Economics

This paper studies the identification and estimation of unconditional policy effects when the treatment is binary and endogenous. We first characterize the asymptotic bias of the unconditional regression estimator that ignores the endogeneity and elaborate on the channels that the endogeneity can render the unconditional regressor estimator inconsistent. We show that even if the treatment status is exogenous, the unconditional regression estimator can still be inconsistent when there are common covariates affecting both the treatment status and the outcome variable. We introduce a new class of marginal treatment effects (MTE) based on the influence function of the functional underlying the policy target. We show that an unconditional policy effect can be represented as a weighted average of the newly defined MTEs over the individuals at the margin of indifference. Point identification is achieved using the local instrumental variable approach. Furthermore, the unconditional policy effects are shown to include the marginal policy-relevant treatment effect in the literature as a special case. Methods of estimation and inference for the unconditional policy effects are provided. In the empirical application, we estimate the effect of changing college enrollment status, induced by higher tuition subsidy, on the quantiles of the wage distribution.

We study the identification and estimation of treatment effect parameters in weakly separable models. In their seminal work, Vytlacil and Yildiz (2007) showed how to identify and estimate the average treatment effect of a dummy endogenous variable when the outcome is weakly separable in a single index. Their identification result builds on a monotonicity condition with respect to this single index. In comparison, we consider similar weakly separable models with multiple indices, and relax the monotonicity condition for identification. Unlike Vytlacil and Yildiz (2007), we exploit the full information in the distribution of the outcome variable, instead of just its mean. Indeed, when the outcome distribution function is more informative than the mean, our method is applicable to more general settings than theirs; in particular we do not rely on their monotonicity assumption and at the same time we also allow for multiple indices. To illustrate the advantage of our approach, we provide examples of models where our approach can identify parameters of interest whereas existing methods would fail. These examples include models with multiple unobserved disturbance terms such as the Roy model and multinomial choice models with dummy endogenous variables, as well as potential outcome models with endogenous random coefficients. Our method is easy to implement and can be applied to a wide class of models. We establish standard asymptotic properties such as consistency and asymptotic normality.

Empirical economic research crucially relies on highly sensitive individual datasets. At the same time, increasing availability of public individual-level data makes it possible for adversaries to potentially de-identify anonymized records in sensitive research datasets. Most commonly accepted formal definition of an individual non-disclosure guarantee is referred to as differential privacy. It restricts the interaction of researchers with the data by allowing them to issue queries to the data. The differential privacy mechanism then replaces the actual outcome of the query with a randomised outcome. The impact of differential privacy on the identification of empirical economic models and on the performance of estimators in nonlinear empirical Econometric models has not been sufficiently studied. Since privacy protection mechanisms are inherently finite-sample procedures, we define the notion of identifiability of the parameter of interest under differential privacy as a property of the limit of experiments. It is naturally characterized by the concepts from the random sets theory. We show that particular instances of regression discontinuity design may be problematic for inference with differential privacy as parameters turn out to be neither point nor partially identified. The set of differentially private estimators converges weakly to a random set. Our analysis suggests that many other estimators that rely on nuisance parameters may have similar properties with the requirement of differential privacy. We show that identification becomes possible if the target parameter can be deterministically located within the random set. In that case, a full exploration of the random set of the weak limits of differentially private estimators can allow the data curator to select a sequence of instances of differentially private estimators converging to the target parameter in probability.

We consider structural vector autoregressions subject to 'narrative restrictions', which are inequality restrictions on functions of the structural shocks in specific periods. These restrictions raise novel problems related to identification and inference, and there is currently no frequentist procedure for conducting inference in these models. We propose a solution that is valid from both Bayesian and frequentist perspectives by: 1) formalizing the identification problem under narrative restrictions; 2) correcting a feature of the existing (single-prior) Bayesian approach that can distort inference; 3) proposing a robust (multiple-prior) Bayesian approach that is useful for assessing and eliminating the posterior sensitivity that arises in these models due to the likelihood having flat regions; and 4) showing that the robust Bayesian approach has asymptotic frequentist validity. We illustrate our methods by estimating the effects of US monetary policy under a variety of narrative restrictions.

We provide a geometric formulation of the problem of identification of the matching surplus function and we show how the estimation problem can be solved by the introduction of a generalized entropy function over the set of matchings.

This paper provides nonparametric identification results for random coefficient distributions in perturbed utility models. We cover discrete and continuous choice models. We establish identification using variation in mean quantities, and the results apply when an analyst observes aggregate demands but not whether goods are chosen together. We require exclusion restrictions and independence between random slope coefficients and random intercepts. We do not require regressors to have large supports or parametric assumptions.

We provide new results showing identification of a large class of fixed-T panel models, where the response variable is an unknown, weakly monotone, time-varying transformation of a latent linear index of fixed effects, regressors, and an error term drawn from an unknown stationary distribution. Our results identify the transformation, the coefficient on regressors, and features of the distribution of the fixed effects. We then develop a full-commitment intertemporal collective household model, where the implied quantity demand equations are time-varying functions of a linear index. The fixed effects in this index equal logged resource shares, defined as the fractions of household expenditure enjoyed by each household member. Using Bangladeshi data, we show that women's resource shares decline with household budgets and that half of the variation in women's resource shares is due to unobserved household-level heterogeneity.

We establish nonparametric identification in a class of so-called index models using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions characterizing the model compared to existing strategies; in particular, it does not require any large support conditions on the regressors of our model. We apply the general identification result to additive random utility and competing risk models.

In this paper, we establish the sufficient conditions for identifying treatment effects on continuous outcomes in endogenous and multi-valued discrete treatment settings with unobserved heterogeneity. We employ the monotonicity assumption for multi-valued discrete treatments and instruments, and our identification condition is easy to interpret economically. Our result contrasts with related work by Chernozhukov and Hansen (2005) with regard to this. In addition, we identify the local treatment effects in multi-valued treatment settings and derive a closed-form expression of the identified treatment effects. We provide examples to illustrate the usefulness of our result.

This paper shows how to use a randomized saturation experimental design to identify and estimate causal effects in the presence of spillovers--one person's treatment may affect another's outcome--and one-sided non-compliance--subjects can only be offered treatment, not compelled to take it up. Two distinct causal effects are of interest in this setting: direct effects quantify how a person's own treatment changes her outcome, while indirect effects quantify how her peers' treatments change her outcome. We consider the case in which spillovers occur only within known groups, and take-up decisions do not depend on peers' offers. In this setting we point identify local average treatment effects, both direct and indirect, in a flexible random coefficients model that allows for both heterogenous treatment effects and endogeneous selection into treatment. We go on to propose a feasible estimator that is consistent and asymptotically normal as the number and size of groups increases. We apply our estimator to data from a large-scale job placement services experiment, and find negative indirect treatment effects on the likelihood of employment for those willing to take up the program. These negative spillovers are offset by positive direct treatment effects from own take-up.