Movements in Exchange Rates and Relative Price Levels in the Netherlands and Britain over the Past Four Centuries

James R. Lothian
Graduate School of Business
Fordham University
New York, NY 10023
tel (212) 636-6147; fax (212)765-5573; email
September 15, 1998

During the course of the last ten years, economists' views of the purchasing power parity relationship have undergone a gradual but nevertheless substantial change. As the 1990s began, the consensus view was that purchasing power parity did not hold to any meaningful degree, that real exchange rates were too variable and otherwise ill-behaved for PPP to have any merit either as a predicative tool or in analysis of historical behavior. Today, in contrast, PPP is seen by most international economists as a useful first approximation, at least over the long run.

Underlying this dramatic turnabout in views is the substantial body of empirical work produced during the past decade, that unlike earlier research, has been largely supportive of PPP. Nevertheless, a number of questions remain to be answered. Most pressing perhaps is the reason for the long lags in adjustment of real exchange rates uncovered in most studies. These lags which generally have estimated half lives of three to five years appear much longer than would be consistent with existing theories of exchange-rate determination. A second is whether the exchange-rate regime matters. Much of the recent evidence supporting PPP comes from studies using long historical time series. Without spelling out exactly why this should be a problem, a number of economists have argued that it is in fact one. Yet another question concerns the effects of real variables such as productivity growth and the terms of trade on real exchange rates and the PPP relationship. A final issue is whether the existing body of empirical evidence is truly representative of behavior more generally. Sample selection bias, some have argued, has worked in favor of PPP, since most of the evidence supporting it has come from studies of countries at similar stages of economic development and with what arguably have been other similar real characteristics (Froot and Rogoff, 1995). The scope for permanent disturbances to operate has therefore been much more limited than in the population as whole.

The problem in each of these instances is one of experimental design, of obtaining the right data and of using tests that are suitable for those data . Standard time-series methods generally require long spans of data, often a century or more, simply to detect the mean-reverting behavior in real exchange rates indicative of long-run PPP (Lothian and Taylor, 1997). Using such methods to test or otherwise evaluate how the behavior of real exchange rates may have changed through time - say, as a result of differences in monetary regimes - or to test the possible influence of slowly-changing real factors on real exchange rates - for instance, productivity differentials - obviously requires even longer samples.

To that end we have collected exchange-rate and price-level data for the long period 1628-1998 for the Netherlands and Great Britain, countries that over this near four century long span have at times differed substantially in terms of the pace at which their economies were developing, have had a variety of exchange rate regimes, and have quite obviously experienced an even greater variety of real shocks of differing orders of magnitude. For two-thirds of this period (1628-1870) the price-level data for the Netherlands are only available in the form of bi-annual averages; for the remainder of the period annual data are available. We therefore have used two samples in our analysis, the bi-annual data for the full period (a total of 186 observations) and the annual data for the later 1871-1998 sub-period (128 observations). In this version of the paper, we focus exclusively on the full-period data. In analyzing these two bodies of data we use techniques ranging from simple graphical analysis, which given the long span of these data is, we believe, of more than usual interest, to regressions and time-series analysis.

1. Theoretical considerations

According to the purchasing power parity (PPP) theorem the logarithm of the nominal exchange rate, et, the foreign-currency price of a unit of domestic currency (here the guilder price of one pound sterling) will equal the difference in the logarithms of the foreign (Dutch) and domestic (British) price levels at time t, pne,t - puk,t :

et = pne,t - puk,t . (1)

Purchasing power parity has been rationalized both as an offshoot of the law of one price, and as an equilibrium condition in a variety of macroeconomic models. These range from simple open-economy versions of the quantity theory of money to Lucas's (1982) two-country, cash-in-advance model. Under fixed exchange rates, PPP provides a description of international price behavior. It implies equality between the two countries' price levels and is thus the macroeconomic analogue to the microeconomic law of one price. Under floating exchange rates, in contrast, it's principal applicability is to exchange-rate behavior, changes in exchange rates being seen as directly related to changes in relative price levels.

In both instances, the PPP relationship generally is regarded as having much greater relevance over the long run than over the short run. Over shorter time horizons, the effects of shocks can be quite substantial; in the long run, however, they appear to dissipate greatly. For this to be the case, monetary shocks, which in principle should be transitory in their effects, have to be almost totally dominant. Real shocks, which can have permanent effects, either have to be of minor importance, to have only transitory impacts, or both.

A stochastic version of equation (1) that has proven useful in describing this behavior takes the form:

et = _ + _1 pne,t + _2 puk,t +_t . (2)

Here the error term _t follows the autoregressive process

_t = $ _t-1 + _t , (3)

where $<1 and _t is an iid(0,&2) disturbance. With _1 = - _2 = 1, the real exchange rate qt (qt é et - pne,t + puk,t) reverts over time to its (constant) mean value _. Correspondingly, the exchange-rate adjusted ratio of the two countries' price levels reverts to that same constant.

An alternative, and arguably more realistic characterization would allow for permanent shocks as well as the transitory shocks in (3). The fact that tests based on (3) very often reject the hypothesis that $=1 and therefore find it to be an adequate representation, however, suggests that these permanent components generally are small relative to the transitory, though not necessarily non-existent.

II. Empirical evidence

Figure 1 plots the biannual figures for the logs of the two countries' price levels, the Dutch adjusted by the nominal exchange rate, and the log real exchange rate, the linear combination of the two. Several features of the chart deserve comment. The first is the quite close correspondence over both the very long term and the short term between the movements in the two price-level measures. We can see this both in the chart and in the right-most column of Table 1 which shows the correlations between the two price-level measures both for the half-century sub-periods and for the full period. An additional feature of the chart to notice is the often substantial variations in the real exchange rate over shorter but nevertheless rather lengthy periods as well as the step-like movements of an even longer duration that we see in several instances. The shorter term volatility is of course a feature shared with other real- exchange-rate data. These apparent longer term shifts are something that we investigate below. A third is what appears to be mean-reverting behavior when the real exchange rate is examined over the sample period as a whole. Again this is a feature shared with other data. It is also one that we also go on to investigate in greater detail. A final thing to notice in both Figure 1 and Table 1 is the time pattern of real-exchange-rate volatility. Measurement error in prices doubtless is greater in the first half of the sample period than in the second. Nevertheless, there is no indication of greater volatility under the recent float than in other time periods. The factor arithmetically responsible for the volatility, however, is different - relative price levels were the culprits earlier, while nominal exchange rates play that role now.

The regressions summarized in Table 2 speak to two of these issues in particular, the questions of mean reversion and of long-lived shifts in the mean. These regressions were of the form:

et = _ + _ qt-1 +21 D1 + ... 2k Dk + _t , (4)

where the Diss are dummy variables for 50-year sub-periods, _, _ and the 2is are coefficients to be estimated and _t is a disturbance The DF test of the hypothesis _=1 is a test for mean reversion; tests of the hypotheses that the 2is are zero are tests for the absence of shifts in the mean of q. We report only the results of DF tests and not those of ADF tests which include lagged differences of q as regressors since all such lagged terms were statistically insignificant in the additional regressions that we ran. In each instance, we reject the hypothesis that _=1. However, we also reject the hypothesis that the intercept of the regression is unchanged through time. We find a sizable upward shift in the real exchange rate in the nineteenth century, an increase in the real value of sterling. Additionally we find evidence of a downward shift in the seventeenth century, an increase in the real value of the guilder. By the second half of the twentieth, however, the average real exchange rate appears to have returned to its average value in the seventeenth. This can be seen both in Figure 1 and Table 1. It was further confirmed in an additional series of regressions in which we included dummies for the other fifty year periods but that we do not report here.

In this sense there is no contradiction between the two sets of findings. The question, however, is what economic inferences to draw from them. Clearly there is a highly persistent component of the real exchange rate, one that on anything other than this long data set would appear to be permanent. Our inclination is to view the two shifts that the regressions have pointed to as productivity related. The move to the higher real exchange rate in the nineteenth century comes during the height of Britain's industrial revolution and well after the golden age of industrialization in the Netherlands. The latter took place in the seventeenth century and carried over into the middle of the eighteenth century or thereabouts. This was also a period of substantial political turmoil for Britain, both internally and externally. It would not be surprising on this score alone to see a currency that was undervalued relative to PPP, as sterling appeared to be during that era.

A final point to notice here is the much higher estimated autoregressive coefficient in the regressions including the dummy variables. In the regression without any dummy variables the coefficient is .905, suggesting a near glacial speed of adjustment to equilibrium of slightly under ten per cent over a two year period. In the two regressions including the dummies the estimated coefficients, in contrast, are .794 and .722, roughly twice as fast and three times as fast respectively. The difference between the two sets of estimates suggests that one reason for the generally slow estimated speeds of adjustment may be failure to account for shifts of the sort seen in these data. In the presence of persistent (though not permanent) shocks to the real exchange rate, simple autoregressive models like those used here and in many other empirical studies of PPP, will be subject to specification bias and will imply slower adjustment to transitory shocks than is actually the case. Clearly this issue deserves further investigation.

III. Conclusions

The principal conclusion of this study to date is the resiliency of the simple purchasing-power- parity model and relatedly of the law of one price at the macroeconomic level. Perhaps not surprisingly, both take some heavy body blows during this close to four-century long sample period. In the end, however, they emerge surprisingly unscathed. Real factors , which over this long span of years have undergone truly major changes, appear at times to have had substantial effects on real exchange rates and hence PPP. Those effects, however, ultimately do not seem to have lasted. Adam Smith's dictum that there is "much ruin in a nation" appears to apply here as elsewhere. What makes this in turn quite remarkable is the long period for which this is the case.

Table 1: Summary statistics for biannual data

		  q 	pne-puk	  e	pne-e	  p	Correl
1628-1649	2.259 	 0.153 	2.413 	1.699 	2.833 	0.694 
1650-1699	2.198 	 0.167 	2.364 	1.793 	3.991 	0.807 
1700-1749	2.097 	 0.254 	2.350 	1.860 	3.957 	0.710 
1750-1799	2.251 	 0.117 	2.369 	1.968 	4.220 	0.664 
1800-1849	2.634 	-0.203 	2.431 	2.096 	4.730 	0.866 
1850-1899	2.541 	-0.057 	2.485 	2.062 	4.603 	0.898 
1900-1949	2.358 	-0.003 	2.356 	2.484 	4.842 	0.834 
1950-1998	2.294 	-0.507 	1.787 	4.766 	7.060 	0.995 
1628-1998	2.334 	-0.022 	2.312 	2.389 	3.599 	0.981 

Std. Dev.	0.178 	 0.248 	0.220 	1.009 	1.203 	
Standard Deviations						
1628-1649	0.090 	0.111 	0.042 	0.076 	1.158 	
1650-1699	0.063 	0.061 	0.032 	0.088 	0.107 	
1700-1749	0.070 	0.078 	0.015 	0.072 	0.099 	
1750-1799	0.137 	0.117 	0.043 	0.078 	0.176 	
1800-1849	0.091 	0.112 	0.099 	0.181 	0.161 	
1850-1899	0.066 	0.071 	0.010 	0.100 	0.139 	
1900-1949	0.205 	0.123 	0.177 	0.361 	0.350 	
1950-1998	0.146 	0.435 	0.521 	1.138 	1.045 	
1628-1998	0.209 	0.297 	0.293 	1.059 	1.549

Note: Variables are in log form and are as defined as in the text.
Correl denotes the correlation coefficient between the exchange-
rate adjusted Dutch price level, pne-e, and the British price level,
 puk.  The standard deviations at the bottom of the upper half  of
the table are of  the sub-period means about the grand mean.

	Table 2. Real exchange rate regressions

Const.	  qt-1	D162   D171	D18	DF 	R2

0.224	 0.905 				-3.104	0.826 
3.115	29.47	 				0.087

0.644	 0.722 	-0.037 	-0.068 	0.076 	-5.844	0.847 
5.890 	15.19	-1.927 	-3.307 	3.756	 	0.082 
0.464 	 0.794 			0.071 	-4.698	0.837 
4.702 	18.06 			3.444 		0.085
Note: D162, D171 and D18 are dummy variables taking 
the value 1 for the periods 1650-99, 1700-49, and 
1800-99, respectively, and zero otherwise; t values are 
beneath the coefficients. DF is the Dickey-Fuller statistic.
Values of -2.89 and -3.51 are significant at the .05 and .01 levels. 


1 See e.g. Lothian and Taylor (1996) and the reviews of this literature in Rogoff (1996) and Taylor (1995).

2 On this issue see Taylor (1996) who uses a broad sample of countries and obtains results very similar to those obtained for the highly industrialized countries used in most other studies.

3 The data and their sources are described in a separate appendix available from the authors on request.

4 Froot, Kim and Rogoff (1996) in their study of individual commodity prices for Britain and the Netherlands since Medieval times reach quite similar conclusions to ours with regard both to the time pattern and proximate causes of shorter term volatility. Interestingly, they find that most of the exchange-rate-adjusted relative prices that they examine are subject to long swings but ultimately seem to mean revert.

5 David Papell in a series of coauthored papers has documented similar phenomena for other time periods and other exchange rates. See, for example, Culver and Papell (1995).

6 Here see Israel (1995) as well as the brief summary of Dutch experience in Kindelberger (1996, p.89-104).


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