Robust Estimation with Nonrandom Measurement Error and Weak Instruments

Author:

Betz Timm

Abstract

Two common problems in applications of two-stage least squares (2SLS) are nonrandom measurement error in the endogenous variable and weak instruments. In the presence of nonrandom measurement error, 2SLS yields inconsistent estimates. In the presence of weak instruments, confidence intervals andp-values can be severely misleading. This article introduces a rank-based estimator, grounded in randomization inference, which addresses both problems within a unified framework. Monte Carlo studies illustrate the deficiencies of 2SLS and the virtues of the rank-based estimator in terms of bias and efficiency. A replication of a study of the effect of economic shocks on democratic transitions demonstrates the practical implications of accounting for nonrandom measurement error and weak instruments.

Publisher

Cambridge University Press (CUP)

Subject

Political Science and International Relations,Sociology and Political Science

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3. BC also provide reduced-form regressions, linking rainfall to democratic transitions, which are not discussed in the following. In a separate paper, I provide a more extended discussion as well as a replication of Miguel, Satyanath, and Sergenti (2004), who use rainfall as an instrument to evaluate the effect of economic shocks on the onset of civil conflict. Their main findings from 2SLS are corroborated by the rank-based HL estimates. See, however, Ciccone (2011), who points out several problems with the specification of Miguel, Satyanath, and Sergenti (2004).

4. An alternative explanation for the differences between the 2SLS and the HL point estimates would be the presence of unusually high outcomes on the dependent variable. If the “unusual” outcomes are considered aberrant, then the rank-based estimate is still preferable. However, Keele, McConnaughy, and White (2012, 489) point out that, if one has reason to believe that the “unusual” outcomes are accurately reflecting the relationship in the data (and hence are due to “unusual” values of the treatment), then a mean-based estimate might be preferable to a rank-based estimate, since the “unusual” observations may contain particularly valuable information. In the sample of BC, the difference between the rank-based HL estimates and the mean-based 2SLS cannot be explained by dropping the most extreme observations.

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