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Estimation and inference in adaptive learning models with slowly decreasing gains

  • This paper develops techniques of estimation and inference in a prototypical macroeconomic adaptive learning model with slowly decreasing gains. A sequential three-step procedure based on a `super-consistent' estimator of the rational expectations equilibrium parameter is proposed. It is shown that this procedure is asymptotically equivalent to first estimating the structural parameters jointly via ordinary least-squares (OLS) and then using the so-obtained estimates to form a plug-in estimator of the rational expectations equilibrium parameter. In spite of failing Grenander's conditions for well-behaved data, a limiting normal distribution of the estimators centered at the true parameters is derived. Although this distribution is singular, it can nevertheless be used to draw inferences about joint restrictions by applying results from Andrews (1987) to show that Wald-type statistics remain valid when equipped with a pseudo-inverse. Monte-Carlo evidence confirms the accuracy of the asymptotic theory for the finite sample behaviour of estimators and test statistics discussed here.

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Metadaten
Author:Alexander Mayer
URN:urn:nbn:de:hbz:992-opus4-6955
Series (Serial Number):WHU – Working Paper Series in Economics (WP 18/03)
Publisher:WHU - Otto Beisheim School of Management
Place of publication:Vallendar
Document Type:Working Paper
Language:English
Date of Publication (online):2018/07/09
Date of first Publication:2018/07/09
Release Date:2018/07/09
Tag:Adaptives Lernen; Nichtstationäre Regression; Rationale Erwartung; Singuläre Verteilung
Adaptive learning; Non-stationary regression; Rational expectation; Singular limiting-distribution
Page Number:73
Institutes:WHU Economics Group / Chair of Econometrics and Statistics
JEL-Classification:C Mathematical and Quantitative Methods / C1 Econometric and Statistical Methods: General / C12 Hypothesis Testing
C Mathematical and Quantitative Methods / C2 Single Equation Models; Single Variables / C22 Time-Series Models; Dynamic Quantile Regressions (Updated!)
C Mathematical and Quantitative Methods / C5 Econometric Modeling / C51 Model Construction and Estimation
D Microeconomics / D8 Information, Knowledge, and Uncertainty / D83 Search; Learning; Information and Knowledge; Communication; Belief
Licence (German):Copyright for this publication