COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1702 Nonparametric Structural Estimation via Continuous Location
Shifts Peter C.B. Phillips and Liangjun Su June 2009 Recent work by Wang and Phillips (2009b, c) has shown that ill posed inverse problems
do not arise in nonstationary nonparametric regression and there is no need for
nonparametric instrumental variable estimation. Instead, simple Nadaraya Watson
nonparametric estimation of a (possibly nonlinear) cointegrating regression equation is
consistent with a limiting (mixed) normal distribution irrespective of the endogeneity in
the regressor, near integration as well as integration in the regressor, and serial
dependence in the regression equation. The present paper shows that some closely related
results apply in the case of structural nonparametric regression with independent data
when there are continuous location shifts in the regressor. In such cases, location shifts
serve as an instrumental variable in tracing out the regression line similar to the random
wandering nature of the regressor in a cointegrating regression. Asymptotic theory is
given for local level and local linear nonparametric estimators, links with nonstationary
cointegrating regression theory and nonparametric IV regression are explored, and
extensions to the stationary strong mixing case are given. In contrast to standard
nonparametric limit theory, local level and local linear estimators have identical limit
distributions, so the local linear approach has no apparent advantage in the present
context. Some interesting cases are discovered, which appear to be new in the literature,
where nonparametric estimation is consistent whereas parametric regression is inconsistent
even when the true (parametric) regression function is known. The methods are further
applied to establish a limit theory for nonparametric estimation of structural panel data
models with endogenous regressors and individual effects. Some simulation evidence is
reported. |
