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COINTEGRATING POLYNOMIAL REGRESSIONS: FULLY MODIFIED OLS ESTIMATION AND INFERENCE

Published online by Cambridge University Press:  16 June 2015

Martin Wagner  and
Seung Hyun Hong
Martin Wagner*
Affiliation:
Technical University Dortmund and Institute for Advanced Studies and Bank of Slovenia
Seung Hyun Hong
Affiliation:
Korea Institute of Public Finance
*
*Address correspondence to Martin Wagner, Faculty of Statistics, Technical University Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany, e-mail: [email protected]
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Abstract

This paper develops a fully modified OLS (FM-OLS) estimator for cointegrating polynomial regressions, i.e., regressions that include as explanatory variables deterministic variables, integrated processes, and integer powers of integrated processes. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The paper extends the fully modified estimator of Phillips and Hansen (1990) from cointegrating regressions to cointegrating polynomial regressions. The FM-OLS estimator has a zero-mean Gaussian mixture limiting distribution that allows for standard asymptotic inference. Wald and LM specification tests as well as a KPSS-type test for cointegration are derived. The theoretical analysis is complemented by a simulation study which shows that this FM-OLS estimator, as well as tests based upon it, perform well in the sense that the performance advantages over OLS are largely similar to the performance advantages of FM-OLS over OLS in standard cointegrating regressions.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 5 , October 2016 , pp. 1289 - 1315
Copyright
Copyright © Cambridge University Press 2015 

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