Real exchange rates exhibit important low-frequency fluctuations. This makes the analysis of real exchange rates at all frequencies a more sound exercise than the typical business cycle one, which compares actual and simulated data after the Hodrick-Prescott filter is applied to both. A simple two-country, two-good model, as described in Heathcote and Perri (2002), can explain the volatility of the real exchange rate when all frequencies are studied. The puzzle is that the model generates too much persistence of the real exchange rate instead of too little, as the business cycle analysis asserts. Finally, we show that the introduction of adjustment costs in production and in portfolio holdings allows us to reconcile theory and this feature of the data.
This paper challenges the conventional wisdom that a baseline international real business cycle (IRBC) two-country, two-good model, such as the one described in Heath-cote and Perri (2002), cannot generate either enough volatility or enough persistence in the real exchange rate (RER) when compared to the data. When the object of interest is RER ‡uctuations at all frequencies, instead of business cycle (BC) frequencies only, this model can explain the standard deviation of the U.S. dollar RER. However, the model implies a higher persistence of the RER than in the data.
We advocate that analyzing RER ‡uctuations at all frequencies is a more compelling exercise than just studying the BC ones. Spectral analysis shows that most of the variance of the RER in the data can be assigned to low-frequency movements (about 70 percent), while movements at BC frequencies account for only a small share of the RER ‡uctuations (just 25 percent). The baseline IRBC model accounts for the area below the spectrum of the RER, i.e., its standard deviation, but not for its shape, since it places a larger share of ‡uctuations of the RER in low-frequency movements than in the data. We call this shortcoming of the model the “excess persistence of RER”puzle. We show that extending the model to consider adjustment costs in the composition of domestic and imported intermediate input and portfolio adjustment costs helps to solve this puzzle (i.e., replicating the shape of the spectrum) while still explaining the standard deviation of the RER (i.e., the area below the spectrum).
Since the seminal works of Backus, Kehoe, and Kydland (1992) and Baxter and Crucini (1995), the IRBC literature has been preoccupied with explaining the international transmission of shocks, the cyclical comovement of variables across countries, and the behavior of international relative prices. As in the real business cycle (RBC) literature, the IRBC literature mainly concentrates on explaining the BC ‡uctuations of the data. The success of the model is measured by its ability to reproduce selected second moments of Hodrick-Prescott (HP) …ltered data, which removes trends and low-frequency movements. Other papers use instead the band-pass …lter, as described in Baxter and King (1999) or Christiano and Fitzgerald (2003). The researcher compares the second moments of actual data with those implied by arti…cial data generated by the model after the same detrending procedure has been applied to both. One of the most relevant facts in the HP-…ltered data is that international relative prices are more volatile than output and highly persistent. IRBC models with reasonable calibrations have a hard time reproducing these features. In earlier work Backus, Kehoe and Kydland
(1994) and Stockman and Tesar (1995) showed that IRBC models cannot match the volatility of the HP-…ltered terms of trade, while, in a more recent contribution, Heath-cote and Perri (2002) have pointed out the standard IRBC model’s inability to explain the volatility and persistence of the HP-…ltered RER.
In this paper, we …rst argue that analyzing only the BC ‡uctuations of the RER leads researchers to miss a large part of the story. The reason is as follows. The top panel of Figure 1 plots the (log) U.S. dollar RER along with its implied HP-…ltered “trend” using a bandwidth of 1600. Just from eyeballing, it is evident that most of the ‡uctuations in the U.S. dollar RER have been low-frequency movements. This observation is con…rmed by the spectral analysis that we perform in Section II: most of the variation of the RER in the data is at frequencies lower than BC ‡uctuations (it is 70 percent for the U.S. dollar, and between 60 to 75 percent depending on the currency we examine). These low-frequency movements are removed by HP-…ltering.
Second, motivated by the argument above, we propose to analyze the ‡uctuations of the RER at all frequencies instead. Therefore, we need to consider a model able to generate low-frequency ‡uctuations in the RER. Our baseline model is an extension of the two country, two-good model of Heathcote and Perri (2002) in which stochastic processes for total factor productivity (TFP) are non-stationary but cointegrated across countries. We show that the model can explain about 80 percent of the standard deviation of the RER in the data while closely matching the volatility of output growth when we use a benchmark calibration of the model, including a value of 0:85
for the elasticity of substitution between intermediate inputs in the production of the …nal good. However, in the model, the RER is too persistent and the spectrum places too much weight on low-frequency ‡uctuations (in the model 85 percent of the variance is caused by low-frequency ‡uctuations while it is 70 percent in the data). In order to solve this shortcoming, we extend the model with adjustment costs in the use of intermediate imported inputs for the production of the …nal good (see Erceg, Guerrieri, and Gust, 2006). The presence of these costs allows us to combine a low short-run elasticity of substitution between imported and domestic intermediate goods, which is needed to increase the volatility of the RER at BC frequencies, with a higher long-run elasticity, which is needed to reduce the excessive volatility of the RER at low frequencies.
We show how these input adjustment costs, together with portfolio adjustment costs,help to solve the puzzle by increasing the impact response of the RER in the short run while reducing it at long-run horizons in the model.
The paper is organized as follows: Section II presents the spectral analysis of the U.S. dollar RER as well as that of other main currencies. Section III discusses the related literature, while Section IV presents a baseline IRBC model. Section V presents the calibration and the results of the baseline model. In Section VI, we present the extensions to the model and show how they help reconcile theory and evidence. Section VII concludes.
IMF.Author/Editor: Rabanal,Pau;Rubio-Ramirez, Juan F.Series: Working Paper No. 12/13
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