نوسانات نرمال نرخ ارز، نوسانات قیمت نسبی کلان، و نرخ ارز واقعی

We model real exchange rate, nominal exchange rate, and relative price volatility using real and nominal factors. We analyze these volatility measures across developing and industrialized countries. We find that the inclusion of nominal factors achieves a sizable reduction in the real exchange rate volatility spread between developing and industrialized countries. In addition, we find that nominal factors matter to real exchange rate volatility in the short run and the long run, and that for developing countries, a higher share of real exchange rate volatility stems from relative price volatility.

It has been thirteen years since Rogoff (1996) raised two important pieces of a puzzle for research in purchasing power parity: (1) slow convergence of deviations from purchasing power parity; and (2) short run deviations from purchasing power parity that are large and volatile. The pieces of the puzzle pose a contradiction – slow convergence implies that real factors like tastes and technology are responsible for the deviations and the slow pace of convergence, yet real factors, because they are slow to change, cannot explain short-run volatility which would be better explained by nominal (monetary) shocks. While much work has been directed at the first piece of the puzzle, the second piece of the puzzle is arguably more important to understand than the first because of its implications for trade, investment, and economic growth. Yet, real exchange rate volatility has received sporadic attention, at best.1 This is our focus. We build on the work of Hausmann et al. (2006) who find the volatility of real exchange rates of developing countries is 2.5 times higher than for industrialized countries, even when controlling for real shocks. Like their model, our model includes real factors but, we also include domestic and external monetary and financial factors and government and trade balances. Using our model, we also explore nominal exchange rate and relative price volatility. Theoretical models of sticky-prices and asset markets dating back to Dornbusch (1976) explicitly address nominal exchange rate and relative price behavior. These models impute behavior to the real exchange rate in the short run and the long run owing to differences in the speed of adjustment between nominal exchange rates and relative prices. So, it seems useful to decompose real exchange rate volatility into its separate components. The Mundell–Fleming model with sticky prices also provides a link between nominal exchange rates and real exchange rates. By investigating the components of real exchange rate volatility separately, we distinguish our work from many others. Engel and Morley, 2001, Mark and Sul, 2001 and Ng, 2003, and Cheung et al. (2004) – who study the components of the real exchange rate – are exceptions. We also conduct a simple variance decomposition of the real exchange, after controlling for real and nominal factors. The decomposition of the residual variance allows us to calculate the contributions of unexplained nominal exchange rate volatility, unexplained relative price volatility, and their covariance to the residual portion of real exchange rate volatility. Our analysis produces several noteworthy results. Three main findings emerge. With the inclusion of nominal factors, our model substantially reduces the real exchange rate volatility spread between developing and developed countries and helps explain Hausmann et al.'s (2006) finding. We also find evidence that nominal factors matter in both the short and long run. Nominal factors can have long-lived (at 5 years) effects on the volatility of the real exchange rate. This finding is consistent with the range of half-life estimates reported for real exchange rate mean reversion. We also find that for developing countries, a much larger share of real exchange rate volatility stems from relative price volatility than for industrialized countries. The finding persists in both the short run and the long run. We conjecture that institutional differences, particularly with respect to central banks and national treasuries may be responsible.

The aim of this paper was to take a closer look at two empirical puzzles – high real exchange rate volatility noted by Rogoff (1996) and real exchange rate volatility that is higher in developing than industrialized countries, even when controlling for factors that might explain the difference. We explore these puzzles in two ways. First, we expand the set of factors theorized to be important to real exchange rates to include a broad set of nominal factors. Second, leaning on the overshooting exchange rate model, we treat the real exchange rate as a composite of the nominal exchange rate and relative price and investigate their separate contributions to real exchange rate volatility in the short run and the long run. We view this as a major contribution of our work. We started by examining the unconditional volatilities of the real and nominal exchange rates and the relative price. We found that while nominal and real exchange rates exhibit similar (and high) volatility in industrialized countries, the same was not true of developing countries. In developing countries, nominal exchange rate volatility was about 1.5–2 times higher than real exchange volatility. We also found that relative prices in both developing and industrialized countries are less volatile than nominal exchange rates. We then attempted to explain the differences in unconditional volatilities by specifying equations for the real exchange rate, the nominal exchange rate, and relative prices. For purposes of residual variance decomposition, these equations were identically specified. This afforded a straightforward variance decomposition which highlighted the contributions of residual nominal exchange rate and relative price variance to residual real exchange rate volatility. While the residual variance decomposition is straightforward, we view it as novel and a minor contribution of our work. We specified six models, beginning with a base model that excluded nominal factors. Then, we sequentially introduced three sets of nominal factors. Our analysis showed that the puzzle reported in Hausmann et al. (2006) is substantially reduced, but not eliminated, with the inclusion of nominal factors, particularly M2 and interest rate changes. Our focus then turned to the residual volatilities from these equations and a decomposition of the residual variance of the real exchange rate. We showed that even after controlling for real and nominal factors and country characteristics, nominal exchange rate volatility contributes substantially to real exchange rate volatility in the short run and the long run for both developing and industrialized countries. But, we find that real exchange rate volatility differences between the two country groups are likely driven by differences in relative price dynamics. We argue that relative price dynamics require further study. We also documented a negative covariance between the residual nominal exchange rates and relative prices for developing and industrialized countries in the short run and the long run. The negative covariance is important in the sense that it is able to offset volatility in the real exchange rate. One weakness of our study is that regressions for the nominal exchange rate and relative price included the same control variables as for the real exchange rate. Our future work will attempt to redress this problem by entertaining specifications more directly related to research on nominal exchange rate and relative price behavior.