Openness and Real Exchange Rate Volatility: In Search of an Explanation

Abstract

The puzzle that real exchange rates are less volatile in open economies is an important challenge to exchange rate theory. Adjustment of domestic prices to nominal exchange rate movements can account for only a small proportion of this effect. Real and nominal shocks display no obvious correlation with openness. It is shown here that real effective exchange rates are more strongly mean-reverting in more open economies, even after controlling for exchange rate regime effects. This is predicted by the theory of current account sustainability, because of its emphasis on ratios to GDP rather than to trade flows.

Appendix

1.1 A theoretical model

In this Appendix, we explore the idea that volatility is related to the strength of signals of misalignment at a given deviation from equilibrium, based on the model of Frankel and Froot (1986a, b).

In Frankel and Froot’s model, the foreign exchange market is populated by “fundamentalists” and “chartists”, who supply exchange-rate forecasts to portfolio managers (see Jeanne and Rose 2002, and Kubelec 2004, for similar models). The log of the exchange rate (foreign currency units per unit of domestic currency) at time t is denoted s _t. Portfolio managers are the only agents active in the foreign exchange market, and generate their own forecasts as a weighted average of the two groups of forecasters. Chartists believe that exchange rates are non-stationary and use some ARIMA (p, 1, q) model to generate forecasts. Fundamentalists believe that exchange rates will revert to equilibrium at some predetermined rate, but it is realistic to assume that they are not certain what the equilibrium is, since even estimates by economists have quite wide confidence intervals (Bénassy-Quéré et al. 2004; Wren-Lewis and Driver 1998). Suppose that fundamentalist j believes at time t that the equilibrium is $\overline{s} _{{jt}} ,$ and let the mean of these beliefs across all fundamentalists be $\overline{s} _{t}$ (it is at this point that the model diverges from that of Frankel and Froot (1986a, b), who assume that $\overline{s}$ is known but that w varies according to the past forecasting performance of the two groups). The log of the exchange rate as forecast at time t by the chartists, fundamentalists and portfolio managers are respectively $s^{c}_{{t + 1}} ,$ $s^{f}_{{t + 1}}$ and $s^{m}_{{t + 1}} .$ Then we have

$$ s^{m}_{{t + 1}} = ws^{f}_{{t + 1}} + {\left( {1 - w} \right)}s^{c}_{{t + 1}} $$

(2)

$$ s^{f}_{{t + 1}} = s_{t} + \mu {\int\limits_{j = 0}^1 {{\left( {\overline{s} _{{jt}} - s_{t} } \right)}} }\,dj = \mu \overline{s} _{t} + {\left( {1 - \mu } \right)}s_{t} $$

(3)

Equation 2 expresses portfolio managers’ forecasts as a weighted average of those of fundamentalists and chartists, and Eq. 3 represents fundamentalists’ average forecast as a constant rate of mean reversion to the average of their beliefs about the equilibrium rate. As in Frankel and Froot (1986a) and Engel and West (2005), the actual exchange rate is determined in a generic way consistent with a wide range of models, as the sum of the fundamentals (z) and a term based on the expected level of the exchange rate:

$$ s_{t} = as^{m}_{{t + 1}} + z_{t} $$

(4)

Substituting from Eqs. 2 and 3 and rearranging yields:

$$ s_{t} = \frac{{a{\left( {1 - w} \right)}s^{c}_{{t + 1}} + aw\mu \overline{s} _{t} + z_{t} }} {{1 - aw{\left( {1 - \mu } \right)}}} $$

(5)

Equation 5 says that the exchange rate is a linear combination of (a) the fundamentals, (b) chartists’ forecasts, and (c) fundamentalists’ beliefs about the equilibrium. Note that, if fundamentalists believe the rate of mean-reversion to be faster (μ is larger), the exchange rate will be closer to its equilibrium value.

If we assume that chartists’ forecasts are uncorrelated with the fundamentals or with fundamentalists’ estimates of the equilibrium, then

$$ \operatorname{var} {\left( s \right)} = \frac{{{\left( {a{\left( {1 - w} \right)}} \right)}^{2} \operatorname{var} {\left( {s^{c} } \right)} + {\left( {aw\mu } \right)}^{2} \operatorname{var} {\left( {\overline{s} } \right)} + 2aw\mu \operatorname{cov} {\left( {\overline{s} ,z} \right)} + \operatorname{var} {\left( z \right)}}} {{{\left( {1 - aw{\left( {1 - \mu } \right)}} \right)}^{2} }} $$

(6)

Both the numerator and the denominator of Eq. 6 are increasing in μ. Because chartists’ forecasts are not tied down by the fundamentals, it is likely that var${\left( {\overline{s} } \right)}$ and var(z) are small compared with var(s ^c). In that case, provided that w is not too close to one (i.e. chartists matter), var(s) will be decreasing in μ. In other words if fundamentalists believe that mean-reversion is stronger, the real exchange rate will be less volatile.