# Nominal exchange rate volatility, relative price volatility, and the real exchange rate

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JEL codes:F3F4

to change, cannot explain short-run volatility which would be better explained by nominal (monetary)shocks.

While much work has been directed at the rst piece of the puzzle, the second piece of thepuzzle is arguably more important to understand than the rst because of its implications fortrade, investment, and economic growth. Yet, real exchange rate volatility has received sporadic

* Corresponding author. Tel.: 1 803 777 7419; fax: 1 803 777 6876.E-mail address: boucher@moore.sc.edu (J.B. Breuer).

Contents lists available at ScienceDirect

Journal of International Moneyand Finance

Journal of International Money and Finance 29 (2010) 8408561. Introduction

It has been thirteen years since Rogoff (1996) raised two important pieces of a puzzle for research inpurchasing 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 puzzlepose a contradiction slow convergence implies that real factors like tastes and technology areresponsible for the deviations and the slow pace of convergence, yet real factors, because they are slowKeywords:Real exchange rateNominal exchange rateVolatilityVariance0261-5606/$ see front matter 2009 Elsevier Ltdoi:10.1016/j.jimonn.2009.11.002We model real exchange rate, nominal exchange rate, and relativeprice volatility using real and nominal factors. We analyze thesevolatility measures across developing and industrialized countries.We nd that the inclusion of nominal factors achieves a sizablereduction in the real exchange rate volatility spread betweendeveloping and industrialized countries. In addition, we nd thatnominal factors matter to real exchange rate volatility in the shortrun and the long run, and that for developing countries, a highershare of real exchange rate volatility stems from relative pricevolatility.

2009 Elsevier Ltd. All rights reserved.a b s t r a c tNominal exchange rate volatility, relative price volatility,and the real exchange rate

Srideep Ganguly, Janice Boucher Breuer*

Department of Economics, University of South Carolina, Columbia, SC 29208, USA

journal homepage: www.elsevier .com/locate/ j imfd. All rights reserved.

attention, at best.1 This is our focus. We build on the work of Hausmann et al. (2006) who nd thevolatility of real exchange rates of developing countries is 2.5 times higher than for industrializedcountries, even when controlling for real shocks. Like their model, our model includes real factorsbut, we also include domestic and external monetary and nancial factors and government and

S. Ganguly, J.B. Breuer / Journal of International Money and Finance 29 (2010) 840856 841trade 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 nominalexchange rate and relative price behavior. These models impute behavior to the real exchange rate inthe short run and the long run owing to differences in the speed of adjustment between nominalexchange rates and relative prices. So, it seems useful to decompose real exchange rate volatility into itsseparate components. The MundellFleming model with sticky prices also provides a link betweennominal exchange rates and real exchange rates. By investigating the components of real exchange ratevolatility separately, we distinguish our work from many others. Engel and Morley (2001), Mark andSul (2001), 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 andnominal factors. The decomposition of the residual variance allows us to calculate the contributions ofunexplained nominal exchange rate volatility, unexplained relative price volatility, and their covari-ance to the residual portion of real exchange rate volatility.

Our analysis produces several noteworthy results. Three main ndings emerge. With the inclusionof nominal factors, our model substantially reduces the real exchange rate volatility spread betweendeveloping and developed countries and helps explain Hausmann et al.s (2006) nding. We also ndevidence 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 nding is consistent with therange of half-life estimates reported for real exchange rate mean reversion. We also nd that fordeveloping countries, a much larger share of real exchange rate volatility stems from relative pricevolatility than for industrialized countries. The nding persists in both the short run and the long run.We conjecture that institutional differences, particularly with respect to central banks and nationaltreasuries may be responsible.

2. Data and unconditional volatilities

The real exchange rate by denition consists of two components, namely the nominal exchange rateand the relative price differential as expressed in Eq. (1):

r s p (1)

where r is the log real exchange rate expressed as units of domestic goods per unit of foreign goods, s isthe log nominal exchange rate expressed as domestic currency per unit foreign currency, and p is thelog of the price of a foreign basket of goods divided by the price of a domestic basket of goods. In whatfollows, we exploit Eq. (1) to explore the inuence of nominal exchange rate volatility and relative pricevolatility on real exchange rate volatility.

2.1. Data

We collect data on real effective exchange rates for fty countries for the period 19802000.This is the same sample period studied by Hausmann et al. (2006) to which we compare several ofour results. There are 22 industrialized countries in the data set and 28 developing countries.2 We

1 Contributions include Edwards (1987), Cote (1994), Hausmann and Gavin (1996), McKenzie (1999), Hau (2000, 2002), Clark,Tamirisa, and Wei (2004), and Hausmann et al. (2006).

2 Since some of the nominal effective exchange rates are calculated using unit labor costs, we are constrained to selecting

a set of countries for which unit labor cost data is available.

also collect data on nominal effective exchange rates.3 From data on real and nominal effectiveexchange rates, we back out data on effective relative consumer price indices (or unit labor costs,depending on the IFS computation for real effective exchange rates).4 Appendix A provides thedetails.

We use effective exchange rates, rather than bilateral rates as effective exchange rates measure

developing countries than industrialized countries in the short run and about 3 times higher in the

S. Ganguly, J.B. Breuer / Journal of International Money and Finance 29 (2010) 840856842long run.A comparison of unconditional real and nominal exchange rate volatilities across column one of

Tables 1 and 2 show that they are about equal for industrialized countries in the short run but not fordeveloping countries. In the short run, the real exchange rate volatility of industrialized countries is0.052 and nominal volatility is 0.055. For developing countries, it is 0.121 versus 0.182. This empiricalobservation contrasts with the heuristic that nominal and real exchange rate volatilities should benearly the same in the short run, owing to price stickiness. This result re-emerges when we considerresidual volatilities.

3 Zanello and Desruelle (1997) provide a detailed explanation and critique of how effective exchange rates are constructed.4 For 18 of the industrialized countries, the trade-weighted (or effective) relative price index is calculated using unit labor

costs (ULC). The remainder of the relative price indices is based on CPI calculations. McDermott (1996) show that real effectiveexchange rates based on unit labor costs are highly correlated with those computed using consumer price indices. It is possible,the international competitiveness of a country against all its trade partners. The use of an effectiveexchange rate helps to avoid potential biases which may be associated with the choice of basecountry in bilateral real exchange rate analysis (Kent and Naja, 1998; Cashin and McDermott,2004). The exchange rate series are measured such that an increase in the real or nominalexchange rate of country j implies a depreciation of country js currency relative to a trade-weighted currency. The relative price index is measured such that an increase in it implies anincrease in the price index of country js trading partners relative to country js price index. (SeeAppendix A for details).

2.2. Short run and long run unconditional volatilities

We start with the simplest possible measure of volatility: the standard deviation of the n-periodgrowth rate of a series, represented by the following equation:

Volatilityj var

xj;t xj;tn

nq

(2)

where xj,t is the log real effective exchange rate, the log nominal effective exchange rate, or the logrelative price for country j, and where n 1 for 1-year volatility measures and n 5 for 5-yearvolatility measures. The 1-year volatility measures represent the short run and the 5-year measuresthe long run.

As a starting point, we report unconditional 1-year and 5-year real exchange rate volatilities aver-aged over the sample period and averaged across developing countries, industrialized countries, andfor the combined set of countries in the rst column of Table 1.

The difference in volatilities for developing and industrialized countries as well as their ratio is alsoreported. The ratio shows that the real exchange rates of developing countries are about 2.2 timesmorevolatile than industrialized countries. The p-values show that the difference is statistically signicant atthe 1-year and 5-year horizons.

Next, we report measures of the unconditional volatilities of the nominal effective exchange rateand relative prices. These are reported in column one of Tables 2 and 3. In Table 2, the entries revealthat the nominal exchange rate of developing countries is about 3.5 times the volatility of industri-alized countries in the short run and the long run, and that this difference is signicant at the 5% level.In Table 3, it can be seen that developing country relative price volatilities are 4 times higher inhowever, that over longer time periods for rapidly growing economies, wage costs will increase at a faster pace than CPIs.

Table 1Unconditional and residual real exchange rate volatilities.

One-year residual volatilitiesOne-yearunconditionalvolatility

Model 1Base Model

Model 2Model 1domestic monetaryshocks

Model 3Model 1govt and tradebalance shocks

Model 4Model 1nancial sector shocks

Model 5Model 2 govtand trade balance shocks

Model 6Model 5nancial sector shocks

Combined 0.092 0.083 0.072 0.082 0.079 0.073 0.070Developing 0.121 0.105 0.088 0.105 0.101 0.088 0.086Industrialized 0.055 0.055 0.052 0.052 0.057 0.053 0.053Difference 0.066 0.050 0.036 0.053 0.044 0.039 0.033Ratio 2.218 1.904 1.707 2.036 1.778 1.682 1.621t-Statistic 4.345 3.700 3.58 3.380 3.290 2.15 1.93P-value 0.000 0.001 0.018 0.001 0.002 0.037 0.06

Five-year residual volatilitiesOne-yearunconditionalvolatility

Model 1base model

Model 2Model 1domestic monetaryshocks

Model 3Model 1govt and tradebalance shocks

Model 4Model 1nancial sector shocks

Model 5Model 2 govtand trade balance shocks

Model 6Model 5nancial sector shocks

Combined 0.095 0.083 0.063 0.07 0.071 0.060 0.058Developing 0.127 0.110 0.077 0.087 0.090 0.071 0.068Industrialized 0.068 0.050 0.044 0.047 0.052 0.045 0.047Difference 0.059 0.060 0.032 0.040 0.038 0.025 0.021Ratio 1.88 2.194 1.718 1.848 1.720 1.564 1.452t-Statistic 3.23 3.760 3.22 3.160 3.440 2.32 2.06P-value 0.001 0.001 0.002 0.003 0.001 0.025 0.046

Note: Unconditional volatilities are measured as the standard deviation of the growth rate in the real exchange rate, nominal exchange rate, or relative price ratio. See Eq. (2). The residualvolatilities are calculated as the 1- or 5-year standard deviation from the residuals obtained from specications of Eq. (3).

S.Ganguly,J.B.Breuer

/Journal

ofInternational

Money

andFinance

29(2010)

840856843

Table 2Unconditional and residual nominal exchange rate volatilities.

One-year residual volatilitiesOne-yearunconditionalvolatility

Model 1base model

Model 2Model 1domestic monetary shocks

Model 3Model 1 govtand trade balance shocks

Model 4Model 1nancial sector shocks

Model 5Model 2 govtand trade balance shocks

Model 6Model 5nancial sector shocks

Combined 0.128 0.105 0.085 0.104 0.105 0.085 0.085Developing 0.182 0.143 0.110 0.144 0.145 0.108 0.112Industrialized 0.052 0.059 0.053 0.053 0.064 0.054 0.055Difference 0.129 0.084 0.056 0.091 0.081 0.054 0.057Ratio 3.47 2.443 2.057 2.699 2.269 2.005 2.05t-statistic 3.228 4.380 3.39 4.500 4.360 2.83 3.07P-value 0.001 0.000 0.001 0.000 0.000 0.006 0.003

Five-year residual volatilitiesOne-yearunconditionalvolatility

Model 1base Model

Model 2Model 1domestic monetary shocks

Model 3Model 1 govtand trade balance shocks

Model 4Model 1nancial sector shocks

Model 5Model 2 govtand trade balance shocks

Model 6Model 5nancial sector shocks

Combined 0.162 0.111 0.076 0.87 0.102 0.070 0.072Developing 0.236 0.151 0.098 0.115 0.136 0.085 0.088Industrialized 0.067 0.061 0.048 0.052 0.070 0.048 0.055Difference 0.168 0.090 0.049 0.063 0.066 0.037 0.032Ratio 3.48 2.486 2.024 2.194 1.936 1.757 1.590t-Statistic 2.719 4.350 4.28 3.480 3.140 2.84 2.69P-value 0.002 0.072 0.0001 0.062 0.070 0.006 0.01

Note: Unconditional volatilities are measured as the standard deviation of the growth rate in the real exchange rate, nominal exchange rate, or relative price ratio. See Eq. (2). The residualvolatilities are calculated as the 1- or 5-year standard deviation from the residuals obtained from specications of Eq. (4).

S.Ganguly,J.B.Breuer

/Journal

ofInternational

Money

andFinance

29(2010)

840856844

Table 3Unconditional and residual relative price level volatilities.

One-year residual volatilitiesOne-yearunconditionalvolatility

Model 1Base model

Model 2 Model 1domestic monetary shocks

Model 3Model 1 govtand trade balance shocks

Model 4Model 1nancial sector shocks

Model 5Model 2 govtand trade balance shocks

Model 6Model 5nancial sector shocks

Combined 0.089 0.076 0.053 0.075 0.079 0.052 0.053Developing 0.134 0.109 0.074 0.107 0.118 0.071 0.078Industrialized 0.032 0.037 0.025 0.036 0.041 0.026 0.026Difference 0.101 0.072 0.048 0.071 0.077 0.044 0.051Ratio 4.14 2.924 2.889 2.975 2.872 2.684 2.912t-Statistic 2.58 3.980 4.9 4.220 4.070 4.13 4.78P-value 0.001 0.000 0.0001 0.000 0.000 0.0001 0.0001

Five-year residual volatilitiesOne-yearunconditionalvolatility

Model 1Base model

Model 2Model 1domestic monetary shocks

Model 3Model 1 govtand trade balance shocks

Model 4Model 1nancial sector shocks

Model 5Model 2 govtand trade balance shocks

Model 6Model 5nancial sector shocks

Combined 0.149 0.093 0.055 0.069 0.86 0.049 0.051Developing 0.207 0.1...

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