Nonparametric Econometrics

Abstract

This book systematically and thoroughly covers the vast literature on the nonparametric and semiparametric statistics and econometrics that has evolved over the last five decades. Within this framework this is the first book to discuss the principles of the nonparametric approach to the topics covered in a first year graduate course in econometrics, e.g. regression function, heteroskedasticity, simultaneous equations models, logit-probit and censored models. Nonparametric and semiparametric methods potentially offer considerable reward to applied researchers, owing to the methods' ability to adapt to many unknown features of the data. Professors Pagan and Ullah provide intuitive explanations of difficult concepts, heuristic developments of theory, and empirical examples emphasizing the usefulness of the modern nonparametric approach. The book should provide a new perspective on teaching and research in applied subjects in general and econometrics and statistics in particular.

A distribution dynamics approach to regional GDP convergence in unified Germany

“…where K(•) is the Gaussian kernel function and h is the bandwidth (see Silverman, 1986, andPagan andUllah, 1999 for introductions to this field of data analysis). In our benchmark estimations displayed in Figure 2, we have chosen the bandwidth h optimally according to Silverman's (1986, formula 3.31) rule of thumb.…”

Testing the null hypothesis of no regime switching with an application to GDP growth rates

“…The Mean Integrated Square Error (MISE) optimal value of the bandwidth for density estimation is of the form cn −1/5 , where c depends on the second derivative of the PDF. It simplifies to c = 1.06σ, provided that the normal kernel function is used and that the data is distributed according to N (µ, σ 2 ) (see, for example, Pagan and Ullah (1999)). However, Silverman (1986) reports that the choice c = 0.9min (σ, R/1.34), where R is the interquartile range, performs better in the case of a mixture of normals.…”

“…Second, provided that h n = o n −1/5 , and that some additional technical conditions found in Robinson (1983) (see also Pagan and Ullah (1999)) hold, under the null, the asymptotic distribution of f n is given by…”

Program Evaluation and Research Designs

“…There are a number of ways of estimating derivatives nonparametrically (Fan and Gijbels, 1996;Pagan and Ullah, 1999), or one could alternatively attempt to approximate the function E [Y |V = v] for D < 0 with a loworder global polynomial. We recognize that, in practical empirical applications, estimates of higher order derivatives may be quite imprecise.…”