Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors

This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the nite-sample theory of weighted-average power (WAP) tests with normal errors and a known long-run variance. We introduce two weights which are invariant to orthogonal transformations of the instruments; e.g., changing the order in which the instruments appear. While tests using the MM1 weight can be severely biased, optimal tests based on the MM2 weight are naturally two-sided when errors are homoskedastic. We propose two boundary conditions that yield two-sided tests whether errors are homoskedastic or not. The locally unbiased (LU) condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness. The strongly unbiased (SU) condition is more restrictive than LU, but the associated WAP tests are easier to implement. Several tests are SU in nite samples or asymptotically, including tests robust to weak IV (such as the Anderson-Rubin, score, conditional quasi-likelihood ratio, and I. Andrews' (2015) PI-CLC tests) and two-sided tests which are optimal when the sample size is large and instruments are strong. We refer to the WAP-SU tests based on our weights as MM1-SU and MM2-SU tests. Dropping the restrictive assumptions of normality and known variance, the theory is shown to remain valid at the cost of asymptotic approximations. The MM2-SU test is optimal under the strong IV asymptotics, and outperforms other existing tests under the weak IV asymptotics.

Asymptotic efficiency in an instrumental variable model

Esta dissertação se propõe ao estudo de inferência usando estimação por método generalizado dos momentos (GMM) baseado no uso de instrumentos. A motivação para o estudo está no fato de que sob identificação fraca dos parâmetros, a inferência tradicional pode levar a resultados enganosos. Dessa forma, é feita uma revisão dos mais usuais testes para superar tal problema e uma apresentação dos arcabouços propostos por Moreira (2002) e Moreira & Moreira (2013), e Kleibergen (2005). Com isso, o trabalho concilia as estatísticas utilizadas por eles para realizar inferência e reescreve o teste score proposto em Kleibergen (2005) utilizando as estatísticas de Moreira & Moreira (2013), e é obtido usando a teoria assintótica em Newey & McFadden (1984) a estatística do teste score ótimo. Além disso, mostra-se a equivalência entre a abordagem por GMM e a que usa sistema de equações e verossimilhança para abordar o problema de identificação fraca.

Invariant tests in an instrumental variables model with unknown data generating process

In this work we focus on tests for the parameter of an endogenous variable in a weakly identi ed instrumental variable regressionmodel. We propose a new unbiasedness restriction for weighted average power (WAP) tests introduced by Moreira and Moreira (2013). This new boundary condition is motivated by the score e ciency under strong identi cation. It allows reducing computational costs of WAP tests by replacing the strongly unbiased condition. This latter restriction imposes, under the null hypothesis, the test to be uncorrelated to a given statistic with dimension given by the number of instruments. The new proposed boundary condition only imposes the test to be uncorrelated to a linear combination of the statistic. WAP tests under both restrictions to perform similarly numerically. We apply the di erent tests discussed to an empirical example. Using data from Yogo (2004), we assess the e ect of weak instruments on the estimation of the elasticity of inter-temporal substitution of a CCAPM model.

Wald tests for IV regression with weak instruments

This dissertation deals with the problem of making inference when there is weak identification in models of instrumental variables regression. More specifically we are interested in one-sided hypothesis testing for the coefficient of the endogenous variable when the instruments are weak. The focus is on the conditional tests based on likelihood ratio, score and Wald statistics. Theoretical and numerical work shows that the conditional t-test based on the two-stage least square (2SLS) estimator performs well even when instruments are weakly correlated with the endogenous variable. The conditional approach correct uniformly its size and when the population F-statistic is as small as two, its power is near the power envelopes for similar and non-similar tests. This finding is surprising considering the bad performance of the two-sided conditional t-tests found in Andrews, Moreira and Stock (2007). Given this counter intuitive result, we propose novel two-sided t-tests which are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test of Moreira (2003).

Testing production functions used in empirical growth studies

We estimate and test two alternative functional forms, which have been used in the growth literature, representing the aggregate production function for a panel of countries: the model of Mankiw, Romer and Weil (Quarterly Journal of Economics, 1992), and a mincerian formulation of schooling-returns to skills. Estimation is performed using instrumental-variable techniques, and both functional forms are confronted using a Box-Cox test, since human capital inputs enter in levels in the mincerian specification and in logs in the extended neoclassical growth model.

Mobilidade e consequências de longo prazo do serviço doméstico no Brasil

O trabalho doméstico é a ocupação da maioria das trabalhadoras brasileiras. São cerca de 6 milhões de mulheres empregadas nesta ocupação. Este estudo tem como objetivo analisar a mobilidade ocupacional e as conseqüências em termos de rendimento destas trabalhadoras. O objetivo do trabalho é examinar até que ponto o fato de tido o primeiro emprego como empregada doméstica afeta as trabalhadoras na escolha futura de suas ocupações. Estima-se o efeito do primeiro emprego como trabalhadora doméstica sobre a probabilidade de ter a ocupação de doméstica atualmente. O método escolhido foi o de variáveis instrumentais de modo a controlar o viés de endogeneidade entre a escolha da primeira ocupação e a ocupação atual. Os instrumentos escolhidos foram: número de escolas por criança em idade escolar, número de professores por escola e PIB per capita. Supõe-se que estes instrumentos sejam proxies para os custos diretos da educação e para o custo de oportunidade das mulheres. Os resultados mostram que o fato de ter tido como primeiro emprego o trabalho doméstico aumenta a probabilidade das trabalhadoras permanecerem nesta mesma ocupação em comparação com quem não começou como doméstica. Quando o resultado é comparado com a estimação pelo Método de Mínimos Quadrados, ou seja, sem controlar por um possível viés de endogeneidade, o resultado é três vezes maior. Estes resultados sugerem uma imobilidade ocupacional onde a escolha de inserção como empregada doméstica pode levar a uma armadilha de ocupação. Para tentar identificar possíveis efeitos que a primeira ocupação de doméstica pode ter sobre os rendimentos das trabalhadoras na sua ocupação atual a estimação pelo método de mínimos quadrados mostrou que o primeiro emprego como doméstica teria como efeito diminuir em 13% os rendimentos das trabalhadoras em comparação com quem não começou como doméstica. Já a estimação pelo método de variáveis instrumentais não mostrou um efeito estatisticamente significante. Além disso, também não foram encontrados resultados estatisticamente significantes quando a amostra foi restringida apenas para trabalhadoras que não tinham a ocupação atual de doméstica. Estes resultados sugerem que apesar da imobilidade ocupacional observada, não haveria diferenças em relação do rendimento atual das trabalhadoras.

The missing link: using the NBER recession indicator to construct coincident and leading indices economic activity

We use the information content in the decisions of the NBER Business Cycle Dating Committee to construct coincident and leading indices of economic activity for the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We establish that our index performs better than other currently popular coincident indices of economic activity.

The missing link: using the NBER recession indicator to construct coincident and leading indices economic activity

We use the information content in the decisions of the NBER Business Cycle Dating Committee to construct coincident and leading indices of economic activity for the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We establish that our index performs better than other currently popular coincident indices of economic activity.

The missing link: using the NBER recession indicator to construct coincident and leading indices economic activity

We use the information content in the decisions of the NBER Business Cycle Dating Committee to construct coincident and leading indices of economic activity for the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We compare the performance of our index with other currently popular coincident indices of economic activity.

Contributions to the Theory of Optimal Tests

This paper considers tests which maximize the weighted average power (WAP). The focus is on determining WAP tests subject to an uncountable number of equalities and/or inequalities. The unifying theory allows us to obtain tests with correct size, similar tests, and unbiased tests, among others. A WAP test may be randomized and its characterization is not always possible. We show how to approximate the power of the optimal test by sequences of nonrandomized tests. Two alternative approximations are considered. The rst approach considers a sequence of similar tests for an increasing number of boundary conditions. This discretization allows us to implement the WAP tests in practice. The second method nds a sequence of tests which approximate the WAP test uniformly. This approximation allows us to show that WAP similar tests are admissible. The theoretical framework is readily applicable to several econometric models, including the important class of the curved-exponential family. In this paper, we consider the instrumental variable model with heteroskedastic and autocorrelated errors (HAC-IV) and the nearly integrated regressor model. In both models, we nd WAP similar and (locally) unbiased tests which dominate other available tests.

Child labor and learning

This paper investigates the impact of working while in school on learning outcomes through the use of a unique micro panel dataset of Brazilian students. The potential endogeneity is addressed through the use of di erence-in-di erence and instrumental variable estimators. A negative e ect of working on learning outcomes in both math and Portuguese is found. The e ects of child work range from 3% to 8% of a standard deviation decline in test score which represents a loss of about a quarter to a half of a year of learning on average. We also explore the minimum legal age to entry in the labor market to induce an exogenous variation in child labor status. The results reinforce the detrimental e ects of child labor on learning. Additionally, it is found that this e ect is likely due to the interference of work with the time kids can devote to school and school work.

Environmental regulation, technology adoption and structural transformation: evidence from Brazilian sugarcane industry

We estimate the effects of the adoption of mechanized agriculture led by a new environmental regulation on structural change of local labor markets within a large emerging country, Brazil. In 2002, the state of S\~{a}o Paulo passed a law outlying the timeline to end sugarcane pre-harvest burning in the state. The environmental law led to the fast adoption of mechanized harvest. We investigate if the labor intensity of sugarcane production decreases; and, if so, if it leads to structural changes in the labor market. We use satellite data containing the type of sugarcane harvesting -- manual or mechanic harvest -- paired with official labor market data.%, also geomorphometric data base for our instrumental variable correction. We find suggestive evidence that mechanization of the field led to an increase in utilization of formal workers and a reduction in formal labor intensity in the sugarcane sector. This is partially compensated by an increase in the share of workers in other agricultural crops and in the construction and services sector. Although we find a reduction in employment in the manufacturing sector, the demand generated by the new agro-industries affected positively the all sectors via an increase in workers' wage.

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.

Tributação de energia elétrica e bem-estar social: uma análise regional

Os reflexos da tributação sobre o setor elétrico ultrapassam as questões meramente arrecadatórias de estados, municípios e União, envolvem toda a produção do país e o bem-estar de sua população. Neste contexto, e com o intuito de trazer as questões de eficiência e redistributividade ao ambiente de tributação de energia elétrica, o presente trabalho pretende apresentar um panorama da tributação atual do consumo residencial de energia elétrica, principalmente em relação ao ICMS, juntamente com um cálculo simplificado de alíquotas considerando dois modelos de tributação ótima, estabelecidos por F. R. Ramsey e Diamond e Mirrlees, a partir dos quais é possível realizar comparações em relação ao modelo atual e sintetizar uma visão nacional de uma tributação realizada em sua maior parte regionalmente. O primeiro modelo considera apenas eficiência na definição das alíquotas aplicadas aos produtos, partindo da premissa de que todos os consumidores são idênticos e não há preocupações com equidade. As elasticidades necessárias para aplicação do critério de Ramsey são estimadas a partir de dados em painel das 64 distribuidoras de energia elétrica do país, utilizando um modelo em dois estágios com variável instrumental. O segundo modelo, proposto por Diamond e Mirrlees, incorpora a equidade na modelagem, introduzindo a diferenciação entre os indivíduos.