Testing the nominal-to-real transformation |
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| Institution: | 1. Department of Banking and Financial Management, University of Piraeus, Greece;2. Department of Economics and Finance, University of New Orleans, 2011 Administration Building, 2000 Lakeshore Drive, New Orleans, LA 70148, United States;1. Department of Geology, Colby College, Waterville, ME 04901, USA;2. Council for Geosciences, Private Bag X112, Silverton, Pretoria 001, South Africa;1. Urweltmuseum GEOSKOP/Burg Lichtenberg (Pfalz), Burgstrasse 19, 66871 Thallichtenberg, Germany;2. Saurierwelt Paläontologisches Museum, Alte Richt 7, D-92318 Neumarkt, Germany;3. Museum für Naturkunde Magdeburg, Otto-von-Guericke-Str. 68-73, 39104 Magdeburg, Germany;4. Department of Earth and Environmental Sciences, University of Pavia, Via Ferrata 1, I-27100 Pavia, Italy;5. Evolutionary Studies Institute, School for Geosciences, University of the Witwatersrand, Private Bag 3 Wits, Johannesburg 2050, South Africa;6. Iziko South African Museum of Cape Town, P.O. Box 61, Cape Town 8000, South Africa;7. Department of Earth Sciences, Albany Museum, Rhodes University, Grahamstown 6139, South Africa;8. Department of Geology, University of Johannesburg, Kingsway Ave, Auckland Park, Johannesburg 2092, South Africa;9. PO Box 360, Clarens 9707, South Africa |
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| Abstract: | This paper establishes the necessary and sufficient condition for nominal-to-real data transformations routinely used in empirical work to reduce the order of integration of an I(2) vector process while retaining the cointegrating relations among the variables. The condition potentially fails in a direction which is often dealt with by assumption in applied work. In this case, the transformed process satisfies a well-specified vector equilibrium model, yet I(1) inference and interpretation based on the real transformed system are invalidated. An easy-to-implement sequential test of the transformation based on I(1) cointegration methods demonstrates good size and power properties. An empirical example illustrates the need to test the nominal-to-real transformation. |
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