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PPP Strikes Back: Aggregation and the Real Exchange Rate^

Imbs, J., Mumtaz, H, Ravn, M., Rey. H.
Date Published: February 2005
Imbs, Jean, et al. "PPP strikes back: Aggregation and the real exchange rate." The Quarterly Journal of Economics 120.1 (2005): 1-43.

Heterogeneity in the dynamics of sectoral prices explains why aggregate price indices mean-revert slowly. When we account for this heterogeinity, the PPP puzzle is no more.

Imbs, Jean, et al. "PPP strikes back: Aggregation and the real exchange rate." The Quarterly Journal of Economics 120.1 (2005): 1-43.
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^The paper is part of the project “Exchange Rates, International Relative Prices, and Macroeconomic Models”, funded by the ESRC (grant no.L138 25 1043).

Copyright The Author(s) 2005. Published by Oxford University Press, on behalf of President and Fellows of Harvard College. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Previous December 2002 incarnation in NBER WP 9372, CEPR DP3715

Our paper has generated quite a debate. Get a summary here below [Posted 11 October 2003: includes our email correspondence with Charles Engel between December 2002 and June 2003]. Here is our reply to Chen and Engel (April 2004).

The PPP Controversy - A Summary of the Debate surrounding "PPP Strikes Back" [correspondance with Charles Engel between December 2002 and June 2003]
A number of issues on our PPP paper were raised during discussions and seminar presentations, most prominently by Charles Engel. We are posting here the documents summarizing the exercises we conducted in response to these comments. The punchline is that our result on an aggregation bias in the persistence of real exchange rates (a) is robust, (b) can be generalized, and (c) is important empirically.
(a) Data and sensitivity analysis.
We use Eurostat data. This dataset is often argued to contain a number of errors, and one might be tempted to think this is a reason for our much lower estimates of real exchange rate persistence.
However, measurement error does not affect our results: The aggregation bias is pervasive. The two notes here and here go through the details of the analysis. Here is also a direct answer to a note posted by Julian di Giovanni on this issue.
Technically: One needs to be careful with the econometric specification. The Random Coefficient estimator is a generalization of Random Effects, the Mean Group estimator generalizes Fixed Effects. They are equivalent to each other asymptotically. Just as in standard panels, appropriate tests should be implemented when deciding which estimator to implement. Longer time series call for a Mean Group estimator, which implies a large and positive aggregation bias. We also implement a variety of corrections to the Eurostat data (inclusive of some suggested by Charles Engel himself). Our results stand in all cases.
(b) A generalization of the proof for the existence of an aggregation bias.
The analytical proof in the paper assumed cross-sectional independence of the errors of relative prices. As shown in this note however, the same result obtains even when allowing for correlation in the errors. It is only under extreme and unrealistic assumptions on the cross-sectional dependence that the sign of the bias can reverse. Thanks are due to Charles Engel for forcing us to develop this more general and elegant proof.
(c) Is the aggregation bias empirically important?
Estimating the persistence of autoregressive processes in panel data is always related to two types of biases: The aggregation bias that we discuss and the Nickell "small-sample" attenuating bias. The question is which dominates. This first note uses Monte-Carlo simulations to show the aggregation bias dominates in most relevant cases. In this more recent note, we dedicate some time to the treatment of explosive roots at the sectoral level, and whether their inclusion influences the magnitude of the aggregation bias. We show they are innocuous: estimates of the aggregation bias when explosive roots are excluded are almost identical to our original results. We also point to existing research showing that, in Monte-Carlo simulations, a (fixed effects) intercept should be included in both the Data Generating Process (DGP) and the simulated estimates. Including it only in the latter severely magnifies the small-sample bias, as shown in this gauss program.
Technically: Explosive processes are innocuous because we estimate directly the autoregressive parameters, rather than the half lives which would indeed be infinite. It is important to deal correctly with the intercept when deriving the properties of the Fixed Effects estimator. The correct exercise is to allow for fixed effects in both the DGP and the empirical model. In that case the aggregation bias dominates. Without fixed effects in the DGP, the Nickell attenuating bias is aggravated and can potentially dominate. It is also important to note that the aggregation bias survives even with a large time-series dimension (as in our paper), while the small sample attenuating bias disappears as the time-series grows.

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