Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints

Abstract

We derive testable implications of instrument validity in just identified treatment effect models with endogeneity and consider several tests. The identifying assumptions of the local average treatment effect allow us to both point identify and bound the mean potential outcomes (i) of the always takers under treatment and (ii) of the never takers under non-treatment. The point identified means must lie within their respective bounds, which provides us with four testable inequality moment constraints. Furthermore, we use dominance/equality restrictions on potential outcomes across subpopulations to increase the power to detect violations of instrument validity. Finally, we adapt our testing framework to the identification of distributional features (as local quantile treatment effects). A brief simulation study and an application to labor market data are also provided.

Testing the validity of the compulsory schooling law instrument

“…Considering health-and income-related outcomes as well as various numbers of cohorts, the test does not provide evidence for the invalidity of the instrument. As a word of caution, we acknowledge that even asymptotically, the approach of Huber and Mellace (2015) cannot detect all possible violations of IV validity when the complier share is larger than zero. 2…”

“…We note that the first stage effect is statistically significant at the 5% level in any scenario considered. The last column 'p-val' provides the p-value when implementing the test based on the method by Chen and Szroeter (2014) and 999 bootstrap replications, see Huber and Mellace (2015) for details. We see that for any outcome and sample specification, the p-values are far from any conventional level of significance.…”

“…To provide statistical insights on the IV validity of CSL, we jointly test random instrument assignment, monotonicity of education in the instrument, and the instrument exclusion restriction by applying the method of Huber and Mellace (2015) to data from the Survey of Health, Ageing and Retirement in Europe (SHARE). 1 These assumptions are necessary for identifying the local average treatment effect (LATE) on those who change their schooling decision in reaction to a change in CSL, the so-called compliers in the denomination of Angrist, Imbens, and Rubin (1996).…”

“…Section 2 briefly reviews the testing approach of Huber and Mellace (2015). Section 3 describes our data.…”

Evidence on the Production of Cognitive Achievement from Moving to Opportunity

“…Further research can investigate whether tests of A3 and A4 generalize from those already established in the one-dimensional case (Angrist and Imbens (1995), Huber and Mellace (2015), Mourifié and Wan (2016)). As discussed in Heckman and Vytlacil (2005), A3 and A4 are necessary for identification but not for the definition of causal effects.…”