Efficient estimation of a semiparametric partially linear varying coefficient model

In this paper we propose a general series method to estimate a semiparametric partially linear varying coefficient model. We establish the consistency and \sqrtn-normality property of the estimator of the finite-dimensional parameters of the model. We further show that, when the error is conditionally homoskedastic, this estimator is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator of the finite-dimensional parameter reaches the semiparametric efficiency bound of this model. A small-scale simulation is reported to examine the finite sample performance of the proposed estimator, and an empirical application is presented to illustrate the usefulness of the proposed method in practice. We also discuss how to obtain an efficient estimation result when the error is conditional heteroskedastic.Comment: Published at http://dx.doi.org/10.1214/009053604000000931 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

MONEY GROWTH AND INFLATION IN THE UNITED STATES

Specification tests reject a linear inflation forecasting model over the period 1959 2002. Based on this finding, we evaluate the out-of-sample inflation forecasts of a fully nonparametric model for 1994 2002. Our two main results are that: (i) nonlinear models produce much better forecasts than linear models, and (ii) including money growth in the nonparametric model yields marginal improvements, but including velocity reduces the mean squared forecast error by as much as 40%. A threshold model fits the data well over the full sample, offering an interpretation of our findings. We conclude that it is important to account for both nonlinearity and the behavior of monetary aggregates when forecasting inflation.