A test for instrumental variable validity using a correlation restriction

DiTraglia and García-Jimeno (2021) demonstrate that the correlation coefficients between an IV, an endogenous regressor, and the outcome variable must satisfy a specific joint constraint determined by their relationships with the structural error term. We exploit this constraint to develop a novel Correlation Restriction test that becomes feasible when the direction of endogeneity bias is known. Our test quantifies the probability of instrument orthogonality to the structural error across the plausible range of endogeneity magnitudes, providing researchers with a previously unavailable diagnostic tool in the frequentist setting. Through simulations and applications to diverse empirical settings including returns to education, criminal recidivism, and development economics, we establish that our method reliably identifies invalid instruments and characterizes the endogeneity range over which valid instruments maintain their exogeneity. This approach contributes to instrumental variable methods by transforming a key identification assumption from an untestable assertion into an empirically verifiable condition.