Appendix 1: Empirical evidence about exchange rates

(See Section 3 (a) (ii) Noisy Asset Values.)

There has been considerable concern within the economics profession about the high volatility of nominal exchange rates, the close relationship between real and nominal exchange rate changes, and the failure of macroeconomic models to perform better than a random walk model of the exchange rate. For example:

“Existing structural models have little in their favour beyond theoretical coherence. Positive results, when they are found, are often either fragile, or unconvincing in that they rely on implausible theoretical or empirical models. For these reasons, we, like much of the profession, are doubtful of the value of further time-series modelling of the exchange rate at high or medium frequencies using macroeconomic models.

…the Meese and Rogoff analysis at short horizons has never been convincingly overturned or explained. It continues to exert a pessimistic effect on the field of empirical exchange rate modelling in particular and international finance in general.”

(Frankel and Rose, 1995, pp1704-5)

In this appendix I briefly discuss three aspects of this literature.

(a) Meese and Rogoff (1983), and short term exchange rate forecasts.

Meese and Rogoff examined the forecasting performance of several different macroeconomic models, including explicitly structural models and time-series vector autoregressions. They compared the forecasting performance of these models with the forecasting performance of a simple random walk model over 1 month, 3 month, 6 month and 12 month horizons for the three major exchange rates. They also compared the random walk with the appropriate forward rates, thus implicitly comparing the forecast with that of uncovered interest parity. They summarise their findings as follows:

“We find that a random walk model would have predicted major-country exchange rates during the recent floating rate period as well as any of our candidate models. Significantly, the structural models fail to improve on the random walk model in spite of the fact that we base their forecasts on actual realise values of future explanatory variables.” Meese and Rogoff (1983 p3)

This result is clearly a severe set back to exchange rate models: quite simply, macroeconomic phenomena are hard-pressed to explain short term movements in exchange rates.

The short term failure is perhaps best seen in two firmly held “beliefs” of many economists: that purchasing power parity should hold, and that uncovered interest rate parity should hold. The former theory says that physical good arbitrage should result in prices in different countries being equal, up to differences in taxes and transactions costs. There is evidence that price levels in different countries eventually do converge, but the length of time this takes is extraordinarily slow - on average it takes four years for half of the difference in price levels to be eliminated (Rogoff 1996). The latter theory suggests that when interest rates are high in one country compared to another, the exchange rate should depreciate over time so that expected returns are equal. This relationship does not hold at short horizons either, with evidence suggesting that exchange rates appreciate rather than depreciate over short horizons. (Froot and Thaler 1990, Lewis 1995).

(b) Long Term Exchange Rate Movements and Macroeconomic Fundamentals.

Despite the poor relationship between macroeconomic fundamentals and the exchange rate in the short term, in the longer term there does seem to be a stronger link. Flood and Taylor (1996) present the results of the cross-sectional relationship between changes in prices and changes in the exchange rate relative to the US over time for 21 industrial countries, 1973 – 1992. They estimate the relationship when the change in each variable is calculated over 1 year (420 observations), 5 years (84 observations), 10 years (42 observations), and 20 years (21 observations). Scatter-plots of the data are reproduced below. As is clear from the scatter-plots, there is little apparent relationship at annual horizons and only a weak relationship at 5 year horizons; not until 10 and 20 year horizons is it apparent that exchange rates move to offset price movements. At short horizons, noise dominates signal.

The authors conduct a similar exercise examining the relationship between exchange rate movements and uncovered interest parity, using 3 year bond rates. Again they find that the fundamental relationship is much stronger over longer periods than shorter periods, that is currencies with high nominal interest rates tend to depreciate over time.

(c) Real Variable Volatility by Exchange Rate Regime.

It has long been realised - in fact it is almost definitional - that nominal exchange rate volatility is higher under flexible exchange rate regimes than fixed exchange rate regimes. What has been surprising in the post-Bretton Woods era is that nominal exchange rates have been so volatile, and that this volatility has passed through almost one for one to real exchange rate volatility[44]. Perhaps even more surprising is that there has been no systematic change in the volatility of any other real variables. Flexible exchange rates just seem to increase the volatility of real exchange rates.

Baxter and Stockman (1989) were amongst the first to document the lack of differences in real variable volatility between exchange rate regimes by comparing the volatility of real variables in the pre and post Bretton Wood’s era.

“We have been unable to find evidence that the cyclic behaviour of real macroeconomic aggregates depends systematically on the exchange-rate regime. The only exception is the well-known case of the real exchange rate. ….

We found that the volatility of exports, imports, and the real exchange rate increased in the post-1973 period for most of the countries in our sample. However, these increases were no more common in countries on a floating exchange rate regime after 1973 than in countries which chose to fix their exchange rate.” Baxter and Stockman (1989, p399)

They also compared the volatility of real variables in countries that changed their exchange rate regimes at other times, notably Canada in the 1950s and Ireland in 1979. Again, they found that the real exchange rate was the only variable that had a significant change in volatility.

Flood and Rose (1995) followed up this idea by modelling the exchange rate as follows

where e_t is the exchange rate and i_t and i_t^* are domestic and foreign interest rates. They compared the volatility of the left hand side and the volatility of the two terms on the right hand side across exchange rate regimes. When moving from fixed exchange rate regimes to flexible exchange rate regimes, the volatility of the left hand side increases by a much greater factor than the volatility of the function on the right; consequently they reject the idea that it is possible to express the exchange rate as a simple function of macroeconomic variables.[45] From this they concluded that the critical determinants of exchange rate volatility are not macroeconomic, because no macroeconomic variables have volatility dependent on the exchange rate regime.