Partial Distributional Policy Effects

In this paper, we propose a method to evaluate the effect of a counterfactual change in the unconditional distribution of a single covariate on the unconditional distribution of an outcome variable of interest. Both fixed and infinitesimal changes are considered. We show that such effects are point identified under general conditions if the covariate affected by the counterfactual change is continuously distributed, but are typically only partially identified if its distribution is discrete. For the latter case, we derive informative bounds making use of the available information. We also discuss estimation and inference.counterfactual distribution, partial identification, nonseparable model

Identification of Unconditional Partial Effects in Non Separable Models.

This note demonstrates identification of Unconditional Partial Effects introduced by Firpo, Fortin, and Lemieux (2009) in nonseparable triangular models with endogenous regressors via a control variable approach, as employed by Imbens and Newey (2009).

Misspecification Testing in a Class of Conditional Distributional Models

We propose a specification test for a wide range of parametric models for the conditional distribution function of an outcome variable given a vector of covariates. The test is based on the Cramer-von Mises distance between an unrestricted estimate of the joint distribution function of the data, and a restricted estimate that imposes the structure implied by the model. The procedure is straightforward to implement, is consistent against fixed alternatives, has non-trivial power against local deviations of order n^-1/2 from the null hypothesis, and does not require the choice of smoothing parameters. In an empirical application, we use our test to study the validity of various models for the conditional distribution of wages in the US.Cramer-von Mises distance, quantile regression, distributional regression, location-scale model, bootstrap, wage distribution

Identification of Unconditional Partial Effects in Non Separable Models

This note demonstrates identification of Unconditional Partial Effects introduced by Firpo, Fortin, and Lemieux (2009) in nonseparable triangular models with endogenous regressors via a control variable approach, as employed by Imbens and Newey (2009)

The Value of Knowing the Propensity Score for Estimating Average Treatment Effects

In a treatment effect model with unconfoundedness, treatment assignments are not only independent of potential outcomes given the covariates, but also given the propensity score alone. Despite this powerful dimension reduction property, adjusting for the propensity score is known to lead to an estimator of the average treatment effect with lower asymptotic efficiency than one based on adjusting for all covariates. Moreover, knowledge of the propensity score does not change the efficiency bound for estimating average treatment effects, and many empirical strategies are more efficient when an estimate of the propensity score is used instead of its true value. Here, we resolve this "propensity score paradox" by demonstrating the value of knowledge of the propensity score. We show that by exploiting such knowledge properly, it is possible to construct an efficient treatment effect estimator that is not affected by the "curse of dimensionality", which yields desirable second order asymptotic properties and finite sample performance. The method combines knowledge of the propensity score with a nonparametric adjustment for covariates, building on ideas from the literature on double robust estimation. It is straightforward to implement, and performs well in simulations. We also show that confidence intervals based on our estimator and a simple variance estimate have remarkably robust coverage properties with respect to the implementation details of the nonparametric adjustment step

Semiparametric estimation of binary response models with endogenous regressors

In this paper, we propose a two-step semiparametric maximum likelihood (SML) estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach. The first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals. In the second step, the latter are added as control variates to the outcome equation, which is in turn estimated by SML. We establish the estimator’s n-consistency and asymptotic normality. In a simulation study, we compare the properties of our estimator with those of existing alternatives, highlighting the advantages of our approach

Unconditional Partial Effects of Binary Covariates

In this paper, we study the effect of a small ceteris paribus change in the marginal distribution of a binary covariate on some feature of the unconditional distribution of an outcome variable of interest. We show that the RIF regression techniques recently proposed by Firpo, Fortin, and Lemieux (2009) do not estimate this quantity. Moreover, we show that such parameters are in general only partially identified, and derive straightforward expressions for the identified set. The results are implemented in the context of an empirical application that studies the effect of union membership rates on the distribution of wages

Semiparametric Estimation with Generated Covariates

In this paper, we study a general class of semiparametric optimization estimators of a vector-valued parameter. The criterion function depends on two types of infinite-dimensional nuisance parameters: a conditional expectation function that has been estimated nonparametrically using generated covariates, and another estimated function that is used to compute the generated covariates in the first place. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root-n consistent and asymptotically normal, and derive a general formula for the asymptotic variance.semiparametric estimation, generated covariates, profiling, propensity score