Wednesday, August 10, 2022

Instrumental Variables in Practical Application

I have always been fascinated by Alwyn Young's paper,  "Consistency without Inference:  Instrumental Variables in Practical Application."   On-line appendix.  Glad to see that it's now published in the European Economic Review.  Note the key role of non-white disturbances.

From the intro:

The economics profession is in the midst of a “credibility revolution” (Angrist and Pischke 2010) in which careful research design has become firmly established as a necessary characteristic of applied work.  A key element in this revolution has been the use of instruments to identify causal effects free of the potential biases carried by endogenous ordinary least squares regressors.  The growing emphasis on research design has not gone hand in hand, however, with equal demands on the quality of inference.  Despite the widespread use of Eicker (1963)-Hinkley (1977)-White (1980) heteroskedasticity robust covariance estimates and their clustered extensions, the implications of non-iid error processes for the quality of inference, and their interaction in this regard with regression and research design, has not received the attention it deserves.  Heteroskedastic and correlated errors in highly leveraged regressions produce test statistics whose dispersion is typically much greater than believed, exaggerating the statistical significance of both 1st and 2nd stage tests, while lowering power to detect meaningful alternatives.  Furthermore, the bias of 2SLS relative to OLS rises as predicted second stage values are increasingly determined by the realization of a few errors, thereby eliminating much of the benefit of IV.  This paper shows that these problems exist in a substantial fraction of published work. 

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