Model specification test with correlated but not cointegrated variables |
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| Institution: | 1. Department of Economics, Texas A&M University, College Station, TX 77843-4228, United States;2. Department of Economics, University of Southern California, Los Angeles, CA 90089-0253, United States;3. School of Economics, Southern University of Finance & Economics, Chengdu, China;1. MIT, United States;2. University of Arizona, United States;1. Department of Finance, Kellogg School of Management, Northwestern University, Evanston, IL 60208, United States;2. Department of Economics, Duke University, Durham, NC 27708, United States;1. Department of Economics, University of Washington, Box 353330, Seattle, WA 98195, United States;2. Department of Economics, Korea University, Anam-dong, Sungbuk-gu, Seoul 136-701, Republic of Korea;1. Department of Economics, U.C.L.A., 8283 Bunche Hall, Mail Stop: 147703, Los Angeles, CA 90095, USA;2. Department of Economics, M.I.T., 50 Memorial Drive, E52-391, Cambridge, MA 02142, USA;3. Centre for Microdata Methods and Practice, Institute for Fiscal Studies, 7 Ridgmount Street, London WC1E 7AE, UK;4. Faculty of Economics, University of Cambridge, Austin Robinson Building, Sidgwick Avenue, Cambridge CB3 9DD, UK;5. Economics and Finance Department, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand |
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| Abstract: | Many macroeconomic and financial variables show highly persistent and correlated patterns but are not necessarily cointegrated. Recently, Sun et al. (2011) propose using a semiparametric varying coefficient approach to capture correlations between integrated but non cointegrated variables. Due to the complication arising from the integrated disturbance term and the semiparametric functional form, consistent estimation of such a semiparametric model requires stronger conditions than usually needed for consistent estimation for a linear (spurious) regression model, or a semiparametric varying coefficient model with a stationary disturbance. Therefore, it is important to develop a testing procedure to examine for a given data set, whether linear relationship holds or not, while allowing for the disturbance being an integrated process. In this paper we propose two test statistics for detecting linearity against semiparametric varying coefficient alternative specification. Monte Carlo simulations are used to examine the finite sample performances of the proposed tests. |
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| Keywords: | Specification test Spurious regression Varying coefficient Kernel estimation |
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