Inference in differences-in-differences with few treated groups and heteroskedasticity

Differences-in-Differences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, we show that when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under-) over-reject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we can model the heteroskedasticity of a linear combination of the errors. We show that this assumption can be satisfied without imposing strong assumptions on the errors in common DID applications. With many pre-treatment periods, we show that this assumption can be relaxed. Instead, we provide an alternative inference method that relies on strict stationarity and ergodicity of the time series. Finally, we consider two recent alternatives to DID when there are many pre-treatment periods. We extend our inference methods to linear factor models when there are few treated groups. We also derive conditions under which a permutation test for the synthetic control estimator proposed by Abadie et al. (2010) is robust to heteroskedasticity and propose a modification on the test statistic that provided a better heteroskedasticity correction in our simulations.

Inference in differences-in-differences with few treated groups and heteroskedasticity

Differences-in-Differences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, we show that when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under-) over-reject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we know how the heteroskedasticity is generated, which is the case when it is generated by variation in the number of observations per group. With many pre-treatment periods, we show that this assumption can be relaxed. Instead, we provide an alternative application of our method that relies on assumptions about stationarity and convergence of the moments of the time series. Finally, we consider two recent alternatives to DID when there are many pre-treatment groups. We extend our inference method to linear factor models when there are few treated groups. We also propose a permutation test for the synthetic control estimator that provided a better heteroskedasticity correction in our simulations than the test suggested by Abadie et al. (2010).

A Higher order and stable method for the numerical integration of Random Differential Equations

Trabalho apresentado no Congresso Nacional de Matemática Aplicada à Indústria, 18 a 21 de novembro de 2014, Caldas Novas - Goiás

A organização social e o acesso à cultura: o caso das bibliotecas parque do Estado do Rio de Janeiro

Esta dissertação procura analisar qual a contribuição das Organizações Sociais para o acesso a direitos culturais, a partir da experiência das Bibliotecas Parque do Estado do Rio de Janeiro, em especial a de Manguinhos e a da Rocinha. Ciente de que as formas de cooperação para a efetivação de direitos culturais são múltiplas e que precisam ser pensadas a partir da inter-relação de vários atores e aspectos, todas invariavelmente necessitam desaguar em molduras de gestão viabilizadoras do acesso à cultura. A pesquisa adota o método do estudo de caso, valendo-se de pesquisas bibliográfica, documental e de campo. Apresenta o cenário de construção dos direitos culturais, em larga expansão no Brasil, e destaca que, para materializá-los, torna-se necessário estudar, avaliar e adotar modelos organizacionais alternativos aos tradicionais que caracterizam a administração pública direta e indireta. Aborda o campo da gestão e dos direitos culturais no contexto das três principais reformas do aparelho do Estado Republicano, ocorridas nas décadas de 30, 60 e 90, com ênfase na última, que incorpora a teoria da Nova Gestão Pública, base desta dissertação. Focaliza a Organização Social como modelo opcional à gestão de instituições ou programas culturais, a partir da realidade existente, das motivações, das vantagens e das perspectivas e aduz uma narrativa acerca do processo de concepção da legislação do estado do Rio de Janeiro. Verifica como surgiram esses equipamentos culturais e como se deu a formação da rede de Bibliotecas Parque. Descreve o processo de implantação das Organizações Sociais de Cultura no estado e apresenta o gestor das bibliotecas e sua relação com a secretaria de Cultura. Conclui que há necessidade de aperfeiçoamento de mecanismos de gestão, a fim de que o modelo possa, de fato, oferecer contribuição para o acesso a direitos culturais.