Article

Purchasing Power Parity and the Balance of Payments: Some Empirical Evidence

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1977
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The advent of floating exchange rates and the substantial changes in relative prices and exchange rates in recent years have renewed interest in the purchasing-power-parity (PPP) theory of the exchange rate. Its main tenet is that, with some caveats, the equilibrium exchange rate is determined by the PPP relationship and that, if left to float freely, the exchange rate will tend to the PPP equilibrium. This paper addresses itself to the disequilibrium theory implied by the PPP theory. What can be said about the disequilibrium in periods that are too short to allow full exchange rate adjustment, or during which the monetary authorities intervene in exchange markets to maintain the exchange rate at disequilibrium levels? In particular, what is the relationship between disequilibrium in the exchange rate and disequilibrium in the balance of payments accounts?

This paper attempts to find evidence for the hypothesis that a country with an overvalued (undervalued) currency will tend to find itself in balance of payments deficit (surplus). This hypothesis is tested by constructing a relative price index (RPI) that may be used to judge the relative overvaluation or undervaluation of 14 industrial countries for the period 1963:111 to 1974: IV. Section I provides some historical background by presenting the movements of a measure of the RPI for the period 1963:1 to 1976:1. One of the more controversial issues in the literature of the PPP theory is the question of the appropriate RPI. Section II touches upon this issue and provides the theoretical background for a relationship between the RPI and the balance of payments accounts. Section III tests a specific functional form of the above hypothesis and presents the results for eight alternative measures of the RPI. Section IV presents a summary and the conclusions of the paper. The Appendix details the data sources and transformations used in this paper.

I. The Relative Price Index

The use of the RPI has a long tradition, beginning with Cassel (1925), who computed it to find the average undervaluation or overvaluation of the dollar for the time period 1919–24. The relative price index is defined as the ratio of domestic (P) to foreign (PF) price indices multiplied by an index of the exchange rate (domestic over foreign currency units), which is the ratio of the actual exchange rate (R) to the exchange rate for the base period of the price indices (R0). A currency is deemed undervalued or overvalued as the relative price index diverges from one; consequently the RPI is henceforth defined as equal to the relative price index minus one, under the assumption that the base period (1970) was an equilibrium period.

As discussed below, the empirical measure of the RPI will vary according to the indices and the weights used in its construction. Chart 1 shows the historical movement of one such measure of the RPI, where the domestic price is measured by the consumer price index and foreign prices by the rest of the industrial world’s wholesale price index, weighted by income shares. The index is measured in percentage points where the base period (1970) is equal to zero.

Chart 1.Fourteen Industrial Countries: Relative Price Index, 1963–761

1 Ratio of domestic price index to the rest of the world wholesale price index, income weighted. The base year for all indices is 1970 (RPI1970 = 0).

The 14 countries have been divided into two groups, one of which can be identified as a deutsche mark group, in that the behavior of the group as a whole parallels that of the Federal Republic of Germany. For this latter group, this measure of the RPI exhibits an upward trend throughout the whole of the period. Inspection shows that, for this group, movements of the RPI were smoother in the period up to 1973 than in the ensuing period. In this latter period, it is possible to detect one major cycle in the movements of the RPI and perhaps the beginning of another, milder cycle. Hitting the initial peak in 1973: IV, and the trough a year later, the RPI for this group of countries seems to reach a new peak in 1975:11, with a subsequent decline later in the year and a mild recovery by 1976:I.1

For the other group, there is no general pattern. For both Japan and Switzerland, there is a strong trend during the period as a whole and, for the latter country, the RPI exhibits the same cyclical behavior in the 1973:1–1976:1 period as the deutsche mark group. The United States and Canada show fairly similar patterns of initial relative stability of the RPI, up to 1971 for the United States and up to 1973 for Canada, with a subsequent decline in the RPI. For both the United Kingdom and France, this measure of the RPI shows cumulative increases in periods before, and strong decreases after, par value changes in the exchange rates. For the floating exchange rate period, France, and, to some extent, the United Kingdom, participated in the 1973:IV–1975:II cycle of the RPI. The RPI of the last country to be reviewed, Italy, shows stable behavior up to 1973, with a recognizable downward trend in the subsequent period while participating in the general cycle described above.

One of the interesting outcomes of this historical review is that it points out the existence of a general RPI cycle during the floating exchange rate period. Since the income weights give U. S. prices a strong role in the determination of the rest of the world’s RPI, the natural reaction is to ascribe this cycle to a changing position of the United States vis-à-vis the rest of the world. Since the purpose of this paper is not to explain the movements of the RPI, but rather to point out their existence, the discussion is limited to showing that these movements not only have increased during the floating exchange rate period but also have existed for the period 1963–76 as a whole.

The traditional use of the RPI is as a tool with which to judge the undervaluation or overvaluation of a currency with respect to the base period. If the base period is an equilibrium one, and the RPI shows an overvaluation of 20 per cent, then, presumably, a 20 per cent devaluation of the exchange rate would restore the exchange rate to an equilibrium position. Chart 1 has shown that the RPI will change over time, and that disequilibrium positions can be maintained for relatively long periods of time.

These observations prompt the question of the implications of a disequilibrium position of the RPI. Given that the actual exchange rate can deviate from the equilibrium exchange rate, what economic forces come into play to return the exchange rate to equilibrium as predicted by the PPP theory? In a floating exchange rate system, the PPP theory assumes that the exchange rate will change sufficiently to restore equilibrium, at least in the long run. But what of periods in which the exchange rate does not change accordingly—that is, in the short run or in periods when a par value system holds? Will there be other forces in the economy working to re-establish equilibrium?

One such force is the balance of payments. Deficits in the current account indicate that there has been a diversion of demand from domestic to foreign goods. The change in demand then has a deflationary effect on the domestic economy, and consequently changes the relationship between domestic and foreign prices in the desired direction. On the other hand, a deficit in the overall balance of payments has a deflationary effect on the economy as a whole, as there is a loss in international reserves that affects both the demand for and supply of money. As both the balance of payments and the RPI are endogenous variables within a general equilibrium system, this paper attempts to explore the relationship between movements in the balance of payments and movements in the RPI—the subject of the next section.

II. RPI and the Balance of Payments—Alternative Theories

The traditional application of the PPP theory is with respect to exchange rate equilibrium. This paper uses the dual of this theory to explore the relationship between RPI disequilibrium and balance of payments disequilibrium. As in the traditional application, a controversy can arise as to what the underlying structural model is that supports this theory and what, consequently, are the appropriate empirical proxies for the RPI.2 There are essentially two approaches to this underlying model. One emphasizes the role of commodity markets, while the other emphasizes the role of the asset market in the determination of the exchange rate and balance of payments.

The first approach—the elasticity approach—finds a relationship between the RPI and the trade balance through the export and import functions. Different variations of this approach advocate different empirical proxies for the RPI. In the simplest case, the RPI is identified with the terms of trade, where the domestic price is the price of exports and the foreign price is the price of imports. In this case, both prices are traded goods prices. In another version of this approach, it is assumed that there is only one traded good, in which case the RPI is identified as the ratio of nontraded to traded goods prices.

In the asset approaches—the absorption and monetary approaches—an excess supply of financial assets (money) causes a trade (overall) balance deficit as the economy exports this excess of assets (money). Concurrently, in the presence of a nontraded good, the excess supply of assets will cause an excess demand for the nontraded good and thus increase the RPI. In the case of a small country, the excess supply of assets does not affect traded goods prices and the RPI is identified as the ratio of nontraded to traded goods prices. In the case of a large country, its excess demand for, and supply of, assets affects the behavior of the rest of the world. As these effects become incorporated into the model, the RPI becomes a ratio of domestic to foreign general price levels. Indeed, their model may even suggest that the ideal RPI is a ratio of the nontraded goods prices for the domestic and foreign economies.

In empirical work, reasonable proxies for traded and nontraded goods prices are not generally available, so the discussion turns to the appropriateness of using the more generally available indices. This paper uses only the consumer and wholesale price indices, excluding from consideration other indices, such as gross national product (GNP) deflators and wage indices. These limitations must be taken into account in interpreting the results reported in this paper. Typically, the wholesale price index is expected to reflect traded goods prices, while the consumer price index is a more general price index that contains both traded and nontraded goods prices. One of the aims of this paper is to investigate which is the proper proxy for the RPI. If the exchange rate system during the period of analysis had been one of freely floating exchange rates, it might have been possible to test directly the appropriate RPI by comparing it with the exchange rate, which, by definition, would always be an equilibrium rate. However, for most of the last decade, exchange rates have been fixed at official par values or, at least, have been determined in a managed floating system where there was discretionary intervention in the exchange markets by the monetary authorities. By performing the test on the dual of the exchange rate—the balance of payments—some evidence is gathered as to the appropriateness of different RPI proxies. Using the two available indices, the wholesale and consumer prices indices, the following four types of RPI proxies are constructed: the ratios of (1) the domestic consumer price index to the foreign consumer price index (c/c), (2) the domestic consumer price index to the foreign wholesale price index (c/w), (3) the domestic wholesale price index to the foreign consumer price index (w/c), and (4) the domestic wholesale price index to the foreign wholesale price index (w/w).

However, a further complication must be added to the empirical test of the PPP hypothesis. The foreign price index is not the price index of just one country, but rather is a weighted average of many countries’ price indices and, thus, an additional source of controversy arises in the choosing of the appropriate weights.3 Here only two weighting schemes are explored—trade weights and income weights. The trade weights are the ratios of the bilateral imports from, and exports to, the jth country to the total trade of the ith country. The income weights are the jth country’s gross national product divided by the aggregate industrial countries’ gross national products, excluding the ith country. Both sets of weights are calculated from 1970 data, the base year for all indices in this paper. Combining the two sets of weights with the four combinations of consumer and wholesale price indices, eight RPI measures are constructed. These RPI measures can be related to the balance of payments. However, which is the appropriate measure of the balance of payments—the trade balance or the overall balance of payments? The elasticity approach would lead one to expect a relationship between the RPI and the trade balance, while some versions of the asset approach (a monetary approach) might lead one to expect the relationship to hold for the overall balance of payments. In this paper, both relationships are investigated.

III. Hypothesis Testing

The above comments suggest a relationship between the RPI, measured in various ways, and two measures of the balance of payments. The task of this section is to set up the test for this hypothesis and present the results. However, before doing this, further definition of both the variables and the hypothesis is required.

The balance of payments measures used here are the trade and overall balances, both denominated in domestic currency units. The dependent variable used is the ratio (BP) of the balance of payments to potential GNP. This procedure has a dual purpose. First, it permits comparability of the results across countries by standardizing the balance of payments by the “size” of the country.4 The ensuing result is that one may consider the coefficients of the independent variables as pseudoelasticities that measure the change in the balance of payments as a percentage of potential GNP for a one-period shock to the independent variable. Second, it allows for comparability across time. As the economy grows, the same change in the RPI would be expected to engender a larger change in the balance of payments at the end, than at the beginning, of the period.5

The theories discussed above are all framed in the context of a full-employment economy. In fact, the industrial countries tested have not maintained full employment; this has necessitated the introduction of a variable that measures the cyclical position of each country. However, since the concern of this paper is the cyclical effects on the balance of payments, it seems more reasonable to judge the country’s business cycle relative to that of the rest of the world.6 For this purpose, a relative business cycle index (RCY) is constructed, the details of which are given in Appendix I. The other independent variable is the relative price index. As discussed above, eight different measures are constructed for this index.

Given that there is a hypothetical relationship between the RPI and the balance of payments, what functional form or lag structure should this relationship take? The theories that have led to the development of the relationship are of little help in formulating an empirically testable functional form. The fact that the variables are allowed to take negative values prevents any log-linear formulation from being tested, and a linear formulation is adopted instead. However, the issue of an appropriate lag distribution still remains. Fortunately, there have been some empirical findings that suggest that the impact effect of a change in the RPI will be different from the long-run effect. This is the J-curve effect following a devaluation, which involves an initial balance of payments deterioration and subsequent improvement.7 This observation establishes the first criterion for the lag structure—that the impact effect be allowed to have a sign different from that of the long-run effect. For this purpose, it is sufficient to introduce both the current and the one-period-lagged independent variables in a Koyck-type of lag structure. However, this type of lag structure is judged to be too restrictive, in that the greatest effect is constrained to occur in the short run. The generalization of the Koyck-type lag to a second-order lag function is sufficient to allow the lag weights to increase in the medium run.8 For these reasons, the following formulation was adopted:

For ease of computation of the long-run effect, equation (2) is transformed into equation (3) without changing its statistical properties

where Δ is the first-difference operator. Since, in this formulation, serial correlation in the error term biases the coefficients, and the Durbin-Watson statistic is not useful in detecting first-order serial correlation in the presence of lagged dependent variables, the error term is assumed to be generated by a first-order autoregressive process

where et ˜ N(0,σ2)

One of the purposes of performing these regressions is to gather evidence on the proper construction of the RPI and RCY. There are eight measures of the RPI and two of the RCY where the weights (either trade or income) are common to both. In this paper, a goodness-of-fit (R¯2) criterion was used to rank the different alternatives, and the “best” regression was chosen for each country. Table 1 reports these results for the trade balance, and Table 2 reports them for the overall balance.

Table 1.Fourteen Industrial Countries: Results of Best Regressions Estimating the Trade Balance of Payments

CountryWeights 1Hypothesis2b0b1b2b3b4t1t2ρR¯2
United StatesIncomec/c−0.020.35−3.842.50−3.961.08−0.13−0.160.86
(0.47)3(0.91)(2.16)(2.03)(1.59)(7.04)(0.82)(1.09)
United KingdomTradec/w−4.8227.31−5.1525.79−16.62−0.12−0.290.730.73
(4.83)(3.49)(0.69)(1.69)(1.63)(0.80)(1.84)(6.89)
AustriaIncomew/w−8.63−25.7517.12−11.89−4.25−0.26−0.520.810.54
(5.88)(2.51)(2.40)(0.91)(0.52)(2.00)(3.67)(9.03)
BelgiumTradec/w−0.3432.50−36.01−11.564.39−0.420.170.030.35
(0.91)(3.20)(1.61)(0.54)(0.20)(2.83)(1.12)(0.31)
DenmarkTradew/c−4.06−4.20−34.4113.86−14.680.080.060.200.23
(4.46)(0.92)(2.52)(1.32)(2.00)(0.53)(0.44)(1.40)
FranceIncomew/w−0.26−6.179.22−5.203.480.250.140.370.55
(1.10)(2.58)(2.19)(1.31)(1.36)(1.61)(0.75)(2.65)
Germany, Fed. Rep.Incomec/c0.683.22−1.13−10.56−3.400.660.07−0.160.80
(2.61)(2.96)(0.37)(2.70)(0.44)(3.93)(0.48)(1.04)
ItalyIncomec/w−0.745.8667.55−15.5611.860.900.500.030.77
(3.37)(1.12)(5.90)(2.35)(1.72)(6.46)(3.19)(0.19)
NetherlandsIncomec/w−7.5230.03−3.42−22.6928.310.08−0.770.200.74
(11.26)(8.35)(0.27)(1.58)(1.95)(0.78)(8.11)(1.28)
NorwayIncomew/w−5.1111.6542.79−10.99−55.690.72−0.22−0.410.43
(2.98)(1.76)(1.58)(0.64)(3.15)(4.68)0.58)(3.08)
SwedenIncomec/w0.1925.18−21.65−1.3811.67−0.04−0.210.370.54
(0.64)(4.58)(2.05)(0.11)(1.02)(0.27)(1.42)(2.84)
SwitzerlandIncomew/w−1.74−2.6015.43−7.560.620.360.280.350.72
(2.40)(1.00)(2.50)(0.91)(0.10)(2.37)(1.96)(2.58)
CanadaIncomec/w1.229.66−16.10−31.2534.740.41−0.25−0.180.42
(4.66)(3.59)(1.88)(3.10)(2.94)(3.02)(1.92)(1.26)
JapanTradew/c0.30−3.403.61−1.69−12.780.73−0.06−0.100.84
(2.84)(3.51)(1.17)(0.80)(2.99)(4.42)(0.42)(0.70)

The RPI and RCY variables are ratios of domestic to foreign prices and of domestic to foreign income cycle positions, respectively. The weight indicates the weight used in constructing the foreign variable.

For definitions of ratios, see Section II of the text.

Figures in parentheses are t-statistics.

The RPI and RCY variables are ratios of domestic to foreign prices and of domestic to foreign income cycle positions, respectively. The weight indicates the weight used in constructing the foreign variable.

For definitions of ratios, see Section II of the text.

Figures in parentheses are t-statistics.

Table 2.Fourteen Industrial Countries: Results of Best Regressions Estimating the Overall Balance of Payments

CountryWeights 1Hypothesis2b0b1b2b3b4t1t2ρR¯2
United StatesIncomec/w−0.182.47−16.90−24.4311.52−0.37−0.460.560.49
(0.81) 3(1.43)(3.96)(3.97)(1.87)(3.01)(3.49)(4.42)
United KingdomTradec/c−0.02−1.0335.3019.22−8.660.71−0.04−0.330.29
(0.08)(0.30)(2.13)(0.90)(0.39)(4.22)(0.24)(2.18)
AustriaTradew/w0.080.316.390.39−4.660.35−0.47−0.780.37
(2.86)(0.31)(3.20)(0.22)(2.03)(2.98)(3.86)(9.16)
BelgiumIncomec/c0.39−7.0338.622.97−10.400.82−0.54−0.760.18
(2.16)(1.95)(2.88)(0.34)(0.58)(6.12)(4.52)(7.80)
DenmarkTradec/c0.26−9.1427.30−13.94−0.100.41−0.50−0.350.16
(1.22)(1.78)(1.30)(1.25)(0.01)(2.87)(0.01)(1.68)
FranceIncomec/w0.32−7.641.4824.65−8.060.230.030.020.25
(1.02)(1.33)(0.16)(2.51)(1.07)(1.41)(0.19)(0.02)
Germany, Fed. Rep.Tradew/c1.19−7.53−7.37−0.22−25.180.28−0.45−0.400.06
(3.08)(1.23)(0.37)(0.01)(0.84)(1.97)(3.13)(2.94)
ItalyTradew/w−1.96−65.9787.95−22.20−8.84−0.42−0.480.850.29
(1.03)(2.84)(4.31)(1.31)(0.85)(3.48)(3.52)(10.58)
NetherlandsIncomec/w0.896.11−11.3526.87−8.000.16−0.29−0.260.12
(2.95)(2.59)(0.71)(2.10)(0.42)(0.99)(1.80)(1.76)
NorwayIncomew/w1.30−7.0217.9832.33−30.04−0.16−0.16−0.520.28
(4.21)(1.49)(0.77)(3.14)(1.81)(1.04)(0.98)(3.88)
SwedenTradec/c1.2144.87−38.131.95−6.00−0.24−0.290.840.33
(1.19)(2.24)(2.69)(0.12)(0.60)(1.71)(2.03)(10.52)
SwitzerlandIncomew/c4.83−22.9548.0867.16−21.13−0.01−0.77−0.910.68
(7.49)(4.49)(2.18)(3.53)(0.75)(0.11)(7.78)(15.41)
CanadaIncomec/c0.520.0623.75−15.027.270.36−0.43−0.600.08
(2.43)(0.01)(1.90)(1.23)(0.47)(2.73)(3.22)(5.18)
JapanIncomew/c1.21−14.54−8.13−7.39−15.670.46−0.42−0.520.58
(4.12)(4.18)(1.12)(1.69)(1.95)(3.38)(3.16)(4.08)

See footnote 1, Table 1.

See footnote 2, Table 1.

See footnote 3, Table 1.

See footnote 1, Table 1.

See footnote 2, Table 1.

See footnote 3, Table 1.

Of the two sets of weights, income weights are preferred. For the trade balance, 10 of the 14 countries show this weight while, for the overall balance, 8 countries have better fits using this weight. These results are somewhat surprising, in that it is trade rather than income weights that are generally used. It is particularly interesting that the strong dominance of income over trade weights appears in the trade balance rather than in the overall balance.

As for the proper choice of the RPI measure, the evidence is less clear. As Table 3 shows, the trade balance results indicate that the (c/w) (which appeared in six countries) and the (w/w) (which appeared in four countries) measures for the RPI are the better measures. This evidence can be taken as a strong indication that the best proxy for the foreign price index is a weighted average of the wholesale price indices in the rest of the world. On the other hand, the domestic price index may be proxied by either the consumer or the wholesale price index, depending on the country. The more traditional PPP measure (c/c) appears in only two countries as their best measure.

Table 3.Tabulation of the Signs Estimated for the Long-Run Effect of Alternative Measures of the Relative Price Index (RPI)1
Trade BalanceOverall Balance
RPI(+)(−)Total(+)(−)Total
c/c1*,1-21*3*,15
c/w5*,1-61*,113
w/c-1*,12-2*,13
w/w1*2*,1411*,13
Total95410
Sources: Tables 1, 2, and 3.

The superscript * indicates significant coefficients.

Sources: Tables 1, 2, and 3.

The superscript * indicates significant coefficients.

The results for the overall balance of payments are more heterogeneous. Perhaps not surprisingly for those who hold to the monetary approach, the (c/c) measure does better than the others, but the evidence is not strong enough to suggest that this measure should be advocated as the generally appropriate measure. Thus, if any conclusions are to be drawn from this section, one should be that care should be taken to choose the appropriate RPI for each country to be investigated, as there does not seem to be one measure that performs universally better than others. Also, if the RPI must be standardized for all countries, it seems best to choose the (c/w) measure for work related to the trade balance and the (c/c) measure for work related to the overall balance, where both measures are income weighted.

The results also provide some interesting evidence on another account. The simple model for the balance of payments described by equation (3) explains the trade balance much better than the overall balance. Moreover, with some exceptions, the R¯2 for the trade balance regressions seem to be inversely related to the size of the country. These two pieces of evidence may be construed as supporting the asset view of the PPP theory. In this view, the change in the RPI reflects the change in the net domestic savings of the economy—that is, the trade balance. Whether this change in net domestic savings affects the capital or the overall balance will depend on some omitted variables, such as interest rates or net domestic credit creation, which describe the behavior of the asset markets. Thus, given that additional variables are needed to describe the split of the current account into the capital and overall balance, it is not surprising that the trade balance regressions perform uniformly better than the overall balance regressions.

An interesting exception to this rule is Switzerland, where the trade balance shows an R¯2 of 0.72 and the overall balance shows one of 0.68. One of the conclusions that may be drawn from the evidence is that this country’s balance of payments accounts are not strongly influenced by internal variables and, thus, the simple model delineated above describes this economy relatively well. On the other hand, the case of the Federal Republic of Germany shows the most contrasting results. The trade balance shows an R¯2 of 0.80, while for the overall balance it is 0.06. Given that no other country shows such a large difference, one may draw the conclusion that the Federal Republic of Germany is particularly active in manipulating the capital and overall balances through asset market policies (i.e., open market operations) that do not seem to be very important in determining the trade balance. The asset approach also suggests that the extent of the RPI’s influence on the trade balance depends on the country’s ability to affect its internal price level while maintaining a constant foreign price level. The smaller and more open the country is, the less likely it is that this may happen; therefore, it is not surprising to see that the smaller countries do not perform as well as the larger countries.

However, the goodness-of-fit does not affect the test of the proposition that the RPI and the balance of payments are related. Given that this relationship may not be contemporaneous, it is its lag distribution that must be investigated. For this purpose, equation (3) is transformed into equation (5).9

where the weights, Wp(i) and Wy(i) are given by

Wp(0) = b1 + b2

Wp(1) = b2 + t1Wp(0)

Wi(j) = t1Wi(j − 1) + t2W(j − 2)

Ww(0) = b3 + b4

Ww(0) = b4 + t1Ww(0)

i = p, y; j = 2, …, n

and the cumulative, or long-run, effects, βp and βy, are given by

As equation (5) shows, there is no single statistic that measures the effect of the RPI or RCY on the balance of payments, since it depends on time. However, investigating the lag distribution is quite a difficult procedure, since the regression results are consistent with a variety of lag distributions. The approach taken in this study is to calculate the confidence intervals for the impact and long-run effects of the independent variables. These results are presented in Table 4. Though sufficient for some purposes, these statistics do not provide enough information about the lag distribution. One shortcoming of these statistics is that, even if there are no impact or long-run effects, there may be significant medium-term effects that are not measured by these statistics. A step toward remedying this shortcoming is to display, by means of Chart 2, the lag distributions corresponding to the point-of-sample estimates. Since there are other distributions that are consistent with the regression results, these lag distributions can be taken only as representative of a class of distributions. However, when used in conjunction with the impact and long-run effect statistics, they permit some confidence to be placed in the conclusions derived.

Table 4.Fourteen Industrial Countries: Impact Effects, Long-Run Effects, and Average Lag of RPI and RCY
RPIRCY
Trade BalanceOverall BalanceTrade BalanceOverall Balance
CountryWp(0)βp1θp2Wp(0)βpθpWy(0)βyθyWy(0)βyθy
United−3.49*36.599.14−14.43*1.352.24−1.4646.9311.68−12.91*13.35*2.07
States(1.97)4(0.90)(3.52)(1.40)(0.61)(0.70)(2.21)(4.34)
United22.16*19.32*0.9234.28*−3.131.599.1818.251.5210.5758.732.40
Kingdom(2.94)(4.67)(2.11)(0.29)(0.89)(1.61)(0.43)(0.75)
Austria−8.63−14.43*2.796.70*0.282.14−16.15*−6.672.32−4.37*0.352.19
(1.24)(2.29)(3.28)(0.31)(1.97)(0.92)(1.87)(0.22)
Belgium−3.5125.85*2.7431.59*−9.70*2.93−7.17−9.190.47−7.434.102.97
(0.17)(3.62)(2.66)(1.82)(0.40)(0.53)(0.50)(0.35)
Denmark−38.60*−4.890.5418.16−8.37*2.50−0.8116.141.18−14.04−12.762.13
(3.04)(0.98)(0.95)(1.90)(0.11)(1.24)(1.57)(1.29)
France3.05−10.13*1.48−6.16−10.230.571.72−8.551.5516.5933.010.70
(0.75)(2.16)(0.73)(1.40)(0.67)(1.29)(2.33)(2.20)
Germany, Fed.2.0911.90*3.30−14.90−6.441.89−13.95*−38.98*2.63−25.40−0.192.03
Rep.(0.73)(3.39)(0.77)(1.24)(2.05)(2.86)(0.86)(0.01)
Italy73.42*9.892.5321.98−34.68*2.74−3.70−26.24*2.83−31.04*−11.672.08
(6.61)(1.23)(1.15)(2.68)(0.57)(2.40)(3.12)0.33)
Netherlands26.61*17.79*6.68−5.245.40*1.595.6213.447.3218.8723.76*1.09
(2.13)(10.18)(0.33)(2.85)(0.39)(1.61)(1.00)(2.35)
Norway54.44*23.30*1.0010.96−5.321.02−66.68*−21.961.052.2924.51*1.42
(2.23)(2.25)(0.49)(1.49)(3.92)(0.77)(0.16)(3.41)
Sweden3.5320.20*1.446.7429.29*1.7910.29−1.111.02−4.051.271.44
(0.36)(5.28)(0.48)(2.03)(0.93)(0.11)(0.38)(0.12)
Switzerland12.84*−7.221.8625.13−12.88*6.90−6.94−20.992.6446.0337.71*6.55
(2.34)0.01)(1.28)(4.75)(1.18)(1.03)(1.63)(3.68)
Canada−6.4411.48*1.4570.01*−10.96*4.473.49−37.12*1.7156.4133.30*4.07
(0.80)(4.12)(2.59)(3.47)(0.30)(2.97)(1.85)(2.74)
Japan0.21−10.33*2.79−22.67*−15.17*1.64−14.48*5.151.23−23.06*−7.71*1.75
(0.08)(4.46)(3.90)(8.27)(3.24)(0.88)(2.79)(1.87)

Instantaneous (Wp(0)) and cumulative (βp) changes in the balance of payments as a percentage of potential GNP owing to a one-period shock to the corresponding index.

The average lag statistic.

The asterisk indicates that the coefficient is significantly different from zero at a 90 per cent confidence level.

The parentheses indicate t-statistics calculated by the method given by Klein (1953), p. 258.

Instantaneous (Wp(0)) and cumulative (βp) changes in the balance of payments as a percentage of potential GNP owing to a one-period shock to the corresponding index.

The average lag statistic.

The asterisk indicates that the coefficient is significantly different from zero at a 90 per cent confidence level.

The parentheses indicate t-statistics calculated by the method given by Klein (1953), p. 258.

Chart 2.Lag Distributions of Relative Price Index (RPI)1

1 The vertical axis plots the value of the lag weight—Wp(i)—and the horizontal axis plots its lag period—i—in terms of quarters.

*Indicates that the impact effect—Wp(0)—or the long-run effect—βp—is significant at least at a 90 per cent level.

One of the more important statistics gathered here is that of the long-run, or cumulative, effect of the RPI on the balance of payments. Although it is commonly expected to be negative, there need not be any sign designated a priori for the RPI’s long-run effect, since its sign depends on the approach taken and the underlying source of the disturbance assumed.

The following examples are attempts to illustrate this point. Taking the RPI as the ratio of the price of exportables to price of importables in a simple elasticity approach, the sign of the long-run effect will be positive or negative, depending on what caused the change in the RPI. If the change was caused by a change in the terms of trade, then the shift in productive resources will expand exports, and the shift in consumption demand will increase imports; depending on which effect is stronger, there will be either a positive or a negative long-run effect. This contrasts with the more common view, which assumes that the increase in export prices is due to an increase in exporters’ costs of production and that, because of the resulting decrease in their “competitiveness,” a trade balance deficit is expected.

Similarly, in the asset approach, the commonly held view is that there is a negative relationship between the RPI and the balance of payments. As in the introductory example in Section II, an excess supply of domestic assets will tend to cause an increase in the RPI, viewed as the ratio of nontraded to traded goods prices, and a balance of payments deficit. On the other hand, an exogenous increase in the RPI will generally be associated with an increase in the general price index that, in turn, will cause an excess demand for assets and a balance of payments surplus as the real value of nominally denominated assets decreases. Thus, these rather simple examples lead to the conclusion that no sign can be designated a priori for the long-run effect of the RPI.

These examples also serve to point out a caveat in the interpretation of the results presented in this paper. It is shown above that the sign, and therefore the value, of the long-run coefficient of the RPI depends on the source of disturbance operating on the RPI. Consequently, if more than one disturbance affects the RPI, the estimated coefficient is best interpreted as the average effect of the separate disturbances. Furthermore, since different disturbances may predominate at different times, it is likely that the true coefficient will vary with time and that the estimated coefficient will represent an average effect over time.

The results indicate, that there is a relationship between the RPI, appropriately defined, and the trade balance. All countries report a significant impact and/or a long-run effect. For the overall balance, the evidence is less conclusive, in that only 11 of the 14 countries report some significant effect. Perhaps the most interesting evidence is that the sign of the long-run effect tends to be positive for the trade balance and negative for the overall balance. As tabulated in Table 3, the trade balance results show nine positive signs, seven of which are significant. On the other hand, the overall balance results show ten negative signs, six of which are significant.

Following arguments similar to those stated above for the long-run effect, the impact effect of the RPI on the balance of payments can be expected to have either a positive or negative sign. The results show that, for nine countries, the impact effect has a positive sign for both measures of the balance of payments, of which about half are significant. However, it is also interesting to note that, for five countries in the trade balance results and nine countries in the overall balance results, the impact effect has a different sign from that of the long-run effect. As mentioned at the beginning of this section, this sign reversal is to be expected, particularly for the trade balance. Embodied in the J-curve literature is the expected reaction of a positive impact effect with a negative long-run effect on the trade balance, as is observed in this study for France, Switzerland, and Japan. However, the reverse effect—a negative impact, and a positive long-run, effect—is observed for the United States and Canada. Similar results occur for the overall balance of payments. Here, there are nine sign changes, of which seven show the expected (positive to negative) sign change. Thus, although initially conceived for the trade balance, the expectations of changes in the sign of the impact and long-run effects are better supported by the results of the overall balance of payments.

Finally, in addition to the impact and long-run effects, the means of the lag distributions of the RPI are presented in Chart 2. With the exception of a few cases that show unreasonable cyclical behavior, the lag distributions seem to be well behaved; the occurrence of sign changes in the lag weights seems also to be well supported. Another rather remarkable aspect of the results presented in this study is the speed with which the effects of the RPI are felt on the balance of payments. Indeed, much of the evidence suggests that the changes in the RPI and the balance of payments may be viewed as occurring almost contemporaneously. The supportive evidence for this remark is given by the average lag statistic. Since the usual computation of this statistic leads to incongruous results for the type of lag distributions presented here—that is, with both positive and negative lag weights allowed—the average lag statistic (θ) is computed by using the absolute values of the weights; the results are reported in Table 4.

The majority of the countries show an average lag of one to three quarters. Indeed, some cases show very quick responses, with an average lag of less than one quarter. The longest average lags are for the United States (9.2 quarters), the Federal Republic of Germany (3.3 quarters), and the Netherlands (6.7 quarters) for the trade balance and Switzerland (6.9 quarters) for the overall balance. Aside from these exceptions, all other average lags are less than three quarters, emphasizing the quickness of the balance of payments response to changes in the RPI.

A by-product of this study is the evidence it provides for the effects of the RCY. For the trade balance, six countries have significant coefficients for the impact and/or the long-run effect, all of which have a negative sign. For the overall balance, nine countries have at least one significant effect, where the impact effects tend to be negative and the long-run effects tend to be positive. Indeed, there is one case—the United States—that reports a significant negative impact effect and a significant positive long-run effect, suggesting that a change in the sign of the RCY lag weights can also occur. Since, by construction, both the RPI and the RCY have their lag distributions determined by the coefficient on the lagged dependent variable, they tend to have the same sort of lag distributions. In general, the RCY distributions have a smaller average lag than those of the RPI distributions. Finally, the size of the long-run coefficients for both the RCY and the RPI are fairly similar.

IV. Summary and Conclusions

The PPP theory suggests that when a country’s currency is overvalued, as measured by the RPI, it should be facing a balance of payments deficit or a depreciating currency. Motivated by this reasoning, the possibility of using the RPl as a forecasting tool for the balance of payments was envisioned. This paper is an initial step toward this purpose. The main task taken up here is to find supportive evidence for a simple and well-behaved relationship between the RPI and the balance of payments. Given that there is no well-established empirical proxy for the RPI, the secondary task is to identify the alternative measures of the RPI that perform best for each country. In this paper, eight proxies for the RPI are investigated. Finally, the literature on this topic recognizes that the relationship between the RPI and the balance of payments should be formulated in terms of full employment. In order to account for the effect of the cyclical nature of economic activity, an additional variable is introduced—the RCY.

The main conclusion of this study is that the relationship between the RPI and the balance of payments, though statistically significant, is quite complex. Consequently, the straightforward use of the PPP theory as a model of balance of payments determination does not seem to be warranted by the results of this study. Indeed, some of the results contradict commonly held expectations. It is commonly held that an increase in the RPI will cause a deterioration in the balance of payments in the long run—a hypothesis that is borne out by these results when the overall balance is used as the measure of the balance of payments. On the other hand, when the trade balance is used (a measure that shows a clearer relationship to the RPI than does the overall balance), the results indicate that an increase in the RPI tends to improve the balance of payments. This rather unusual result serves best to highlight the complexity of the relationship between the RPI and the balance of payments—a relationship that may change both in strength and sign, depending on the underlying source of the disturbance in the RPI.

This paper estimates distributed lag functions of the RPI and the RCY variables with respect to each of two measures of the balance of payments (the trade and overall balances), using data from 14 industrial countries for the period 1963:111 to 1974:IV. The results indicate that the following caveats should be considered in any discussion of the relationship between the RPI and the balance of payments. First, the appropriate measure of the RPI is important, since the results are highly sensitive to it. Second, the relationship involves rather complex lag distributions of the RPI that allow for reversals in the signs of the lag weights. Finally, while the R¯2 of the trade balance results are reasonably satisfactory (about 0.80) for the larger countries, such a simple model of balance of payments determination has low explanatory power for the smaller countries and for the overall balance of payments.

Thus, while there is evidence of a relationship between the balance of payments and the RPI, it is unlikely that much benefit can be reaped from using the latter as a forecast tool for the balance of payments. Not only has the RPI been unable to satisfactorily explain the past history of the balance of payments, but the latter’s reactions to changes in the RPI seem to be complex and short-lived, both characteristics that reduce the usefulness of the RPI as a forecasting tool. These results may not be very surprising, since, after all, the balance of payments would be expected to react to a variety of stimuli that are not embodied in the RPI. It seems fair to say that, particularly for the overall balance, a model of balance of payments determination must include other variables that have been left out of this study. Further research along these lines, then, should either construct more comprehensive reduced forms of the balance of payments determination models or actually estimate the structural models that give rise to the expectation of a relationship between the balance of payments and the RPI measures.

APPENDIX

This Appendix contains the data transformations and the data sources used. All indices have the year 1970 as the base period.

transformations

Weights

The two weights used are the trade and income weights, both of which are constructed for 1970 data. The trade weights are derived by taking the ratios of the sum of imports and exports to and from the ith country with respect to the sum of total imports and exports of the ith country, using figures taken from Direction of Trade, which is published by the International Monetary Fund. The income weights are the ratios of the jth country’s GNP to the total GNP of the rest of the world as viewed by the ith country, both in dollar terms. The rest of the world’s GNP for the ith country is the sum of the GNP of all the countries in this study less the GNP of the ith country.

Relative Cycle Index (RCY)

The construction of this index is the most complex of all the transformations. The purpose of this index is to measure the business cycle position of the ith country with respect to the rest of the world. For this purpose, an industrial production index is chosen to be the relevant indicator of economic activity, and the ratio of current to potential industrial activity is selected as the relevant measure of the business cycle. This ratio is calculated for every country and a weighted average is constructed to make up a business cycle index for the rest of the world, where what the rest of the world is depends on the particular country compared. Potential industrial production is measured principally by a 17-quarter geometric moving average, on the grounds that the “typical” cycle has a period of roughly four years. Given the limitation that data are available for all countries only from 1961:1 to 1974: IV, this procedure permits the construction of the index only up to 1972; IV; consequently, a different procedure was used for the period 1973:1 to 1974: IV. A time trend is fitted to the industrial production index (in logarithms) for the period 1970: IV to 1974: IV and the resulting trend is spliced into the potential production series calculated above. By choosing the time period for the regression to be the moving average period, a smooth splicing is guaranteed since the fitted trend must go through the mean of the sample. The country’s business cycle measure is simply the ratio of the actual industrial production index to the potential industrial production index. For each country, the business cycle measure for the rest of the world is the weighted average of all other countries’ business cycles, where the weights used are either trade or income weights. The relative business cycle measure is simply the ratio of the country’s business cycle index to the comparable index for the rest of the world.

Foreign Price Index

This index is constructed in two steps. First, the price indices for the individual countries are transformed into dollar, rather than domestic currency, indices; then, a weighted average is used to construct the foreign price index. There are two price indices used in this study—the consumer and wholesale price indices—and two weights—the trade and income weights—that imply four measures of the foreign price index. The domestic currency price index is transformed into a dollar price index by multiplying it by an exchange rate index (the actual exchange rate divided by the average exchange rate prevailing in 1970).

Relative Price Index (RPI)

As explained in the text, this index is the ratio of the domestic and foreign price indices. Since there are four foreign price indices, there are four RPIs.

Balance of Payments (BP)

The dependent variable used is constructed by dividing the balance of payments measure (defined below) by GNP and multiplying the quotient by the domestic business cycle index. This procedure is equivalent to standardizing the balance of payments for potential output. The two balance of payments measures are the trade and overall balances. The trade balance is the difference between the seasonally adjusted value of exports (f.o.b.) and imports (c.i.f.), both measured in domestic currency. The overall balance is defined as the change in the net foreign assets of the country, and is also measured in domestic currency.

sources

Data are taken from International Financial Statistics, with the exception of bilateral trade weights, which are calculated from data taken from Direction of Trade.

BIBLIOGRAPHY

Mr. Brillembourg, economist in the Special Studies Division of the Research Department, is a graduate of Harvard University and of the University of Chicago.

For some countries, the data for 1976:1 is based on Fund staff estimates of the price indices.

For reference on the doctrinal history of PPP, see Frenkel (1976) and Officer (1975).

See Rhomberg (1975).

Depending on the approach taken, this standardization takes into account either the different sizes of countries’ trade sectors (the United States being an outlier because of the relatively small size of its trade sector) or, in an asset approach, the different sizes of countries’ asset portfolios.

This procedure, in effect, constrains the income elasticity to be one. This constraint is imposed for the sake of maintaining a simple hypothesis and a reasonable approximation of the true elasticity.

This procedure again constrains the elasticities of the domestic and foreign cycles to be of the same magnitude but opposite in sign. Aside from simplifying the hypothesis, it avoids the problems owing to the high correlation between the two measurements of the business cycle. The alternative specification of including the rest of the world’s business cycle index separately was also tried, but was not reported since the results were very similar to those reported above; only Denmark and Canada have their lag distribution affected.

For the literature discussing this effect, see Mikesell and Goldstein (1975), Masera (1974), Magee (1973), and Williamson (1973).

See Griliches (1967). By introducing both the current and the lagged independent variables, the lag structure of the RPI can be made quite dissimilar to that of the RCY; in particular, the average lags need not be equal. Nevertheless, a caveat is in order. While this formulation goes part way in estimating separate lag structures for the two independent variables, the two lag structures are related, and, consequently, biases may be introduced in the estimated lag structures if the true lag structures are very dissimilar.

The balance of payments is redefined so that it is in equilibrium when the RPI and RCY are zero—that is, when BP* is equal to BP less b0. This redefinition is necessary only because the base year for the indices was chosen without regard to the balance of payments equilibrium.

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