RDP 9811: Effective Real Exchange Rates and Irrelevant Nominal Exchange-Rate Regimes 2. Re-examining Existing Evidence

In this section of the paper we show that the results of previous studies are driven partly by their reliance on bilateral RERs. We focus on Mussa's seminal paper by reproducing his results, using his sample of countries and his nominal exchange rate classification scheme, looking first at bilateral RERs and then at effective RERs.

We tested the hypothesis of no difference in the variance of monthly percentage changes in the RER across different nominal exchange-rate regimes using F-tests. To do this we used two different methods. First, we assumed that for a given exchange-rate regime, observations of monthly changes in the RER across all countries were the result of independent draws from the same distribution. This assumption allowed observations of RER changes from a given regime to be pooled across countries. In this way the relative variance of changes in the RER could be compared across regimes. In addition to providing a convenient summary measure of the variance of the RER within each regime, this method was advantageous because it allowed us to include observations from countries that had experienced only one regime in the sample period. The disadvantage of this pooling method was that the assumption of a single distribution may be incorrect for countries which might have very different ‘underlying’ characteristics (and it may be impossible to control for these differences).

For the second method, observations of RER changes were assumed to be drawn from distributions which varied across countries. This justifies separate within-country comparisons of the variance of monthly changes in the RER across different regimes.

Mussa (1986) analysed the behaviour of bilateral RERs (versus the US dollar) of 15 industrialised countries. The Bretton Woods era was used to identify the fixed exchange-rate regime. He described the post-Bretton Woods period as being a floating exchange-rate regime for these industrialised countries. His main result was that the variance of the quarterly changes in the bilateral RERs was on average almost 14 times higher under the floating exchange-rate regime than under the fixed exchange-rate regimes. We replicated Mussa's results using the two methodologies described above for monthly bilateral RERs.[9] The left panel of Figure 2 illustrates the pooled variance of changes in the bilateral RER for each regime.[10] The variance of bilateral RER changes was a lot higher post-Bretton Woods than during Bretton Woods; the ratio of the pooled variances was 12 to 1.[11] This difference was significant at the 5 per cent level.

Figure 2: Variance of Monthly RER Changes
Mussa's sample of industrialised countries
Figure 2: Variance of Monthly RER Changes

Notes: The bilateral RER was based on the US dollar and the CPI. The effective RER variance estimates included the United States and placed Austria in the Bretton Woods (that is, fixed exchange rate) regime for the full sample; likewise for Ireland until December 1978.

We also conducted F-tests on the ratio of the variances of bilateral RER changes across nominal exchange-rate regimes within each country. All of these tests (not reported here) conclusively indicated a higher variance under floating exchange rates than fixed exchange rates for every country in the sample. Therefore, the within country results support the results of the pooled analysis, namely, that bilateral RERs displayed systematically higher short-term volatility post-Bretton Woods compared with during Bretton Woods.

The pooled and within-country tests were repeated on this set of countries using effective RERs. The issue of the classification of the nominal exchange-rate regimes was more difficult in the case of effective RERs than in the case of bilateral RERs. For instance, the Austrian schilling was fixed against the US dollar under Bretton Woods and then floating against the US dollar post-Bretton Woods. This is a natural way of classifying the nominal exchange-rate regime for the purpose of examining the behaviour of the Austrian bilateral RER (relative to the US). However, when analysing the Austrian effective RER, it is natural to classify the nominal exchange-rate regime as fixed both during and after Bretton Woods – that is, fixed first against the US dollar and later fixed against the Deutsche Mark.

Mussa accounted for these problems by considering more than one bilateral RER for a given country. In contrast, we classified countries' exchange-rate regimes according to whether the country was fixing its exchange rate against any major currency and not just against the US dollar. Also, we added the US to the sample of countries. The results from pooling countries together are shown in the right panel of Figure 2 (a description of the data is provided in Section 3). The variance of changes in the effective RER post-Bretton Woods was less than three times the variance during Bretton Woods.[12] This difference was significant at the 5 per cent level, although it was clearly smaller for effective RERs than for bilateral RERs.

Results of within country F-tests are shown in Table 1. In contrast to the pooled results, three countries, Denmark, France and the Netherlands, showed no evidence of a significant difference in the variance of the monthly changes in the effective RER across nominal exchange-rate regimes. (Notice that the high variance of changes in the RER for Japan post-Bretton Woods pushed up the level of the pooled variance – excluding Japan from the sample reduced the pooled variance post-Bretton Woods from 2.7 to 2.5, but did not alter the result of the pooled F-test.)

Table 1: F-Tests for Differences in Variances of Effective RERs Across Nominal Exchange-rate Regimes(a)
  Country Bretton Woods Variance Post-Bretton Woods Variance F-Test(b) Direction(c)
1 Austria 1.51(d)      
2 Belgium 0.39 0.68 1.77* +
3 Canada 0.07 1.11 14.83* +
4 Denmark 0.71 0.89 1.25 0
5 France 1.45 1.58 1.09 0
6 Germany 0.85 1.45 1.70* +
7 Ireland 1.11 2.16 1.95* +
8 Italy 0.38 1.54 4.03* +
9 Japan 1.08 5.38 5.00* +
10 Netherlands 0.61 0.78 1.27 0
11 Norway 0.72 1.15 1.61* +
12 Sweden 1.34 2.02 1.50* +
13 Switzerland 0.35 2.21 6.32* +
14 United Kingdom 2.46 3.95 1.61* +
15 United States 0.17 2.39 14.29* +

Notes: (a) Variances are based on monthly percentage changes in the effective RER.
(b) * indicates significance at the 5 per cent level.
(c) A positive (negative) sign indicates that the variance is significantly higher (lower) for the Bretton Woods regime. A zero indicates no significant difference in the variance across regimes.
(d) Austria had a fixed exchange rate over the full sample period. Therefore, only one variance over the whole sample period is reported.

In summary, the ratio of the short-term volatility of the RER under floating versus fixed regimes was about 12 to 1 for bilateral RERs, but the ratio was less than 3 to 1 for effective RERs. Furthermore, within country tests showed that for three of the 14 countries in the sample, there was no significant difference in the short-term volatility of the effective RER during and after Bretton Woods.[13] In other words, increased RER volatility post-Bretton Woods is no longer as conspicuous when we consider effective RERs.

As we mentioned above, a major problem with this sample of industrialised countries is that most of the changes in the exchange-rate regimes occurred at the same time (around the collapse of the Bretton Woods system). This is troubling because it is not clear that a finding of different behaviour of the RER is due to a change in nominal exchange-rate regimes or other contemporaneous changes in the world economy.

In Section 4 we examine the behaviour of the effective RER across a larger set of countries using data well after the collapse of the Bretton Woods system. For this data set, changes in nominal exchange-rate regimes were not strongly correlated over time.


The bilateral RERs were based on Consumer Price Indices. Nominal exchange rates (versus the US dollar) were monthly averages throughout the paper (from the IMF, International Financial Statistics). We did not include Luxembourg in our sample. For the following countries we followed Mussa by representing the Bretton Woods regime as the period up to December 1970 and the post-Bretton Woods regime as the period from March 1973 onwards: Austria, Belgium, Denmark, France, Germany, Italy, Japan, the Netherlands, Norway, Sweden, Switzerland and the United Kingdom. Ireland was fixed against the pound sterling until December 1978, hence it was included in the Bretton Woods (fixed) regime up to that time and in the post-Bretton Woods (flexible) regime after that time. Following Mussa, Canada was included in the Bretton Woods regime from August 1962 until March 1970 and in the post-Bretton Woods regime from April 1970 onwards. The question of transitions between regimes was avoided here, as in Mussa, by excluding observations around the time of the breakdown of Bretton Woods. This issue is discussed in more detail in Section 4. [9]

Mussa's original sample period was from 1957 to 1984. Our effective RERs start in 1960, and we found it was straightforward to extend Mussa's regime classification scheme up to December 1990. Beyond that, Mussa's classification scheme becomes ambiguous for many European countries which dabbled with fixed exchange rates for a time (especially Sweden, the United Kingdom and Italy). [10]

The ratio of the average variance is lower than Mussa's result due to slightly different sample periods, the use of monthly instead of quarterly data, and slightly different regime classifications for Ireland and Canada. [11]

This was robust to using exactly the same set of countries and the same nominal regime classifications used by Mussa (that is, as in the left panel of Figure 1). [12]

The IMF (1984) show that the average of month-to-month changes in the effective RER more than doubled for France post-Bretton Woods, however, this study makes no comparison of the variance of these short-term changes in the effective RER. [13]