Some recent developments on nonparametric econometrics

Abstract

In this paper we survey some recent developments of nonparametric econometrics in the following areas: (i) Nonparametric estimation of regression models with mixed discrete and continuous data; (ii) Nonparametric models with nonstationary data; (iii) Nonparametric models with instrumental variables; (iv) Nonparametric estimation of conditional quantile functions. In each of the above areas we also point out some open research problems. Forthcoming in Advances in Econometrics * We thank the referees for their careful reading of the manuscript and for their helpful comments. We also thank the Econometric Seminar audiences at the University of Guelph, and the participants in the Advances in Econometrics conference for helpful comments on this paper.

Partially varying coefficient instrumental variables models

“…It is well documented in the literature that for ordinary semiparametric models, a profile likelihood approach is useful and is semiparametrically efficient; see S peckman (1988), C ai (2002a, 2002b), and F an and H uang (2005) for details. For the detailed procedures on how to apply the profile likelihood approach to estimate Θ p ; see C ai , G u and L i (2009). Therefore, we conjecture that the profile least squares estimate for Θ p described above should be ‐consistent and semiparametrically efficient.…”

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

“…If there is no X t (only U t ) in (2), then (2) reduces to the ordinary nonparametric quantile regression model which has been studied extensively; see Cai (2002a) and Cai, Gu and Li (2009). Further, if X t2 = 1 in (2), then model (2) includes a partially linear quantile model explored by He and Shi (1996), He and Liang (2000) and Lee (2003) as a special case.…”

“…More recently, nonparametric and semiparametric quantile regression models have attracted a great deal of research attention due to their greater flexibility than tightly specified parametric models. See, for example, Chaudhuri (1991), He and Shi (1996), Chaudhuri, Doksum and Samarov (1997), He, Ng and Portnoy (1998), Yu and Jones (1998), Koenker, Ng and Portnoy (1998), He and Ng (1999), He and Liang (2000), He and Portnoy (2000), Honda (2000Honda ( , 2004, Khindanova and Rachev (2000), Cai (2002a), De Gooijer andGannoun (2003), Kim (2007), Lee (2003), Yu and Lu (2004), Horowitz and Lee (2005), Cai and Xu (2008), Cai, Gu and Li (2009) and references therein for recent statistics and econometrics literature.…”

Economies of diversification in the US credit union sector

“…In fact, since Equation 13 nests Equation 14, we can formally discriminate between the two specifications by means of a nonparametric likelihood ratio test, which we discuss in more detail in Section 5. For an excellent review of the existing pooled nonparametric (kernel and spline) quantile regression models, see Cai, Gu, and Li (2009). 14 That is, based on Cai et al's (2013) specification, some of the parameter functions in B r, (·) would have been assumed to be constant and not dependent on a "contextual" variable z it .…”