Most of the empirical literature on purchasing power parity (PPP) and real exchange rate (RER) persistence focuses on the analysis of aggregate RER data, where the latter are constructed with aggregate price indices. After years of close scrutiny, the general consensus is that aggregate RERs may converge to parity in the long run, but that the rate at which this happens is very slow, with half-lives (HL) in the range of 3 to 5 years (Frankel and Rose, 1996, Lothian and Taylor, 1996 and Murray and Papell, 2005). Thus, while the high volatility of real exchange rates could potentially be explained by monetary or financial shocks, the rate of reversion to parity seems to be too slow to be compatible with plausible nominal rigidities, giving rise to the so-called PPP puzzle (Rogoff, 1996).
Several avenues have been pursued to shed more light on this issue. A recent literature has focused on the analysis of disaggregate real exchange rates, cf. Crucini and Shintani (2008), Imbs et al. (2005), Crucini et al. (2005), Cheung et al. (2001), Yang (1997), Knetter (1993), etc. One of the common findings of these papers is that there is a considerable degree of heterogeneity across sectors. With respect to sectoral persistence and its relation with that observed at the aggregate level, the empirical findings appear to be disparate. Some authors have found large divergences between sectoral and aggregate reversion rates. Using Eurostat data, Imbs et al. (2005) report standard HL estimates for aggregate RERs in the range of 3-5 years and considerably lower HL estimates, around 1 year, when sectoral data is employed.
They claim that the PPP puzzle arises as a consequence of an aggregation bias that affects aggregate estimates due to the high degree of heterogeneity in sectoral RERs which neither standard time series nor panel data techniques are able to control. On the other hand, it has also been pointed out that the aggregation bias appears not to be a robust feature in the data. Crucini and Shintani (2008) analyze a micro-panel of local currency prices of individual retail goods and services in major cities and find that the median level of persistence (across goods) is similar to that obtained for the aggregate RER (HL around 12-19 months).
The theoretical results recently presented in Mayoral (2008) help to clarify the contrasting empirical findings outlined above. She has studied the relations between measures of persistence computed at different aggregation levels and has shown that there is a tight link between them. In particular, in a linear setting similar to that consider in Imbs et al. (2005) and Crucini and Shintani (2008), it has been proven that the impulse response function (IRF) computed with aggregate data equals the average of the sectoral impulse responses. A similar relation holds for the scalar measures associated with the IRF, such as the cumulative impulse response (CIR). Gadea and Mayoral (2009) have used these results to show that, in fact, this relation between IRFs holds very closely for Imbs et al. (2005)’s dataset, implying that aggregate and average sectoral speeds of reversion to parity are very similar.
These theoretical results are the starting point of this paper. They imply that, since aggregate persistence -as measured by the IRF or the associated scalar tools- is completely determined by the behavior of the sectors, the aggregate HL or CIR can be estimated by using either aggregate or sectoral data. However, by using sectoral data, it will be possible to decompose aggregate persistence into the persistence of its different subcomponents, obtaining, thereby, a lot of valuable information about the sources of aggregate persistence. Another interesting implication of these results is that they unveil the nature of the relation between sectoral and aggregate persistence: the aggregate response to a shock is the average of the individual responses and, since averages are very non-robust measures, a situation where most sectors present quick reversion to parity but where a few of them are highly persistent, is compatible with a highly persistent aggregate RER.
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Aggregate real exchange rate persistence through the lens of sectoral data
