Pascal Lavergne

Nonparametric Significance Testing

A procedure for testing the signicance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has a nhp2/2 standard normal limiting distribution, where p2 is the dimension of the complete set of regressors. Our test is one-sided, consistent against all alternatives and detect local alternatives approaching the null at rate slower than n-1/2 h-p2/4. Our Monte-Carlo experiments indicate that it outperforms the test proposed by Fan and Li (1996).

Nonparametric Selection of Regressors: The Nonnested Case

We propose a consistent and directional testing procedure for discriminating between two sets of regressors without specifying the functional form of the regressions or the distribution of the residuals. Our test statistic uses the empirical mean square error from a nonparametric (kernel) regression.

Data-Driven Rate-Optimal Specification Testing in Regression Models

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/sqrt(n). Asymptotic critical values come from the standard normal distribution and bootstrap can be used in small samples. A general formalization allows to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.

Welfare Losses Due to Market Power: Hicksian versus Marshallian Measurement

This paper warns against the use of Marshallian welfare loss in applied analysis of market power. We show how to compute the Hicksian deadweight loss from an ordinary demand. Then, from an experiment using real data on twenty-one sectors of the French food industry, we find that the Marshallian deadweight loss poorly approximates the exact Hicksian measure. Hence, it is advisable to use the latter in applied welfare analysis. Copyright 2001, Oxford University Press.

Selection of regressors in econometrics: parametric and nonparametric methods selection of regressors in econometrics

The present paper addresses the selection-of-regressors issue into a general discrimination framework. We show how this framework is useful in unifying various procedures for selecting regressors and helpful in understanding the different strategies underlying these procedures. We review selection of regressors in linear, nonlinear and nonparametric regression models. In each case we successively consider model selection criteria and hypothesis testing procedures.

A Significance Test for Covariates in Nonparametric Regression

We consider testing the significance of a subset of covariates in a nonparamet- ric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the null hypothesis, so that the curse of dimensionality is mitigated. The test statistic is asymptotically pivotal and the rate of which the test detects local alternatives depends only on the dimension of the covariates under the null hy- pothesis. We show the validity of wild bootstrap for the test. In small samples, our test is competitive compared to existing procedures.

An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression

We propose a new estimator of unconditional residual variance in nonparametric regression based on the integral of squared residuals. We show its consistency in l} under general conditions and derive a nonparametric decomposition of the variance formula. Monte-Carlo experiments suggest that the estimator has good small sample properties.

The Hot Air in R2: Comment

In a recent contribution to this journal, McGuirk and Driscoll warn applied econometricians about blind use of R2 in model selection. Relying on some simulations, they illustrate three claims. First, they show that correctly specified models may have a low R2. Second they exemplify that misspecified models may have a high R2. These two remarks are rather trivial and do not deserve much com-