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Over the last three decades much research in empirical and theoretical economics has been carried on under various assumptions. For example a parametric functional form of the regression model, the heteroskedasticity, and the autocorrelation is always as­ sumed, usually linear. Also, the errors are assumed to follow certain parametric distri­ butions, often normal. A disadvantage of parametric econometrics based on these assumptions is that it may not be robust to the slight data inconsistency with the particular parametric specification. Indeed any misspecification in the functional form may lead to erroneous conclusions. In view of these problems, recently there has been significant interest in 'the semiparametric/nonparametric approaches to econometrics. The semiparametric approach considers econometric models where one component has a parametric and the other, which is unknown, a nonparametric specification (Manski 1984 and Horowitz and Neumann 1987, among others). The purely non­ parametric approach, on the other hand, does not specify any component of the model a priori. The main ingredient of this approach is the data based estimation of the unknown joint density due to Rosenblatt (1956). Since then, especially in the last decade, a vast amount of literature has appeared on nonparametric estimation in statistics journals. However, this literature is mostly highly technical and this may partly be the reason why very little is known about it in econometrics, although see Bierens (1987) and Ullah (1988).



The Asymptotic Efficiency of Semiparametric Estimators for Censored Linear Regression Models

This paper presents numerical comparisons of the asymptotic mean square estimation errors of semiparametric generalized least squares (SGLS), quantile, symmetrically censored least squares (SCLS), and tobit maximum likelihood estimators of the slope parameters of censored linear regression models with one explanatory variable. The results indicate that the SCLS estimator is less efficient than the other two semiparametric estimators. The SGLS estimator is more efficient than quantile estimators when the tails of the distribution of the random component of the model are not too thick and the probability of censoring is not too large. The most efficient semiparametric estimators usually have smaller mean square estimation errors than does the tobit estimator when the random component of the model is not normally distributed and the sample size is 500–1,000 or more.
Joel L. Horowitz

Nonparametric Kernel Estimation Applied to Forecasting: An Evaluation Based on the Bootstrap

The results reported in this paper lend support to the nonparametric approach to estimating regression functions. This conclusion is based on a comparison of two sets of eight quarterly forecasts of U.S. hog supply generated by a well specified parametric dynamic model and by nonparametric kernel estimation. Despite the relatively small sample size, the nonparametric point forecasts are found to be as accurate as the parametric forecasts according to the mean square error and mean absolute error criteria. Bootstrap resampling is used to estimate the distributions of the forecast errors. The results of this exercise favour the nonparametric forecasts, which are found to have a tighter distribution.
Giancarlo Moschini, David M. Prescott, Thanasis Stengos

Calibrating Histograms with Application to Economic Data

In this paper the problem of automatic calibration of histograms by cross-validation is considered, assuming the true underlying density is continuous with continuous first derivative. The histogram is one of the simpliest semiparametric estimators used by economists, but it is surprisingly difficult to construct histograms with small estimation errors. Cross-validation algorithms attempt, to automatically determine histogram bin widths that are nearly optimal with respect to mean integrated squared error. Alternative philosophies and approaches of cross-validation for histograms are presented. It is shown that the classical Sturges’ rule performs poorly and that cross-validation is a relatively difficult task. Understanding the performance of cross-validation algorithms in this simple setting should prove valuable when cross-validating other more complex semiparametric procedures.
David W. Scott, Heinz-Peter Schmitz

The Role of Fiscal Policy in the St. Louis Model: Nonparametric Estimates for a Small Open Economy

This paper reevaluates the efficacy of monetary and fiscal policies and bidirectional causality between income and each of the policy instruments used in the St. Louis model for aggregate demand using nonparametric (or infinite parametric) spectral methods. We proceed by estimating the strength of the correlations (or partial coherences) between income and each of the policy instruments over various frequencies. Then we obtain the corresponding band regression and Hannan’s efficient estimates of both the lead and lag coefficients in the St. Louis model. The analysis is carried out with seasonally adjusted quarterly data and is divided into the flexible, fixed, and managed flexible exchange rate regimes.
We find that while estimates from parametric regressions yield the standard conclusions for the St. Louis model, results from the nonparametric analysis are quite different. Specifically, the results of our analysis reveal that (i) both monetary and fiscal instruments are strongly correlated with income over cycles of 10 quarters or longer for the most recent period of the managed flexible exchange rate regime, and (ii) bidirectional causality exists between income and the fiscal policy instrument. These results suggest that both monetary and fiscal policy have a long-lasting effect on aggregate demand and that bidirectional causality exists between income and policy instruments. An explanation for the existence of bidirectional causality might be that the Canadian government generally pursued a purposeful discretionary fiscal policy during the post-World War II period. Furthermore, it appears that discretionary policy action may have been anticipated by rational, farsighted, and forward-looking economic agents. Finally, our results for the flexible exchange rate and fixed rate regimes are in agreement with the Mundell-Fleming view of the role of monetary fiscal policy in an open economy.
Baldev Raj, Pierre L. Siklos

Automatic Smoothing Parameter Selection: A Survey

This is a survey of recent developments in smoothing parameter selection for curve estimation. The first goal of this paper is to provide an introduction to the methods available, with discussion at both a practical and also a nontechnical level, including comparison of methods. The second goal is to provide access to the literature, especially on smoothing parameter selection, but also on curve estimation in general. The two main settings considered here are nonparametric regression and probability density estimation, although the points made apply to other settings as well. These points also apply to many different estimators, although the focus is on kernel estimators, because they are the most easily understood and motivated, and have been at the heart of the development in the field.
J. S. Marron

Bayes Prediction Density and Regression Estimation — A Semiparametric Approach

This paper is concerned with the Bayes estimation of an arbitrary multivariate density, f(x), xR k . Such an f(x) may be represented as a mixture of a given parametric family of densities h(x|θ) with support in R k, where θ (in R d) is chosen according to a mixing distribution G. We consider the semiparametric Bayes approach in which G, in turn, is chosen according to a Dirichlet process prior with given parameter a. We then specialize these results when f is expressed as a mixture of multivariate normal densities θ(x|μ, Λ) where μ is the mean vector and Λ is the precision matrix. The results are finally applied to estimating a regression parameter.
R. C. Tiwari, S. R. Jammalamadaka, S. Chib

Nonparametric Estimation and Hypothesis Testing in Econometric Models

In this paper we systematically review and develop nonparametric estimation and testing techniques in the context of econometric models. The results are discussed under the settings of regression model and kernel estimation, although as indicated in the paper these results can go through for other econometric models and for the nearest neighbor estimation. A nontechnical survey of the asymptotic properties of kernel regression estimation is also presented. The technique described in the paper are useful for the empirical analysis of the economic relations whose true functional forms are usually unknown.
Aman Ullah

Some Simulation Studies of Nonparametric Estimators

This paper constructs a number of Monte Carlo studies to assess the quality of various nonparametric estimators that have been proposed recently for the estimation of nonlinear econometric models. We consider both kernel and Fourier series based methods of estimation, and also examine techniques that have been suggested to improve the bias properties of the kernel estimator. The two models examined are a production function and a model emphasising the effects of risk. The Fourier estimator does very well in estimating the first of these, but not the second, while the kernel estimator shows substantial bias for the first, which is only partially alleviated by the procedures advocated for bias correction, and good results for the second.
Y. Hong, A. Pagan

Estimating a Hedonic Earnings Function with a Nonparametric Method

In this paper we apply the nonparametric approach of Bierens and Hartog (1988) to estimating and testing an earnings function which emphasizes the simultaneous impact of supply characteristics (like education) and demand characteristics (like job level). The data support this emphasis and point to significant non-linearities. In particular, job level comes out as an important variable.
Joop Hartog, Herman J. Bierens


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