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.

Notation:

• Q_x = volume of exports

• Q_NT = volume of production of nontraded goods

• Q = fixed volume of total output

• D_M = volume of imports

• D_NT = real domestic expenditure on nontraded goods

• D = total real domestic expenditure

• P_x = export price index, in local currency

• P_M = import price index, in local currency

• P_Q = GDP deflator

• P_D = domestic expenditure deflator

Price and income elasticities are defined as follows:

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:

The terms of trade and real exchange rate are defined as

and

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

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

and the real exchange rate can be expressed as

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

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 W_T and W_θ, 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

where

and

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

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 = −W_TW_θ 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 W_θ and W_T 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 W_θ and W_T 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 W_T 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:

$\begin{array}{ccc}\ln {(X/PX)}_t-\ln Q_t=& {\alpha }_0+{\alpha }_1\left(L\right)\ln {(PX/PQ)}_t\hfill & \\ & +{\alpha }_2\ln {(QF/QFT)}_t\hfill & \\ & +{\alpha }_3\ln {(Q/QT)}_t+{\alpha }_{4}TD\hfill & \left(15\right)\end{array}$

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

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

¹Standard errors are in parentheses. All estimates are by ordinary least squares.

²For 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.

³Lags of cyclical variables are indicated where used.

⁴This weight is spread over both current and lagged levels of the regressor.

⁵Country definitions of TD1 and TD2, and of DUM1 and DUM 2, are given in Appendix I.

⁶First 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.

Table 1.

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

Country		Australia			Denmark			Finland		Ireland		New Zealand
Dependent variable		$\ln \left(\frac{XA/PX}{Q}\right)$	$\ln \left(\frac{XR/PX}{Q}\right)$	$\ln \left(\frac{XM/PX}{Q}\right)$	$\ln \left(\frac{XA/PX}{Q}\right)$	$\ln \left(\frac{XR/PX}{Q}\right)$	$\ln \left(\frac{XM/PX}{Q}\right)$	$\ln \left(\frac{XR/PX}{Q}\right)$	$\ln \left(\frac{XM/PX}{Q}\right)$	$\ln \left(\frac{XA/PX}{Q}\right)$	$\ln \left(\frac{XM/PX}{Q}\right)$	$\ln \left(\frac{(XA+XR)/PX}{Q}\right)$ 2	$\ln \left(\frac{XM/PX}{Q}\right)$
Lag weights on relative price	(t)	0.141		0.015		0.327	0.787			0.087	−0.002		0.041
ln(PX/PQ)	(t−1)	0.255	0.205	0.249	0.150	−0.024				0.103	0.083		0.272
	(t−2)	0.298	0.295	0.244	0.292	0.008			0.100	0.106	0.134		0.384
	(t−3)	0.270	0.291		0.332	0.255		0.258	0.363	0.098	0.152	0.053	0.376
	(t−4)	0.170	0.193		0.271	0.546		0.758	0.434	0.077	0.135	0.229	0.248
	(t−5)				0.107	0.713		0.882	0.313	0.045	0.084	0.278
	(t−6)					0.588		0.629				0.202
Total weight		1.134	0.984	0.507	1.152	2.414	0.787	2.527	1.209	0.515	0.587	0.762	1.321
		(0.279)	(0.485)	(0.715)	(0.540)	(0.683)	(0.424)	(1.063)	(0.438)	(0.116)	(0.169)	(0.568)	(0.816)
ln(Q/QT)3					−2.406	−1.566	−0.901	−0.422 (−1)	−0.363			−0.501	−1.209 (−1)
					(0.593)	(0.994)	(0.728)	(0.664)	(0.356)			(0.855)	(0.492)
Δln(Q/QT)		−0.818 (−1)	−0.511	−1.833						−0.396(−1)	−0.577 (−1)
		(0.709)	(0.747)	(1.200)						(0.579)	(0.331)
ln(QF/QFT)			2.571		3.719	5.541	1.565		0.493		4.0034		0.120
			(0.910)		(1.130)	(1.625)	(1.101)		(0.935)		(0.718)		(1.201)
Δln(QF/QFT)		1.640 (-2)	2.776	1.192				5.7034		0.233		1.193
		(0.652)	(0.953)	(1.470)				(2.128)		(0.598)		(0.840)
CNST		−3.781	−3.865	−6.527	−3.418	−7.023	−4.625	−1.786	−4.127	−2.138	−4.480	−2.238	−6.833
		(0.162)	(0.357)	(1.055)	(0.484)	(0.604)	(0.448)	(0.580)	(0.150)	(0.046)	(0.023)	(0.314)	(0.276)
TD		0.022	0.022		0.028	0.097		−0.030		0.133	0.099	0.009
		(0.006)	(0.013)		(0.017)	(0.021)		(0.017)		(0.002)	(0.001)	(0.009)
TDl 5				0.133			0.103		0.113				0.092
				(0.047)			(0.019)		(0.008)				(0.012)
TD2				0.015			0.032						0.221
				(0.009)			(0.009)						(0.033)
DUM1		0.217	0.059					−0.190	−0.125	0.089	0.083	−0.105
		(0.043)	(0.040)					(0.065)	(0.047)	(0.052)	(0.023)	(0.042)
DUM2		−0.188	−0.124									−0.190
		(0.029)	(0.043)									(0.052)
ρ				0.411		−0.294		0.752		−0.531	−0.640
				(0.252)		(0.224)		(0.076)		(0.205)	(0.215)
${\overline{R}}^2$		0.826	0.886	0.920	0.794	0.813	0.983	0.759	0.970	0.748	0.998	0.879	0.990
SEE		0.040	0.037	0.062	0.031	0.048	0.037	0.058	0.033	0.044	0.026	0.035	0.064
D-W		2.67	2.47	1.43	2.11	2.16	1.55	1.43	2.15	2.47	2.55	1.72	2.24
Poly characteristics6		(2, 2, 2.07)	(2, 2, 2.48)	(2, 2, 1.45)	(2, 0, 2.91)	(3, 2, 4.16)	(0, 0, 0)	(2, 2, 4.75)	(2, 2, 3.79)	(2, 2, 2.21)	(2, 2, 3.01)	(2, 2, 4.82)	(2, 2, 2.39)
and F-test		F3,8=0.62	F2,6=2.02	F1,9=0.44	F2,11=0.06	F4,9=1.22	…	F2,7=1.34	F2,9=0.74	F4,8=2.10	F4,8=14.50**	F2,11=0.23	F3,9=2.41
t-test on unit Q elasticity		t10=1.48	t7=2.26	t9=0.51	…	…	…	t8=1.60	t10=0.63	t11=1.35	t11=0.59	…	t11=0.06
Sample period		1963-80	1965-80	1964-80	1961-80	1961-80	1961-80	1964-80	1964-80	1962-80	1961-80	1961-80	1963-80

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

¹Standard errors are in parentheses. All estimates are by ordinary least squares.

²For 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.

³Lags of cyclical variables are indicated where used.

⁴This weight is spread over both current and lagged levels of the regressor.

⁵Country definitions of TD1 and TD2, and of DUM1 and DUM 2, are given in Appendix I.

⁶First 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.

View Table

Table 1.

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

Country		Australia			Denmark			Finland		Ireland		New Zealand
Dependent variable		$\ln \left(\frac{XA/PX}{Q}\right)$	$\ln \left(\frac{XR/PX}{Q}\right)$	$\ln \left(\frac{XM/PX}{Q}\right)$	$\ln \left(\frac{XA/PX}{Q}\right)$	$\ln \left(\frac{XR/PX}{Q}\right)$	$\ln \left(\frac{XM/PX}{Q}\right)$	$\ln \left(\frac{XR/PX}{Q}\right)$	$\ln \left(\frac{XM/PX}{Q}\right)$	$\ln \left(\frac{XA/PX}{Q}\right)$	$\ln \left(\frac{XM/PX}{Q}\right)$	$\ln \left(\frac{(XA+XR)/PX}{Q}\right)$ 2	$\ln \left(\frac{XM/PX}{Q}\right)$
Lag weights on relative price	(t)	0.141		0.015		0.327	0.787			0.087	−0.002		0.041
ln(PX/PQ)	(t−1)	0.255	0.205	0.249	0.150	−0.024				0.103	0.083		0.272
	(t−2)	0.298	0.295	0.244	0.292	0.008			0.100	0.106	0.134		0.384
	(t−3)	0.270	0.291		0.332	0.255		0.258	0.363	0.098	0.152	0.053	0.376
	(t−4)	0.170	0.193		0.271	0.546		0.758	0.434	0.077	0.135	0.229	0.248
	(t−5)				0.107	0.713		0.882	0.313	0.045	0.084	0.278
	(t−6)					0.588		0.629				0.202
Total weight		1.134	0.984	0.507	1.152	2.414	0.787	2.527	1.209	0.515	0.587	0.762	1.321
		(0.279)	(0.485)	(0.715)	(0.540)	(0.683)	(0.424)	(1.063)	(0.438)	(0.116)	(0.169)	(0.568)	(0.816)
ln(Q/QT)3					−2.406	−1.566	−0.901	−0.422 (−1)	−0.363			−0.501	−1.209 (−1)
					(0.593)	(0.994)	(0.728)	(0.664)	(0.356)			(0.855)	(0.492)
Δln(Q/QT)		−0.818 (−1)	−0.511	−1.833						−0.396(−1)	−0.577 (−1)
		(0.709)	(0.747)	(1.200)						(0.579)	(0.331)
ln(QF/QFT)			2.571		3.719	5.541	1.565		0.493		4.0034		0.120
			(0.910)		(1.130)	(1.625)	(1.101)		(0.935)		(0.718)		(1.201)
Δln(QF/QFT)		1.640 (-2)	2.776	1.192				5.7034		0.233		1.193
		(0.652)	(0.953)	(1.470)				(2.128)		(0.598)		(0.840)
CNST		−3.781	−3.865	−6.527	−3.418	−7.023	−4.625	−1.786	−4.127	−2.138	−4.480	−2.238	−6.833
		(0.162)	(0.357)	(1.055)	(0.484)	(0.604)	(0.448)	(0.580)	(0.150)	(0.046)	(0.023)	(0.314)	(0.276)
TD		0.022	0.022		0.028	0.097		−0.030		0.133	0.099	0.009
		(0.006)	(0.013)		(0.017)	(0.021)		(0.017)		(0.002)	(0.001)	(0.009)
TDl 5				0.133			0.103		0.113				0.092
				(0.047)			(0.019)		(0.008)				(0.012)
TD2				0.015			0.032						0.221
				(0.009)			(0.009)						(0.033)
DUM1		0.217	0.059					−0.190	−0.125	0.089	0.083	−0.105
		(0.043)	(0.040)					(0.065)	(0.047)	(0.052)	(0.023)	(0.042)
DUM2		−0.188	−0.124									−0.190
		(0.029)	(0.043)									(0.052)
ρ				0.411		−0.294		0.752		−0.531	−0.640
				(0.252)		(0.224)		(0.076)		(0.205)	(0.215)
${\overline{R}}^2$		0.826	0.886	0.920	0.794	0.813	0.983	0.759	0.970	0.748	0.998	0.879	0.990
SEE		0.040	0.037	0.062	0.031	0.048	0.037	0.058	0.033	0.044	0.026	0.035	0.064
D-W		2.67	2.47	1.43	2.11	2.16	1.55	1.43	2.15	2.47	2.55	1.72	2.24
Poly characteristics6		(2, 2, 2.07)	(2, 2, 2.48)	(2, 2, 1.45)	(2, 0, 2.91)	(3, 2, 4.16)	(0, 0, 0)	(2, 2, 4.75)	(2, 2, 3.79)	(2, 2, 2.21)	(2, 2, 3.01)	(2, 2, 4.82)	(2, 2, 2.39)
and F-test		F3,8=0.62	F2,6=2.02	F1,9=0.44	F2,11=0.06	F4,9=1.22	…	F2,7=1.34	F2,9=0.74	F4,8=2.10	F4,8=14.50**	F2,11=0.23	F3,9=2.41
t-test on unit Q elasticity		t10=1.48	t7=2.26	t9=0.51	…	…	…	t8=1.60	t10=0.63	t11=1.35	t11=0.59	…	t11=0.06
Sample period		1963-80	1965-80	1964-80	1961-80	1961-80	1961-80	1964-80	1964-80	1962-80	1961-80	1961-80	1963-80

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

¹Standard errors are in parentheses. All estimates are by ordinary least squares.

²For 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.

³Lags of cyclical variables are indicated where used.

⁴This weight is spread over both current and lagged levels of the regressor.

⁵Country definitions of TD1 and TD2, and of DUM1 and DUM 2, are given in Appendix I.

⁶First 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.

XA =	exports of agricultural goods	SITC 0+1
XR =	exports of raw materials	SITC 2 + 4
XF =	exports of fuels	SITC 3
XM =	exports of manufactures	SITC 5-8

View Table

XA =	exports of agricultural goods	SITC 0+1
XR =	exports of raw materials	SITC 2 + 4
XF =	exports of fuels	SITC 3
XM =	exports of manufactures	SITC 5-8

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

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

Table 2.

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

	Australia		Denmark		Finland		Ireland		New Zealand
	Share	Elasticity	Share	Elasticity	Share	Elasticity	Share	Elasticity	Share		Elasticity
Agriculture	0.359	1.134	0.395	1.152	0.038	…	0.524	0.515	0.528
											0.762
Raw materials	0.347	0.984	0.075	2.414	0.238	2.527	0.063	…	0.344
Fuels	0.072	…	0.022	…	0.012	…	0.012	…	0.007		…
Manufactures	0.222	0.507	0.508	0.787	0.712	1.209	0.401	0.587	0.121		1.321
Total		0.861		1.037		1.462		0.505			0.824

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

View Table

Table 2.

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

	Australia		Denmark		Finland		Ireland		New Zealand
	Share	Elasticity	Share	Elasticity	Share	Elasticity	Share	Elasticity	Share		Elasticity
Agriculture	0.359	1.134	0.395	1.152	0.038	…	0.524	0.515	0.528	View Expanded
											0.762
Raw materials	0.347	0.984	0.075	2.414	0.238	2.527	0.063	…	0.344
Fuels	0.072	…	0.022	…	0.012	…	0.012	…	0.007		…
Manufactures	0.222	0.507	0.508	0.787	0.712	1.209	0.401	0.587	0.121		1.321
Total		0.861		1.037		1.462		0.505			0.824

¹The “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

$\begin{array}{ccc}\ln {(M/PM)}_t=& {\beta }_0+{\beta }_1\ln {(Q\mathrm{.}PQ/PD)}_t+{\beta }_2\left(L\right)\ln {(PM/PD)}_t\hfill & \\ & +{\beta }_3\ln {(Q/QT)}_t+{\beta }_{5}TD\hfill & \left(16\right)\end{array}$

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

¹Standard errors are in parentheses. All estimates are by ordinary least squares.

²No estimates of any accuracy could be obtained for the volume of Australia’s fuel imports as a result of significant variations in domestic production.

³Country definitions of DUM1, DUM2, and DUM3 are given in Appendix I.

Table 3.

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

Country	Australia2	Denmark		Finland		Ireland		New Zealand
Dependent variable	ln(MNF/PMNF)	ln(MNF/PMNF)	ln(MF/PMF)	ln(MNF/PMNF)	ln(MF/PMF)	ln(MNF/PMNF)	In(MF/PMF)	In(MNF/PMNF)	In(MF/PMF)
ln(PMNF/PD)	−0.410			−0.952		−0.817
	(0.130)			(0.196)		(0.363)
ln(PMNF/PD)−		−0.481						−0.580
		(0.188)						(0.381)
ln(PMF/PD)			−0.133		−0.205		−0.344		−0.199
			(0.039)		(0.087)		(0.048)		(0.048)
ln(PMF/PD)−1					−0.196
					(0.086)
ln (Q.PQ/PD)	1.034	1.249	0.905	1.242
	(0.043)	(0.138)	(0.055)	(0.043)
ln(Q.PQ/PD)−1					1.597	1.461	0.879	1.114	0.671
					(0.221)	(0.191)	(0.098)	(0.147)	(0.128)
ln(Q/QT)−1			1.268
			(0.354)
Δln(Q/QT)	0.650	0.517			1.267			1.391
	(0.612)	(0.348)			(0.664)			(1.026)
Δln(Q/QT)−1				1.858		1.903			0.558
				(0.442)		(0.677)			(0.747)
CNST	−2.331	−2.827	−2.483	−2.774	−5.591	−4.616	−1.696	−2.870	−0.413
	(0.170)	(0.739)	(0.296)	(0.187)	(1.011)	(1.555)	(0.805)	(1.328)	(1.187).
DUM1 3	0.132	−0.085				0.048		−0.208
	(0.036)	(0.023)				(0.028)		(0.076)
DUM2	0.157							−0.161
	(0.053)							(0.085)
DUM3	−0.175
	(0.055)
p					0.429	0.756
					(0.202)	(0.155)
${\overline{R}}^2$	0.974	0.987	0.967	0.980	0.814	0.839	0.806	0.927	0.570
SEE	0.050	0.032	0.038	0.049	0.073	0.056	0.073	0.072	0.074
D-W	1.81	1.66	2.01	1.61	2.13	1.49	1.83	2.12	2.01
Sample period	1961-80	1964-80	1961-80	1961-80	1962-80	1961-80	1961-80	1962-80	1961-80

¹Standard errors are in parentheses. All estimates are by ordinary least squares.

²No estimates of any accuracy could be obtained for the volume of Australia’s fuel imports as a result of significant variations in domestic production.

³Country definitions of DUM1, DUM2, and DUM3 are given in Appendix I.

View Table

Table 3.

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

Country	Australia2	Denmark		Finland		Ireland		New Zealand
Dependent variable	ln(MNF/PMNF)	ln(MNF/PMNF)	ln(MF/PMF)	ln(MNF/PMNF)	ln(MF/PMF)	ln(MNF/PMNF)	In(MF/PMF)	In(MNF/PMNF)	In(MF/PMF)
ln(PMNF/PD)	−0.410			−0.952		−0.817
	(0.130)			(0.196)		(0.363)
ln(PMNF/PD)−		−0.481						−0.580
		(0.188)						(0.381)
ln(PMF/PD)			−0.133		−0.205		−0.344		−0.199
			(0.039)		(0.087)		(0.048)		(0.048)
ln(PMF/PD)−1					−0.196
					(0.086)
ln (Q.PQ/PD)	1.034	1.249	0.905	1.242
	(0.043)	(0.138)	(0.055)	(0.043)
ln(Q.PQ/PD)−1					1.597	1.461	0.879	1.114	0.671
					(0.221)	(0.191)	(0.098)	(0.147)	(0.128)
ln(Q/QT)−1			1.268
			(0.354)
Δln(Q/QT)	0.650	0.517			1.267			1.391
	(0.612)	(0.348)			(0.664)			(1.026)
Δln(Q/QT)−1				1.858		1.903			0.558
				(0.442)		(0.677)			(0.747)
CNST	−2.331	−2.827	−2.483	−2.774	−5.591	−4.616	−1.696	−2.870	−0.413
	(0.170)	(0.739)	(0.296)	(0.187)	(1.011)	(1.555)	(0.805)	(1.328)	(1.187).
DUM1 3	0.132	−0.085				0.048		−0.208
	(0.036)	(0.023)				(0.028)		(0.076)
DUM2	0.157							−0.161
	(0.053)							(0.085)
DUM3	−0.175
	(0.055)
p					0.429	0.756
					(0.202)	(0.155)
${\overline{R}}^2$	0.974	0.987	0.967	0.980	0.814	0.839	0.806	0.927	0.570
SEE	0.050	0.032	0.038	0.049	0.073	0.056	0.073	0.072	0.074
D-W	1.81	1.66	2.01	1.61	2.13	1.49	1.83	2.12	2.01
Sample period	1961-80	1964-80	1961-80	1961-80	1962-80	1961-80	1961-80	1962-80	1961-80

¹Standard errors are in parentheses. All estimates are by ordinary least squares.

²No estimates of any accuracy could be obtained for the volume of Australia’s fuel imports as a result of significant variations in domestic production.

³Country 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

¹Reported shares are 20-year averages. Estimates of elasticities are taken from Table 3.

²Default value for the Australian income elasticity of demand for fuel imports is taken as 1.0.

Table 4.

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

		Australia		Denmark		Finland		Ireland		New Zealand
		Nonfuels	Fuels	Nonfuels	Fuels	Nonfuels	Fuels	Nonfuels	Fuels	Nonfuels	Fuels
Shares		0.915	0.085	0.849	0.151	0.826	0.174	0.893	0.107	0.883	0.117
Price elasticities		−0.410	…	−0.481	−0.133	−0.952	−0.401	−0.817	−0.344	−0.580	−0.199
Total price
	elasticity	−0.375		−0.428		−0.856		−0.766		−0.535
Income elasticities2		1.034	1.0	1.249	0.905	1.242	1.597	1.461	0.879	1.114	0.671
Total income
	elasticity	1.031		1.197		1.304		1.399		1.062

¹Reported shares are 20-year averages. Estimates of elasticities are taken from Table 3.

²Default value for the Australian income elasticity of demand for fuel imports is taken as 1.0.

View Table

Table 4.

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

		Australia		Denmark		Finland		Ireland		New Zealand
		Nonfuels	Fuels	Nonfuels	Fuels	Nonfuels	Fuels	Nonfuels	Fuels	Nonfuels	Fuels
Shares		0.915	0.085	0.849	0.151	0.826	0.174	0.893	0.107	0.883	0.117
Price elasticities		−0.410	…	−0.481	−0.133	−0.952	−0.401	−0.817	−0.344	−0.580	−0.199
Total price
	elasticity	−0.375		−0.428		−0.856		−0.766		−0.535
Income elasticities2		1.034	1.0	1.249	0.905	1.242	1.597	1.461	0.879	1.114	0.671
Total income
	elasticity	1.031		1.197		1.304		1.399		1.062

¹Reported shares are 20-year averages. Estimates of elasticities are taken from Table 3.

²Default 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.