arXiv subjects

Javier Alejo

Publications and source records attributed to Javier Alejo.

6 recordsLinked to original sources

arXiv2024

Endogenous Heteroskedasticity in Linear Models

Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous regressors, i.e., endogenous heteroskedasticity. To address the inconsistency of the two-stage least squares estimator in this scenario, and recover the causal parameters of interest, we develop a framework for practical estimation and inference based on the control function approach allowing for discrete and continuous regressors. In particular, we suggest a simple two-step estimation procedure. We establish the limiting properties of the estimator, namely, consistency and asymptotic normality. In addition, we develop practical valid inference methods by proposing an estimator for the asymptotic variance-covariance matrix, and formally establishing its consistency. Monte Carlo simulations provide evidence on the finite-sample performance of the proposed methods and evaluate different implementation strategies. We revisit an empirical application on job training to illustrate the methods.

econ.EM↗

arXiv2023

Unconditional Quantile Partial Effects via Conditional Quantile Regression

This paper develops a semi-parametric procedure for estimation of unconditional quantile partial effects using quantile regression coefficients. The estimator is based on an identification result showing that, for continuous covariates, unconditional quantile effects are a weighted average of conditional ones at particular quantile levels that depend on the covariates. We propose a two-step estimator for the unconditional effects where in the first step one estimates a structural quantile regression model, and in the second step a nonparametric regression is applied to the first step coefficients. We establish the asymptotic properties of the estimator, say consistency and asymptotic normality. Monte Carlo simulations show numerical evidence that the estimator has very good finite sample performance and is robust to the selection of bandwidth and kernel. To illustrate the proposed method, we study the canonical application of the Engel's curve, i.e. food expenditures as a share of income.

econ.EM↗

arXiv2022

A first-stage representation for instrumental variables quantile regression

This paper develops a first-stage linear regression representation for the instrumental variables (IV) quantile regression (QR) model. The quantile first-stage is analogous to the least squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, conditional on the endogeneous and exogenous covariates, and the instruments as well, at a given quantile. We also show that the required Jacobian identification conditions for IVQR models are embedded in the quantile first-stage. We then suggest inference procedures to evaluate the adequacy of instruments by evaluating their statistical significance using the first-stage result. The test is developed in an over-identification context, since consistent estimation of the weights for implementation of the first-stage requires at least one valid instrument to be available. Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power in finite samples. An empirical application illustrates that checking for the statistical significance of the instruments at different quantiles is important. The proposed procedures may be specially useful in QR since the instruments may be relevant at some quantiles but not at others.

econ.EM↗

arXiv2021

Quantile Regression under Limited Dependent Variable

A new Stata command, ldvqreg, is developed to estimate quantile regression models for the cases of censored (with lower and/or upper censoring) and binary dependent variables. The estimators are implemented using a smoothed version of the quantile regression objective function. Simulation exercises show that it correctly estimates the parameters and it should be implemented instead of the available quantile regression methods when censoring is present. An empirical application to women's labor supply in Uruguay is considered.

econ.EM↗

arXiv2021

A decomposition method to evaluate the `paradox of progress' with evidence for Argentina

The `paradox of progress' is an empirical regularity that associates more education with larger income inequality. Two driving and competing factors behind this phenomenon are the convexity of the `Mincer equation' (that links wages and education) and the heterogeneity in its returns, as captured by quantile regressions. We propose a joint least-squares and quantile regression statistical framework to derive a decomposition in order to evaluate the relative contribution of each explanation. The estimators are based on the `functional derivative' approach. We apply the proposed decomposition strategy to the case of Argentina 1992 to 2015.

econ.EM↗

arXiv2021

RIF Regression via Sensitivity Curves

This paper proposes an empirical method to implement the recentered influence function (RIF) regression of Firpo, Fortin and Lemieux (2009), a relevant method to study the effect of covariates on many statistics beyond the mean. In empirically relevant situations where the influence function is not available or difficult to compute, we suggest to use the \emph{sensitivity curve} (Tukey, 1977) as a feasible alternative. This may be computationally cumbersome when the sample size is large. The relevance of the proposed strategy derives from the fact that, under general conditions, the sensitivity curve converges in probability to the influence function. In order to save computational time we propose to use a cubic splines non-parametric method for a random subsample and then to interpolate to the rest of the cases where it was not computed. Monte Carlo simulations show good finite sample properties. We illustrate the proposed estimator with an application to the polarization index of Duclos, Esteban and Ray (2004).

econ.EM↗