Journal of Economic Literature (JEL) Code(s)
This paper studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspeciﬁed through the use of a proxy regressor in place of the true regressor. Such regressions arise naturally in linear and nonlinear regressions where the regressor suﬀers from measurement error or where the true regressor is a latent variable. The model considered allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable. Such a framework includes correctly speciﬁed systems as well as misspeciﬁed models in which the actual regressor serves as a proxy variable for the true regressor. The system is therefore intermediate between nonlinear nonparametric cointegrating regression (Wang and Phillips, 2009a, 2009b) and completely misspeciﬁed nonparametric regressions in which the relationship is entirely spurious (Phillips, 2009). The asymptotic results relate to recent work on dynamic misspeciﬁcation in nonparametric nonstationary systems by Kasparis and Phillips (2012) and Duﬀy (2014). The limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and ﬁnancial time series.
Wang, Qiying; Phillips, Peter C.B.; and Kasparis, Ioannis, "Latent Variable Nonparametric Cointegrating Regression" (2017). Cowles Foundation Discussion Papers. 167.