Broken Instruments

Abstract

Repeated use of the same potentially related instrumental variables by a literature can "collectively invalidate" these instruments. This paper examines two ways in which this can happen. First, when instruments sharing significant sources of variation are used to instrument multiple distinct covariates, it is increasingly likely the exclusion restriction was not satisfied in any individual specification from the outset. Second, when a variable is documented to affect many outcomes that are likely to be highly or even mildly persistent, using lagged values of that variable as an instrument is likely to violate the exclusion condition. This paper produces a dataset of approximately 960 instrumental variables papers from 1995-2019 in highly-ranked economics general interest and field journals. We find six groups of commonly-used instruments whose literatures, taken together, suggest they are likely to fail the strict exogeneity condition: (i) elevation and bodies of water (ii) sibling structure (iii) ethnicity/ethnolinguistic fractionalization (iv) religion (v) weather and (vi) immigrant enclaves. Taken together, these potentially related instruments have been used in 86 “top five" publications and 317 well-ranked field or general interest journals, with 189 total uses cataloged from 2011 onwards. We propose a Hausman-like test for suspect regressions and discuss its asymptotic properties. We then apply it to two IV papers, finding little reason to be concerned about one, and tentative evidence to be concerned about the other.

Keywords: instrumental variables, commonly-used instruments, exclusion restriction, repeated-use instruments

JEL Classification: C13, C26, C36