"Aggregation Bias" DOES Explain the PPP Puzzle

Abstract

This article summarizes our views on the role of an "aggregation bias" in explaining the PPP Puzzle, in response to the several papers recently written in reaction to our initial contribution. We discuss in particular the criticisms of Imbs, Mumtaz, Ravn and Rey (2002) presented in Chen and Engel (2005). We show that their contentions are based on: (i) analytical counter-examples which are not empirically relevant; (ii) simulation results minimizing the extent of "aggregation bias"; (iii) unfounded claims on the impact of measurement errors on our results; and (iv) problematic implementation of small-sample bias corrections. We conclude, as in our original paper, that "aggregation bias" goes a long way towards explaining the PPP puzzle.

PPP Strikes Back: Aggregation And the Real Exchange Rate

“…8. In Imbs, Mumtaz, Ravn, and Rey [2004], we detail the reasons why the small sample bias is limited in our data set.…”

“…A simple example of conditions under which Corollary 2.1 is satisfied is when the CPI weights are similar, the innovation variances are similar and the covariances between the innovations are similar and positive (see Imbs, Mumtaz, Ravn, and Rey [2004] for details). 16 We note that such families of restrictions (broadly defined) are plausible for sectoral price data.…”

“…But pursuing this route will be impossible in most cases, for lack of degrees of freedom, unless the 11. This is a log-linear approximation to the CPI-based real exchange rate when CPI weights are equal across countries (see Appendix A1 in Imbs, Mumtaz, Ravn, and Rey [2004]). …”

Non-Linear Adjustment in Law of One Price Deviations and Physical Characteristics of Goods

“…I assume two thresholds 19 for each good. Since there is no a-priori reason for t ijg to have different effects in appreciation and depreciation, I also assume symmetry: γ…”

“…In a smooth threshold autoregressive model reversion occurs for any deviation and its strength rises in the size of the deviation (for references see, i.a., Tong 1990; Granger and Teräsvirta 1993). 19 One threshold following sufficient appreciation, another one after depreciation. 20 Confidence intervals forβ g,in are constructed using the method in Hansen (1997).…”