Bounds on functionals of the distribution treatment effects

Bounds on the distribution function of the sum of two random variables with known marginal distributions obtained by Makarov (1981) can be used to bound the cumulative distribution function (c.d.f.) of individual treatment effects. Identification of the distribution of individual treatment effects is important for policy purposes if we are interested in functionals of that distribution, such as the proportion of individuals who gain from the treatment and the expected gain from the treatment for these individuals. Makarov bounds on the c.d.f. of the individual treatment effect distribution are pointwise sharp, i.e. they cannot be improved in any single point of the distribution. We show that the Makarov bounds are not uniformly sharp. Specifically, we show that the Makarov bounds on the region that contains the c.d.f. of the treatment effect distribution in two (or more) points can be improved, and we derive the smallest set for the c.d.f. of the treatment effect distribution in two (or more) points. An implication is that the Makarov bounds on a functional of the c.d.f. of the individual treatment effect distribution are not best possible.

Inequality treatment effects

This paper presents semiparametric estimators for treatment effects parameters when selection to treatment is based on observable characteristics. The parameters of interest in this paper are those that capture summarized distributional effects of the treatment. In particular, the focus is on the impact of the treatment calculated by differences in inequality measures of the potential outcomes of receiving and not receiving the treatment. These differences are called here inequality treatment effects. The estimation procedure involves a first non-parametric step in which the probability of receiving treatment given covariates, the propensity-score, is estimated. Using the reweighting method to estimate parameters of the marginal distribution of potential outcomes, in the second step weighted sample versions of inequality measures are.computed. Calculations of semiparametric effciency bounds for inequality treatment effects parameters are presented. Root-N consistency, asymptotic normality, and the achievement of the semiparametric efficiency bound are shown for the semiparametric estimators proposed. A Monte Carlo exercise is performed to investigate the behavior in finite samples of the estimator derived in the paper.

Efficient semiparametric estimation of quantile treatment effects

This paper presents calculations of semiparametric efficiency bounds for quantile treatment effects parameters when se1ection to treatment is based on observable characteristics. The paper also presents three estimation procedures forthese parameters, alI ofwhich have two steps: a nonparametric estimation and a computation ofthe difference between the solutions of two distinct minimization problems. Root-N consistency, asymptotic normality, and the achievement ofthe semiparametric efficiency bound is shown for one ofthe three estimators. In the final part ofthe paper, an empirical application to a job training program reveals the importance of heterogeneous treatment effects, showing that for this program the effects are concentrated in the upper quantiles ofthe earnings distribution.

Effects on school enrollment and performance of a conditional transfers program in Mexico

We study the effects of a conditional transfers program on school enrollment and performance in Mexico. We provide a theoretical framework for analyzing the dynamic educational decision and process inc1uding the endogeneity and uncertainty of performance (passing grades) and the effect of a conditional cash transfer program for children enrolled at school. Careful identification of the program impact on this model is studied. This framework is used to study the Mexican social program Progresa in which a randomized experiment has been implemented and allows us to identify the effect of the conditional cash transfer program on enrollment and performance at school. Using the mIes of the conditional program, we can explain the different incentive effects provided. We also derive the formal identifying assumptions needed to provide consistent estimates of the average treatment effects on enrollment and performance at school. We estimate empirically these effects and find that Progresa had always a positive impact on school continuation whereas for performance it had a positive impact at primary school but a negative one at secondary school, a possible consequence of disincentives due to the program termination after the third year of secondary school.

Identification and estimation of interventions using changes in inequality measures

This paper presents semiparametric estimators of changes in inequality measures of a dependent variable distribution taking into account the possible changes on the distributions of covariates. When we do not impose parametric assumptions on the conditional distribution of the dependent variable given covariates, this problem becomes equivalent to estimation of distributional impacts of interventions (treatment) when selection to the program is based on observable characteristics. The distributional impacts of a treatment will be calculated as differences in inequality measures of the potential outcomes of receiving and not receiving the treatment. These differences are called here Inequality Treatment Effects (ITE). The estimation procedure involves a first non-parametric step in which the probability of receiving treatment given covariates, the propensity-score, is estimated. Using the inverse probability weighting method to estimate parameters of the marginal distribution of potential outcomes, in the second step weighted sample versions of inequality measures are computed. Root-N consistency, asymptotic normality and semiparametric efficiency are shown for the semiparametric estimators proposed. A Monte Carlo exercise is performed to investigate the behavior in finite samples of the estimator derived in the paper. We also apply our method to the evaluation of a job training program.

Semiparametric estimation and inference using doubly robust moment conditions

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step. The key difference is that we do not impose any parametric restriction on the nuisance functions that are estimated in a first stage, but retain a fully nonparametric model instead. We call these estimators semiparametric doubly robust estimators (SDREs), and show that they possess superior theoretical and practical properties compared to generic semiparametric two-step estimators. In particular, our estimators have substantially smaller first-order bias, allow for a wider range of nonparametric first-stage estimates, rate-optimal choices of smoothing parameters and data-driven estimates thereof, and their stochastic behavior can be well-approximated by classical first-order asymptotics. SDREs exist for a wide range of parameters of interest, particularly in semiparametric missing data and causal inference models. We illustrate our method with a simulation exercise.

Essays in Corporate Bankruptcy

Esta tese é composta por três ensaios sobre o mercado de crédito e as instituições que regem bancarrota corporativa. No capítulo um, trazemos evidências que questionam a ideia de que maiores níveis de proteção ao credor sempre promovem desenvolvimento do mercado de crédito. Desde a publicação dos artigos seminais de La Porta et al (1997,1998), a métrica de proteção ao credor que os autores propuseram -- o índice de proteção ao credor -- tem sido amplamente utilizada na literatura de Law and Finance como variável explicativa em modelos de regressão linear em forma reduzida para determinar a correlação entre proteção ao credor e desenvolvimento do mercado de crédito. Neste artigo, exploramos alguns problemas com essa abordagem. Do ponto de vista teórico, essa abordagem geralmente supõe uma relação monotônica entre proteção ao credor e expansão do crédito. Nós apresentamos um modelo teórico para um mercado de crédito com seleção adversa em que um nível intermediário de proteção ao credor é capaz de implementar equilíbrios first best. Este resultado está de acordo com diversos outros artigos teóricos, tanto em equilíbrio geral quanto em equilíbrio parcial. Do ponto de vista empírico, tiramos proveito das reformas realizadas por alguns países durante as décadas de 1990 e 2000 para implementar uma estratégia inspirada na literatura de treatment effects e estimar o efeito sobre o valor de mercado e sobre a dívida de: i) permitir automatic stay a firmas em recuperação; e ii) conceder aos credores o direito de afastar os administradores. Os resultados que obtivemos apontam para um impacto positivo de automatic stay sobre todas as variáveis que dependem do valor de mercado da firma. Não encontramos efeito sobre dívida, e não encontramos efeitos significativos do direito de afastar administradores sobre valor de mercado ou dívida. O capítulo dois avalia as consequências empíricas de uma reforma na lei de falências sobre um mercado de crédito pouco desenvolvido. No início de 2005, o Congresso Nacional brasileiro aprovou uma nova lei de falências, a lei 11.101/05. Usando dados de firmas brasileiras e não-brasileiras, nós estimamos, usando dois modelos diferentes, o efeito da reforma falimentar sobre variáveis contratuais e não-contratuais de dívida. Ambos os modelos produzem resultados similares. Encontramos um aumento no volume total de dívida e na dívida de longo prazo, e uma redução no custo de dívida. Não encontramos efeitos significativos sobre a estrutura de propriedade da dívida. No capítulo três, desenvolvemos um modelo estimável de equilíbrio em search direcionado aplicado ao mercado de crédito, modelo este que pode ser usado para realizar avaliações ex ante de mudanças institucionais que afetem o crédito (como reformas em leis de falência). A literatura em economia há muito reconhece uma relação causal entre instituições (como leis e regulações) e desenvolvimento dos mercados financeiros. Essa conclusão qualitativa é amplamente reconhecida, mas há pouca evidência de sua importância quantitativa. Com o nosso modelo, é possível estimar como contratos de dívida mudam em resposta a mudanças nos parâmetros que descrevem as instituições da economia. Também é possível estimar o impacto sobre investimentos realizados pelas firmas, bem como caracterizar a distribuição do tamanho, idade e produtividade das firmas antes e depois da mudança institucional. Como ilustração, realizamos um exercício empírico em que usamos dados de firmas brasileiras para simular o impacto de variações na taxa de recuperação de créditos sobre os valores médios e totais de dívida e capital das firmas. Encontramos dívida crescente e capital quase sempre também crescente na taxa de recuperação.

Bounds on policy relevant parameters with discrete policy variation

When estimating policy parameters, also known as treatment effects, the assignment to treatment mechanism almost always causes endogeneity and thus bias many of these policy parameters estimates. Additionally, heterogeneity in program impacts is more likely to be the norm than the exception for most social programs. In situations where these issues are present, the Marginal Treatment Effect (MTE) parameter estimation makes use of an instrument to avoid assignment bias and simultaneously to account for heterogeneous effects throughout individuals. Although this parameter is point identified in the literature, the assumptions required for identification may be strong. Given that, we use weaker assumptions in order to partially identify the MTE, i.e. to stablish a methodology for MTE bounds estimation, implementing it computationally and showing results from Monte Carlo simulations. The partial identification we perfom requires the MTE to be a monotone function over the propensity score, which is a reasonable assumption on several economics' examples, and the simulation results shows it is possible to get informative even in restricted cases where point identification is lost. Additionally, in situations where estimated bounds are not informative and the traditional point identification is lost, we suggest a more generic method to point estimate MTE using the Moore-Penrose Pseudo-Invese Matrix, achieving better results than traditional methods.

Três ensaios sobre o mercado de trabalho no Brasil

Esta tese é composta por três artigos e uma nota, sendo um em cada capítulo. Todos os capítulos enquadram-se na área de Microeconomia Aplicada e Economia do Trabalho. O primeiro artigo estende o modelo tradicional de decomposição das flutuações na taxa de desemprego de Shimer (2012), separando o emprego formal do informal. Com essa modificação, os principais resultados da metodologia se alteram e conclui-se que os principais fatores para a queda do desemprego na última década foram (i) a queda na taxa de participação, principalmente pela menor entrada na força de trabalho; (ii) o aumento da formalização, atingido tanto pelo aumento da probabilidade de encontrar um trabalho formal quanto pela probabilidade de deixar a condição de empregado formal. O segundo capítulo apresenta estimativas para o retorno à educação no Brasil, utilizando uma nova metodologia que não necessita de variáveis de exclusão. A vantagem do método em relação a abordagens que utilizam variáveis instrumentais é a de permitir avaliar o retorno médio para todos os trabalhadores (e não somente os afetados pelos instrumentos) e em qualquer instante do tempo. Face aos resultados, concluímos as estimativas via MQO subestimam o retorno médio. Discute-se possíveis explicações para esse fenômeno. O terceiro artigo trata da terceirização da mão de obra no Brasil. Mais especificamente, mede-se o diferencial de salários entre os trabalhadores terceirizados e os contratados diretamente. Os resultados de uma comparação não condicional indicam que os terceirizados têm salário médio 17% menor no período 2007 a 2012. Porém, com estimativas que levam em conta o efeito fixo de cada trabalhador, esse diferencial cai para 3,0%. Além disso, o diferencial é bastante heterogêneo entre os tipos de serviços: aqueles que utilizam trabalhadores de baixa qualificação apresentam salário menores, enquanto nas ocupações de maior qualificação os terceirizados têm salários iguais ou maiores do que os diretamente contratados. Mais ainda, as evidencias apontam para a diminuição do diferencial ao longo do tempo no período analisado. Finalmente, a nota que encerra a tese documenta dois aspectos relevantes e pouco conhecidos da Pesquisa Mensal de Emprego do IBGE que podem levar a resultados imprecisos nas pesquisas que utilizam esse painel se não forem tratados adequadamente.

Lighting and violent crimes: evaluating the effect of an electrification policy in rural Brazil on violent crime reduction

This paper estimates the effect of lighting on violent crime reduction. We explore an electrification program (LUZ PARA TODOS or Light for All - LPT) adopted by the federal government to expand electrification to rural areas in all Brazilian municipalities in the 2000s as an exogenous source of variation in electrification expansion. Our instrumental variable results show a reduction in homicide rates (approximately five homicides per 100,000 inhabitants) on rural roads/urban streets when a municipality moved from no access to full coverage of electricity between 2000 and 2010. These findings are even more significant in the northern and northeastern regions of Brazil, where rates of electrification are lower than those of the rest of the country and, thus, where the program is concentrated. In the north (northeast), the number of violent deaths on the streets per 100,000 inhabitants decreased by 48.12 (13.43). This moved a municipality at the 99th percentile (75th) to the median (zero) of the crime distribution of municipalities. Finally, we do not find effects on violent deaths in households and at other locations. Because we use an IV strategy by exploring the LPT program eligibility criteria, we can interpret the results as the estimated impact of the program on those experiencing an increase in electricity coverage due to their program eligibility. Thus, the results represent local average treatment effects of lighting on homicides.

Revisiting the synthetic control estimator

The synthetic control (SC) method has been recently proposed as an alternative to estimate treatment effects in comparative case studies. The SC relies on the assumption that there is a weighted average of the control units that reconstruct the potential outcome of the treated unit in the absence of treatment. If these weights were known, then one could estimate the counterfactual for the treated unit using this weighted average. With these weights, the SC would provide an unbiased estimator for the treatment effect even if selection into treatment is correlated with the unobserved heterogeneity. In this paper, we revisit the SC method in a linear factor model where the SC weights are considered nuisance parameters that are estimated to construct the SC estimator. We show that, when the number of control units is fixed, the estimated SC weights will generally not converge to the weights that reconstruct the factor loadings of the treated unit, even when the number of pre-intervention periods goes to infinity. As a consequence, the SC estimator will be asymptotically biased if treatment assignment is correlated with the unobserved heterogeneity. The asymptotic bias only vanishes when the variance of the idiosyncratic error goes to zero. We suggest a slight modification in the SC method that guarantees that the SC estimator is asymptotically unbiased and has a lower asymptotic variance than the difference-in-differences (DID) estimator when the DID identification assumption is satisfied. If the DID assumption is not satisfied, then both estimators would be asymptotically biased, and it would not be possible to rank them in terms of their asymptotic bias.