Antonio F. Galvao

Convergence or divergence in Latin America? A time series analysis

This article investigates the occurrence of per capita income convergence in 19 Latin American countries. We apply a time series approach to test for stochastic convergence and β-convergence based on structural breaks unit root tests, where the dates of breaks are unknown and determined endogenously. This approach is essential since it does not impose common break dates and parameter homogeneity among countries. In fact, the econometric methodology employed attempts to provide what was lacking in previous works. As a consequence, unlike prior studies the results indicate that there is substantial evidence in favor of conditional convergence in Latin America. We show that this evidence is even greater when analyzing South and Central America separately.This article investigates the occurrence of per capita income convergence in 19 Latin American countries. We apply a time series approach to test for stochastic convergence and β-convergence based on structural breaks unit root tests, where the dates of breaks are unknown and determined endogenously. This approach is essential since it does not impose common break dates and parameter homogeneity among countries. In fact, the econometric methodology employed attempts to provide what was lacking in previous works. As a consequence, unlike prior studies the results indicate that there is substantial evidence in favor of conditional convergence in Latin America. We show that this evidence is even greater when analyzing South and Central America separately.

Threshold Quantile Autoregressive Models

This article studies estimation and asymptotic properties of Threshold Quantile Autoregressive processes. In particular, we show the consistency of the threshold and slope parameter estimators for each quantile and regime, and derive the asymptotic normality of the slope parameter estimators. A Monte Carlo experiment shows that the standard ordinary least squares estimation method is not able to detect important nonlinearities produced in the quantile process. The empirical study concentrates on modelling the dynamics of the conditional distribution of unemployment growth after the second world war. The results show evidence of important heterogeneity associated with unemployment and strong asymmetric persistence of unemployment growth in the higher quantiles.

Estimation of Censored Quantile Regression for Panel Data With Fixed Effects

This article investigates estimation of censored quantile regression (QR) models with fixed effects. Standard available methods are not appropriate for estimation of a censored QR model with a large number of parameters or with covariates correlated with unobserved individual heterogeneity. Motivated by these limitations, the article proposes estimators that are obtained by applying fixed effects QR to subsets of observations selected either parametrically or nonparametrically. We derive the limiting distribution of the new estimators under joint limits, and conduct Monte Carlo simulations to assess their small sample performance. An empirical application of the method to study the impact of the 1964 Civil Rights Act on the black–white earnings gap is considered. Supplementary materials for this article are available online.

Efficient minimum distance estimator for quantile regression fixed effects panel data

This paper develops a new minimum distance quantile regression (MD-QR) estimator for panel data models with fixed effects. The proposed estimator is efficient in the class of minimum distance estimators. In addition, the MD-QR estimator is computationally fast, especially for large cross-sections. We establish consistency and explicitly derive the limiting distribution of the MD-QR estimator for panels with large number of cross-sections and time-series. The limit theory allows for both sequential and joint limits. Monte Carlo simulations are conducted to evaluate the finite sample performance of the estimator. The simulation results confirm that the MD-QR approach produces approximately unbiased estimators with small variances, and is computationally advantageous. Finally, we illustrate the use of the estimator with a simple application to the investment equation model.

Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large

This article considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, n, and the number of time periods, T, are large. We first clarify the probability limit of the FE estimator and argue that this probability limit can be regarded as a pseudo-true parameter. We then establish the asymptotic distributional properties of the FE estimator around the pseudo-true parameter when n and T jointly go to infinity. Notably, we show that the FE estimator suffers from the incidental parameters bias of which the top order is O(T− 1), and even after the incidental parameters bias is completely removed, the rate of convergence of the FE estimator depends on the degree of model misspecification and is either (nT)− 1/2 or n− 1/2. Second, we establish asymptotically valid inference on the (pseudo-true) parameter. Specifically, we derive the asymptotic properties of the clustered covariance matrix (CCM) estimator and the cross-section bootstrap, and show that they are robust to model misspecification. This establishes a rigorous theoretical ground for the use of the CCM estimator and the cross-section bootstrap when model misspecification and the incidental parameters bias (in the coefficient estimate) are present. We conduct Monte Carlo simulations to evaluate the finite sample performance of the estimators and inference methods, together with a simple application to the unemployment dynamics in the U.S.

Tests for skewness and kurtosis in the one-way error component model

This paper derives tests for skewness and kurtosis for the panel data one-way error component model. The test statistics are based on the between and within transformations of the pooled OLS residuals, and are derived in a moment conditions framework. We establish the limiting distribution of the test statistics for panels with large cross-section and fixed time-series dimension. The tests are implemented in practice using the bootstrap. The proposed methods are able to detect departures away from normality in the form of skewness and kurtosis, and to identify whether these occur at the individual, remainder, or both error components. The finite sample properties of the tests are studied through extensive Monte Carlo simulations, and the results show evidence of good finite sample performance.

Dynamic Quantile Models of Rational Behavior

This paper develops a dynamic model of rational behavior under uncertainty, in which the agent maximizes the stream of future τ-quantile utilities, for τ ∈ (0, 1). That is, the agent has a quantile utility preference instead of the standard expected utility. Quantile preferences have useful advantages, including the ability to capture heterogeneity and allowing the separation between risk aversion and elasticity of intertemporal substitution. Although quantiles do not share some of the helpful properties of expectations, such as linearity and the law of iterated expectations, we are able to establish all the standard results in dynamic models. Namely, we show that the quantile preferences are dynamically consistent, the corresponding dynamic problem yields a value function, via a fixed point argument, this value function is concave and differentiable, and the principle of optimality holds. Additionally, we derive the corresponding Euler equation, which is well suited for using well-known quantile regression methods for estimating and testing the economic model. In this way, the parameters of the model can be interpreted as structural objects. Therefore, the proposed methods provide microeconomic foundations for quantile regression methods. To illustrate the developments, we construct an intertemporal consumption model and estimate the discount factor and elasticity of intertemporal substitution parameters across the quantiles. The results provide evidence of heterogeneity in these parameters.

On Testing the Equality of Mean and Quantile Effects

Abstract This paper proposes tests for equality of the mean regression (MR) and quantile regression (QR) coefficients. The tests are based on the asymptotic joint distribution of the ordinary least squares and QR estimators. First, we formally derive the asymptotic joint distribution of these estimators. Second, we propose a Wald test for equality of the MR and QR coefficients considering a single fixed quantile, and also describe a more general test using multiple quantiles simultaneously. A very salient feature of these tests is that they produce asymptotically distribution-free nature of inference. In addition, we suggest a sup-type test for equality of the coefficients uniformly over a range of quantiles. For the estimation of the variance-covariance matrix, the use sample counterparts and bootstrap methods. An important attribute of the proposed tests is that they can be used as a heteroskedasticity test. Monte Carlo studies are conducted to evaluate the finite sample properties of the tests in terms of size and power. Finally, we briefly illustrate the implementation of the tests using Engel data.

Uniformly Semiparametric Efficient Estimation of Treatment Effects With a Continuous Treatment

This article studies identification, estimation, and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption. We show identification of the parameters of interest, the dose–response functions, under the assumption that selection to treatment is based on observables. We propose a semiparametric two-step estimator, and consider estimation of the dose–response functions through moment restriction models with generalized residual functions that are possibly nonsmooth. This general formulation includes average and quantile treatment effects as special cases. The asymptotic properties of the estimator are derived, namely, uniform consistency, weak convergence, and semiparametric efficiency. We also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice. Monte Carlo simulations show that the proposed methods have good finite sample properties. Finally, we apply the proposed methods to estimate the unconditional average and quantile effects of mothers’ weight gain and age on birthweight. Supplementary materials for this article are available online.

A NEW CHARACTERIZATION OF THE NORMAL DISTRIBUTION AND TEST FOR NORMALITY

We study the asymptotic covariance function of the sample mean and quantile and derive a new and surprising characterization of the normal distribution: the asymptotic covariance between the sample mean and quantile is constant across all quantiles, if and only if the underlying distribution is normal. This is a powerful result and facilitates statistical inference. Utilizing this result, we develop a new omnibus test for normality based on the quantile-mean covariance process. Compared to existing normality tests, the proposed testing procedure has several important attractive features. Monte Carlo evidence shows that the proposed test possesses good finite sample properties. In addition to the formal test, we suggest a graphical procedure that is easy to implement and visualize in practice. Finally, we illustrate the use of the suggested techniques with an application to stock return datasets.