Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity

• Main Authors: HONG, Seong Hyun, Peter C. B. PHILLIPS
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2010
• Subjects: Noncentral chi(2) distribution; Nonlinear cointegration; RESET test; Specification test; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1812; https://ink.library.smu.edu.sg/context/soe_research/article/2811/viewcontent/Testing_Linearity_Cointegrating_PPP_av.pdf
• Institution: Singapore Management University

This article shows that when applied to nonstationary time series, the conventional Regression Error Specification Test (RESET) leads to severe size distortion and its asymptotic distribution involves a mixture of noncentral chi(2) distributions. Nonstationarity introduces bias terms in the limit distribution, and appropriate corrections for the bias are presented leading to a modified RESET test that has a central chi(2) limit distribution. In simulations, this modified test is shown to have power not only against nonlinear cointegration but also against the absence of cointegration. In an empirical illustration, the linear purchasing power parity (PPP) specification is tested using five Organization for Economic Cooperation and Development (OECD) countries.