τ1))(2.23)which depends on the concavity or convexity of B (·) around τ1.In summary, the main characteristics of the model holds when I assumethat the worker cannot save. The main difference with respect to the modelwith savings is that in this case the worker cannot smooth consumption, andtherefore the short and long-run utility gains from working in the formalsector are clearly separated.2.4.1 Numerical exampleFigure 2.3 presents a numerical example of the utility gains for the modelwith no savings. The example uses the assumptions listed in Section 2.3.1,except that in this case I assume that the representative agent cannot save.Relative to the utility gains presented in Figure 2.1, the dependence of theutility gains with respect to formal-sector experience is associated with the652.5. Separation rate less than onechanges of pension wealth, regardless of the level of pension wealth. Theincrease in current consumption by working in the formal sector is 10 percent(the wage gap), while the gains associated with future consumption dependon the change of pension wealth only. For example, for workers with a fewperiods of formal- sector experience, the changes of the replacement rateare close to zero, implying that the utility gains they perceive are only theincrease in current consumption.2.5 Separation rate less than oneThe versions of the model presented above assume that the worker loses hisjob by the end of the period. In this section, I use the framework fromSection 2.4 to analyze a scenario in which the worker loses his job withprobability q < 1. To simplify the analysis, I assume that the separationprobability is equal in both the formal and the informal sector.Because the worker loses his job with probability q, the worker’s decisionalso depends on the sector he worked in a − 1. Let xa denote an i.i.d.Bernoulli random variable that indicates whether the worker lost his job atthe end of the previous period (i.e., q = P (xa = 1)).Since the retiree is not affected by the separation results, his optimalconsumption plan is the same as that discussed in Section 2.4. When theagent is a worker, though, his consumption and labor supply plan dependson whether he loses his job. If the worker does not lose his job, then hechooses a consumption and formal-sector labor supply plan that solvesva (τa−1, ha−1, xa = 0) = maxcau (ca) + βEva+1 (τa, ha−1, xa+1) (2.24)subject toca = wia + ha−1(wfa (1− tc − tp)− wia)τa = τa−1 + ha−1.Similarly, if the worker loses his job at the end of a − 1, his problem662.5. Separation rate less than onebecomesva (τa−1, ha−1, xa = 1) = maxca,hau (ca)− haψa + βEva+1 (τa, ha, xa+1) (2.25)subject toca = wia + ha(wfa (1− tc − tp)− wia)τa = τa−1 + ha.Thus, when the representative worker does not lose his job in the previousperiod, he does not take any new decision about his formal-sector laborsupply; when he loses his job, the previous formal-sector labor supply doesnot affect his decision.Because the worker cannot save, his optimal consumption plan in bothcases is equal to his income. Conditional on xa = 0, the value function isva (τa−1, ha−1, 0) = u(wia + ha−1(wfa (1− tc − tp)− wia))+βEva+1 (τa−1 + ha−1, ha−1, xa+1) .(2.26)Additionally, conditional on xa = 1, the worker consumes his entire in-come and chooses to work in the formal sector ifu¯a (τa−1) = u(wfa (1− tc − tp))− u (wia)+β (Eva+1 (τa−1 + 1, 1, xa+1)− Eva+1 (τa−1, 0, xa+1)) ≥ ψa,(2.27)and therefore the ex-ante probability that a worker works in the formal sectorisP (ha = 1| τa−1, xa = 1) = G (u¯a (τa−1)) . (2.28)Using equations (2.26) to (2.28), the expected value function conditional672.6. Defined-contribution pension planon τa−1 and ha−1 = h ∈ {0, 1} isEva (τa−1, h, xa) = (1− q)u(wia + h(wfa (1− tp − tc)− wia))+(1− q)βEva+1 (τa−1 + h, h, xa+1) +q(u(wia)+ βEva+1 (τa−1, 0, xa+1))qG (u¯a (τa−1))E ( u¯a (τa−1)− ψa| u¯a (τa−1) ≥ ψa)(2.29)Since the worker consumes all his pension wealth when retired, the differ-ence Ev3 (τ2 + 1, 1, x3) − Ev3 (τ2, 0, x3) = u (B (τ2 + 1)) − u (B (τ2)) is non-negative. Using this result and equation (2.29),Eva (τa−1 + 1, 1, xa)− Eva (τa−1, 0, xa) = (1− q) u¯a (τa−1) ≥ 0. (2.30)Therefore, the long-run utility gains from working in the formal sector arealways non-negative. As a result, u¯a (τa−1) possesses the same properties asthe threshold defined in equation (2.21). The main difference in this caseis that the aggregate formal-sector labor supply will be determined by thecombination of past and present decisions.2.6 Defined-contribution pension planThe previous sections analyze the effect of a defined-benefit pension planon formal-sector labor supply. Although defined-benefit plans are commonacross Latin America, some countries have changed from defined-benefit pen-sion plans to combinations of defined-benefit and defined-contribution (indi-vidual account) plans. For instance, Chile has had an exclusive individualaccount plan since early 1980s, and Colombia and Peru implemented dualsystems in which both defined-contribution and defined-benefit plans coexist(Bosch et al., 2013).In this section, I use the framework presented in the previous sectionassuming an individual account pension plan, in which a pension fund in-vests the worker’s contributions in the capital market, and the principal andreturns constitute the worker’s income after retirement.682.6. Defined-contribution pension planThe setup of the model is the same as that presented in Section 2.3,except for the definition of the pension plan. Let Ba denote the pensionwealth of the representative agent at age a. When the agent retires (a = 3),his optimal consumption and saving plan is the solution ofv3 (B2, A2) = maxc3,A3u (c3) (2.31)subject toA3 = (1 + r) (A2 +B2)− c3. (2.32)Because the agent does not have bequest motives, the optimal solution is toconsume all his income, setting A3 = 0 and c3 = (1 + r) (A2 +B2). In whatfollows, I assume that financial assets and pension wealth have the samereturn in the financial market.When the agent is working (a ∈ {0, 1}), his optimal consumption, saving,and formal-sector labor supply plan is the solution ofva (Ba−1, Aa−1) = maxca,Aa,hau (ca)− ψaha + βEva+1 (Ba, Aa) (2.33)subject toAa = (1 + r)Aa−1 + wia + ha(wfa (1− tc − tp)− wia)− ca (2.34)Ba = (1 + r)Ba−1 + hatpwfa (2.35)with Ba−1 and Aa−1 given. The agent’s pension wealth is the agent’s accu-mulated pension wealth up to age a− 1 plus the additional per-period con-tribution that he makes when working in the formal sector (equation (2.35)).The solution of the agent’s problem follows similar arguments as thosepresented in Section 2.3. Using backward induction, the agent’s optimal692.6. Defined-contribution pension planconsumption and saving plan conditional on h2 isc2 =11 + β((1 + r)A1 + wi2 + h2(wf2 (1− tc)− wi2))+1 + r1 + βB1 (2.36)A2 =β1 + β((1 + r)A1 + wi2 + h2(wf2 (1− tc)− wi2))− 1 + r1 + βB1− h2tpwf2 (2.37)The optimal consumption and saving plan differs from the plan presentedin equations (2.7) to (2.10). Under the individual account plan the agentinternalizes the relationship between his present contribution to the pen-sion system and its impact on future pension benefits. As a result, theagent’s consumption does not depend on the pension contribution rate tp(equation (2.36)), and an increase of pension wealth of tpwf2 is offset by areduction in financial wealth (equation (2.37)).The value function conditional on sector choice isvi2 (B1, A1) = (1 + β)u(ci2)= v˜i2 (B1, A1) (2.38)vf2 (B1, A1) = (1 + β)u(cf2)− ψ2 = v˜f2 (B1, A1)− ψ2, (2.39)which implies that the agent chooses to work in the formal sector ifu¯2 (B1, A1) = v˜f2 (B1, A1)− v˜i2 (B1, A1) ≥ ψ2. (2.40)Equation (2.40) summarizes the gains from working in the formal sector.In contrast to the environment with a defined-benefit pension plan, the gainsin the model with an individual account plan are associated with the increaseof the agent’s lifetime income by the wage gap wf2 (1− tc) − wi. Becausefinancial assets and pension wealth are perfect substitutes, other potentiallong run gains associated with the increase of the pension wealth are offset bya reduction in financial assets. Following a similar analysis that the presentedin the Appendix B.1, it is possible to show that this behavior holds whenthe worker is young (a = 1).Although the long run gains from working in the formal sector are off-702.7. Final remarksset by changes in financial wealth, the utility gains from working in theformal sector are positive as long as wf2 (1− tc) > wi. Moreover, using equa-tions (2.38) and (2.39), the utility gains are decreasing in both, the level offinancial assets and pension wealth.The results presented in this section show that an individual accountpension plan has a limited effect on formal-sector labor supply when finan-cial and pension wealth are perfect substitutes. However, this one-to-onerelationship between financial and pension wealth depends on frictions af-fecting the economy. For example, credit constraints, minimum pensionsguarantees, and differential returns of assets and pension wealth, may affectthe degree of substitution between financial and pension wealth and maygenerate effects on formal-sector labor supply.2.7 Final remarksThis chapter describes the analysis of formal-sector labor supply for workersunder a life-cycle setting. The analysis extends the discussion presented inChapter 1, in which I provide empirical evidence of the effects of changes inpension wealth on pre-retirement formal-sector labor supply.The central piece of the model is the threshold u¯, which is the valuationthe worker places to the gains from working one more period in the formal-sector. The gains from working in the formal sector are divided in two: short-run gains, represented by the wage gap the worker receives, and long-rungains, represented by the increase in future pension benefits. As I show underdifferent specifications, as long as either the wage gap or the change in the(defined-benefit) pension plan is positive, working one period in the formalsector represents a gain in utility. Everything else constant, the gains fromworking in the formal sector are decreasing in the level of financial wealth(assets), while its relationship with respect to the formal-sector experiencedepends on the specific pension plan. In contrast, when the pension benefitsare related to an defined-contribution pension plan, the long-run gain fromworking in the formal sector is offset by a one-to-one reduction of financialassets. As a result, the utility gains in an individual account system comes712.7. Final remarksfrom the increase in the lifetime income of the wage gap.Although the model presents the formal-sector labor supply in a stylizedframework, its structure and implications can be extended to other contexts.For example, the model allows to study the interaction of pension programs,such as individual account pensions with minimum pension guarantees, andsocial pensions. The features of the model also provide a basic setup for thestudy of welfare consequences of pension programs in economies with a largeinformal sector.72Table 2.1: Pros and cons of working in the formal sectorPros Cons– Higher wages – Pay contribution– Mandated benefits – Preference for informal jobs∗– Pension benefits – Low valuation of benefits∗– Formal-sector jobs are scarce∗∗Participation shock in the modelNotes: This table presents the factors in favor and against working in the formal sector.For workers, a formal-sector job provides a wage greater than the wage in the informalsector and mandated benefits, such as health care and severance payments. In addition,formal-sector workers may be entitled to pension benefits in the future, depending ontheir time of contribution. However, there are factors that prevent workers from gettinga formal-sector job. First, working in the formal sector implies that workers have to paycontributions to the mandated benefits system. Second, some workers may prefer to workin the informal sector, due to time flexibility and desires of being independent. Third,because of the existence of substitutes for the mandated benefits, workers may have lowvaluation for the benefits provided by the formal sector. Finally, labor market frictionsand regulations may prevent workers from finding formal-sector jobs.73Figure 2.1: Simulation results, model with savings0.1.2.3Gains from working in the formal sector0 .5 1 1.5 2Formal-sector experienceA1 = -0.5A1 = 0A1 = 5Notes: This Figure shows the utility gains from working in the formal sector (u¯2 (τ1, A1))in a simulated scenario where the representative agent can save. The utility gains arecomputed for age 2, following equations (2.7) to (2.13) from Section 2.3 for three differentvalues of A1. I assume a logarithmic utility function, wf = 1.2, wi = 1, tc = tp = 0,and B (τ1) =(1 +(1 + e−2(τ1−1))−1)wf2. The utility gains from working in the formalsector are a function of the agent’s formal-sector experience, and follows closely the slopeof the pension benefits received in age a = 3. Moreover, it is a decreasing function of thelevel of financial wealth. Keeping everything else constant, the marginal gains from thewage gap and the increase in pension wealth become less important when the agent hasmore financial wealth.74Figure 2.2: Replacement rate0.2.4.6.81Replacement rate0 .5 1 1.5 2Formal-sector experienceNotes: The Figure shows the replacement rate (the fraction of the formal-sector wage theretiree receives as pension benefits) used in the examples presented in Sections 2.3 and 2.4.75Figure 2.3: Simulation results, model with no savings0.1.2.3Gains from working in the formal sector0 .5 1 1.5 2Formal-sector experienceNotes: This Figure shows the utility gains from working in the formal sector (u¯2 (τ1)) ina scenario where the representative agent cannot save. The utility gains are computed forage 2, following equation (2.21) from Section 2.4. I assume a logarithmic utility function,wf = 1.2, wi = 1, tc = tp = 0, and B (τ1) =(1 +(1 + exp−2(τ1−1))−1)wf2. In this case,the utility gains from working in the formal sector are a function of the wage gap and thechange of the pension wealth, regardless of the level of the agent’s pension wealth.76Chapter 3Labor Demand Responses toPayroll Taxes in an Economywith Wage Rigidity3.1 IntroductionA major challenge faced by developing economies is how to create a strongsocial insurance system while minimizing its distortionary effects on the econ-omy (Levy, 2008). In this challenge, payroll taxation plays a prominent roleas a policy instrument. On one hand, a payroll tax provides benefits toworkers in the form of insurance and may be used to finance the provision ofpublic goods. On the other hand, if the incidence of payroll taxes is borneby registered employers complying with regulation (formal employers),22 apayroll tax may discourage the creation of formal-sector jobs. A payroll taxmay increase the cost of labor in the formal sector, reducing formal-sector la-bor demand and reallocating labor towards less-productive, low-quality jobsin the informal (unregulated) sector. Empirical evidence from Brazil andColombia shows that the increase of payroll taxes has been a determinant inthe rise of informal-sector employment in both countries (Santa María et al.,2009; Ulyssea, 2010).The literature has identified three main determinants of the incidence22In what follows, I define informal sector as the set of firms and workers that do notcomply with government regulation, such as the payment of mandated contributions andtaxes. A firm operating in the informal does not pay taxes (including payroll taxes), but itis subject to fines if it is inspected. Regarding workers, informal-sector workers do not paycontributions to the mandated benefit and insurance systems, but they are not coveredby mandated benefits and other insurance included in the regulation.773.1. Introductionof payroll taxes: the tax-benefit link of payroll taxes, the elasticity of laborsupply, and the existence of factors that prevent wages from adjusting, suchas the minimum wage (Gruber, 2000). When wages are flexible, a one-to-one valuation of the benefits funded from payroll tax revenues or an inelasticlabor supply will allow payroll taxes to pass-through fully to wages with noemployment effects. Ultimately, the incidence of payroll taxes depends onthe interaction of those three factors, which is an empirical question.In this chapter, I analyze the incidence of payroll taxes in Colombia, aneconomy in which the labor market institutions prevent wages from adjustingto changes in payroll taxes. Colombia’s economy is characterized by majordistortions in the wage adjustment process. To begin with, the Colombianminimum wage is binding for a large fraction of the population (Bell, 1997).About 40 percent of workers in the formal sector work for the minimumwage. In addition, about 50 percent of the labor force works in the informalsector. The large informal sector mitigates the pass-through from payrolltaxes to wages, as a reduction in the formal-sector wage reduces the gainsfrom working in the formal sector. The wage rigidity suggests that payrolltax incidence is borne mostly by Colombian formal-sector employers.In this paper, I estimate incidence of payroll taxes on the Colombianlabor market by using an exogenous reduction of payroll taxes. In 2011, theColombian government introduced the First Job Act, which reduced payrolltaxes for new workers younger than 28 by 11 percentage points (on a basis of42 percent). Since the reduction in payroll taxes had no effect on the benefitsthat workers received (the deducted taxes were used to finance public goods),I interpret this reduction as a shock to the formal-sector labor demand.Using the exogenous variation caused by the First Job Act, I implementregression discontinuity and differences-in-differences identification strategieson a new source of administrative data for formal-sector employment. Inboth strategies, I compare the number of new workers and hiring wages forworkers younger and older than 28 years of age. Consistent with the idea thatthe incidence of payroll taxes is borne by employers, I find that the reductionof payroll taxes brought about by the First Job Act increased formal-sectorlabor demand for young workers by 3.4 percent while having no significant783.1. Introductioneffect on wages. The estimated impacts are similar across firms of all sizes,and are concentrated more in workers with no previous experience in theformal sector, men, and workers living in less developed regions.This chapter contributes to the literature on the incidence of payroll taxesby examining a context where labor market institutions lead to wage rigidity.As a result, the incidence of payroll taxes is borne by employers. The litera-ture on the incidence of payroll taxes includes a number of papers that lookat the incidence of payroll taxes in developing economies. Two of the mostrelevant papers are those by Gruber (1997), who analyzes the impact of thereduction of payroll taxes in Chile in the early 1980s, and Kugler and Kugler(2009), who analyze the impact of the increase of payroll taxes in Colom-bia in the early 1990s. While Gruber (1997) finds full pass-through fromtaxes to wages in Chile, Kugler and Kugler (2009) find partial pass-throughand employment effects in Colombia. Kugler and Kugler (2009) highlightthe importance of wage rigidity as a potential driver of their results. Byusing data at the individual level, I am able to analyze those effects directly.The empirical approach of this Chapter is similar to the used in Cruces,Galiani, and Kidyba (2010), as I identify the incidence of payroll taxes bycomparing the response of similar workers facing different payroll tax ratesin the same time period, an identification strategy frequently unavailable inprevious studies.As an additional contribution to the literature on the incidence of payrolltaxes, I recover the elasticity of formal-sector labor demand. Based on theestimation results and a standard economic model, I obtain an estimate ofthe elasticity of the formal-sector labor demand of −0.44. Because the wagedistribution of new workers is concentrated around the minimum wage, theelasticity is informative of the labor demand response around the minimumwage. Thus, my results imply that an increase of 10 percent of the minimumwage reduces formal-sector employment by 4.4 percent. This implication isspecific for the Colombian context, as the minimum wage is binding for alarge fraction of formal-sector workers (about 40%), which makes likely thatthe results are driven by changes in the formal-sector labor demand only.The rest of the chapter is organized as follows: Section 3.2 discusses793.2. Conceptual frameworkthe basic framework used in the analysis of the incidence of payroll taxes.Section 3.3 presents the institutional setting of the Colombian labor mar-ket, payroll taxes, and the First Job Act. Section 3.4 describes the dataused in the estimation and the identification strategy. Section 3.5 shows theestimation results, and Section 3.6 sets out the conclusions.3.2 Conceptual frameworkThe literature that examines the incidence of payroll taxes has a long his-tory. The framework is set out by Summers (1989) and Gruber and Krueger(1991). It emphasizes that the incidence of payroll taxes depends on theextent to which these can be passed-through to wages. In particular, if achange in payroll taxes is offset by a change in wages, payroll taxes do notgenerate distortions in the labor market. Further, the extent of the pass-through from payroll taxes to wages depends on the elasticity of the laborsupply and the tax-benefit link, i.e., the workers’ valuation of the benefitsthey perceive from payroll taxes.In a competitive labor market with homogeneous agents and employerpayroll taxes, the market equilibrium is given by the relationshipD (w (1 + t)) = S (w (1 + αt)) (3.1)where D (w (1 + t)) and S (w (1 + αt)) represent the aggregate labor demandand supply, w is the equilibrium wage, t is the employer payroll tax rate,and α represents the valuation that workers have for the benefits financedwith payroll taxes. The inclusion of payroll taxes implies that the worker’swage and the cost that the firm pays for this worker are different, as the firmhas to pay the payroll tax rate t. Similarly, the benefits perceived for theworker are higher than the worker’s wage, as he receives the wage plus thebenefits financed with payroll taxes, that the worker values at rate α. Asa result, labor demand is a function of the total labor cost w (1 + t), whilelabor supply is a function of the total worker’s compensation w (1 + αt).Gruber (1997) shows that, under this setup, a change in the employer803.2. Conceptual frameworkpayroll tax has effects on the equilibrium level of employment and wages.Using total differentiation on equation (3.1), the response of the equilibriumwages and employment to a change in the employer payroll tax is given bydwwdt=α (1 + t)ϕ− (1 + αt) η(η − ϕ) (1 + αt) (1 + t) (3.2)dDDdt= η(dwwdt+11 + t)=η1 + t(ϕ (α− 1)(η − ϕ) (1 + αt)). (3.3)In equations (3.2) and (3.3), η = D′w(1+t)D and ϕ = S′w(1+αt)S stand for theelasticity of labor demand and supply respectively.23From the previous analysis, employer payroll taxes do not have effectson employment (i.e.,dDDdt = 0) as long as the pass-through from taxes towages is equal to − 11+t . This result holds in two cases: First, if labor supplyis perfectly inelastic (ϕ = 0), then all the incidence of payroll taxes is onworkers. Second, if the worker’s valuation from the payroll tax equals thecost paid by the employer (α = 1) then the increase in taxes is offset by aproportional reduction in wages, leaving employment unchanged (Summers,1989).Along with an inelastic labor supply and a one-to-one tax-benefit link, afull pass-through from payroll taxes to wages requires that wages can adjustto changes in payroll taxes. However, this is not always the case in developingeconomies. In particular, the existence of a binding minimum wage and alarge informal (unregulated) sector prevents wages from adjusting to changesin taxes, which in turn generates employment effects even when the laborsupply is inelastic.A binding minimum wage is a common characteristic of Latin Americaneconomies, particularly Colombia (Bell, 1997; Maloney and Nuñez, 2004). Ifthe minimum wage is binding, payroll taxes cannot pass-through to wages,and the incidence of payroll taxes is borne by employers (Gruber, 2000).The extent of the effect of the minimum wage on tax incidence depends on23Equation (3.2) differs from the equation presented by Gruber (1997) because I assumea positive employer payroll tax and a zero employee payroll tax. I show in Section 3.3.1that these assumptions are a good approximation for the Colombian case.813.2. Conceptual frameworkhow binding the minimum wage is, an effect which is country-specific. Forexample, in Gruber’s (1997) examination of payroll taxes in Chile, he arguesthat the minimum wage is not a relevant factor given that it is relatively lowand affects only a small fraction of workers. In contrast, Kugler and Kugler(2009) find a limited pass-through in Colombia, which is consistent with thefact that the minimum wage is binding for a large fraction of Colombianworkers (Bell, 1997).The model presented above predicts that, when the minimum wage isbinding, the employment effect of an increase of payroll taxes is negative.Using equation (3.3), the employment effect of a change in payroll taxes isdDDdt=η1 + t. (3.4)A second characteristic frequently found in developing economies is aformal (regulated) sector co-existing with an informal sector. Typically, theinformal sector is composed of small firms and self-employed workers thatsurvive in the market by evading taxes and other regulations (La Porta andShleifer, 2014; Meghir et al., 2015). Most remain unregistered because theyare not productive enough to afford the cost of regulation, they are smallenough to avoid detection by tax authorities, or they do not see the benefitof registering (Maloney, 2004; Perry et al., 2007).The existence of the informal sector may mitigate the pass-through frompayroll taxes to wages. To illustrate the effect of the informal sector on thepass-through from payroll taxes to wages, I follow Levy (2008) and analyzea two-sector labor market where one sector (the informal) does not complywith labor regulation. I assume that workers do not have a preference forworking in either of the two sectors, and that they do not value the benefitsfrom payroll taxes. As a result, the equilibrium wage is the same for bothsectors, and the equilibrium in the labor market is given byDf (w (1 + t)) +Di (w) = S (w) , (3.5)where Di (·) and Df (·) represent the labor demand in the formal and infor-823.2. Conceptual frameworkmal sector, and S (·) is the aggregate labor supply.Figure 3.1 presents an example of the equilibrium effect of a reductionof payroll taxes in an economy with an informal sector. I assume that theaggregate labor supply is inelastic and equal to Lm, and that a worker alwaysgets a job in either the formal or the informal sector. The formal-sector labordemand is represented by the curve Df0 (drawn from left to right), while theinformal-sector labor demand is represented by the curve Di0 (drawn fromright to left, starting at Lm). The initial equilibrium is denoted by thepoint A, where the wage received by workers in both sectors is the same(w∗i0 = w∗f0).A reduction of payroll taxes shifts formal-sector labor demand curve tothe right by ηf1+tdt to Df1 , where ηf stands for the elasticity of formal-sectorlabor demand and t is the employer payroll tax. In the new equilibrium, thereduction of payroll taxes increases wages in both sectors and reallocates em-ployment from the informal to the formal sector (point B). Overall, the effecton formal-sector employment caused by the reduction of the payroll taxes(Lf∗1 − Lf∗0)is smaller than that observed in a case of a binding minimumwage(ηf1+tdt), but larger than that observed in a case with full pass-throughfrom taxes to wages and no informal sector (0). The magnitude of the effectdepends on the relative elasticity of the formal and informal sector labordemand curves.In general, using total differentiation on equation (3.5), the wage andformal-sector employment effects of a change in payroll taxes aredwwdt=−δηf(δηf + (1− δ) ηi − ϕ) (1 + t) (3.6)dDfDfdt= ηf(dwfwfdt+11 + t)=ηf1 + t((1− δ) ηi − ϕδηf + (1− δ) ηi − ϕ), (3.7)where δ = Df (w(1+t))Df (w(1+t))+Di(w)is the fraction of workers employed in the formalsector, and ηf and ηi are the elasticity of labor demand in the formal andinformal sectors. Equation (3.7) implies that payroll taxes have employmenteffects even with an inelastic aggregate labor supply (ϕ = 0). Assuming833.3. Institutional backgroundϕ = 0, the magnitude of the effect depends on the relative elasticity of labordemand and the size of the formal sector. Payroll taxes do not have an effecton the size of the formal sector if the demand for labor in the informal sectoris relatively inelastic(ηiηf→ 0)or the size of the informal sector is relativelysmall (δ → 1).3.3 Institutional background3.3.1 Colombian payroll taxes and labor marketThe labor market institutions in Colombia exhibit characteristics that sug-gest that the incidence of payroll taxes is borne by formal-sector employers.A weak tax-benefit link, a binding minimum wage, and a large informal sec-tor lead to a potentially large effect of payroll taxes on the generation offormal-sector employment.Table 3.1 presents a summary of payroll taxes levied in 2010. It showsthe employer and employee tax rate on the basis of contribution, and noteswhether the contribution rate is applied to the provision of benefits forworkers. The total payroll tax rate represents between 46 to 54 percentof a worker’s monthly wage, and is divided into three components: insur-ance, family benefits, and public goods. The insurance component formsthe largest part of the payroll tax rate (37 to 45 percentage points), andprovides insurance for workers in the event of negative health shocks, oldage, disability, and unemployment. Of the 12.5 percent deducted for healthcare insurance, 2 percentage points go to finance the public health care sys-tem. The family benefits component (4 percentage points) goes to FamilyBenefits funds, which are non-profit organizations responsible for providingbenefits to workers, such as child allowances, access to recreation facilities,and subsidies for housing. The public goods component of the contribution(5 percentage points) funds a public education institution with a focus ontechnical programs (SENA), and the government agency responsible for pro-viding child protection and family services (ICBF). Most of the payroll taxrate is paid by the employer (38 to 46 percentage points).843.3. Institutional backgroundAlthough the level of the Colombian payroll tax rate is similar to otherdeveloped and Latin American economies (Corbacho, Fretes Cibils, and Lora,2013; OECD., 2016), the structure of the payroll tax system may result in adistortionary effect on the labor market. To begin with, the tax-benefit linkis weak, given that the benefits deriving from payroll taxes depend on beingable to work in the formal sector and personal characteristics, and are notproportional to the worker’s contribution. For example, because the healthcare insurance covers the worker and his family, benefits from health careinsurance depend on the worker’s family size and their health rather thanhis actual contribution. Moreover, unless workers place enough value on thesocial benefit provided by the public good component of the payroll taxes,they will not give up part of their wage to fund them (Summers, 1989).Additionally, the binding minimum wage implies that the tax incidence–for a significant portion of Colombian workers– is fully borne by employ-ers. In their comparison of wage distribution for Latin American economies,Maloney and Nuñez (2004) show that Colombia has a particularly bindingminimum wage. When compared to seven Latin American economies,24 thewage distribution in Colombia exhibits the second highest minimum wage- tomedian-wage ratio, the lowest standard deviation, and the highest skewnesscoefficient. Taken together, the results presented by Maloney and Nuñez(2004)indicate that the distribution of wages in Colombia is concentratedaround the minimum wage and it is more concentrated than other LatinAmerican economies. The binding minimum wage is confirmed by the re-sults presented Table 3.2 (discussed in detail in Section 3.4), which showsthat about 40 percent of formal-sector workers earn the minimum wage.A third factor preventing wages from adjusting to changes in payrolltaxes is the large size of the informal sector. The informal sector so char-acteristic of the Colombian economy is explained by a number of factors.Firms are inclined to operate informally given weak enforcement of registra-tion requirements, large differences in costs of labor between the formal andinformal sector, and a low valuation given to the benefit of operating in theformal sector (Santa María et al., 2009). As Mondragón-Vélez, Peña, and24Argentina, Bolivia, Brazil, Chile, Honduras, Mexico and Uruguay.853.3. Institutional backgroundWills (2010) show, employment in the informal sector accounts for between50 to 60 percent of total employment in Colombia, mostly less-educated peo-ple working as a self-employed or as a salaried-worker in a small firm. Thesepatterns are similar to those found in other Latin American countries (Perryet al., 2007).3.3.2 First Job ActIn order to encourage the generation of formal-sector jobs, the Colombiangovernment enacted the First Job Act (Law 1429 of 2010). The Act had twoobjectives: to increase formal-sector employment of workers facing difficultiesin finding formal-sector jobs, and to increase the registration rate of smallfirms.The first component of the Act provided tax credits to existing firms forhiring workers under the age of 28. Starting in January 2011, employers coulddeduct from their corporate taxes 11 percentage points of the payroll taxespaid for these new workers. The tax credits were temporary, allowing theemployer to claim the benefit for up to two years. The deducted contributionscorrespond to payroll taxes used to fund public goods (SENA, ICBF, and thepublic health care system) and Family Benefits funds. A worker’s eligibilitywas based on the age at which employment commenced. For example, if theworker was hired when he was 27 years and 11 months old and continuedworking in the same firm, the firm would still be able to claim the taxcredits.25 Because the intention of the Act was to encourage the creation ofnew jobs, eligibility for tax credits was conditional on the firm increasing itstotal payroll by the end of the year.The second component of the Act provided incentives for new firms em-ploying up to 50 workers. The Act defined new firms as those registered after25The Act included other groups of eligible workers: women 40 and above without aformal job in the last 12 months; people with disabilities; heads of households eligible forsocial assistance programs; low-wage workers, up to 1.5 times the minimum wage, who hadnot worked in the formal sector; refugees; demobilized guerrilla soldiers, and paramilitarymembers. When a worker met more than one of the eligibility criteria, the exemptionsapply once. Due to the lack of information needed in order to identify these workers, Irestrict my analysis to workers under the age of 28.863.4. Empirical strategyJanuary 2011, and did not distinguish between new entrants and existing un-registered firms. New registered firms were exempt from paying corporatetaxes (33 percent), along with 11 percentage points of the payroll taxes of alltheir workers (SENA, ICBF, Family Benefits, and public health care), andregistration fees. The exemptions were temporary, allowing full exemptionfor the first two years and partial exemptions for the following three years.The prospect of a reduction in payroll taxes resulted in a positive shockin the demand for workers under the age of 28. After the Act was enacted,the total labor cost (wage plus payroll taxes) of eligible workers declinedby 11 percent. In contrast, the Act had a limited effect on labor supplybecause the reduction in payroll taxes had no effect on the benefits thatworkers received. Most of the reduction in payroll taxes was associated withcontributions used to fund public goods. In addition, given that firms werestill required to contribute to the Family Benefits funds, the workers continuereceiving the benefits from the contributions to the Family Benefits funds.Given my focus on identifying the effects of payroll taxes on formal-sectoremployment, I restrict my analysis to the effect of the reduction of payrolltaxes for workers below the age of 28. Although the First Job Act reducedpayroll taxes for new registered firms, it also reduced corporate taxes andregistration fees. As a result, I am not able to distinguish the causal effect ofthe reduction in payroll taxes on employment from the effect of reductions inthe corporate tax rate and registration fees on employment for new entrants.3.4 Empirical strategy3.4.1 Data and sample selectionTo investigate the effects of payroll taxes on the formal-sector labor market, Iuse the PILA dataset covering the period between 2010 and 2012. The PILAis an employer-employee dataset obtained from the system used to collectpayroll taxes. From the taxes reported in Table 3.1, all but the severancesavings contributions are collected monthly through the PILA system. Be-cause formal-sector employers pay payroll taxes and mandated contributions,873.4. Empirical strategythe dataset collects information for the universe of formal-sector workers.The PILA dataset includes information with respect to the type of em-ployer (public or private), the type of worker (independent or employee),days worked (typically 30 per month), job location, and the worker’s wage,gender, and date of birth.26 Although the dataset covers all formal-sectoremployment, there are problems with some of the identifiers for employersand employees. To avoid false transitions, I fill in job spells in cases where amatch is missing in a month but the dataset records the same match withina three-month window. In addition, I drop employers with extremely largevariations in the number of workers. After processing, the PILA datasetcontains 3.6 million private-sector employer-employee matches per month.The sample selection is based on characteristics of both the employersand the employees, and the conditions of the First Job Act. With respect toemployers, I restrict the sample to employers appearing in the entire sample(January 2010 to December 2012). Because these employers were registeredbefore January 2011, they became eligible for tax credits only when hiringnew workers below the age of 28. These employers are likely to be morestable and less likely to be affected by the entry effects associated with theprovision of additional benefits as set out by the Act. The final samplecontains 126,855 employers, which account for 57 percent of private-sectoremployers and 87 percent of formal-sector employment between 2010 and2012.With respect to employees, I restrict the sample to workers aged 26 to29, hired between February 2010 and December 2012. I focus on new formal-sector workers, defined as workers reported by the first time in a formal-sectorfirm. Since the Act reduced payroll taxes for new workers only, workersyounger than 28 who did not change their job after January 2011 were noteligible for the tax credit. Regarding the selection of workers by age group,I also restrict the sample to those aged 26 to 29 to mitigate concerns aboutsystematic differences in the time trends of formal-sector employment by ageor cohort (e.g., college enrollment decisions for workers 25 and younger).26Date of birth and gender were added by the Ministry of Health based on the employeeID number. About 0.4 percent of the sample do not have information about these variables.883.4. Empirical strategyTable 3.2 presents summary statistics for the selected sample of employ-ers. The table shows the average employment composition and wages byage group for all workers and for new workers, between February 2010 andDecember 2012. Table 3.2 shows that workers aged 26 to 29 share similarcharacteristics, while exhibiting noticeable differences with other age groups.In particular, relative to the total population,27 workers aged 26 to 29 havethe highest participation on both total formal-sector employment (22 per-cent) and entry into the formal-sector (1 percent). The result is consistentwith previous evidence for Latin American economies, where young workersenter into the labor market in salaried-informal jobs, switch in their adult-hood to salaried-formal jobs and, after accumulating experience, switch toinformal self-employment (Perry et al., 2007). Despite noticeable differencesin age composition, the distribution of employment in other demographiccharacteristics is similar across age groups. Except for the higher prevalenceof men older than 30, the fraction of men and the regional distribution aresimilar across age groups.The bottom part of Table 3.2 shows summary statistics for the wagedistribution of formal-sector workers. To reduce the effect of extreme ob-servations on the summary statistics, I trim the top and bottom 1 percentwages based on the monthly wage distribution. The first noticeable char-acteristic of the wage distribution is the binding minimum wage, especiallyfor new workers. About 36 percent of workers older than 25 earn exactlythe minimum wage and this fraction reaches 50 percent for the group ofnew workers. The average and median wage show a positive gradient overage, yet the median wage is just 20 percent larger than the minimum wage.Comparing the wage distribution of new workers with the wage distributionfor all workers, the wage distribution of new workers is more concentratedtowards the minimum wage. On average, new workers earn less, and theirwage distribution exhibits a lower standard deviation. These differences sug-gest that less-skilled workers are more prevalent in the new workers groupthan in the full sample.27To compute the fraction of total population, I used the total urban population by agefrom the Colombian Census of 2005. I describe the 2005 Census in Chapter 1.893.4. Empirical strategyIn summary, workers aged 26 to 29 are at their prime age for workingin the formal-sector. In spite of the fact that new hires share similar de-mographic characteristics with workers with more tenure in the firm, theirwages tend to be located near the minimum wage. The importance of theminimum wage in shaping the wage distribution is remarkable, and this mayplay a key role in preventing taxes from passing through wages even afterthe reduction of payroll taxes.3.4.2 Identification strategyTo measure the causal effect of changes in payroll taxes on formal-sector em-ployment and wages, I use the variation across age and time induced by theFirst Job Act to implement two identification strategies. In both strategies,I analyze the behavior of employment and wages of workers younger than28 relative to the behavior of workers 28 and older. I focus on labor marketindicators for workers in the month that they were hired, so I am estimatingthe effects of payroll taxes on employment generation and hiring wages.The first strategy is a regression discontinuity design (RD). I identify theemployment and wage effect of payroll taxes by comparing those indicatorsfor new workers just below and just above 28. I group workers aged 26 to29 hired after January 2011 by age group (a) and month of entry (m0) andrun regressions of the formya,m0 = α0 + ρRDI (a < 0) +2∑k=1(αk + α˜kI (a < 0)) · ak + ua,m0 . (3.8)In equation (3.8), ya,m0 is the labor market outcome for age group a andmonth of entry m0, a = age − 28 is normalized age (in quarters), and I (·)is the indicator function. The polynomial∑2k=1(αkak + α˜kakI (a < 0)) ac-counts for the relationship between the labor market indicators and age.Under the identification assumption that determinants of formal-sector em-ployment evolve smoothly around the eligibility threshold, ρRD is the causaleffect of the reduction of payroll taxes on the outcome of interest (Imbensand Lemieux, 2008).903.4. Empirical strategyAn additional identification assumption is required for the causal effect ofthe reduction of payroll taxes on employment. Because I have the universeof formal-sector workers, estimates of equation (3.8) are based on countsof formal-sector workers instead of measures of formal-sector employmentrelative to the entire population. As a result, the identification strategyrelies on the assumption that the density of the overall population by ageevolves smoothly around the eligibility threshold. If so, the estimates basedon the density of formal-sector employees identify the changes in formal-sector employment caused by the reduction of payroll taxes instead of achange in the population by age.The second identification strategy is a differences-in-differences design(DD). I identify the employment and wage effect of payroll taxes by compar-ing these indicators for new workers younger and older than 28 who startedworking in a formal-sector firm before and after the entry of the First JobAct. Using information for workers entering formal-sector firms by age group(a) and month of entry (m0), I run regressions of the form28ya,m0 = βa + βm0 + ρDDI (a < 0) · I (m0 ≥ 2011 : 01) + va,m0 (3.9)where the variables are defined in equation (3.8). Under the identificationassumption that determinants of formal-sector employment do not changedifferentially across the treatment and control groups around the reform,ρDD is the causal effect of the reduction in payroll taxes on formal-sectoremployment for workers younger than 28.I use three indicators to estimate employment and wage effects of thereduction of payroll taxes caused by the entry of the First Job Act. Giventhat I only had access to information about formal-sector workers, I estimateformal-sector employment effects based on the density of new workers by ageper month of entry. To compute the density, I count the number of workershired in month m0 by age group, normalized by the total number of workersaged 26 to 29 hired in month m0. To measure formal-sector wage effects, I28I restrict the sample to workers in the month they enter into the formal-sector firm(m0). Because of that, each new formal-sector match appears only once in the sample.913.4. Empirical strategyuse the average log wage and the fraction of new workers with wage equalto the minimum wage by age-month cell. For the wage regressions, I weighteach average by the number of observations per cell.A limitation of using the density of new entrants as dependent variableis that ρRD and ρDD do not allow a straightforward interpretation. Thedensity of new entrants is computed as the fraction of workers of a given agegroup relative to the total number of entrants aged 26 to 29. As a result,the estimated effects ρRD and ρDD are relative to the total formal-sectoremployment for this particular group. To estimate employment effects, I userelative measures using estimates of equations (3.8) and (3.9). For the RDstrategy, I use the test statistic proposed by McCrary (2008) and computethe employment effect as the log difference of the density just below and justabove 28. Using estimates from equation (3.8), I estimate the relative effecton formal-sector employment asγRD = log(α0 + ρRD)− log (α0) . (3.10)For the DD strategy, I normalize the average difference in the density offormal-sector employment by the density of workers aged 28 in December2010 (one month before the First Job Act took place). Using estimates fromequation (3.9), I estimate the employment effect of the reduction of payrolltaxes asγDD =ρDDβ28 + β2012:12. (3.11)In both cases, I compute the standard errors of the employment effects byusing the delta method.Because the minimum wage is binding for a large fraction of new workers,the expected sign for the employment effect of the reduction of payroll taxesis positive, but the expected sign for the wage effect is ambiguous. To see this,note that if the workers productivity is not constant, a reduction of payrolltaxes has two effects on workers with productivity close to the minimum wage(Kramarz and Philippon, 2001). On one hand, some workers who wouldhave entered earning the minimum wage will receive a higher wage. This923.5. Estimation resultseffect reduces the fraction of workers at the minimum wage and increasesthe average wage. On the other hand, the reduction allows the entry ofnew minimum wage workers who were not productive enough to work at theoriginal labor cost level. This effect increases the fraction of workers at theminimum wage and reduces the average wage. Thus, the overall effect of thereduction of the payroll taxes on wages around the minimum wage dependson the relative magnitude of these offsetting effects.3.5 Estimation results3.5.1 Identification checksThe regression discontinuity identification strategy relies on the assumptionthat the unobserved determinants of formal-sector employment and wagesevolve smoothly around the eligibility threshold. This assumption could beundermined if the estimated effect of the policy could be confounded bychanges in other covariates that might influence the outcome (Imbens andLemieux, 2008).To test the extent in which other observable characteristics may changearound the eligibility threshold, I analyze labor market outcomes and ob-servable characteristics of workers entering into formal-sector firms betweenFebruary and December 2010. Because the First Job Act took place in Jan-uary 2010, the distribution and characteristics of entrants should not beaffected by the fact that the worker is under the age of 28.Table 3.3 presents estimates of equation (3.9) for observable charac-teristics of the new entrants (panel A) and the formal-sector employmentand wages in 2010 (panel B). Observable characteristics found in the PILAdataset are gender and whether the worker starts a new job in a firm withless than 10 workers.29 Panel A presents regression discontinuity estimatesusing as dependent variables the fraction of male formal-sector workers andthe fraction of formal-sector workers entering into a small firm (10 workers29Since the Act could have differential effects by gender and firm size after its entry, itis not possible to implement this test for 2011 and 2012.933.5. Estimation resultsor less). The results show that there are no systematic differences in thoseobservable categories between workers just below and just after the eligibilitythreshold of the First Job Act.Panel B of Table 3.3 presents estimates of the employment and wageeffects for 2010. Since the Act took place before in January 2011, estimatesfor 2010 provide evidence of differential changes in wages and employmentassociated with other factors different from the entry of the First Job Act.The estimation results show that there is no significant employment effect.However, there is a significant difference in the average wage around the ageof 28 before the entry of the First Job Act. The significant effect is notrobust to alternative estimators and control functions.3.5.2 Baseline resultsTable 3.4 reports estimates of the employment and wage effects of the re-duction of payroll taxes for the sample of new workers aged 26 to 29. Thetable presents estimates of the employment effects and wage effects using re-gression discontinuity (RD) and differences-in-differences (DD) identificationstrategies. For each strategy, the columns present the effect of the reductionof payroll taxes on employment, on average wages, and on the fraction ofworkers earning the minimum wage. All estimates are presented in percent-age points. I allow for correlated errors by age group over time by clusteringthe standard errors by age group (16 clusters).Table 3.4 shows that the main adjustment to the reduction of payrolltaxes for new workers younger than 28 was through employment rather thanwages. In both strategies, I find a positive and significant effect on em-ployment and a small and insignificant effect on the average wage and thefraction of new formal-sector workers earning the minimum wage. The es-timates from the RD strategy indicate that, at the boundary, the reductionof payroll taxes increased employment for workers aged 28 by 1.14 percent.Similarly, the DD strategy indicates that the reduction of payroll taxes in-creased employment of workers younger than 28 by 3.38 percent. The RDresults are robust to the specification of the control function, alternative es-943.5. Estimation resultstimators and bandwidth selections. Similarly, the DD estimation results arerobust to the inclusion of time trends by age group to control for differen-tial entry rates of younger workers to the formal-sector. The results of therobustness tests are presented in Appendix C.The bottom part of Table 3.4 presents estimates of the effects of the FirstJob Act for new workers, in which I allow that the effect of the Act changesper year. The results show that firms responded slowly to the implementationof the reduction of payroll taxes, as the estimated employment effects werelarger in 2012 than in 2011. The RD employment effects are estimated withlow precision, and it is not possible to reject the null hypothesis that theemployment effects per year are the same (p-value: 0.169). In contrast, theemployment effect from the DD strategy is significant for both years, andsignificantly larger in 2012 (p-value for the difference between employmenteffects per year: 0.013). On average, the estimated employment effect basedon the differences-in-differences strategy is about 4.5 percent in 2012.Graphical evidence for the RD identification strategy is presented in Fig-ure 3.2. The top panel presents the estimated density of formal-sector em-ployment by age group in the year before and two years after the entry of theFirst Job Act. In 2010, there is no visible difference at the density of employ-ment around the age of 28, however there is a positive and significant effectafter the entry of the First Job Act. The density of employment in 2011-12tends to be more volatile for workers above the age of 28, which is reflectedon the wider confidence bands after the entry of the policy. With respectto average wages, there is no observable difference between wages aroundthe discontinuity threshold, that in fact is observed in 2010. Although thisdifference is not robust to the specification of the control function, the resultcasts doubts on the RD identification strategy.To further investigate the differences in the employment effects over time,I compute the time trend of the estimated employment effects for the DDstrategy. Figure 3.3 presents estimates of γDD in which I allow that theemployment effect changes by semester, using the second semester of 2010953.5. Estimation resultsas base category. Specifically, I estimate the equationya,m0 = βa + βm0 + ρDDh[m0]I (a < 0) · I (m0 ≥ 2011 : 01) + va,m0 (3.12)where h [m0] stands for the semester associated with month of entry m0.Based on estimates of ρDDh[m0], I compute the employment effects followingequation (3.11). The employment effect takes larger values only after thesecond semester of 2011, consistent with the idea that it took some timefor the firms to implement the First Job Act. Moreover, the estimated ef-fect for the first half of 2010 suggests that, prior to the entry of the FirstJob Act there were no significant differences in the trends for workers in thetreatment and control group. This result provides evidence to support thecommon-trend assumption required for the differences-in-differences identi-fication strategy.In light of the discussion presented in Section 3.2, the estimation resultssuggest that effect of the reduction in payroll taxes was not passed-throughhigher wages. Taking the estimated employment effect from the DD strat-egy(γˆDD = 0.0338), the reduction in payroll taxes (dt = −0.11), and theemployer payroll tax rate (t ≈ 0.42),30 equation (3.4) implies an elasticity offormal-sector labor demand of ηf = −0.44. This is likely a lower bound ofthe actual elasticity, as not all firms can claim the tax credit (so dt may becloser to zero). The elasticity is in the middle range of previous estimatesfound in the literature, which vary between -0.65 and -0.3 (Arango Thomas,Gómez, and Posada, 2009; Bell, 1997; Cardenas and Bernal, 2004; Robertsand Skoufias, 1997). In contrast to these previous studies, the estimatedelasticity does not rely on specific functional forms for labor demand, but onthe zero wage effect of the reduction of payroll taxes.Differences between identification strategiesAlthough both identification strategies find positive and significant employ-ment effects and no wage effects, the magnitude of the RD employment30I assume t = 0.42, as it is the middle point of the employer payroll tax rate (seeTable 3.1).963.5. Estimation resultseffects are smaller than the DD employment effects. Those differences maybe explained by the limited external validity of the RD identification strat-egy under heterogeneous treatment effects. As Imbens and Lemieux (2008)point out, regression discontinuity designs provide the average effect for thesubpopulation located at the boundary (in this case, new hires aged 28).However, if the treatment effect is heterogeneous, the conclusions drawnfrom this strategy cannot be extrapolated to other subpopulations.To test the role of heterogeneity in driving the differences between iden-tification strategies, I estimate employment effects by age group using adifferences-in-differences strategy. I estimate employment effects based onequation (3.11), allowing γDD to change by age group (grouped in 6-monthbins), and using new hires aged 28 as the base group. Figure 3.4 presents theestimates by age group. Under the homogeneity hypothesis, the coefficientslocated to the left of 28 should be equal. However, the estimate for the groupjust below 28 is smaller than the average effects for younger workers, and it issignificantly different from the other average effects (p-value:<0.01). More-over, as Table C.2 in the Appendix shows, the aggregate results are robustto the inclusion of time trends by age group, suggesting that the effect is notthe result of differential time trends between young and old workers. Thus,the results indicate that employment effects were larger for younger work-ers. This result may explain part of the difference between the estimatedemployment effects.Figure 3.4 provides additional information to test the robustness of theDD identification strategy. Since the First Job Act affected new workersyounger than 28, the estimated effects for older age groups should not beaffected for the entry of the First Job Act. The coefficients above 28 are notsignificantly different from zero (p-value 0.193), which provides supportingevidence of the robustness of the DD results.3.5.3 Heterogeneity analysisPrevious section shows that the effect of the reduction in payroll taxes foryounger workers exhibits heterogeneous effects over time and over age groups.973.5. Estimation resultsNext, I analyze whether the effects is heterogeneous with respect to otherobservable characteristics available in the data. To take into account theaverage effects over the whole group of workers younger than 28, I presentresults for the differences-in-differences identification strategy.I estimate the response of the formal-sector labor market to changes inpayroll taxes along four dimensions. First, I look at whether the significantemployment effect reported before corresponds to an actual increase of em-ployment, or whether it corresponds to a reallocation from younger workersto new formal-sector jobs. I test this by grouping new workers on the basisof their presence in the PILA dataset before (regardless of the type of job). Ithen estimate the employment and wage effects for workers with and withoutformal-sector experience.Panel A of Table 3.5 presents the estimated employment and wage ef-fects obtained by using the differences-in-differences identification strategy.Although the employment effects are significant for workers with and withoutformal-sector experience, the larger employment effects are for new formal-sector workers. The estimated employment effect for workers with and with-out previous experience in the formal sector are 3.6 and 7.5 percent, andthe difference is statistically significant (p-value: 0.014). Contrary to theaggregate results, the average effect on starting wages for new formal-sectorworkers is positive and significant. However, the estimated increase in wagesis relatively small compared to the employment effects (0.78 percent).Second, I examine the effects of the reduction of payroll taxes on em-ployment and wages by gender. Men and women have different labor forceand formal-sector participation patterns over their life cycle (Perry et al.,2007). Although men and women are in their prime age for both types ofparticipation, fertility and household decisions might differentially affect thetime trends for men and women, which may confound my results.Panel B of Table 3.5 presents the estimation results by gender. Bothgroups exhibit positive and significant employment effects, while the wageeffects are small and estimated with low precision. The employment effectsare higher for men than for women, 4.7 versus 2.7 percent, yet their differenceis only statistically significant at 10 percent level (p-value: 0.072).983.5. Estimation resultsThird, I analyze the effects of the reduction of payroll taxes on employ-ment and wages by region. Geographical variation has received increasingattention in the literature concerned with determinants and consequencesof the informal sector (Almeida and Carneiro, 2012; Gerard and Gonzaga,2014). Economies with low levels of economic development tend to exhibitlarger informal sectors (La Porta and Shleifer, 2014). Regions characterizedby lower economic development tend towards smaller and less productivefirms, with lower levels of enforcement of labor regulation.Panel C of Table 3.5 presents the estimation results by region. I split thesample between developed regions, comparing the largest industrial regionsof the country (Bogota/Cundinamarca, Antioquia, and Valle) versus the restof the country.31 The estimated employment effects are large and significantfor both regions. Employment effects are larger for developing regions, sug-gesting that formal-sector labor demand is more elastic in less developedregions. Nonetheless, the standard errors of the estimates are large enoughto fail to reject the null of equality of employment effects (p-value: 0.13).Finally, I analyze the effects of the reduction of payroll taxes on employ-ment and wages by firm size. Small firms tend to hire low-skilled workersand pay lower wages. Taking into account the binding minimum wage inColombia, it is more likely that the wage distribution for workers in smallfirms is more concentrated around the minimum wage. Figure 3.5 showsthat this is certainly the case. The figure presents the average fraction ofworkers earning the minimum wage by firm size. To maintain consistencyin the composition of the sample over time, I define firm size based on thenumber of workers reported in January 2010. Although the minimum wage isbinding for firms of all sizes, small formal-sector firms are more likely to paythe minimum wage than larger firms. About 60 percent of workers in firmswith 1 to 10 workers earn the minimum wage, and this figure drops to 35percent for firms with more than 100 workers. A similar pattern is observed31According to official reports from the Colombian Statistics Office (DANE), developedregions account for 60 percent of the total GDP and about 45 percent of the total popu-lation. Moreover, as I show in Chapter 1, developed regions exhibit larger formal-sectoremployment rates than developing regions.993.6. Final remarksin the distribution of hiring wages, where about 70 percent of new workersin firms with 1 to 10 workers earn the minimum wage. Thus, because theminimum wage is more binding for small firms, a reduction in payroll taxesshould have larger effects for them.Panel D of Table 3.5 presents the estimation results by firm size. Theresults suggest that the response of labor demand to changes in payroll taxeswas similar across firm sizes. Estimates of employment effects oscillate be-tween 3.0 and 3.5 percent, and I fail to reject the null hypothesis of equalityof employment effects (p-value: 0.918). Wage effects are small and insignif-icant for all firms. Taken together, the reduction in payroll taxes had awidespread positive impact in the formal-sector labor demand.3.6 Final remarksIn this chapter, I analyze the response of formal-sector labor demand to pay-roll taxes in an economy with wage rigidity. In developing economies, payrolltaxes may have large distortionary effects, given the likelihood that their in-stitutional characteristics will have employers bearing all the incidence of thepayroll tax.In particular, I analyze the incidence of payroll taxes in the formal-sectorin Colombia. Colombia is an example of an economy with labor marketinstitutions that prevents payroll taxes from passing-through wages. Onone hand, it has a strong wage rigidity. It exhibits one of the most bindingminimum wages in the region and half of the labor force works in the informalsector. On the other hand, the majority of the payroll tax system has a lowtax-benefit link, which leaves workers less willing to give up part of theirwage in exchange for access to the benefits from payroll taxes.To estimate the incidence of payroll taxes on the Colombian formal sectorI use the First Job Act. Starting in 2011, the Act reduced payroll taxes fornew workers under the age of 28. The Act has two useful aspects for theidentification of the incidence of payroll taxes. First, it modified payrolltaxes for only a subpopulation of workers, which allows the identification ofemployment and wage effects by using group variation over time. Second,1003.6. Final remarksthe Act reduced taxes that did not provide a direct benefit for workers, andthus the variation induced by the Act can be interpreted as a shock in theformal-sector labor demand.I estimate the payroll tax incidence by applying two identification strate-gies (regression discontinuity and differences-in-differences) to a new sourceof administrative data for the formal sector. I estimate effects of the reduc-tion of payroll taxes on both formal-sector employment and wages. Consis-tent with the idea that the incidence of payroll taxes is borne by employers,I find that the reduction of payroll taxes increased formal-sector demandfor young workers by 3.38 percent and no significant effect on wages. Theestimated employment and wage effects are consistent across different speci-fications and subsamples. The estimated impacts are similar across firms ofall sizes, and are concentrated more in workers with no previous experiencein the formal sector, in male workers, and in workers living in less developedregions.Using the estimates from the differences-in-differences strategy and thechange in payroll taxes, I find that the implied elasticity of demand in theformal sector is -0.44. Because the wage distribution of new workers is con-centrated around the minimum wage, the elasticity is informative with re-spect to the labor demand response around the minimum wage. Thus, theestimation results indicate that an increase of 10 percent of the minimumwage reduces formal-sector employment by 4.4 percent. This implication iscountry-specific, as the Colombian minimum wage is binding for a large frac-tion of formal-sector workers, which makes likely that the results are drivenby changes in the formal-sector labor demand only.The results show that changes in payroll taxes are an effective policy toolfor generating formal-sector employment when the institutional arrangementprevents labor market from passing-through payroll taxes to wages. The gen-eralization of these results is not straightforward, though, because such gen-eralization would depend on the particular type of rigidity affecting the labormarket. Nonetheless, this paper shows the importance of understanding thewage-setting process in order to better measure the extent and efficacy oflabor market policies.101Table 3.1: Payroll taxes in Colombia, 2010% of monthly Total Employer Employee Benefits forwage tax rate tax rate Worker OtherA. InsuranceHealth care 12.5 8.5 4.0 10.5 2.0Workplace safety 0.4-8.7 0.4-8.7 – 0.4-8.7 –Pension benefits 16.0 12.0 4.0 16.0 –Severance savings 8.1 8.1 – 8.1 –B. Family Benefits fundsFamily benefits 4.0 4.0 – 4.0 –C. Public goodsSENA/ICBF 5.0 5.0 – – 5.0Total 46.0-54.3 38.0-46.3 8.0 39.0-47.3 7.0Notes: This Table presents a summary of the payroll taxes paid by Colombian firms andworkers in the formal sector. It shows the employer and employee payroll tax rates, andthe distribution of the rate between services provided to the worker and the financing ofpublic goods. SENA is a public education institution with a focus on technical programsand training, ICBF is the government agency responsible for providing child protectionand family services, and Family Benefits funds are non-profit organizations responsible forproviding benefits to workers, such as child allowances, access to recreation facilities, andsubsidies for housing.102Table 3.2: Summary statistics, average 2010-2012All workers New workersAge group (years) 20-25 26-27 28-29 30-60 20-25 26-27 28-29 30-60Workers/month (Thousands) 503.0 226.9 237.7 2,069.8 40.6 11.9 10.7 57.7% of total 16.6 7.5 7.8 68.1 33.6 9.8 8.9 47.8% of Population 15.0 21.6 22.6 16.9 1.21 1.13 1.02 0.47Demographic Characteristics (% of total by age group)Men 55.4 55.9 56.2 60.2 56.4 56.9 57.3 61.9Developed regions 70.6 69.2 69.0 68.7 68.8 66.7 66.4 65.8Workers by Employer’s Size in January 2010 (% of total by age group)1-10 workers (97,526 Firms) 9.4 9.4 9.5 12.6 7.9 8.1 8.2 9.911-50 (21,478 Firms) 14.3 14.5 14.5 15.8 12.6 13.1 13.3 14.851-100 (3,506 Firms) 7.6 8.1 8.2 8.6 7.0 7.6 7.9 8.8101-1000 (3,983 Firms) 32.3 34.7 35.5 36.6 30.0 32.4 33.4 35.51000+ (362 Firms) 36.3 33.4 32.4 26.3 42.5 38.7 37.1 31.1Wage distribution (Minimum wage = 1)Average 1.34 1.66 1.80 2.03 1.25 1.48 1.55 1.58Standard Deviation 0.73 1.22 1.49 1.99 0.64 1.06 1.26 1.47Median 1.02 1.13 1.17 1.18 1.00 1.00 1.00 1.00Min. wage earners (%) 46.9 37.6 35.9 37.0 59.8 51.5 50.8 54.7Notes: This Table presents summary statistics from the PILA dataset between February 2010 and November 2012. It compares thedistribution of employment and wages across age groups (columns) for all workers in the firms included in the sample, as well as thesubset of new workers. For the wage distribution statistics, I trim the top and bottom one percent of observations based on the monthlydistribution of wages. “Min. wage earners” refers to the fraction of workers earning the monthly minimum wage.103Table 3.3: Balance tests, 2010A: RD results for predetermined variables, 2010Men Small firmworkerUnder the age of 28 0.20 0.06[0.31] [0.13]Number of cells 176 176Observations 241,368 241,368B: Employment and wage effects for 2010Employment Wage Min. WageUnder the age of 28 1.10 0.61 -0.46[1.24] [0.27]∗∗ [0.32]Number of cells 176 176 176Observations 241,368 236,240 236,240Notes: This Table investigates whether there are factors that affect the validity of theidentification assumptions required for the regression discontinuity (RD) design describedin Section 3.4.2. Each cell reports an RD estimate (escalated by 100) based on a separateregression of a variable observed in 2010 (the year before the entry of the First Job Act).The regressions include a quadratic polynomial on age and its interaction with a treatmentindicator for being under the age of 28 as independent variables (See equation (3.8)). PanelA presents estimates for the composition by gender and firm size between workers justbelow and just after the eligibility threshold of the First Job Act (28 years). Panel Bpresents RD estimates for employment and wage effects. The estimated effect for wagesis significant, but it is not robust to the specification of the control function. Standarderrors clustered by age group in brackets. ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01.104Table 3.4: Estimation results, Regression Discontinuity (RD) and Differences-in-Differences (DD) identificationstrategiesRD strategy DD strategyEmployment Wages Min. Wage Employment Wages Min. WagePanel A. Average effect 2011-2012Lower payroll taxes 1.14 0.02 -0.13 3.38 -0.23 0.07[0.57]∗ [0.36] [0.17] [0.81]∗∗∗ [0.19] [0.23]Panel B. Effects by year2011 0.32 -0.41 -0.04 2.20 0.01 -0.09[0.70] [0.64] [0.46] [1.09]∗ [0.25] [0.28]2012 1.91 0.39 -0.22 4.48 -0.46 0.22[0.88]∗∗ [0.26] [0.21] [0.70]∗∗∗ [0.22]∗ [0.25]Number of cells 384 384 384 560 560 560Observations 549,171 539,220 539,220 790,539 775,460 775,460Notes: This Table presents the estimation results for the employment and wage effects (in percentage points) for the sample of workersentering into formal-sector firms between February 2010 and December 2012. Each cell represents an estimated employment or wageeffect obtained by using regression discontinuity (RD) and differences-in-differences (DD) identification strategies (See Section 3.4 fordetails). “Min. Wage” refers to the average effect on the fraction of workers earning the minimum wage. Panel A displays the estimationresults assuming that the average effect of the policy is constant; Panel B allows that the estimated effects vary by year. Standarderrors clustered by age group in brackets. ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01.105Table 3.5: Estimation results for subsamplesEmployment Wages Min. WageA. Effects by previous experience in the formal sectorPrevious experience 3.64 -0.06 0.05[0.98]∗∗∗ [0.29] [0.30]No previous experience 7.46 0.78 -0.46[1.49]∗∗∗ [0.29]∗∗ [0.38]B. Effects by genderMen 4.23 -0.59 0.06[1.19]∗∗∗ [0.31]∗ [0.31]Women 2.22 0.30 0.04[0.51]∗∗∗ [0.31] [0.39]C. Effects by regionDeveloped 2.73 -0.41 0.30[0.93]∗∗ [0.25] [0.35]Developing 4.72 0.17 -0.47[1.14]∗∗∗ [0.26] [0.35]D. Effects by firm size1–10 workers 3.27 -0.18 0.85[1.55]∗ [0.51] [0.71]11–100 3.03 -0.26 -0.49[1.11]∗∗ [0.45] [0.48]100+ 3.47 -0.21 0.11[0.83]∗∗∗ [0.25] [0.30]Observations 790,539 775,460 775,460Notes: This Table investigates whether the effect of the First Job Act on employmentand wages is heterogeneous by observable characteristics of firms and workers. Eachcell represents an estimated employment or wage effect (in percentage points) obtainedby using a differences-in-differences (DD) identification strategy on the selected sample.“Min. Wage” refers to the average effect on the fraction of workers earning the minimumwage. Panel A analyzes whether the employment effect found in Table 3.4 is the resultof the entry of new formal-sector workers, or the result of reallocating younger workerswho were at one time working in the formal sector. Panel B shows the results by gender.Panel C shows the results by region. Panel D shows the results by firm size, defined as thenumber of workers employed by the firm at the beginning of the sample (January 2010).Standard errors clustered by age group in brackets. ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01.106Figure 3.1: Effect of a reduction of payroll taxes in an economy with aninformal sectorALf*0BLf*1w*0f w*0iw*1f w*1iDf0Df1SupplyDi0LmInformal-sector wageFormal-sector wageLaborNotes: This Figure shows an example of the equilibrium effect of a reduction of payrolltaxes in an economy with an informal sector. I assume that the aggregate labor supply isinelastic and equal to Lm, and that a worker always gets a job in either the formal or theinformal sector. The formal-sector labor demand is represented by the curve Df0 (drawnfrom left to right), while the informal-sector labor demand is represented by the curveDi0 (drawn from right to left, starting at Lm). The initial equilibrium is denoted by thepoint A, where the wage received by workers in both sectors is the same(w∗i0 = w∗f0). Areduction of payroll taxes shifts formal-sector labor demand curve to the right by ηf1+tdt toDf1 , where ηf stands for the elasticity of formal-sector labor demand and t is the employerpayroll tax. In the new equilibrium, the reduction of payroll taxes increases wages in bothsectors and reallocates employment from the informal to the formal sector (point B).Overall, the effect on formal-sector employment caused by the reduction of the payrolltaxes(Lf∗1 − Lf∗0)is smaller than that observed in a case of a binding minimum wage(ηf1+tdt), but larger than that observed in a case with full pass-through from taxes towages and no informal sector (0).107Figure 3.2: Formal-sector employment and wages by age, 2010–2012(a) Density of formal-sector employment (new workers).022.024.026.028.0326 27 28 29 302010.022.024.026.028.0326 27 28 29 302011-12Density of formal-sector employmentWorker's age (years)(b) Average log-wages (new workers)13.413.4513.513.5526 27 28 29 30201013.413.4513.513.5526 27 28 29 302011-12Average formal-sector (log) wageWorker's age (years)Notes: This Figure shows the differences in the density of employment and the averagewages by age before (2010) and after (2011-12) the entry of the First Job Act. Confidencebands (95 percent) were computed by using standard errors clustered by age group (inquarters).108Figure 3.3: Estimated employment effects by Semester, 2010–2012First Job Act took place-10-50510Estimated Effect on Employment (Percent)2010h1 2010h2 2011h1 2011h2 2012h1 2012h2Notes: This Figure investigates whether the employment effect of the First Job Act onemployment changes over time. Each point in the graph represents the estimated employ-ment effect (in percentage points), estimated using a differences-in-differences strategy inwhich I allow that the employment effect varies by semester. I use as a base category thesecond semester of 2010, so the reported coefficients are relative to the difference betweenthe density of entrants younger and older than 28 in that date. Confidence bands are 95percent confidence intervals using standard errors clustered by age group (in quarters).109Figure 3.4: Estimated employment effects by Age Group-202468Estimated Effect on Employment (Percent)26 27 28 29 30Notes: This Figure investigates whether the employment effect of the First Job Act isheterogeneous by age. Each point in the graph represents the estimated employmenteffect (in percentage points) estimated using a differences-in-differences strategy in whichI allow that the employment effect varies by age, grouped in 6-month bins. I use asbase category the group aged 28 to 28.5 years, so the reported coefficients are relativeto the difference between employment for that group. 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To simplifynotation, let uf = u(wf (1− tnom)) and ui = u (wi) denote the utilitylevels the worker receives when working in the formal and informal sector,ur = u(bwf)the utility the worker gets when he retires and is eligible forpension benefits, and u0 = u (0) the baseline utility the worker receives whenhe retires but is not entitled to pension benefits. Thus, u˜ = uf + θf − ui isthe gap (in utility terms) between the formal an informal sector and u¯a (τ) =u˜+ β∆va+1 (τ + 1).Most of the proofs use backward induction.Proposition 1. A replacement rate of b = 1 implies that the worker retiresas soon as he meets the requirements.Proof. Assume b = 1 and τ∗ ≤ R < T . In period T , the value function forretirement is given byvrT (τT−1) =u0 if τT−1 < τ∗ur + θr if τT−1 ≥ τ∗ .The value function if the worker continues working isvwT (τT−1) = ui +G (u˜)E ( u˜− ψT |ψT ≤ u˜) .By assumption u0 < ui, and so the comparison of both value functions117A.1. Model implications and robustness testsimplies that the worker retires when τT−1 ≥ τ∗, andvT (τT−1) =vwT (τT−1) if τT−1 < τ∗vrT (τT−1) if τT−1 ≥ τ∗ .For period T−1, the value function conditional on retirement and workingare equal tovrT−1 (τT−2) =u0 + βvrT (τT−2) if τT−2 < τ∗ur + θr + βvrT (τT−2) if τT−2 ≥ τ∗ .vwT−1 (τT−2) = ui + βvT (τT−2) +G (u¯T−1 (τT−2))×E ( u¯T−1 (τT−2)− ψT−1|ψT−1 ≤ u¯T−1 (τT−2)) .The second term of the latter equation is non negative, which implies thatthe worker does not retire when τT−2 < τ∗. When τT−2 ≥ τ∗, rewritevwT−1 (τT−2) asvwT−1 (τT−2) = (1−G (u¯T−1 (τT−2)))(ui + βvT (τT−2))+G (u¯T−1 (τT−2))(uf + θf + βvT (τT−2 + 1))−G (u¯T−1 (τT−2))E (ψT−1|ψT−1 ≤ u¯T−1 (τT−2))which is strictly less than vrT−1 (τT−2), and therefore the worker retires ifτT−2 ≥ τ∗. A similar analysis applies for a = R,R+ 1, . . . , T − 2.For a ≤ R−1, the worker cannot claim pension benefits even if τa−1 ≥ τ∗.The value function if he retires is vra (τa−1) = u0 + βvra (τa−1), which is lessthan vwa (τa−1). As a result, he does not retire before period R.Proposition 2. The intensity of the search for formal-sector jobs dependson the likelihood of getting retirement benefits.Proof. For simplicity, assume b = 1 so the worker retires as soon as he mets118A.1. Model implications and robustness teststhe requirements. The proof of the proposition has two parts. First, I showthat for workers for whom τ ≥ τ∗ or τ + (T − a+ 1) < τ∗, ∆va (τ + 1) = 0and therefore u¯a (τ) = u˜. Second, I show that ∆va (τ + 1) ≥ 0 for all othervalues of τ , and so u¯a (τ) ≥ u˜ for all τ . As a result, workers who still havea chance of meeting the minimum requirement conditions are the ones whosearch more actively for formal-sector jobs.First, there are two cases in which the accrual value of a period worked inthe formal sector is zero: (i) when workers are vested (τa−1 ≥ τ∗) and whenworkers do not have enough periods to reach τ∗ (τa−1 + (T − a+ 1) < τ∗).For the first part of the proof, note that when a ≥ R and τ ≥ τ∗, theoptimal retirement decision implies that va (τ + 1) = va (τ) = vra (τ) fora = R, . . . T − 1. For the case a = R− 1 and τ ≥ τ∗, condition (1.2) impliesthat uR−1 (τ) = u˜, and therefore the accrual value of an additional periodworked in the formal sector is∆vR−1 (τ + 1) = (1−G (u˜))β∆vR (τ + 1) +G (u˜)β∆vR (τ + 2) = 0.The same argument can be extended for a = τ∗, . . . , R− 2.When τT−1+1 < τ∗, ∆vT (τT−1 + 1) = 0 and u¯T−1 (τ) = u˜ for τ+1 < τ∗.Using backward induction, the result follows.Second, for τ ∈ [τ∗ − (T − a+ 1) , τ∗ − 1], ∆va (τ + 1) ≥ 0. To see this,note first that from the definition of vT (τT−1) presented above, vT (τ + 1) ≥vT (τ) for all τ . For any other period a < T , assume u¯a (τ + 1) ≥ u¯a (τ),and rewrite the first difference of the value function as∆va (τ + 1) = (1−G (u¯a (τ)))β∆va+1 (τ + 1) +G (u¯a (τ + 1))β∆va+1 (τ + 2) +(G (u¯a (τ + 1))−G (u¯a (τ)))×E ( u˜− ψa| u¯a (τ) ≤ ψa ≤ u¯a (τ + 1))≥ (1−G (u¯a (τ)))β∆va+1 (τ + 1) +G (u¯a (τ))β∆va+1 (τ + 2)≥0and thus ∆va (τ + 1) ≥ 0. A similar argument can be used to show the result119A.1. Model implications and robustness testswhen u¯a (τ + 1) ≤ u¯a (τ).Proposition 3. Assume b = 1. Holding all other variables constant, achange in the minimum retirement age R affects the incentives to search forformal-sector jobs. The effect is ambiguous and depends on a and τa−1.Proof. Assume an increase in the minimum age of retirement from R to R′.To characterize the full set of cases, assume that R′ −R ≥ 3. Since b equalsone, workers retire as soon as they meet the requirements, and therefore achange in the minimum age of retirement affects the incentives to search forformal-sector jobs.32Let va (τ) and v′a (τ) denote the value functions for the workers underR and R′. The effect of a change in the minimum retirement age dependson the worker’s age a. For workers with a ≥ R′, there is no labor supplyresponse, as a change in the retirement age does not change their retirementbehavior. Therefore, va (τ) = v′a (τ) for all τ and a = R′, . . . , T .For R ≥ a > R′, the effect of changes in the retirement age the effectis ambiguous. To see this, start with a = R′ − 1. Since ∆vR′ (τ + 1) =∆v′R′ (τ + 1), the long-run gains from retirement do not change for thisgroup, and so u¯R′−1 (τ) = u¯′R′−1 (τ). However, workers with τ ≥ τ∗ areno longer eligible to retire, and so they search for formal-sector jobs. Asa result, vR′−1 (τ) = v′R′−1 (τ) for τ < τ∗ and vR′−1 (τ) ≥ v′R′−1 (τ) forτ ≥ τ∗ (otherwise the retirement decision would not have been optimal).For this age group, there is an increase in formal-sector employment, asthe workers who are not longer eligible to retire search for formal-sectorjobs – driven by short-run gains only. A direct implication of the definitionof v′R′−1 (τ) is that ∆vR′−1 (τ + 1) = ∆v′R′−1 (τ + 1) for τ 6= τ∗ − 1 and∆vR′−1 (τ∗) ≥ ∆v′R′−1 (τ∗).For a = R′ − 2, the change in the incentives to search for formal-sectorjobs depends on τ . The definitions of vR′−1 (τ) and v′R′−1 (τ) imply that32The assumption b = 1 is not a necessary condition for the proof. In order that achange in the minimum retirement age generates changes in the incentives to search forformal-sector jobs, it is necessary that at least a group of workers finds optimal to retirein an age R∗ such that R ≤ R∗ < R′. Otherwise, the minimum retirement age is notbinding and workers do not respond to the change.120A.1. Model implications and robustness testsu¯R′−2 (τ) = u¯′R′−2 (τ) for τ 6= τ∗ − 1 and u¯R′−2 (τ∗ − 1) ≥ u¯′R′−2 (τ∗ − 1).Thus, the effect of a change in the minimum retirement age on the formal-sector labor supply response for is ambiguous, as there is a group that isnot affected by the measure (those with τ ≤ τ∗ − 2), a group that reducesits searching for formal-sector jobs (τ = τ∗ − 1), and a group that increasestheir formal-labor supply, as they would have retired under the previousconditions (τ ≥ τ∗). Using the definition of va (τ), vR′−2 (τ) = v′R′−2 (τ) forτ < τ∗ − 1 and vR′−2 (τ) > v′R′−2 (τ) for τ ≥ τ∗ − 1.Finally, ∆vR′−2 (τ + 1) = ∆v′R′−2 (τ + 1) for τ /∈ {τ∗ − 2, τ∗ − 1} and∆vR′−2 (τ + 1) ≥ ∆v′R′−2 (τ + 1) for τ ∈ {τ∗ − 2, τ∗ − 1} since∆vR′−2 (τ∗ − 1) = ∆vR′−2 (τ∗ − 1)−∆v′R′−2 (τ∗ − 1)= β (vR′−2 (τ∗ − 1)− vR′−2 (τ∗ − 2))− β (v′R′−2 (τ∗ − 1)− v′R′−2 (τ∗ − 2))= β(vR′−2 (τ∗ − 1)− v′R′−2 (τ∗ − 1))≥ 0and∆vR′−2 (τ∗) = ∆vR′−2 (τ∗)−∆v′R′−2 (τ∗)= (1−G (u¯R′−2 (τ∗ − 1)))β∆vR′−1 (τ∗)− (1−G (u¯′R′−2 (τ∗ − 1)))β∆v′R′−1 (τ∗)− (G (u¯R′−2 (τ∗ − 1))−G (u¯′R′−2 (τ∗ − 1)))×E(u˜− ψR′−2| u¯′R′−2 (τ∗ − 1) ≤ ψR′−2 ≤ u¯R′−2 (τ∗ − 1))≥ (1−G (u¯R′−2 (τ∗ − 1)))β(∆vR′−1 (τ∗)−∆v′R′−1 (τ∗))≥ 0.For a = R′−3, the change in the minimum retirement age have the sametype of composition effects as those for a = R′− 2. In this case, the workersthat exhibit a reduction in their formal-sector labor supply are those withτ ∈ {τ∗ − 3, τ∗ − 2, τ∗ − 1}. Again, vR′−3 (τ) = v′R′−3 (τ) for τ < τ∗− 2 andvR′−3 (τ) ≥ v′R′−3 (τ) otherwise. Moreover, ∆vR′−3 (τ + 1) = ∆v′R′−3 (τ + 1)121A.1. Model implications and robustness testsfor τ /∈ {τ∗ − 3, τ∗ − 2, τ∗ − 1} while ∆vR′−3 (τ + 1) ≥ ∆v′R′−3 (τ + 1) forτ ∈ {τ∗ − 3, τ∗ − 2, τ∗ − 1}. The proof of ∆vR′−3 (τ + 1) ≥ ∆v′R′−3 (τ + 1)for τ ∈ {τ∗ − 3, τ∗ − 1} follows the same steps as those for a = R′ − 2. Forτ = τ∗ − 2, difference between the value functions is equal to∆vR′−3 (τ∗ − 1) = ∆vR′−3 (τ∗ − 1)−∆v′R′−3 (τ∗ − 1)= (1−G (u¯R′−3 (τ∗ − 2)))β∆vR′−2 (τ∗ − 1)− (1−G (u¯′R′−3 (τ∗ − 2)))β∆v′R′−2 (τ∗ − 1)+G (u¯R′−3 (τ∗ − 1))β∆vR′−2 (τ∗)−G (u¯′R′−3 (τ∗ − 1))β∆v′R′−2 (τ∗)+(G (u¯R′−3 (τ∗ − 1))−G(u¯′R′−3 (τ∗ − 1)))×E(u˜− ψR′−3| u¯′R′−3 (τ∗ − 1) ≤ ψR′−3 ≤ u¯R′−3 (τ∗ − 1))− (G (u¯R′−3 (τ∗ − 2))−G (u¯′R′−3 (τ∗ − 2)))×E(u˜− ψR′−3| u¯′R′−3 (τ∗ − 2) ≤ ψR′−3 ≤ u¯R′−3 (τ∗ − 2))≥ (1−G (u¯R′−3 (τ∗ − 2)))×β(∆vR′−2 (τ∗ − 1)−∆v′R′−2 (τ∗ − 1))+G(u¯′R′−3 (τ∗ − 1))β (∆vR′−2 (τ∗)−∆v′R′−2 (τ∗))≥ 0.Using backward induction, the implications above apply for all age groupsa = {R, . . . , R′ − 3}.For a < R, the effect of a change in the minimum age for retirementis a reduction of the formal-sector labor supply. In this case, the searchingefforts of two types of workers are not affected by the change in R: work-ers who are too far to retire before R′ (τa−1 + R′ − a < τ∗) and thosewho already met the vesting period (τa−1 ≥ τ∗). For all other workers, thechange in R reduces their labor supply (the proof is similar to the presentedabove). Thus, for a < R, va+1 (τ) = v′a+1 (τ) for τ < τ∗ + (R′ − a+ 1) andva+1 (τ) > v′a+1 (τ) otherwise. In addition, ∆va+1 (τ + 1) ≥ ∆v′a+1 (τ + 1)for τ ∈ {τ∗ − (R′ − a) , . . . , τ∗ − 1} and ∆va+1 (τ + 1) = ∆v′a+1 (τ + 1) oth-erwise.122A.1. Model implications and robustness testsProposition 4. Assume b = 1. Holding all other variables constant, achange in the vesting period τ∗ affects the incentives to search for formal-sector jobs. The effect is ambiguous and depends on a and τa−1.Proof. Given an increase of the vesting period from τ∗ to τ ′, the optimalretirement and searching policy change. Using the arguments presented inpropositions 1 and 2, solving the model by backward induction yields a typeof policy like the one presented before, but it uses τ ′ as a reference pointinstead of τ∗. Thus, the policy function shifts rightwards. The shift generatestwo types of changes within each cohort. Workers with τa−1 ∈ {τ∗, . . . , τ ′}increase their searching efforts, as they are not vested yet, and workers withlow values of τa−1 tend to reduce their efforts, as the probability of reachingthe vesting period goes down.123A.1.ModelimplicationsandrobustnesstestsTable A.1: Robustness test, 2005Men Women(1) (2) (3) (4) (5) (6)A: Least Squares estimator (estimates scaled up by 100)Linear control function -2.79 -2.61 -2.87 -0.84 -0.74 -0.56(Bandwidth 48 months) [0.94]∗∗∗ [0.91]∗∗∗ [0.85]∗∗∗ [0.70] [0.70] [0.70]Quadratic control function -2.62 -2.36 -2.52 -0.18 -0.13 -0.15(Bandwidth 48 months) [1.28]∗∗ [1.34]∗ [1.14]∗∗ [1.03] [1.00] [1.05]B: Logit estimator (estimates scaled up by 100)Linear control function -2.82 -2.84 -2.48 -0.87 -0.77 -0.44(Bandwidth 48 months) [0.96]∗∗∗ [1.04]∗∗∗ [0.74]∗∗∗ [0.71] [0.71] [0.54]Quadratic control function -2.48 -2.39 -2.00 -0.15 -0.10 -0.10(Bandwidth 48 months) [1.27]∗ [1.42]∗ [0.95]∗∗ [1.04] [1.00] [0.80]C: Local linear estimator (estimates scaled up by 100)Local linear -2.64 – – -1.10 – –(Bandwidth 24 months) [1.16]∗∗ [0.94]Local linear -2.80 – – -0.68 – –(Bandwidth 36 months) [1.03]∗∗∗ [0.83]Observations 129,061 129,061 129,061 178,990 178,990 178,990Mean dep. variable (%) 18.1 18.1 18.1 15.7 15.7 15.7Fixed effects Month of High School Month of High Schoolbirth or less birth or lessNotes: Each cell reports an RD estimate based on a separate regression of an indicator variable of whether the person is a salariedworker contributing to the pension system and covered by the contributory health care system versus a polynomial on date of birthand its interaction with a dummy for being born after March-54 (men) and March-59 (women) as independent variables (See equation(1.6)). Columns (1) and (5) present the baseline regressions without any fixed effects, while the other columns include fixed effects totest the sensitivity of the results. The included fixed effects are based on categories of month of birth, educational attainment, andregion. Regressions were computed using the Colombian Census long-form questionnaire dataset (2005). Standard errors clustered bydate of birth (in months) in brackets. * p<0.1, ** p<0.05, *** p<0.01.124A.1.ModelimplicationsandrobustnesstestsTable A.2: Robustness test, 2011Men Women(1) (2) (3) (4) (5) (6)A: Least Squares estimator (estimates scaled up by 100)Linear control function 4.32 3.36 4.32 5.10 4.99 5.10(Bandwidth 730 days) [1.92]∗∗ [1.43]∗∗ [1.92]∗∗ [1.98]∗∗ [1.60]∗∗∗ [1.98]∗∗Quadratic control function 6.79 5.84 6.79 2.03 1.89 2.03(Bandwidth 730 days) [2.39]∗∗∗ [2.04]∗∗∗ [2.39]∗∗∗ [2.17] [1.58] [2.17]B: Local linear estimator (estimates scaled up by 100)Local linear 8.39 – – 3.70 – –(Bandwidth 360 days) [2.24]∗∗∗ [1.63]∗∗Local linear 6.74 – – 3.85 – –(Bandwidth 540 days) [2.05]∗∗∗ [1.69]∗∗Observations 964,558 964,558 964,558 927,691 927,691 927,691Fixed effects Month of Month of Month of Month ofbirth contribution birth contributionNotes: Each cell reports an RD estimate based on a separate regression of the log number of salaried formal workers contributing tothe pension system and the contributory health care system versus a polynomial on date of birth and its interaction with a dummy forbeing born after March-54 (men) and March-59 (women) as independent variables (See equation (1.6)). Columns (1) and (4) presentthe baseline regressions without any fixed effects, while the other columns include fixed effects to test the sensitivity of the results.The included fixed effects are based on categories of month of birth and month of contribution. Regressions were computed using thePILA dataset (2011). Standard errors clustered by date of birth (in months) in brackets. * p<0.1, ** p<0.05, *** p<0.01.125A.1.ModelimplicationsandrobustnesstestsTable A.3: Estimation results with alternative definitions of formal employment,2005Men WomenSalaried- Formal Formal Pension Salaried- Formal Formal Pensionformal worker worker (all) formal worker worker (all)(pension) (Colp) (pension) (Colp)(1) (2) (3) (4) (5) (6) (7) (8)Least Squares estimator (estimates scaled up by 100)Harder qualifying conditions -2.57 -2.71 -2.17 -3.49 -0.16 -0.36 0.02 -0.16(Bandwidth 48 months) [1.42]∗ [1.36]∗∗ [0.90]∗∗ [1.29]∗∗∗ [1.08] [0.91] [0.50] [1.02]Observations 129,061 129,061 129,061 129,061 178,990 178,990 178,990 178,990Mean dep. variable (%) 19.1 22.0 5.5 25.8 16.3 17.6 3.4 20.9Notes: Each cell reports an RD estimate based on a separate regression of formal employment versus a quadratic polynomial on dateof birth and its interaction with a dummy for being born after March-54 (men) and March-59 (women) as independent variables (Seeequation (1.6)). The definitions used are (i) salaried-formal employment based on contributions to the pension system, regardless ofcoverage of the contributory health care system; (ii) formal employment for all workers contributing to the pension and covered by thecontributory health care system, regardless of type of employment; (iii) formal employment for workers contributing to the pensionsystem and covered by the contributory health care system managed by Colpensiones; and (iv) an indicator for all people contributingto the pension system, regardless of their labor force participation. Regressions were estimated using the Colombian Census long-formquestionnaire dataset. Standard errors clustered by date of birth (in months) in brackets. * p<0.1, ** p<0.05, *** p<0.01.126Appendix BAppendix to Chapter 2B.1 Formal-sector labor supply of the youngworkerIn this appendix, I show that the properties of the function u¯a (τa−1, Aa−1)described in Section 2.3 also hold for the young worker (a = 1).Given an initial endowment of formal-sector experience τ0 and assets A0,the problem for the young worker isv1 (τ0, A0) = maxc1,A1,h1u (c1)− ψ1h1 + βEv2 (τ1, A1) (B.1)subject toA1 = (1 + r)A0 + wi1 + h1(wf1 (1− tc − tp)− wi1)− c1 (B.2)τ1 = τ0 + h1 (B.3)where the expected value function Ev2 (τ1, A1) is defined in equation (2.17).The optimal consumption and formal-sector labor supply plan for theyoung worker does not have an analytical solution. However, conditional on aformal-sector labor supply decision being made, the solution is characterizedby the system of equationsu′ (c1) = Eu′ (c2 (τ1, A1)) (B.4)A1 = (1 + r)A0 + wi1 + h1(wf1 (1− tc − tp)− wi1)− c1 (B.5)τ1 = τ0 + h1. (B.6)127B.1. Formal-sector labor supply of the young workerTo find the utility gains from working in the formal sector, I first describethe response of the optimal consumption plan and the value function withto changes in h1. Keeping h1 constant, there exists a consumption plan thatsatisfies equations (B.4) and (B.5). Implicit differentiation on equation (B.4)yields∂c1∂A1=ΨA1u′′ (c1)(B.7)whereΨA1 =(1 + r1 + β)Eu′′ (c2) +(1 + r) g (u¯2 (τ1, A1))(u′(cf2)− u′ (ci2))2 . (B.8)In equation (B.8), g (ψ) is the density function of the random variable ψ.Using the properties of the utility function, equation (B.7) implies that inthe space (A1, c1), the sign of the expression in equation (B.7) is ambiguous.The first term of ΨA1 accounts for the effect that an increase in savings hason future consumption, while the second term accounts for the effect that anincrease in savings has on the ex-ante probability of working in the formalsector in the future. In what follows, I assume that the effect of assets onthe probability of working in the formal sector is small enough, such thatΨA1 ≤ 0. This assumption rules out equilibria where the worker reduces hiscurrent consumption to reduce his sensitivity to the gains from working inthe formal-sector in the future. Thus, assuming ΨA1 ≤ 0, the equilibriumis unique, as the locus defined in equation (B.4) cuts the locus (B.5) frombelow in the (A1, c1) space.Let cf1 , Af1 , ci1, and Ai1 denote the consumption and saving plans condi-tional on working in the formal and the informal sector, respectively. Then,the worker chooses to work in the formal sector ifu¯1 (τ0, A0) = u(cf1)+ βEv2(τ0 + 1, Af0)− (u (ci1)+ βEv2 (τ0, Ai0))= v˜f1 (τ0, A0)− v˜i1 (τ0, A0) ≥ ψ1,(B.9)128B.1. Formal-sector labor supply of the young workerand the ex-ante probability of working in the formal sector is equal toP (h1 = 1| τ0, A0) = G (u¯1 (τ0, A0)) . (B.10)Next, I show that the value function (without utility shocks) is increas-ing in h1, and therefore u¯1 (τ0, A0) is always non-negative. Define v˜1 asv˜1 (τ0, A0) = u (c1)+Ev2 (τ1, A1) evaluated at the optimal consumption plangiven an arbitrary value of h1. Then, the partial derivative of v˜1 (τ0, A0)with respect to h1 is∂v˜1 (τ0, A0)∂h1= u′ (c1)(wf1 (1− tc − tp)− wi1)+β2E(u′ (c2)B′ (τ1))(B.11)where E (u′ (c2)B′ (τ1)) is defined asE(u′ (c2)B′ (τ1))= (1−G (u¯2 (τ1, A1)))u′(ci2)B′ (τ1) +G (u¯2 (τ1, A1))u′(cf2)B′ (τ1 + 1) .(B.12)Due to the assumptions imposed on the utility function, the wage gap,and the pension plan, (B.11) is a non-decreasing function of h1. Thereforeu¯1 (τ0, A0) is always non-negative.Finally, I show two more properties of the threshold u¯1 (τ0, A0): it isdecreasing in the level of assets and its relationship with the formal-sectorexperience is ambiguous. First, the derivative of u¯1 (τ0, A0) with respect toA0 is∂u¯1 (τ0, A0)∂A0= (1 + r)(u′(cf1)− u′ (ci1)) . (B.13)The concavity of the utility function guarantees that the right hand sideof (B.13) is non-positive as long as cf1 ≥ ci1. Using equations (B.4) and (B.5),the partial derivative of c1 with respect to h1 around the optimal consump-tion plan is∂c1∂h1=ΨA1(wf1 (1− tc − tp)− wi1)+ Ψτ1u′′ (c1) + ΨA1, (B.14)where Ψτ1 is the partial derivative of the expected marginal utility with129B.1. Formal-sector labor supply of the young workerrespect to τ1 defined asΨτ1 =β1 + βE(u′′ (c2)B′ (τ1))+βg (u¯2 (τ1, A1))(u′(cf2)− u′ (ci2))×(u′(cf2)B′ (τ1 + 1)− u′(ci2)B′ (τ1)),(B.15)with E (u′′ (c2)B′ (τ1)) defined in a similar way than (B.12). As in the caseof ΨA1 , I assume that the effect of τ1 on G (u¯2 (τ1, A1)) is small enough suchthat Ψτ1 ≤ 0. As a result, the optimal consumption plan is a non-decreasingfunction of h1, and therefore the derivative defined in (B.13) is negative.Second, the derivative of u¯1 (τ0, A0) with respect to τ0 is∂u¯1 (τ0, A0)∂τ0= β2E(u′(c1(τ0 + 1, Af1))B′ (τ0 + 1))− β2E (u′ (c1 (τ0, Ai1))B′ (τ0)) . (B.16)In this case, the sign of (B.16) is ambiguous, as it depends on the curvatureof the utility function and the concavity or convexity of the pension plan.130Appendix CAppendix to Chapter 3C.1 Robustness testIn this Appendix, I show that the estimation results presented in Table 3.4are robust to alternative specifications. In particular, I show that the RDresults are robust to the specification of control functions, estimators andbandwidth selections (Table C.1). Similarly, Table C.2 shows that the DDestimation results are robust to the inclusion of time trends by age group tocontrol for differential entry rates of younger workers to the formal sector.131C.1.RobustnesstestTable C.1: Regression Discontinuity robustness test, 2011-12Employment Wage Fraction at min. wage(1) (2) (3) (4) (5) (6) (7) (8) (9)A: Least Squares estimator (estimates scaled up by 100)Linear control function 1.25 1.24 1.55 0.34 0.26 0.36 -0.04 -0.03 -0.11(Bandwidth 24 months) [0.55]∗∗ [0.56]∗∗ [0.60]∗∗ [0.29] [0.36] [0.31] [0.16] [0.16] [0.17]Quadratic control function 1.14 1.13 1.42 0.02 -0.04 0.17 -0.13 -0.10 -0.26(Bandwidth 24 months) [0.57]∗ [0.57]∗ [0.56]∗∗ [0.36] [0.28] [0.29] [0.17] [0.18] [0.16]B: Local linear estimator (estimates scaled up by 100)Local linear 1.10 – – -0.18 – – 0.07 – –(Bandwidth 12 months) [0.35]∗∗ [0.25] [0.04]Local linear 1.21 – – 0.22 – – -0.08 – –(Bandwidth 24 months) [0.43]∗∗ [0.30] [0.11]Observations 549,171 549,171 549,171 539,220 539,220 539,220 539,220 539,220 539,220Fixed effects Quarter Region Quarter Region Quarter RegionNotes: Each cell reports an estimate (escalated by 100) based on a separate regression of employment or wage as dependent variable. Asindependent variables, I include a polynomial on age (in quarters) and its interaction with a treatment indicator of whether the workeris under the age of 28 (See Section 3.4 for details). Columns (1), (4) and (7) test the robustness of the results to the specification of thecontrol function and estimators, while other columns include fixed effects in the regressions to test the sensitivity of the results. Thefixed effects are based on categories of quarters of entry and job location. Standard errors clustered by age (in quarters) in brackets.∗ p<0.1,∗∗ p<0.05, ∗∗∗ p<0.01.132C.1. Robustness testTable C.2: Estimation results, DD including time trends by age groupEmployment Wages Min. WageLower payroll taxes 3.36 -0.17 0.04[0.88]∗∗∗ [0.19] [0.24]Number of cells 560 560 560Observations 790,539 775,460 775,460Notes: This Table investigates whether the Differences-in-Differences (DD) estimationresults are robust to the introduction of differential trends by age group. Each cell presentsDD estimates for the employment and wage effects (escalated by 100) for the sampleof workers entering into formal-sector firms between February 2010 and December 2012(See Section 3.4 for details). In each regression, I estimate the DD regression includingdifferential time trends by age group. “Min. Wage” refers to the average effect on thefraction of workers earning the minimum wage.∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01.133

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