More efficient tests robust to heteroskedasticity of unknown form

In the presence of heteroskedasticity of unknown form, the Ordinary Least Squares parameter estimator becomes inefficient and its covariance matrix estimator inconsistent. Eicker (1963) and White (1980) were the first to propose a robust consistent covariance matrix estimator, that permits asymptotically correct inference. This estimator is widely used in practice. % Cragg (1983) proposed a more efficient estimator, but concluded thattests based on it are unreliable. Thus, this last estimator has not been used in practice. This paper is concerned with finite sample properties of tests robust to heteroskedasticity of unknown form. Our results suggestthat reliable and more efficient tests can be obtained with the Cragg estimators in small samples.wild bootstrap; heteroskedasticity-robust test; regression model

A better way to bootstrap pairs

In this paper we are interested in heteroskedastic regression models, for which an appropriate bootstrap method is bootstrapping pairs, proposed by Freedman (1981). We propose an ameliorate version of it, with better numerical performance.bootstrap, heteroskedasticity

Bootstrapping heteroskedasticity consistent covariance matrix estimator

Recent results of Cribari-Neto and Zarkos (1999) show that bootstrap methods can be successfully used to estimate a heteroskedasticity robust covariance matrix estimator. In this paper, we show that the wild bootstrap estimator can be calculated directly, without simulations, as it is just a more traditional estimator. Their experimental results seem to conflict with those of MacKinnon and White (1985); we reconcile these two results.wild bootstrap, heteroskedasticity

Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap

In regression models, appropriate bootstrap methods for inference robust to heteroskedasticity of unknown form are the wild bootstrap and the pairs bootstrap. The finite sample performance of a heteroskedastic-robust test is investigated with Monte Carlo experiments. The simulation results suggest that one specific version of the wild bootstrap outperforms the other versions of the wild bootstrap and of the pairs bootstrap. It is the only one for which the bootstrap test gives always better results than the asymptotic test.wild bootstrap ; pairs bootstrap ; heteroskedasticity-robust test ; Monte Carlo simulations

The Role of Economic Space in Decision Making: A Comment

This article is a comment on Margaret Slade (2005).Spatial autocorrelation

Asymptotic and bootstrap inference for inequality and poverty measures

A random sample drawn from a population would appear to offer an ideal opportunity to use the bootstrap in order to perform accurate inference, since the observations of the sample are IID. In this paper, Monte Carlo results suggest that bootstrapping a commonly used index of inequality leads to inference that is not accurate even in very large samples, although inference with poverty indices is satisfactory. We find that the major cause is the extreme sensitivity of many inequality indices to the exact nature of the upper tail of the income distribution. This leads us to study two non-standard bootstraps, the m out of n bootstrap, which is valid in some situations where the standard bootstrap fails, and a bootstrap in which the upper tail is modelled parametrically. Monte Carlo results suggest that accurate inference can be achieved with this last method in moderately large samples.Income distribution; Poverty; Bootstrap inference

The Wild Bootstrap, Tamed at Last

Various versions of the wild bootstrap are studied as applied to regression models with heteroskedastic errors. We develop formal Edgeworth expansions for the error in the rejection probability (ERP) of wild bootstrap tests based on asymptotic t statistics computed with a heteroskedasticity consistent covariance matrix estimator. Particular interest centers on the choice of the auxiliary distribution used by the wild bootstrap in order to generate bootstrap error terms. We find that the Rademacher distribution usually gives smaller ERPs, in small samples, than the version of the wild bootstrap that seems most popular in the literature, even though it does not benefit from the latter's skewness correction. This conclusion, based on Edgeworth expansions, is confirmed by a series of simulation experiments. We conclude that a particular version of the wild bootstrap is to be preferred in almost all practical situations, and we show analytically that it, and no other version, gives perfect inference in a special case.Wild Bootstrap, Heteroskedasticity Consistent Covariance Matrix Estimators, Size distortion

Starting-point bias and respondent uncertainty in dichotomous choice contingent valuation surveys

In this article, we develop a dichotomous choice model with follow-up questions that describes the willingness to pay being uncertain in an interval. The initial response is subject to starting point bias. Our model provides an alternative interpretation of the starting point bias in the dichotomous choice valuation surveys. Using the Exxon Valdez survey, we show that, when uncertain, individuals tend to answer "yes".starting point bias ; preference uncertainty ; contingent valuation

Controlling starting-point bias in double-bounded contingent valuation surveys

In this paper, we study starting point bias in double-bounded contingent valuation surveys. This phenomenon arise in applications that use multiple valuation questions. Indeed, response to follow-up valuation questions may be influenced by the bid proposed in the initial valuation question. Previous research have been conducted in order to control for such an effect. However, they find that efficiency gains are lost when we control for undesirable response effects, relative to a single dichotomous choice question. Contrary to these results, we propose a way to control for starting point bias in double-bounded questions with gains in efficiencycontingent valuation

The Wild Bootstrap, Tamed at Last

In this paper we are interested in inference based on heteroskedasticity consistent covariance matrix estimators, for which the appropriate bootstrap is a version of the wild bootstrap. Simulation results, obtained by a new very efficient method, show that all wild bootstrap tests exhibit substantial size distortion if the error terms are skewed and strongly heteroskedastic. The distortion is however less, sometimes much less, if one uses a version of the wild bootstrap, belonging to a class we call ``tamed'', which benefit from an asymptotic refinement related to the asymptotic independence of the bootstrapped test statistic and the bootstrap DGP. This version always gives better results than the version usually recommended in the literature, and gives exact results for some specific cases. However, when exact results are not available, we find that the rate of convergence to zero of the size distortion of wild bootstrap tests is not very rapid: in some cases, significant size distortion still remains for samples of size~100.