Nonparametric, Semiparametric, and Bootstrap Methods in Econometrics

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This project consists of research on three topics with wide potential empirical application: testing parametric models against nonparametric alternatives, Semiparametric estimation of proportional hazard models with unobserved heterogeneity, and bootstrap methods for econometric models estimated from time series. All build on prior work by the investigator. The first topic is concerned with testing a parametric model of a (possibly vector valued) conditional moment or quartile function against a nonparametric alternative. The research will develop tests that are uniformly consistent over smooth, nonparametric alternative models whose distance from the parametric model converges to zero at the fastest possible rate as the sample size increases. Tests which do not require a priori knowledge of the smoothness of the alternative model will also be developed. These properties provide important practical benefits in terms of power, and the new research will develop tests for more general parametric models and for models based on time-series data. The second topic is concerned with estimating proportional hazard models with unobserved heterogeneity. Neither the baseline hazard function nor the distribution of the unobserved heterogeneity will be assumed to belong to a known, finite-dimensional parametric family of functions. They will be treated nonparametrically. The research will focus particularly on fixed-effects models for panel data, models with covariates that are time varying within spells, and cross-sectional models in which the unobserved heterogeneity is an unknown form of heteroskedasticity. All of the models are relevant to applied research. The third topic is concerned with testing hypotheses about a finite-dimensional parameter that is estimated by the generalized method of moments (GMM) using dependent data. Since first-order approximations can be very inaccurate with the sample sizes found in applications, the true and nominal probabilities that a test rejects a correct null hypothesis can be very different when critical values are based on first-order asymptotic approximations. Similarly, the true and nominal coverage probabilities of confidence intervals based on first-order approximations can be very different. The block bootstrap provides a way to obtain improved approximations with dependent data, but recent research has shown that the amount of improvement is not large. The new research will investigate the use of the sieve bootstrap in which the data generation process is approximated by an expanding sequence of finite-dimensional parametric models, and bootstrap samples are generated by simulation from the sieve approximation. In settings much simpler than those of GMM estimation and testing, it has been found that the sieve bootstrap provides a substantially greater improvement over first-order approximations than does the block bootstrap. The new research will investigate whether the improved performance of the sieve bootstrap extends to the kinds of tests and models to which for which GMM is typically used in economics. In addition, the research will investigate whether iterated versions of the sieve bootstrap can be used to provide asymptotic refinements without the need for heteroskedasticity and autocorrelation consistent (MAC) covariance matrix estimation.