On identification and estimation of Heckman models

In this article, we present commands to enable fixing the value of the correlation between the unobservables in Heckman models. These commands can solve two practical issues. First, for situations in which a valid exclusion restriction is not available, these commands enable exploring how the results could be affected by sample-selection bias. Second, stepping through values of this correlation can verify whether the global maximum of the likelihood function has been found. We provide several commands to fit these and related models with a fixed value of the correlation between the unobservables.

Performance of statistical methods to address treatment non-adherence in pragmatic clinical trials with point-treatment settings: a simulation study

Introduction: The instrumental variable (IV)-based methods (e.g., two-stage least square [2SLS], two-stage residual inclusion [2SRI], and nonparametric causal bound [NPCB]) can be used to address non-adherence in pragmatic trials. These methods require assumptions, e.g., exclusion restriction, although they are known to handle unmeasured confounding. The inverse probability-weighted per-protocol [IPW-PP] method is useful in the same setting but requires different assumptions (no unmeasured confounding). Although all these methods aim to address the same problem, comprehensive simulations to compare their performance are absent in the literature. We performed extensive simulations when (1) confounding is present, (2) confounder is unmeasured but exclusion restriction is met, (3) exclusion restriction is violated, and (4) non-adherence is one-sided and differential. Method: We compared the performance in terms of bias, standard error (SE), mean squared error (MSE), and 95% confidence interval coverage probability. Results: For setting-1, IPW-PP outperforms IV-methods in terms of bias, SE, MSE, and coverage for <80% non-adherence but produces high bias beyond that point. IPW-PP also has high biases, but 2SLS and 2SRI work well for setting-2. For setting-3, 2SLS and 2SRI perform the worst in all scenarios; IPW-PP produces unbiased estimates when necessary confounders are measured and adjusted. For setting-4, IPW-PP has less bias, but 2SLS and 2SRI have higher SE and MSE. NPCB has wider bounds in all scenarios. We also analyze a two-arm trial to estimate the effect of vitamin A supplementation on childhood mortality after addressing non-adherence. Conclusion: We need to be cautious using the IPW-PP when non-adherence is very high or strong unmeasured confounding and should avoid using the IV methods when the exclusion restriction assumption is violated or high differential non-adherence. Since assumptions are different and often untestable for IPW-PP and IV methods, we suggest analyzing data using both methods for a robust conclusion.

Rain, Rain, Go Away: 176 potential exclusion-restriction violations for studies using weather as an instrumental variable

Instrumental variable (IV) analysis assumes that the instrument only affects the dependent variable via its relationship with the independent variable. Other possible causal routes from the IV to the dependent variable are exclusion-restriction violations and make the instrument invalid. Weather has been widely used as an instrumental variable in social science to predict many different variables. The use of weather to instrument different independent variables represents strong prima facie evidence of exclusion violations for all studies using weather as an IV. A review of 217 social science studies reveals 176 variables which have been linked to weather, all of which represent potential exclusion violations. I conclude with practical steps to systematically review existing literature to identify possible exclusion violations when using IV designs. I demonstrate how sensitivity analysis can quantify the vulnerability of a particular IV estimate to exclusion restriction violations in the literature.

Instrument-based estimation with binarised treatments: issues and tests for the exclusion restriction

Summary When estimating local average and marginal treatment effects using instrumental variables (IVs), multivalued endogenous treatments are frequently converted to binary measures, supposedly to improve interpretability or policy relevance. Such binarisation introduces a violation of the IV exclusion if (a) the IV affects the multivalued treatment within support areas below and/or above the threshold and (b) such IV-induced changes in the multivalued treatment affect the outcome. We discuss assumptions that satisfy the IV exclusion restriction with a binarised treatment and permit identifying the average effect of (a) the binarised treatment and (b) unit-level increases in the original multivalued treatment among specific compliers. We derive testable implications of these assumptions and propose tests which we apply to the estimation of the returns to college graduation instrumented by college proximity.

Effects of Rural Electrification on Employment: A Comment on Dinkelman (2011)

This paper replicates and extends the seminal paper by Dinkelman (2011) on the impacts of electrification on female employment. We revisit the validity of the identification strategy that uses the land gradient as an instrumental variable (IV). Our robustness checks cast doubt on the exclusion restriction as the IV drives the outcome variable in non-electrified regions. We also demonstrate that it is more difficult to disentangle the effects of electricity and road infrastructure than the original paper claims, because the IV affects both. We additionally highlight that the IV is weak, consequently preventing interpretation of the point estimates that are used throughout the original paper. The concomitance of a questionable exclusion restriction and a weak IV is particularly problematic. We conclude by arguing that the take-aways of the original paper for policy and the academic literature need to be reconsidered. In general terms, our comment shows the difficulties of using geographical variation as a natural experiment for infrastructure evaluation.

Identifying the discount factor in dynamic discrete choice models

Empirical research often cites observed choice responses to variation that shifts expected discounted future utilities, but not current utilities, as an intuitive source of information on time preferences. We study the identification of dynamic discrete choice models under such economically motivated exclusion restrictions on primitive utilities. We show that each exclusion restriction leads to an easily interpretable moment condition with the discount factor as the only unknown parameter. The identified set of discount factors that solves this condition is finite, but not necessarily a singleton. Consequently, in contrast to common intuition, an exclusion restriction does not in general give point identification. Finally, we show that exclusion restrictions have nontrivial empirical content: The implied moment conditions impose restrictions on choices that are absent from the unconstrained model.