Quantile regression is one of the most important methods to estimate heterogeneous effects on a variable of interest. In many applications there is a subset of covariates of interest, while the rest operate as controls in the regression equation. This work presents a straightforward empirical strategy for situations in which the control variables have a homogeneous effect on the conditional distribution. We develop the asymptotic theory for the proposed estimator and the corresponding inference procedures. An application using environmental pollution data illustrates the method by estimating the Environmental Kuznets Curve.
The package implements methods for detecting structural breaks and estimating break locations for linear multiple regression models under general linear restrictions on the coefficient vector. Restrictions can be within regimes, across regimes, or both, and are supported in two forms: an affine parameterization (Form A: ) and explicit linear constraints (Form B: ). It provides break date estimation with confidence interval, a restricted sup-F test for the null of no structural change, simulation of critical values by Monte Carlo, and a bootstrap restart procedure to reduce the risk of convergence to spurious local optima. It also implements a generalized regression tree (linear model tree) procedure where each leaf contains a linear regression rather than a local average. This note explains the methods and illustrates them with applications.
This paper develops a consistent series-based specification test for semiparametric panel data models with fixed effects. The test statistic resembles the Lagrange Multiplier (LM) test statistic in parametric models and is based on a quadratic form in the restricted model residuals. The use of series methods facilitates both estimation of the null model and computation of the test statistic. The asymptotic distribution of the test statistic is standard normal, so that appropriate critical values can easily be computed. The projection property of series estimators allows me to develop a degrees of freedom correction. This correction makes it possible to account for the estimation variance and obtain refined asymptotic results. It also substantially improves the finite sample performance of the test.
The QR.break package provides methods for detecting, estimating, and conducting inference on multiple structural breaks in linear quantile regression models, based on one or multiple quantiles and applicable to both time series and repeated cross-sectional data. The main function, rq.break() , returns testing and estimation results based on user specifications of the quantiles of interest, the maximum number of breaks allowed, and the minimum length of a single regime. This note outlines the underlying methods and explains how to use the main function with two datasets: a time series dataset on U.S. real GDP growth rates and a repeated cross-sectional dataset on youth drinking and driving behavior. Both datasets are included in the package available on CRAN.
Heteroskedasticity robust standard errors are often presented as a formula that is not directly related to classical standard errors derived under homoskedasticity. This short paper introduces a moment-based result relating these two estimators through the correlation between squared residuals and squared regressors. Though the result does not rely on normality, it admits a simple approximation when all variables are normally distributed. This representation can be useful both for pedagogical purposes in undergraduate courses that do not use matrix algebra and in highlighting the relative magnitude of robust to non-robust standard errors.
