Are 'Nearly Exogenous' Instruments Reliable?

Abstract

Instrumental variable methods are widely used to make inferences about the impact of some variable on economic outcomes; for example, whether or not institutions influence long term growth. However, the test-statistics used for making these inferences are based on the generally unrealistic identifying assumption that the instruments are exogenous. We find that when carefully chosen instruments are more realistically modeled as nearly exogenous, the standard test statistics are unreliable: the t-statistic substantially and unpredictably either over-rejects or under-rejects the null and the Anderson-Rubin test always over-rejects. We show how an Anderson-Rubin test statistic derived from the deleted jackknife procedure developed by Chien-Fu Jeff Wu (1986) can be used to make reliable inferences in small samples when instruments are nearly exogenous. Our procedure adjusts the critical values according to the correlation between the instrument and structural error. We are able to do this both in exactly identified systems as well as the over-identified ones. Furthermore, our test is robust to weak instruments problem. We use this test to confirm and to correct inferences about the impact of institutions in the celebrated work of Daron Acemoglu, Simon Johnson and James Robinson (2001).

Keywords: near exogeneity, instrumental variables, institutional economics

JEL Classification: C10, O5