Strong Consistency of the Least-Squares Estimator in Simple Regression Models with Stochastic Regressors

2013

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“…Nevertheless, Christopeit & Massmann (2013b) prove that strong consistency of the OLS estimator for δ and β does hold for c > 1/2.…”

Section: Asymptotics Of Eigenvaluesmentioning

confidence: 85%

mentioning

confidence: 77%

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A Note on an Estimation Problem in Models with Adaptive Learning

2013

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“…Nevertheless, Theorem 4 implies that the slope estimator is weakly consistent. Under the more stringent conditions of Gaussian error terms, we even have strong consistency, as is shown in Christopeit & Massmann (2012). To make the analysis tractable, the regressor sequence x t is assumed to be constant.…”

Section: Decreasing Gainmentioning

confidence: 95%

Estimating Structural Parameters in Regression Models with Adaptive Learning

2013

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis paper examines the ordinary least squares (OLS) estimator of the structural parameters in a class of stylised macroeconomic models in which agents are boundedly rational and use an adaptive learning rule to form expectations of the endogenous variable. The popularity of this type of model has recently increased amongst applied economists and policy makers who seek to estimate it empirically. Two prominent learning algorithms are considered, namely constant gain and decreasing gain learning. For each of the two learning rules, the analysis proceeds in two stages. First, the paper derives the asymptotic properties of agents' expectations. At the second stage, the paper derives the asymptotics of OLS in the structural model, taken the rst stage learning dynamics as given. In the case of constant gain learning, the structural model eectively amounts to a static, cointegrating or co-explosiveness regression. With decreasing gain learning, the regressors are asymptotically collinear such that OLS does not satisfy, in general, the Grenander conditions for consistent estimability. Nevertheless, this paper shows that the OLS estimator remains consistent in all models considered. It also shows, however, that its asymptotic distribution, and hence any inference based upon it, may be non-standard.

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“…As to be expected, the sufficient conditions for models with stochastic regressors are more restrictive than those for deterministic regressors. A brief account of these results is given in Christopeit & Massmann (2012). Concerning our model, it will turn out that for some cases of both constant and decreasing gain learning the near optimal sufficient condition established in Lai & Wei (1982a) is not satisfied.…”

Section: Introductionmentioning

confidence: 95%

Strong Consistency of the Least Squares Estimator in Regression Models with Adaptive Learning

2017

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