A Note on an Estimation Problem in Models with Adaptive Learning

Norbert Christopeit and Michael Massmann
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Norbert Christopeit: University of Bonn, Germany

No 13-151/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This paper provides an example of a linear regression model with predetermined stochastic regressors for which the sufficient condition for strong consistency of the ordinary least squares estimator by Lai & Wei (1982, Annals of Statistics) is not met. Nevertheless, the estimator is strongly consistent, as shown in a companion paper, cf. Christopeit & Massmann (2013b). This is intriguing because the Lai & Wei condition is the best currently available and is referred to as “in some sense the weakest possible”. Moreover, the example discussed in this paper arises naturally in a class of macroeconomic models with adaptive learning, the estimation of which has recently gained popularity amongst researchers and policy makers.

Keywords: least-squares regression; stochastic regressors; strong consistency; minimal sufficient condition; adaptive learning (search for similar items in EconPapers)
JEL-codes: C22 C51 D83 (search for similar items in EconPapers)
Date: 2013-09-26
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Citations: View citations in EconPapers (2)

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