Nonlinear estimation using estimated cointegrating relations

Article Abstract:

The Granger-Engle procedure consists of two steps. In the first step, a long-run cointegrating relationship is estimated, and in the second stage, this estimated long-run relationship is used to estimate a distributed lag model. This paper establishes the limit distribution of the second-stage estimator if the model estimated in the second stage is other than linear. One may expect that the estimation of the cointegrating relationship does not affect the limit distribution of the second-stage estimator; however, it is shown that unless a regularity condition holds, this intuition is false. Clearly this regularity condition holds in the standard linear case. A simple example where the limit distribution changes is the addition of the square of the cointegrating relationship to the second stage distributed lag model that is estimated by least squares. Surprisingly however, it turns out that if a constant is included in the long-run least-squares regression, the (possibly nonlinear) second-stage estimator will be asymptotically normally distributed. [C] 2001 Elsevier Science S.A. All rights reserved. JEL classification: C22; C32 Keywords: Cointegration; Unit root; Time series; Nonlinearity

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The unbalanced nested error component regression model

Article Abstract:

This paper considers a nested error component model with unbalanced data and proposes simple analysis of variance (ANOVA), maximum likelihood (MLE) and minimum norm quadratic unbiased estimators (MINQUE)-type estimators of the variance components. These are natural extensions from the biometrics, statistics and econometrics literature. The performance of these estimators is investigated by means of Monte Carlo experiments. While the MLE and MINQUE methods perform the best in estimating the variance components and the standard errors of the regression coefficients, the simple ANOVA methods perform just as well in estimating the regression coefficients. These estimation methods are also used to investigate the productivity of public capital in private production. [C] 2001 Published by Elsevier Science S.A. JEL: C23 Keywords: Panel data; Nested error component; Unbalanced ANOVA; MINQUE; MLE; Variance components

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