Linear or Nonlinear Cointegration in the Purchasing Power Parity Relationship?

We test long-run PPP within a general model of cointegration of linear and nonlinear form. Nonlinear cointegration is tested with rank tests of Breitung (2001). We determine first the order of integration of each variable, using monthly data from the post-Bretton Woods era for G-10 countries. In many cases prices are I(2), whereas all exchange rates are I(1). However, there are several countries that have a price level that linearly cointegrates with the US price level so that this combination is I(1). Overall, we find some, though limited, evidence for nonlinear and also linear cointegration in the PPP model.PublishedBacchiocchi, E., and Fanelli, L. (2005), “Testing the purchasing power parity through I(2) cointegration techniques,” Journal of Applied Econometrics, 20, 749–770. Banerjee, A., Cockerell, L., and Russel, B. (2001), “An I(2) analysis of inflation and the markup,” Journal of Applied Econometrics, 16, 221–240. Betts, C., and Devereux, M. (2001), “The international monetary transmission of monetary and fiscal policy in a two country model,” in Obstfeld, M, and G. Calvo (eds.) Essays in Honor of Robert A. Mundell, MIT Press. Breitung, J. (2001), “Rank tests for nonlinear cointegration,” Journal of Business and Economic Statistics, 19, 331–340. Campa, J., and Goldberg, L. (2002), “Exchange rate pass–through into import prices,” NBER Working Paper No. 8934. Choi, I., and Saikkonen, P. (2004), “Testing linearity in cointegrated smooth transition regressions,” Econometrics Journal, 7, 341–365. Cheung, Y.-W., Lai, K.S., and Bergman, M. (2004), “Dissecting the PPP puzzle: the unconventional roles of nominal exchange rate and price adjustments,” Journal of International Economics, 64, 135–150. Cheung, Y.-W., and Lai, K.S. (1993a), “Long–run purchasing power parity during the recent float,” Journal of International Economics, 34, 181–192. Cheung, Y.-W., and Lai, K.S. (1993b), “A fractional cointegration analysis of purchasing power parity,” Journal of Business and Economic Statistics, 11, 103–112. Clarida, R., Gali, J., and Gertler, M. (2000), “Monetary policy rules and macroeconomic stability: Evidence and some theory,” Quarterly Journal of Economics, 115, 147–180. Dickey, D.A., and Pantula,S.G. (1987), “Determining the order of differencing in autoregressive processes,” Journal of Business and Economic Statistics, 5, 455–461. Donnenfeld, S., and Haug, A.A. (2003), “Currency invoicing in international trade: an empirical investigation,” Review of International Economics, 11, 337–345. Elliot, G., and Pesavento, E. (2006) “On the failure of PPP for bilateral exchange rates after 1973”, Journal of Money, Credit, and Banking, 38, 1405–1430. Elliott, G., Rothenberg, T.J., and Stock, J.H. (1996), “Efficient tests for an autoregressive unit root,” Econometrica, 64, 813–836. Engel, C., and Morley, J.C. (2001), “The adjustment of prices and the adjustment of the exchange rate,” NBER Working Paper no. 8550. Granger, C.W.J., and Hallman, J. (1991), “Long memory processes with attractors,” Oxford Bulletin of Economics and Statistics, 53, 11–26. Haug, A. A. (1996), “Tests for cointegration: A Monte Carlo comparison,” Journal of Econometrics, 71, 89–115. Johansen, S. (1995), Likelihood-based inference in cointegrated vector autoregressive models, Oxford University Press. Kilian, L., and Taylor, M.P. (2003), “Why is it so difficult to beat the random walk forecast of exchange rates?” Journal of International Economics, 60, 85–107. Lopez, C., Murray, C.J., and Papell, D.H. (2005), “State of the art unit root tests and purchasing power parity,” Journal of Money, Credit and Banking, 37, 361-369. Lothian, J.R., and Taylor, M.P. (1996), “Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries,” Journal of Political Economy, 104, 488-509. MacKinnon, J.G., Haug, A.A., and Michelis, L, (1999), “Numerical distribution functions of likelihood ratio tests for cointegration,” Journal of Applied Econometrics, 14, 563–577 MacKinnon, J.G. (1996), “Numerical distribution functions for unit root and cointegration tests,” Journal of Applied Econometrics, 11, 601–618. Michael, P., Nobay, A.R., and Peel, D.A. (1997), “Transactions costs and nonlinear adjustment in real exchange rates: an empirical investigation,” Journal of Political Economy, 105, 862–879. Ng, S., and P. Perron (2001), “Lag length selection and the construction of unit root tests with good size and power”, Econometrica, 69, 1519–1554. Pedroni, P. (2001), “Purchasing power parity tests in cointegrated panels,” Review of Economics and Statistics, 83, 727–731. Rapach, D.E. (2003), “International evidence on the long run impact of inflation,”Journal of Money, Credit, and Banking, 35, 23–48. Rogoff, K. (1996), “The purchasing power parity puzzle,” Journal of Economic Literature, 34, 647–668. Schwert, G.W. (1989),“Tests for unit roots: A monte carlo investigation,” Journal of Business and Economic Statistics, 7, 147–59. Sercu, P., Uppal, R., and Van Hulle, C. (1995), “The exchange rate in the presence of transaction costs: implications for tests of purchasing power parity,” Journal of Finance, 50, 1309–1319. Sims, C.A., and Zha, T. (2002), “Macroeconomic switching,” Economic Letter,11, Proceedings from the Federal Reserve Bank of San Francisco, 1–23. Stock, J.H., and Watson, M.W. (1993), “A simple estimator of cointegrating vectors in high order integrated systems,” Econometrica, 61, 783–820. Taylor, A.M., and Taylor, M.P. (2004), “The purchasing power parity debate,” Journal of Economic Perspectives, 18, 135–158. Taylor, M.P. (1988), “An empirical examination of long–run purchasing power parity using cointegration techniques,” Applied Economics, 20, 1369–1381