Two-stage rank estimation of quantile index models

Article Abstract:

This paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable. This class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction, thus allowing for very general forms of conditional heteroscedasticity. A two-stage approach is adopted to estimate the relevant parameters. In the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in Chaudhuri (Journal of Multivariate Analysis 39 (1991a) 246-269; Annals of Statistics 19 (1991b) 760-777) and Cavanagh (1996, Preprint). In the second stage, the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank-based objective function. The proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model. [C] 2001 Elsevier Science S.A. All rights reserved. JEL classification: C13; C14; C24; C41 Keywords: Monotonic transformation; Nonparametric quantile regression; Hetero-scedasticity; Rank regression

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An analysis of housing expenditure using semiparametric models and panel data

Article Abstract:

In this paper we model expenditure on housing for owners and renters by means of endogenous switching regression models for panel data. We explain the share of housing in total expenditure from a household specific effect, family characteristics, constant-quality prices, and total expenditure, where the latter is allowed to be endogenous. We consider both random and fixed effects panel data models. We compare estimates for the random effects model with estimates for the linear panel data model in which selection only enters through the fixed effects, and with estimates allowing for fixed effects and a more general type of selectivity. Differences appear to be substantial. The results imply that the random effects model as well as the linear panel data model are too restrictive. [C] 2001 Elsevier Science S.A. All rights reserved. JEL classification: C14; C33; R21 Keywords: Sample selection; Engel curves; Semiparametric models; Panel data

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The memory of stochastic volatility models

Article Abstract:

A valid asymptotic expansion for the covariance of functions of multivariate normal vectors is applied to approximate autocovariances of time series generated by nonlinear transformation of Gaussian latent variates, and nonlinear functions of these, with special reference to long memory stochastic volatility models, serving to identify the roles played by the underlying Gaussian processes and the nonlinear transformation. Implications for simple stochastic volatility models are examined in detail, with numerical and Monte Carlo calculations, and applications to cyclic behaviour, cross-sectional and temporal aggregation, and multivariate models are discussed. [C] 2001 Elsevier Science S.A. All rights reserved. JEL classification: C22 Keywords: Stochastic volatility; Long memory; Nonlinear functions of Gaussian processes

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