Testing instrument validity for LATE identification based on inequality moment constraints

This paper proposes bootstrap tests for the validity of instrumental variables (IV) in just identified treatment effect models with endogeneity. We demonstrate that the IV assumptions required for the identification of the local average treatment effect (LATE) allow us to both point identify and bound the mean potential outcomes (i) of the always takers (those treated irrespective of the instrument) under treatment and (ii) of the never takers (never treated irrespective of the instrument) under non-treatment. The point identified means must lie within their respective bounds, which provides four testable inequality moment constraints for IV validity. Furthermore, we show that a similar logic applies to testing the assumptions needed to identify distributional features (e.g., local quantile treatment effects). Finally, we discuss how testing power can be increased by imposing dominance/equality assumptions on the potential outcome distributions of different subpopulations.specification test, instrument, treatment effects, LATE, inequality moment constraints.

Sharp IV bounds on average treatment effects under endogeneity and noncompliance

In the presence of an endogenous treatment and a valid instrument, causal effects are (nonparametrically) point identified only for the subpopulation of compliers, given that the treatment is monotone in the instrument. Further populations of likely policy interest have been widely ignored in econometrics. Therefore, we use treatment monotonicity and/or stochastic dominance assumptions to derive sharp bounds on the average treatment effects of the treated population, the entire population, the compliers, the always takers, and the never takers. We also provide an application to labor market data and briefly discuss testable implications of the instrumental exclusion restriction and stochastic dominance.Instrument, noncompliance, principal stratification, nonparametric bounds

Sharp bounds on causal effects under sample selection

In many empirical problems, the evaluation of treatment effects is complicated by sample selection such that the outcome is only observed for a non-random subpopulation. In the absence of instruments and/or tight parametric assumptions, treatment effects are not point identified, but can be bounded under mild restrictions. Previous work on partial identification has primarily focused on the "always selected" (whose outcomes are observed irrespective of the treatment). This paper complements those studies by considering further populations, namely the "compliers" (whose selection states react to the treatment) and the selected population. We derive sharp bounds under various assumptions (monotonicity and stochastic dominance) and provide an empirical application to a school voucher experiment.Causal inference, principal stratification, nonparametric bounds, sample selection

Identify More, Observe Less: Mediation Analysis Synthetic Control

The synthetic control method (SCM) allows estimation of the causal effect of an intervention in settings where panel data on just a few treated units and control units are available. We show that the existing SCM as well as its extensions can be easily modified to estimate how much of the "total" effect goes through observed causal channels. The additional assumptions needed are arguably very mild in many settings. Furthermore, in an illustrative empirical application we estimate the effects of adopting the euro on labor productivity in several countries and show that a reduction in the Economic Complexity Index helped to mitigate the negative short run effects of adopting the new currency in some countries and boosted the positive effects in others.Comment: We have benefited from comments by Simone De Angelis and participants at several seminars, workshops, and conferences. Addresses for correspondence: Giovanni Mellace ([email protected]), and Alessandra Pasquini ([email protected]

Principal Stratification in Sample Selection Problems with Non Normal Error Terms

The aim of the paper is to relax distributional assumptions on the error terms, often imposed in parametric sample selection models to estimate causal effects, when plausible exclusion restrictions are not available. Within the principal stratification framework, we approximate the true distribution of the error terms with a mixture of Gaussian. We propose an EM type algorithm for ML estimation. In a simulation study we show that our estimator has lower MSE than the ML and two-step Heckman estimators with any non normal distribution considered for the error terms. Finally we provide an application to the Job Corps training program

The Finite Sample Performance of Estimators for Mediation Analysis Under Sequential Conditional Independence

Using a comprehensive simulation study based on empirical data, this article investigates the finite sample properties of different classes of parametric and semiparametric stimators of (natural) direct and indirect causal effects used in mediation analysis under sequential conditional independence assumptions. The estimators are based on regression, inverse probability weighting, and combinations thereof. Our simulation design uses a large population of Swiss jobseekers and considers variations of several features of the data-generating process (DGP) and the implementation of the estimators that are of practical relevance. We find that no estimator performs uniformly best (in terms of root mean squared error) in all simulations. Overall, so-called “g-computation” dominates. However, differences between estimators are often (but not always) minor in the various setups and the relative performance of the methods often (but not always) varies with the features of the DGP

Sharp bounds on causal effects under sample selection

In many empirical problems, the evaluation of treatment effects is complicated by sample selection so that the outcome is only observed for a non-random subpopulation. In the absence of instruments and/or tight parametric assumptions, treatment effects are not point identified, but can be bounded under mild restrictions. Previous work on partial identification has primarily focused on the ‘always observed’ (irrespective of the treatment). This paper complements those studies by considering further populations, namely the ‘compliers’ (observed only if treated) and the observed population. We derive sharp bounds under various assumptions and provide an empirical application to a school voucher experiment

Testing instrument validity for LATE identification based on inequality moment constraints

We derive testable implications of instrument validity in just identified treat- ment effect models with endogeneity and consider several tests. The identifying assump- tions 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. Finally, we adapt our testing framework to the identification of distributional features. A brief simulation study and an application to labor market data are also provided

Testing exclusion restrictions and additive separability in sample selection models

Standard sample selection models with non-randomly censored outcomes assume (i) an exclusion restriction (i.e., a variable affecting selection, but not the outcome) and (ii) additive separability of the errors in the selection process. This paper proposes tests for the joint satisfaction of these assumptions by applying the approach of Huber and Mellace (Testing instrument validity for LATE identification based on inequality moment constraints, 2011) (for testing instrument validity under treatment endogeneity) to the sample selection framework. We show that the exclusion restriction and additive separability imply two testable inequality constraints that come from both point identifying and bounding the outcome distribution of the subpopulation that is always selected/observed. We apply the tests to two variables for which the exclusion restriction is frequently invoked in female wage regressions: non- wife/husband’s income and the number of (young) children. Considering eight empirical applications, our results suggest that the identifying assumptions are likely violated for the former variable, but cannot be refuted for the latter on statistical grounds

The Gray Zone

The Gray Zone ∗ Federico Crudu† University of Siena and CRENoS Roberta Di Stefano ‡ Sapienza University of Rome Giovanni Mellace§ University of Southern Denmark Silvia Tiezzi¶ University of Siena March 2022 Abstract On March 23, 2020, in response to the COVID-19 pandemic, Italy declared a nation- wide lockdown. A month earlier, on February 23, the Italian government ordered its military police to seal the borders and declared a Red Zone around 10 municipalities of the province of Lodi and in Vo’ Euganeo, a small town in Padua province. On the same day, Confindustria Bergamo, the province’s industrial association, posted a video on social media against having a lockdown in the area of Bergamo and was supported by key business leaders and local administrators. Despite having a similar infection rate to the Red Zone municipalities, the government decided not to extend the Red Zone to the municipalities of Bergamo province with high infection rates. Bergamo later became one of the deadliest outbreaks of the first wave of the virus in the Western world. What would have happened had the Red Zone been extended to that area? We use the Synthetic Control Method to estimate the causal effect of (not) declaring a Red Zone in the Bergamo area on daily excess mortality. We find that about two-thirds of the reported deaths could have been avoided had the Italian government declared the area a Red Zone