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).

Esta dissertaÁ„o trata do problema de inferÍncia na presenÁa de identiÖcaÁ„o fraca em modelos de regress„o com vari·veis instrumentais. Mais especiÖcamente em testes de hipÛteses com relaÁ„o ao par‚metro da vari·vel endÛgena quando os instrumentos s„o fracos. O principal foco È nos testes condicionais unilaterais baseados nas estatÌsticas de raz„o de m·xima verossimilhanÁa, score e Wald. Resultados tÈoricos e numÈricos mostram que o teste t condicional unilateral baseado no estimador de mÌnimos quadrados em dois est·gios tem uma boa performance mesmo na presenÁa de instrumentos fracamente correlacionados com a vari·vel endÛgena. A abordagem condicional corrige uniformemente o tamanho do teste t e quando a estatÌstica F populacional È t„o pequena quanto dois, o poder do teste È proximo ao power envelope tanto de testes similares quanto de n„o similares. Tal resultado È surpreendente visto a m· performace dos testes tís condicionais bilaterais relatada em ( 6 , Andrews, Moreira and Stock (2007)). Dado esse resultado aparentemente contra intuitivo, apresentamos novos testes tís condicionals bilaterais que s„o aproximadamente n„o viesados e performam, em alguns casos, t„o bem quanto o teste condicional baseado na estatÌstica de raz„o de verossimilhanÁa de ( 19 , Moreira (2003)).