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What is the effect of nominal exchange rate variability on trade? I argue that the methods conventionally used to answer this perennial question are plagued by a variety of sources of systematic bias. I propose a novel approach that simultaneously addresses all of these biases, and present new estimates from a broad sample of countries from 1970 to 1997. The estimates indicate that nominal exchange rate variability has no significant impact on trade flows.

Major changes are reshaping the international monetary system. The Communist Party in China is considering the idea of floating the Chinese yuan and so are several Asian governments.1 In the same direction, although prompted by the drastic collapse of its currency board, Argentina has moved towards a (managed) float. On the other extreme, and after the recent institution of the euro, many countries in Eastern Europe are joining while others are expected to join the euro area. El Salvador and Guatemala have reinforced their peg to the dollar, and Ecuador has dollarized its economy. These recent developments have reinvigorated the policy debate over the pros and cons of different exchange rate systems. One of the issues in the debate is the trade effect of nominal exchange rate variability.2 Proponents of fixed exchange rates have long argued that the risks associated with exchange rate variability discourage economic agents from trading across borders. Opponents have maintained that there are good instruments to hedge against this type of nominal volatility, and hence this effect should be immaterial. The question of the magnitude of the trade effect of exchange rate variability is an empirical one, and the subject of this investigation.3 The economics literature has provided at best mixed results. Most early studies, including Abrahms (1980) and Thursby and Thursby (1987), document a large negative effect of nominal variability on trade.4 Studies from the 1990s, including Frankel and Wei (1993), Eichengreen and Irwin (1996), and Frankel (1997) report negative, albeit quantitatively small effects.5 More recent studies on the effect of currency unions and unilateral dollarizations on trade, however, document large effects. (See, for example, Rose, 2000, Engel and Rose, 2000, Frankel and Rose, 2002, Alesina et al., 2002 and Tenreyro and Barro, 2002). Frankel and Rose (2002) extend the analysis to currency boards, also finding significantly large effects. It could be argued that currency unions involve more than the mere elimination of exchange rate variability, although the case is less clear for currency boards. Furthermore, some critics have contended that countries that have historically been part of a currency union are too small and too poor to make generalizations about the effect of currency unions (boards) in larger countries. These interpretations and criticisms reinforce the need for a second look at the data that is not limited to this extreme type of exchange rate regime. This paper argues that there are several estimation problems in previous studies of the impact of nominal variability (and more generally, of exchange rate regimes) on trade that cast doubt on previous answers. These studies have typically been framed in the context of the “gravity equation” model for trade.6 In its simplest form, the empirical gravity equation states that exports from country i to country j, denoted by Tij, are proportional to the product of the two countries' GDPs, denoted by Yi and Yj, and inversely proportional to their distance, Dij, broadly construed to include all factors that might create trade resistance. Importer and exporter specific effects, sj and si, are added to account for multilateral resistance.7 The gravity equation is then augmented to account for the resistance, α4, created by exchange rate variability, δij, with δij ≥ 0, that is: equation(1) View the MathML sourceTi⁢j=α0·Yiα1·Yjα2·Di⁢jα3·exp(α4si+α5sj+α6δi⁢j)·εi⁢j, Turn MathJax on where εij is an error term, typically assumed to be statistically independent of the regressors, with E(εij|Yi, Yj, Dij, δij, si, sj) = 1, and the α's are parameters to be estimated. The standard practice consists of log-linearizing Eq. (1) and estimating the parameters of interest, in particular α4, by ordinary least squares (OLS) using the equation equation(2) ln(Ti⁢j)=ln(α0)+α1ln(Yi)+α2ln(Yj)+α3ln(Di⁢j)+α4si+α5sj+α4δi⁢j+ln(εi⁢j).ln(Ti⁢j)=ln(α0)+α1ln(Yi)+α2ln(Yj)+α3ln(Di⁢j)+α4si+α5sj+α4δi⁢j+ln(εi⁢j). There are at least four problems with this procedure. First, it is very unlikely that the variance of εij in (1) will be independent of the countries' GDPs and of the various measures of distance. In other words, the error term εij is generally heteroskedastic. Since the expected value of the logarithm of a random variable depends both on its mean and on higher order moments of its distribution, whenever the variance of the error term εij in Eq. (1) depends on the regressors, the expected value of ln(εij) will also depend on the regressors, violating the condition for consistency of OLS. This is simply the result of Jensen's inequality: E(ln ε) ≠ ln E(ε), and E(ln ε) depends on the whole distribution of ε. In particular, if ε is log-normal, E(ln ε) is a function of the mean and variance of ε. Santos Silva and Tenreyro (in press) find this to be a serious source of bias in practical applications of the gravity equation. Second, pairs of countries for which bilateral exports are zero have to be dropped out of the sample, as a result of the logarithmic transformation. In a typical data set, this leads to the loss of over 30% of the data points. This massive sample selection can cause additional biases in the estimation. Third, with a few exceptions, previous studies assume that exchange rate variability is exogenous to the level of trade. Standard endogeneity problems, however, are likely to confound the estimates. For example, two countries willing to increase their bilateral trade through lower exchange rate volatility might undertake additional steps to foster integration (such as lowering regulatory barriers, harmonizing standards of production, and so on). To the extent that these steps cannot be measured in the data, simple OLS estimates will tend to produce a bias. Fourth, there is significant measurement error in official statistics on nominal exchange rates, and hence in the corresponding measures of variability.8 In this paper, I argue that partial corrections of the different biases can lead to misleading answers, and that all biases should be tackled simultaneously. I hence propose an approach to estimation that simultaneously addresses all of these problems. In a nutshell, my approach deals with the problems generated by heteroskedsasticity and zero-trade observations by estimating the trade-volatility relation in levels, instead of logarithms, as is usually done. More specifically, I use a pseudo-maximum likelihood (PML) technique whose efficiency and robustness in the context of gravity equations has been established by Santos Silva and Tenreyro (in press). To deal with the endogeneity and the measurement error of exchange rate variability I then develop an instrumental-variable (IV) version of the PML estimator. The idea behind the IV is as follows. For a variety of reasons (which I review below) many countries find it useful to peg their currency to that of a large, and stable “anchor” country (e.g., the US, France). Two countries that have chosen to peg to the same anchor will therefore experience low bilateral exchange rate variability. I turn this observation into an identification strategy by first estimating the probability that two countries are pegged to the same anchor, and then using this probability as an instrument for their bilateral exchange rate volatility. Crucially, I estimate this “propensity to share a common anchor” by using exclusively information on the relationship between the anchor country and each individual “client” country, so that my instrument only captures reasons for pegging to the anchor country other than the desire to increase bilateral trade among the two clients. In Section 3.2 I elaborate further on this point. Using a broad sample of countries from 1970 to 1997, and after accounting for all sources of bias, the analysis leads to the conclusion that exchange rate variability has no significant impact on trade. The absence of any significant effect goes against the view that stabilization of exchange rates is necessary to foster international trade. As later explained, this result can be rationalized by the fact that exchange rate fluctuations not only create uncertainty or risks, which tend to discourage trade across borders, but they also create profitable opportunities. This finding might also suggest that the availability of forward contracts, currency options, and other alternatives for risk diversification provide sufficient hedging to reduce the potential drawbacks of exchange rate variability on trade. The absence of a significant effect is also consistent with the model proposed by Bacchetta and van Wincoop (2001), who show that in a general equilibrium context, exchange rate stability may have no impact on trade. The remainder of the paper is organized as follows. Section 2 discusses in further detail the problems raised by log-linearization in the presence of heterogeneity, the exclusion of zeroes, and the endogeneity of the regressors. It then presents the PML-IV method to address the various econometric problems. Section 3 studies the effect of exchange rate variability on trade, using different methodologies. Section 4 contains concluding remarks

Does exchange rate variability harm trade? This paper takes a long road to say “no.” However, the long road is not futile: in the quest for an answer, the process uncovers the problems associated with the techniques typically used in empirical applications of the gravity equation. Moreover, the methodological points raised in the paper and the proposed solution can be extended to other contexts where log-linearizations (or, more generally, non-linear transformations) coupled with heteroskedasticity and/or endogeneity threaten the consistency of simple estimators. Examples include production functions and Mincerian regressions for earnings. I argue that all potential sources of bias should be tackled simultaneously and that partial corrections can be highly misleading. I hence develop an IV PPML approach that addresses the various potential biases highlighted in this paper. The instrument I use relies on the fact that many countries find it useful to peg their currency to that of a large, and stable “anchor” country in order to reduce inflation. Hence, two countries that have chosen to peg officially or de facto to the same anchor will tend to experience low bilateral exchange rate variability. This observation motivates the use of the probability that two countries peg their currencies to the same anchor as an instrument for their bilateral exchange rate volatility. Importantly, the propensity to share a common anchor-currency uses information on the relationship between the anchor country and each individual client country so that my instrument only captures reasons for pegging to the anchor country other than the desire to increase bilateral trade between any two clients. The results show that the probability that a client-country pegs its currency to one of the main anchors increases when the client is closer to the anchor, and when they share a common colonial past. Also, the propensity to anchor the currency increases with the size of the anchor and the difference in size between the anchor and the potential client. The paper contributes to the international policy debate by showing that exchange rate variability does not harm export flows. The elimination of exchange rate variability alone, hence, should not be expected to create any significant gain in trade in the aftermath of the recent waves towards stronger pegs.