IN RECENT YEARS frequent calls have been made for adjustment by the developing and small industrial countries to correct external and internal imbalances that have persisted since the time of the first oil shock. Furthermore, it has been claimed that in many cases a shift in the real exchange rate, induced by some combination of demand management and exchange rate policies, would be appropriate. This argument is based on the view that the adverse changes in terms of trade faced by many small specialized economies during the 1970s should, to some extent, be regarded as permanent. It follows that the real exchange rate of such countries should not be supported at historical levels in anticipation of corrective (cyclical) terms of trade movements; rather, they should be adjusted toward new, more sustainable levels.

Abstract

IN RECENT YEARS frequent calls have been made for adjustment by the developing and small industrial countries to correct external and internal imbalances that have persisted since the time of the first oil shock. Furthermore, it has been claimed that in many cases a shift in the real exchange rate, induced by some combination of demand management and exchange rate policies, would be appropriate. This argument is based on the view that the adverse changes in terms of trade faced by many small specialized economies during the 1970s should, to some extent, be regarded as permanent. It follows that the real exchange rate of such countries should not be supported at historical levels in anticipation of corrective (cyclical) terms of trade movements; rather, they should be adjusted toward new, more sustainable levels.

IN RECENT YEARS frequent calls have been made for adjustment by the developing and small industrial countries to correct external and internal imbalances that have persisted since the time of the first oil shock. Furthermore, it has been claimed that in many cases a shift in the real exchange rate, induced by some combination of demand management and exchange rate policies, would be appropriate. This argument is based on the view that the adverse changes in terms of trade faced by many small specialized economies during the 1970s should, to some extent, be regarded as permanent. It follows that the real exchange rate of such countries should not be supported at historical levels in anticipation of corrective (cyclical) terms of trade movements; rather, they should be adjusted toward new, more sustainable levels.

While it may be difficult in many countries to achieve even small real exchange rate movements in the direction of a sustainable equilibrium, there would nevertheless appear to be a need for a better understanding of the size of real exchange rate adjustments that may be required to fully offset a given change in the terms of trade. More specifically, the concern in this paper is to consider the size of real exchange rate adjustments, defined in terms of relative gross domestic product (GDP) deflators, that may be required to offset the trade balance effects of a change in the terms of trade, given that aggregate activity is maintained at some initial preshock level.

In Section I a simple model is developed of a small open economy facing infinite foreign price elasticities and having a fixed level of total output. A comparative static result is then derived that gives the combinations of terms of trade and real exchange rate changes that are required to maintain a given initial trade balance. This result is quantified in Section II, where estimates are obtained of trade elasticities and share parameters for five small industrial countries—Australia, Denmark, Finland, Ireland, and New Zealand. The sensitivity of outcomes is discussed in Section III, largely within the context of intercountry differences in parameter estimates.

I. The Model

There is now a considerable literature on the macroeconomic implications of price shocks arising from commodity markets, but little of this work has considered the situation in which a permanent terms of trade shock is imposed on a small open economy. Models of the open economy have typically included two traded goods, with the domestic economy facing an infinitely elastic supply of a foreign final good but facing a relatively inelastic foreign demand for its own domestic final good. To analyze the effects of an external shock to the relative price of an imported raw material, this framework has been expanded—for example, by Findlay and Rodriguez (1977), Buiter (1978), Bruno and Sachs (1979), and Obstfeld (1980)—to include a third importable good, which is used as an intermediate input into domestic production and which has its price set in relation to the foreign final good. The experiment that is typically conducted within such a framework involves a change in the foreign relative price of the intermediate import. As domestic expenditures and production respond to this shift, the impact of the relative price change may then be traced, inter alia, to shifts in both the real exchange rate and the terms of trade.

In moving to a small open economy model, the exportable domestic product becomes a perfect substitute for the foreign final good, and consequently both importers and exporters become price takers. Within this framework, an external relative price shock is seen as an exogenous shift in the terms of trade. For the overall domestic price level, and hence the real exchange rate, to respond to such a shock, it becomes necessary to distinguish a nontraded good from the two (importable and exportable) traded goods. If, however, the intention is to conduct an empirical analysis within a macroeconomic framework, the prospect is raised of a considerable task of modeling and data collection; for this reason, it is convenient here to adopt a number of simplifying assumptions. First, given that the concern here is not with cyclical fluctuations in aggregate production but with medium-term effects on patterns of production and absorption, it is assumed that total domestic output is fixed. Second, it is assumed that production of traded goods is concentrated in exportables and that absorption of traded goods is concentrated in importables. These latter two assumptions allow substitution possibilities to be characterized by one export supply elasticity and one import demand elasticity.

The four components of supply and demand in the model are given by equations (l)-(4). With supply decisions constrained by a fixed level of total output, the supply of exports is determined as a price-sensitive ratio of total output. The supply of nontraded goods is determined residually in equation (2); in that this assumes perfect substitution in production, the domestic economy may best be seen here as the producer of just one good that is sold both on a protected home market at a monopoly price and on the export market at a fixed world price. On the demand side, the scale variable adopted is nominal output deflated by a domestic expenditure price; absorption is thus affected by changes in purchasing power arising through terms of trade movements. The relative demand price entering the import equation is also deflated by the expenditure price. To maintain internal equilibrium within the model, equation (4) sets the demand for nontradables equal to supply. While the domestic economy’s “nontraded” and export products may be distinguished only as a result of price discrimination between home and export markets, the “non-traded” product is necessarily an imperfect substitute for the imported good.

QX=QX(PX/PQ).Q(1)
QNT=QQX(2)
DM=DM(PM/PD,Q.PQ/PD)(3)
DNT=QNT(4)
D=DM+DNT

Notation:

  • Qx = volume of exports

  • QNT = volume of production of nontraded goods

  • Q = fixed volume of total output

  • DM = volume of imports

  • DNT = real domestic expenditure on nontraded goods

  • D = total real domestic expenditure

  • Px = export price index, in local currency

  • PM = import price index, in local currency

  • PQ = GDP deflator

  • PD = domestic expenditure deflator

Price and income elasticities are defined as follows:

α=lnQX/ln(PX/PQ)η=lnDM/ln(PM/PD)ε=lnDM/ln(Q.PQ/PD)

The price indices for both output and expenditure can be expressed in terms of the three product prices with weights reflecting the shares of exportables and importables in total output and absorption, respectively:

PQ=γPX+(1γ)PNT(5)
PD=σPM+(1σ)PNT(6)

The terms of trade and real exchange rate are defined as

T=PX/PM(7)

and

R=EPQ*/PQ

where E is the nominal exchange rate and * denotes the foreign equivalent. Defining θ as the expenditure price of traded goods relative to the output price, the assumption of no consumption of exportables in the home country implies that

θ=PM/PQ(8)

If δ is taken as the proportion of foreign expenditures for traded goods on goods that are exportable by the home country, the foreign equivalent is

θ*=[(1δ)PM+δPX]/PQ*E(9)

and the real exchange rate can be expressed as

R=[(1δ)+δT]θ/θ*(10)

The measure of the external balance that is to be kept fixed is the local currency trade balance as a proportion of GDP

B=(PXQXPMDM)/Q.PQ

Substituting equations (1), (3), (5), (6), (7), and (8) in this expression and setting the total differential equal to zero, a linear homogeneous equation is obtained1 in dlnT and dlnθ (equation (11)) with arguments WT and Wθ, depending on the two share parameters (γ and σ), the elasticities (α, η, and ε), and the size of the initial current account balance as a proportion of nominal output ( ϕ ).2

Wθdlnθ+WTdlnT=0(11)

where

Wθ=γ(1Φ)σ+αγησ(1σ)(1Φ)(1γ)+εσ(ογ)(1Φ)(1γ)(12)

and

WT=γ+ασησ(1σ)(1Φ)γ/(1γ)εσ(1σ)(1Φ)(1γ)(13)

Condition (11) combined with the real exchange rate expression in equation (10) implies that

dlnRdlnT|dB=0=dlnθdlnT|dB=0dlnθ*dlnT+δ=WT/Wθdlnθ*dlnT+δ(14)

Thus, provided that the relative price (θ*) of foreign traded goods is unaffected by movements in the home country’s terms of trade and provided that the home country’s exports represent a small proportion of total foreign expenditures on traded goods, one may focus on the quantity m = −WTWθ as a measure of the adjustment required to maintain a constant trade balance in the face of a terms of trade shift. For a small specialized economy, δ will certainly tend to be small, and if terms of trade fluctuations emanate primarily from movements in the foreign relative price of the home country’s exports, then the assumption of a fixed θ* will also be acceptable. However, if a terms of trade shock is seen to result primarily from a shift in the foreign relative price of the home country’s imports, the implied change in θ* will not be negligible, and it will become necessary to estimate this change to obtain a proper assessment of the required real exchange rate adjustment. Notwithstanding this caveat, the empirical analysis here does not relate to specific terms of trade shocks, and so, by default, it is assumed that the relative price (θ*) of foreign traded goods remains fixed.

Before going on to derive estimates of m for specific sets of country parameters, it may be of use to discuss briefly the structure of Wθ and WT as defined in equations (12) and (13). Each of these expressions comprises four components representing the four channels in the model through which movements in the real exchange rate and the terms of trade affect the trade balance. The four types of effects are as follows:

(1) Pure valuation effects. These are caused primarily through terms of trade movements but also through real exchange rate adjustments when there is an initial trade account imbalance. If the comparative static result is derived on the alternative basis of a fixed trade balance in foreign currency terms, the only change that is required in the expressions for Wθ and WT in equations (12) and (13) is the elimination of the exchange rate valuation effect, that is, the elimination of the first two terms in equation (12).

(2) Relative price effects on the volume of exports. These are equal in size between the two expressions with equivalent increases of 1 percent in T and θ both leading to increases of γα percent in export volumes.

(3) Relative price effects on import volumes. A terms of trade improvement (increase in T) and a real exchange rate depreciation (increase in θ) both improve the trade balance through this channel, a real depreciation more so than an equivalent terms of trade improvement. The result, that an increase in the terms of trade causes an improvement in the trade balance through an increase in the relative price of imports, is somewhat counterintuitive. It must be recalled, however, that WT represents a partial derivative, giving the trade balance effects of a terms of trade change for a fixed real exchange rate level. If the real exchange rate is allowed to appreciate as the terms of trade improve, then the net effect is a decrease in the relative price of imports, which tends to worsen the trade balance.

(4) Real income effects on import volumes. The trade balance improvement caused by the valuation and substitution effects of a terms of trade improvement are offset to some extent by the income effect, which causes import volumes to increase. The impact of income effects resulting from real exchange rate movements depends on the relative proportions of traded goods in production and expenditure, that is, on the sign of (σ − γ). If, for example, imports represent a greater proportion of domestic expenditures than exports represent as a proportion of total production, then a real depreciation causes a reduction in real income, which tends to improve the trade balance. In the reverse case, a real depreciation tends to worsen the trade balance through this channel.

II. Parameter Estimates for Five Small Industrial Countries

The six parameters entering expressions (12) and (13) are estimated here for each of the five small industrial countries—Australia, Denmark, Finland, Ireland, and New Zealand. The three elasticities are estimated using time-series regressions, while estimates for the three ratios are based on simple historical averages.

regression estimates

Ideally, one wants to estimate export supply and import demand functions that are essentially of the form described in Section I. Given that the expressions in equations (1) and (3) are simple long-run relationships, however, these are modified somewhat in an attempt to allow for the short-term effects of business cycles, lagged relative-price effects, and unusual historical events that would tend to bias elasticity estimates derived from simple static estimating equations. Furthermore, the two equations are disaggregated to allow for parameter differences across broad commodity groupings. Both the export and import estimating equations are reduced form equations in that all right-hand variables are predetermined for this model. They are estimated on annual data extending over the 20-year period from 1960 to 1980.

Export supply

Based on equation (1), the general form adopted here for estimating equations is as follows:

ln(X/PX)tlnQt=α0+α1(L)ln(PX/PQ)t+α2ln(QF/QFT)t+α3ln(Q/QT)t+α4TD(15)

where3

  • X = local currency value of merchandise exports f.o.b.

  • PX = export unit value

  • Q = GDP in constant (1975) prices

  • PQ = GDP deflator

  • QF = index of foreign GDP, in constant prices

  • QT = exponential trend in output, formed as the exponential of predicted values from the regression of ln Q on a constant and a trend

  • QFT = exponential trend in QF, formed in the same manner as QT TD

  • TD = time trend

  • L = lag operator

  • α1(L) = Almon lag polynomial (Estimated long-run relative-price elasticity α = α1(l) = sum of the estimated Almon lag coefficients.)

Thus, the proportion of output exported is given as a function of (1) lagged relative prices intended to capture medium-term substitution effects; (2) domestic and foreign cyclical variables intended to pick up the direct demand effects that circumvent the price mechanism in the short term; and (3) a time trend intended to capture secular shifts in output composition. In the actual estimating equations, kinked trend variables are used where significant shifts in trend growth have occurred during the sample period. Dummy variables are also included to allow for specific historical events. The results presented in Table 1 show that the actual estimating equations include lags and first differences rather than current levels of the cyclical variables wherever these give a better representation of cyclical demand pressures.

In the five countries under consideration, exports are commonly concentrated in a small number of distinct commodity groupings. Consequently, it is considered that the estimates of the aggregate relative-price elasticity may be improved substantially by estimating separate equations of the form (15) for significant export subaggregates that are in one or more of the following four categories of Standard International Trade Classification (SITC):

Table 1.

Five Small Industrial Countries: Estimates of Export Supply Equations, 1961-801

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**Indicates a significant F-test at the 1 percent level; * would indicate a significant F-test at the 5 percent level.

Standard errors are in parentheses. All estimates are by ordinary least squares.

For New Zealand, raw material exports consist mainly of animal and vegetable products that are closely linked to agricultural production. Accordingly, exports of agricultural products and raw materials are treated here in the aggregate.

Lags of cyclical variables are indicated where used.

This weight is spread over both current and lagged levels of the regressor.

Country definitions of TD1 and TD2, and of DUM1 and DUM 2, are given in Appendix I.

First number in parentheses gives degree of polynomial restrictions. The second number gives the type of end-point restriction adopted: 0=none; 1 = near-end zero restriction; 2=far-end zero restriction. The third number gives the estimated average length of lag in years. The F-statistic provides a test of the polynomial lag structure against an unrestricted distributed lag of the same length.

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The intention here is not to focus on relative price movements between these commodity groupings, but rather to allow the magnitudes and lag structures of the same right-hand parameters in equation (15) to vary between the groups and to allow the use of group-specific dummy variables. Thus, apart from equation-specific dummies and variations in the dynamic form of the cyclical variables, the regression set remains as in equation (15) and the overall relative-price elasticity is derived by taking a simple weighted average of the disaggregated elasticity estimates. The weights used to construct the aggregate supply elasticities in Table 2 indicate that those subcategories of exports taken as exogenous contribute negligibly to country totals.

The estimated aggregate supply-price elasticities that are reported in Table 2 are all of a similar magnitude, lying within the range from 0.5 to 1.5. The size of standard errors given in Table 1 indicates that it is the smallest of these elasticities—for Ireland—that is the most precisely determined. The commodity-group elasticities for Ireland have standard errors of about 0.15, compared with an across-country median standard error of approximately 0.4. The time profile of lagged relative-price effects, as revealed in Table 1, is seen to vary widely across commodity groups and countries. The average length of lag, however, is commonly found to lie between two and four years.

In making comparisons with previous elasticity estimates, the numbers obtained here appear to be generally consistent with the small amount of available evidence. Econometric results reported in the economic survey for Denmark (OECD (1979)) include an estimated export volume equation that, while demand based, supports a significant profitability effect with an elasticity in the region of 0.6 to 1.0. In a survey of empirical work on Australia’s balance of payments, Macfarlane (1979) finds agreement that a supply-based model is appropriate for export volumes, but, as a result of difficulties encountered in identifying stable supply functions, he finds that the evidence on export supply-price responses is scant and inconclusive. Evidence on export supply responses for Finland is also scarce, but in this instance it would seem, for example from work by Aurikko (1975), that the small-country assumption has been rejected in favor of a demand-based explanation of export volumes. For New Zealand, a number of estimated export supply-price elasticities are reported in Deane and others (1981, Chap. 25); in general, these elasticities lie within the vicinity of the estimates obtained here. Finally, the available evidence for Ireland is limited, with agricultural supply models having concentrated on overall production rather than on exports. Supply-price elasticities have been estimated by O’Connell (1977) for manufactured exports; these lie in a range (2.0 to 3.0) that is considerably higher than the estimate (0.6) reported in Table 1. However, O’Connell’s estimating equations do not include an output scale variable, and therefore they are not directly comparable with the share supply equations estimated here.

Table 2.

Five Small Industrial Countries: Derivation of Aggregate Export Supply-Price Elasticities, 1960-801

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The “share” reported is the 20-year average. Estimates of elasticities are from Table 1.

Import demand

The demand for import volumes is disaggregated on a simple fuels, nonfuels basis, the main objective being to filter out any spurious effects on aggregate elasticity estimates resulting from the two oil shocks. To achieve this, it is of course necessary to explain the two import components as functions of their own relative prices rather than of a single overall relative price, as used in the disaggregated export equations. However, given that the demand for fuels is expected to be relatively inelastic, separate cross-price effects between fuels and nonfuels are not considered. Estimating equations, based on equation (3), are thus of the form

ln(M/PM)t=β0+β1ln(Q.PQ/PD)t+β2(L)ln(PM/PD)t+β3ln(Q/QT)t+β5TD(16)

where4

  • M = local currency value of merchandise imports f.o.b.

  • PM = import unit value

  • PD = domestic expenditure deflator

and all other variables are as defined for equation (15). Equations of this form are estimated for each of the five countries, with M and PM being replaced by MF and PMF for fuel imports and by MNF and PMNF for nonfuel imports where

  • MF = imports of fuels, in local currency (SITC 3)

  • MNF = imports of nonfuels, in local currency (SITC 0-2, 4-8)

  • PMF = unit value for fuel imports

  • PMNF = unit value for nonfuel imports

As in the export supply equations, cyclical and trend terms are included here in an attempt to account for both direct short-term demand effects and longer-term shifts in tastes and production patterns. In the imports equation, however, only a domestic cyclical variable is included, as fluctuations in foreign output are assumed to have no significant direct effect on the supply of imports available to the five countries under consideration. Table 3 shows that the first difference rather than the level of ln(Q/QT) was generally found to give the best representation of domestic cyclical pressures on import volumes. Estimates of the aggregate income and relative-price elasticities, ε and η, are derived in Table 4 as simple weighted averages of the β1 and (β2 estimates, respectively.

Within the context of the model described in Section I, the estimating equation (16) is in reduced form, but from a statistical viewpoint one may suspect a degree of (negative) reverse causality from import volumes to output and therefore some downward bias in the estimates for both income and relative-price elasticities. For this reason, the import equations were re-estimated using foreign GDP, the terms of trade, and real government expenditure as instrumental variables. The resulting elasticity estimates, however, were similar to the ordinary least-squares estimates reported in Tables 3 and 4.

The lag structures on the relative price effects are of a simple form with no more than two price terms entering each equation and with no lags longer than one period. Such specifications were found to be most suitable following initial experiments with longer polynomial distributed lag structures. The estimated relative-price elasticities are all of a moderate size, lying between − 0.38 and − 0.86. In comparison with estimates from previous studies, the values derived here for Denmark, Finland, and New Zealand seem to be reasonably consistent. However, the surveys by McAleese (1970) and Macfarlane (1979) for Ireland and Australia, respectively, both report demand-price elasticity estimates in the region of − 1 to − 1.5. This discrepancy may be attributed in part to the use here of domestic cyclical variables, which tend to explain variations that might otherwise be picked up by the relative price terms. Furthermore, the studies cited in these surveys were based on data covering earlier historical periods, which tend to yield larger elasticity estimates for the two countries concerned.

Table 3.

Five Small Industrial Countries: Estimates of Import Demand Equations, 1961-801

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Standard errors are in parentheses. All estimates are by ordinary least squares.

No estimates of any accuracy could be obtained for the volume of Australia’s fuel imports as a result of significant variations in domestic production.

Country definitions of DUM1, DUM2, and DUM3 are given in Appendix I.

Table 4.

Five Small Industrial Countries: Derivation of Aggregate Import Demand Price and Income Elasticities, 1960-801

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Reported shares are 20-year averages. Estimates of elasticities are taken from Table 3.

Default value for the Australian income elasticity of demand for fuel imports is taken as 1.0.

The estimated income elasticities of demand for imports are all found to be greater than one, lying between 1.03 for Australia and 1.40 for Ireland. Within the context of a steady-state growth model, a “long-run” income elasticity of demand that differs from one will cause the model to be dynamically unstable, but the present concern is to analyze relative price-induced income effects within a comparative static framework; within this context, a unity restriction is not considered to be appropriate. The income elasticity estimates reported in Table 4 are not inconsistent with comparable estimates derived in previous studies.

RATIO ESTIMATES

The three parameters of the model that remain to be estimated are

  • γ = the share of total domestic output in exports

  • σ = the share of total domestic expenditure in imports

  • ϕ = the current account balance as a proportion of nominal output.

The values adopted for these parameters are the average values of the actual ratios over the last five years (1976-80) of the sample period.5 These numbers serve to characterize the average structure of the five economies over recent history, although it is clear that, in analyzing specific episodes, one may wish to base the parameter estimates on alternative historical periods. Indeed, if the objective is to formulate an appropriate response to a terms of trade shift that has already occurred, it may be of interest to use preshock parameter estimates in expression (13) for WT and post-shock estimates in expression (12) for Wθ. The estimates based on data for 1976-80 are given in Table 5.

Table 5.

Five Small Industrial Countries: Ratio Parameter Estimates, 1976-80

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III. Comparative Static Results

In this section, the parameter estimates presented in Tables 2, 4, and 5 are used to quantify the comparative static relationship, derived in Section I (equation (11)), between changes in the real exchange rate and the terms of trade that have offsetting effects on the trade balance. The quantity used to summarize this relationship is

m=dlnθdlnT|dB=0=WT/Wθ

As discussed in Section I (cf. equation (14)), for any given value of the foreign relative price (θ*) of traded goods, this quantity approximates the percentage real depreciation required to offset the effect of a permanent improvement of 1 percent in the terms of trade.6 The sensitivity of country results is discussed largely within the context of intercountry differences, although variations in price elasticities outside the observed range are also considered. This is seen in Table 6 where values of m are reported both on the basis of best parameter estimates and using a range of alternative import and export price elasticities. The ranges of price elasticities considered—0.0 to 1.5 for exports and 0.0 to −1.0 for imports—correspond roughly to the ranges observed across the five countries, and thus enable comparisons to be made between countries with effects that are due to differences in elasticities neutralized.

Considering briefly the tabulated figures corresponding to econometric elasticity estimates (those boxed in the tables), the absolute m-values are seen to be considerably smaller for the two countries—Finland and Ireland—that have the largest import price and income elasticities. These countries both have price elasticities in the region of −0.8, income elasticities of 1.3 to 1.4, and m-values close to—1. The remaining three countries all have import-price elasticities in the region of −0.4 to −0.5, income elasticities between 1.0 and 1.2, and m-values near −1.3. There is an indication, therefore, that one or both of the import elasticities have a significant bearing on the size of m. The relative importance of the import-price elasticity vis-à-vis the export-price elasticity is supported further by the general pattern of values observed in Table 6 where, at least for nonzero α, the gradient of m by η appears to be steeper than the gradient of m by α. The lesser role of the export-price elasticity α is demonstrated for Ireland, where relatively high import-price and income elasticities dominate a low export-price elasticity to give |m | less than one. In the three countries with relatively steep tradeoffs, | m | may be ranked inversely by the size of |η | ; relatively large export-price and import-income elasticities for Denmark do not significantly affect that country’s trade-off position relative to Australia and New Zealand.

Table 6.

Five Small Industrial Countries: Trade-Offs Between Real Exchange Rate and Terms of Trade

Tabulated m-values give the percentage real depreciation required to offset the trade balance effects of an increase of 1 percent in the terms of trade, for given values of country parameters.1

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Recalling again the definitions of model parameters:

  • α = export supply-price elasticity

  • η = import demand-price elasticity

  • σ = share of merchandise imports in total domestic demand

  • γ = share of merchandise exports in total domestic output

  • ε = income elasticity of demand for imports

  • ϕ = current account balance as proportion of nominal output

Investigating further the relationship between m and the two relative-price elasticities, it is readily apparent from the tabulated figures that the extent of reductions in | m | resulting from absolute increases in one of the elasticities depends inversely on the absolute size of the other. In the situation in which elasticities become large, however, the relationship loses symmetry; the gradient of m with respect to ηapproaches zero as a becomes large, but the gradient of m with respect to a becomes positive for large |η | values. Specifically, with a carrying the same weight in both the Wθ and WT expressions (equations (12) and (13)), increases in a are found to increase the value of | m when | m | is smaller than one. From the tabulated figures, it would appear that this point is reached for every country except Ireland, when η reaches a value in the region of −0.8 to −1.0. For Ireland, | m | approaches one when η equals −0.6. In contrast, the import-price elasticity η always carries a larger weight in Wθ than in WT, and consequently a larger demand-price elasticity almost always reduces |m |.7

Considering briefly the behavior of m-values when both of the relative-price elasticities approach zero, it is apparent from equation (12) that the total real exchange rate effect Wθ comes to be dominated by real income and valuation effects that are small and of uncertain sign. In such a situation, the real exchange rate clearly ceases to be a relevant policy variable and m becomes rather meaningless; accordingly, m-values for α = 0, η = 0 are not tabulated.

While both the valuation effects and the export and import relative-price effects of an improvement in the terms of trade are positive, the terms of trade income effect that operates through import volumes is seen to work in the opposite direction, reducing the need for offsetting real exchange rate adjustments. Income effects resulting directly from real exchange rate adjustments are proportional to (σ − γ) and stabilize the trade balance when this quantity is positive. Such effects, however, are relatively small compared with terms of trade income effects; furthermore, they are more than offset by the direct valuation effects of real exchange rate adjustments that are destabilizing under an initial deficit position. It follows that the income elasticity of demand for imports ε has its primary influence on m through the terms of trade income effect and, therefore, that | m | varies inversely with €. The size of real income changes resulting from terms of trade movements depends mainly on the size of the traded goods sector, and consequently the influence of ε on | m | is greater in those countries with large traded goods sectors.

Evaluating the influence on m owing to the size of the initial trade balance, a worsened initial position—caused, say, by a ceteris paribus increase in α—tends to magnify the stabilizing income and relative-price effects of real exchange rate changes. It also increases the degree to which terms of trade movements are self-correcting. As mentioned earlier, however, the real exchange rate valuation effect becomes more destabilizing as the initial balance position worsens. This effect becomes relatively less important as the size of the traded goods sector increases, but even for Ireland it is large enough so that a worsened initial deficit causes |m| to increase. The net influence of the initial trade balance may be demonstrated in a comparison of the tabulated figures for Denmark and Finland, where, for similar income elasticities and traded goods shares, | m | values corresponding to like price elasticities are found to be higher for that country (Denmark) which has the larger initial deficit position.

To see how the size of the traded goods sector may affect m, it is necessary to look at the general level of cr and y rather than at their difference. The task may be made easier by assuming that both the trade and current accounts are initially in balance. Substituting γ = α and ζ = 0 in equations (12) and (13), the expression for m reduces to

m=WTWθ|σ=γΦ=0=γ(ε+η)(1+α)(αη)(17)

and the absolute value of m ′ is seen to be inversely proportional to γ, provided that (ε + η) is positive. Providing some rationale for this condition, an increase in the size of the traded goods sector leads to near-proportionate increases in all relative-price and valuation effects that are caused by real exchange rate changes and, similarly, proportionate increases in the export relative-price and valuation effects that are caused by terms of trade changes. However, the terms of trade effects working through relative import prices and real income increase more than proportionately with the traded goods share and so, provided that the net impact of these two effects is negative (stabilizing), an increase in the relative size of the traded sector reduces the real exchange rate adjustment required to offset a given terms of trade change. Given that (ε + η) is indeed found to be positive for each of the five countries, one may thus expect to see larger traded goods sectors associated with absolutely smaller m-values. Unfortunately, intercountry differences in tabulated m-values that relate specifically to the size of the traded goods sector are not easily detected, as there is no one country that provides a suitable “control” for any other. However, the table for Australia may be recalculated with ε = 1.304 and 4ϕ= −0.010 and may be compared with the table for Finland to give an indication of differences in m resulting from a traded goods share of 0.26 for Finland as opposed to 0.13 for Australia. Comparing figures based on the Australian relative-price elasticity estimates, the higher traded goods share appears to decrease | m | by approximately 0.06.

While the real exchange rate adjustment to a terms of trade shock may become smaller as the traded goods sector becomes larger, it should be recognized that real exchange rate adjustments also become harder to achieve in that larger movements are required in the relative price of nontraded goods. Using the model equations from Section I, it can be shown that the relative non-traded goods price adjustment associated with any given m-value is

dln(PNT/PQ)dlnT|dB=0=γ(m+1)(1γ)(18)

Considering the simplified definition of m given in equation (17), this expression indicates that an increase in γ will increase the required adjustment in the relative price of nontraded goods even though | m | will tend to fall. Of course, in the extreme case in which the nontraded sector becomes small—that is, γ approaches one—then m approaches − 1 as the real exchange rate becomes more like the inverse of the terms of trade; but trade balance adjustment to a terms of trade shock becomes more nearly impossible as the required change in the price of nontraded goods approaches infinity.

IV. Conclusion

The aim of the foregoing analysis has been to develop a simple framework that may be used to derive an estimate of the real exchange rate correction required to maintain the trade balance of a small open economy under a permanent exogenous shift in the terms of trade. The framework is based on the assumption of an infinite elasticity of demand for exports, stable export supply and import demand functions, and a fixed long-run level of real GDP. Goods are classified as either exportable, importable, or nontraded, and the traded goods sector is assumed to be completely specialized in that no importables are produced and no exportables are consumed. Furthermore, it is assumed that the domestic price level is controlled in the long run, independently of terms of trade and real exchange rate movements.

Based on this list of simplifying assumptions, an economy that is suitable for analysis within the framework should be specialized and also small in that it exerts little influence on world prices for traded goods. To justify the concentration on the trade balance, it should also have a balance on invisibles account that is relatively stable under terms of trade and real exchange rate shocks. A number of both developing and small industrial countries fit this description reasonably well, although the empirical application here was concerned solely with countries from the latter group—Australia, Denmark, Finland, Ireland, and New Zealand.

The relationship between terms of trade changes and “offsetting” real exchange rate changes is summarized by the quantity m, which gives the percentage real depreciation that is required to neutralize the trade balance effects of an increase of 1 percent in the terms of trade. Based on empirical estimates of six model parameters for each of the five countries under consideration, this quantity was found to range between −0.92 for Ireland and −1.37 for Australia.

Of the underlying model parameters, emphasis was placed on the estimation of trade-price and income elasticities. Econometric time-series estimates of export supply and import demand equations yielded export supply-price elasticities between 0.5 and 1.5, and import demand-price elasticities between −0.4 and −0.9. The latter estimates, while spanning a relatively narrow range, were nevertheless found to have a dominant influence on the relative size of m-values. Increases in export supply-price elasticities were seen to reduce the absolute size of m significantly for small import-price elasticities but also to increase the absolute size of m for import-price elasticities that were large enough to reduce | m | below one. As already indicated, however, the estimated import-price elasticities were not so high as to trigger this somewhat perverse relationship.

Income effects, felt in the model through the demand for import volumes, are generated both by terms of trade movements and by real exchange rate adjustments. The real exchange rate income effect is stabilizing when the share of traded goods in domestic demand is greater than the traded goods share in production, but this is usually dominated by the terms of trade income effect, which is always stabilizing. Both types of income effect are influenced directly by the size of the traded goods sector (α, γ) and by the income elasticity of demand for imports e. The parameters measuring traded goods shares were found to range between 0.11 and 0.49, while the income elasticities of import demand fell between 1.03 and 1.40. In both cases, the largest estimates obtained were for Ireland, which indicates that the proportion of adjustment to be achieved through income effects is significantly greater for Ireland than for the remaining countries.

While a larger traded goods sector tends to reduce | m | through larger stabilizing real income effects, there is also an opposite influence resulting from an increase in the terms of trade effect working through the relative import price. The net influence of the traded goods share on the size of | m | nevertheless remains negative, provided that the sum of the income and price elasticities of demand for imports is positive. This condition was met for all five countries, but it was noted that when an increase in the traded goods share reduces the size of the required adjustment to a terms of trade shock, it also makes it more difficult to achieve.

I. Data Sources and Definitions for Regression Analysis

All nondummy variables are derived from data in International Monetary Fund, International Financial Statistics (IFS), unless stated otherwise.

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Dummy variable definitions

Before defining variables on a country-by-country basis, the following examples demonstrate the naming convention adopted.

D71 takes the value 1 in 1971, zero elsewhere.

D7172 takes the value 1 in 1971, 1 in 1972, zero elsewhere.

DD71 takes the value 1 in 1971, − 1 in 1972, zero elsewhere.

TD70 takes the values of a linear trend from 1960 to 1970 and the value of TD70 at 1970 from 1971 to 1980. TD7180 takes the values of a linear trend from 1971 to 1980, zero elsewhere. Variable definitions by country, by equation, are as follows:

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II. Derivation of Equations (11), (12), and (13) as Given in Section I

Model equations required to derive the comparative static result are as follows:

QX=QX(PX/PQ)Q(19)
DM=DM(PM/PD,QPQ/PD)(20)
PQ=γPX+(1γ)PNT(21)
PD=σPM+(1σ)PNT(22)
T=PX/PM(23)
θ=PM/PQ(24)
B=(PXQXPMDM)/PQQ(25)

First obtaining the relevant price ratios, equations (21), (22), (23), and (24) may be used to give

PX/PQ=θT(26)
PNT/PQ=(1γθT)(1γ)(27)
PQ/PD=(1γ)/[σθ(1γ)+(1σ)(1γθT)](28)
PM/PD=θ(1γ)/[σθ(1γ)+(1σ)(1γθT)](29)

Now, setting dB = 0 and taking initial values of QX/Q and DM/Q as γ and σ(1 − ϕ), respectively,8 we have

γdln(PXQXPQQ)=σ(1Φ)dln(PMDMPQQ)(30)

Expanding the total differentials on each side of equation (30) and substituting in the elasticity definitions from Section I:

γ[dln(PXPQ)+αdln(PXPQ)]=σ(1Φ)[dln(PMPQ)+ηdln(PMPD)+εdln(QPQPD)](31)

Making use of equations (26) to (29), and defining all price ratios as having an initial scale of one, equation (31) can be expressed in terms of just dlnθ and dlnT:

γ(α+1)(dlnθ+dlnT)=σ1Φ[(1+η)dlnθ+(ε+η)(γσ)(1γ)dlnθ+(ε+η)(1σ)(1γ)dlnT](32)

Finally, collecting terms and moving everything to the left-hand side, we have

Wθdlnθ+WTdlnT=0

where

Wθ=γ(1Φ)σ+αγησ(1σ)(1Φ)/(1γ)+εσ(σγ)(1Φ)/(1γ)

and

WT=γ+αγησ(1σ)(1Φ)γ/(1γ)εσ(σγ)(1Φ)γ/(1γ)

The partial derivatives Wθ and T are expressed here, as in Section I, with separate additive terms representing valuation effects, export relative-price effects, import relative-price effects, and import income effects, in that order.

REFERENCES

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*

Mr. Spencer, economist in the External Adjustment Division of the Research Department, holds degrees from Victoria University of Wellington and the London School of Economics and Political Science. He is currently on leave of absence from the Reserve Bank of New Zealand.

1

See Appendix II for a full derivation of equations (11), (12), and (13).

2

The initial scale of the current balance, rather than the trade balance, is required to determine the scale of total absorption relative to total output.

3

Data sources for the regression analysis are given in Appendix I.

4

Data sources for the regression analysis are given in Appendix I.

5

Once ϕ is determined from current account and GDP data, then the total domestic demand series used to estimate a is just the GDP series scaled up by (1-ϕ)

6

A real appreciation occurs when θ falls.

7

The only requirement here is that | m | be greater than γ.

8

Recalling that ϕ is the initial current account deficit as a proportion of GNP, (1 − ϕ)Q approximates the scale of total domestic demand and cr(l − ϕ)Q approximates the scale of total imports.