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 and p-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.
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