On modeling heterogeneity in linear models using trend polynomials |
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| Affiliation: | 1. Allegheny College, Department of Economics, Quigley Hall, Box 20, Meadville, PA, 16335, USA;2. Virginia Tech, Department of Economics, Pamplin Hall, Mail Code 0316, Blacksburg, VA, 24061, USA;1. Department of Quantitative Economics, University of Santiago de Compostela, Spain;2. Department of Finance and Accounting, University of Santiago de Compostela, Spain;1. American University of Sharjah, United Arab Emirates;2. ADA University, Azerbaijan;3. Deakin University, Australia;1. INSEEC School of Business & Economics, 27, Avenue Claude Vellefaux, 75010, Paris, France;2. INSEEC School of Business & Economics, H19, Quai de Bacalan, 33070, Bordeaux, France;1. University College Dublin, Ireland;2. City University of Hong Kong and Wilfrid Laurier University, Ireland;3. Dublin City University, Ireland;1. Australian National University, College of Asia and the Pacific, Crawford School of Public Policy, Acton, ACT, 2601, Australia;2. Bangladesh Bank, Head Office, Motijheel, Dhaka, 1000, Bangladesh |
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| Abstract: | The primary aim of the paper is to consider the problems and issues raised when the data exhibit time heterogeneity in the context of linear models. Ignoring time heterogeneity will undermine the reliability of inference and will give rise to untrustworthy evidence. Accounting for it using trend polynomials, however, is non-trivial because it raises several modeling issues. First, when the degree of the polynomial is greater than 4, or so, one needs to deal with the near-multicollinearity problem that arises. The second issue pertains to the type of polynomial that will adequately account for the time heterogeneity. Third, when the trend polynomials are treated as additional regressors, they will give rise to highly misleading statistical results. The paper investigates how different types of polynomials could deal with the near-multicollinearity and the modeling issues they raise, and makes recommendations to practitioners. |
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| Keywords: | Linear model t-Heterogeneity Near-collinearity Trend polynomial Orthogonal polynomial Orthonormal polynomial C18 C22 C51 C52 C58 |
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