Instrument approval by the Sargan test and its consequences for coefficient estimation

Jan F Kiviet,Sebastian Kripfganz

doi:10.1016/j.econlet.2021.109935

Jan F Kiviet, Sebastian Kripfganz

Open Access

https://doi.org/10.1016/j.econlet.2021.109935

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Abstract

Empirical econometric findings are often vindicated by supplementing them with the p-values of Sargan–Hansen tests for overidentifying restrictions, provided these exceed a chosen small nominal significance level. It is illustrated here that the probability that such tests reject instrument validity may often barely exceed small levels, even when instruments are seriously invalid, whereas even minor invalidity of instruments can severely undermine inference on regression coefficients by instrumental variable estimators. These uncomfortable patterns may be aggravated when particular valid or invalid instruments are relatively weak or strong.

Highlights

Many economic relationships are possibly characterized by instantaneous feedbacks
In order to qualify as an e¤ective external instrument, a variable should not be explanatory for the dependent variable, and it should be –preferably strongly –correlated with the potentially endogenous regressors
We examine Sargan test and coe¢ cient estimation outcomes for a simple linear regression model under a range of practically relevant circumstances

Summary

Introduction

Many economic relationships are possibly characterized by instantaneous feedbacks. In that case the dependent variable is endogenous, but some explanatory variables as well. The standard methods to ...nd out whether explanatory variables are endogenous, and – if they are – to cope with them when estimating reaction coe¢ cients, exploit external instrumental variables. In order to qualify as an e¤ective external instrument, a variable should not be explanatory for the dependent variable (its exclusion from the model should be valid), and it should be –preferably strongly –correlated with the potentially endogenous regressors. Veri...cation of the latter property is relatively straightforward, whereas the former is usually tested by the Sargan (1958) test – in relatively simple linear models –or by its generalization, the Hansen (1982) test. Various studies –see, for instance, Hayashi (2000, p.218), Parente and Santos Silva (2012) and Kiviet (2017) –have spelled out a fundamental methodological limitation of these tests, being that they can only verify over-identifying restrictions, while implicitly adopting untestable just-identifying restrictions

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