demand function for volume of imports

The first ingredient of the complete import model is an aggregative relationship expressing the real demand for imports as a function of domestic real expenditure (Y^d), the price of domestic goods (P^d), and the price of imported goods (P^m). Furthermore, it is recognized that domestic goods markets are cleared not only by movements in nominal (quoted) prices but also by changes in a set of nonprice variables, such as waiting times for delivery, discounts, credit terms, and quality standards. These variables should be considered as arguments in the demand function, since they influence the allocation of expenditures between domestic and foreign goods.⁸ Using the symbol W^d to summarize the impact of these nonprice variables, the demand function for imports in volume terms can be written as:

where M and $\overline{M}$ stand for the nominal and real value of imports, respectively. The partial derivatives of f are assumed to be positive with respect to Y^d, P^d, and W^d; and negative with respect to P^m.

Because of the existence of delivery lags and adjustment delays, each independent variable in equation (1) should be interpreted as representing a weighted sum of current and lagged values of that variable. To simplify the notation, it is assumed that the only variables that affect imports with a distributed lag are P^d and P^m. (The empirical analysis presented in Sections III and IV allows, however, for the possibility of lagged effects from all the explanatory variables.) It is also assumed that the function f can be approximated by a log-linear expression. If lower case letters stand for natural logarithms—for example, x = log_e(X)—equation (1) can be rewritten as:

where $\overline{m}=m-p^m$. The a_jis are non-negative weights, and their sum for i = 0, … l is unity. Each α represents a sum of lagged coefficients and can be interpreted as a long-run demand elasticity; α₃ is expected to be negative, while α₁, α₂, and α₄ are expected to be positive.

It may be noted that p^m and p^d are included as separate explanatory variables on the right-hand side of equation (2). In many trade models, the inclusion of a single relative price variable (p^m — p^d) is justified by postulating the absence of “money illusion.” Although the present model does not appeal to this postulate, it is worth noting that this justification is quite dubious on several counts. First, in a world in which imported and domestic goods differ in terms of both price and nonprice characteristics, different reactions to opposite but equal changes in p^m and p^d do not necessarily represent symptoms of “money illusion.” ⁹ Second, the use of a single relative price variable can be justified by the assumption of no money illusion if consumers allocate expenditures among two goods only (say, domestic and imported goods). If, however, consumers face n goods—and hence n prices—the demand function for each of these n goods must include n — 1 relative price variables, even in the absence of money illusion. Finally, there is a practical problem stemming from differences in the construction of unit value and wholesale price indexes. In the United States, unit value indexes are based on Fisher’s formula, while wholesale price indexes are based on Laspeyres’ formula, and it has been shown that these two types of indexes describe different time paths even if the commodity composition remains unchanged.¹⁰ Therefore, even a model that constrains the theoretical elasticities with respect to the “true” prices p^d and p^m to be equal in absolute value should allow the estimated elasticities with respect to the price indexes ${\overline{p}}^d$ and ${\overline{p}}^m$ to differ because of the methodological differences between the two indexes.

The elements of the vector W^d are not subject to direct measurement, although it is shown in Section IV that an adequate proxy for domestic delivery lags of industrial supplies and materials can be specified.¹¹ More generally, it is hypothesized that the intensity of the rationing mechanisms—that is, the magnitude of excess demand at the given (nominal) price—can be expressed as a function of the discrepancy between actual and desired rates of domestic resource utilization¹² denoted by R and $\hat{R}$, respectively.

Chart 1 shows three possible ways to approximate the function g subject to the conditions g^′ > 0 and g(0) = 0. The identity function is the most simplified but not necessarily the most realistic from the economic standpoint. A somewhat more attractive alternative is the nonlinear expression

where ψ is a positive scalar. If ψ = 1, the variable is symmetric with respect to the origin (Chart 1). Such a variable was used by Parrish and DiLullo (1972a) in estimating aggregate import equations for the United States. R was taken to be the ratio of actual to potential gross national product (GNP), and $\hat{R}$ was estimated at 0.97. If ψ > 1, the variable W^d is nonlinear and asymmetric (dotted line in Chart 1). This asymmetry reflects the assumption that, ceteris paribus, the stimulating impact on imports of capacity bottlenecks is larger than the depressive impact resulting from excess capacity. This is likely to occur when, for example, outstanding contracts impose a limit on how far importers can turn from foreign to domestic suppliers in response to an improvement in the nonprice characteristics of domestic goods.

View Full Size

Alternative Versions of the Variable W^d

Citation: IMF Staff Papers 1975, 003; 10.5089/9781451969382.024.A007

• Download Figure
• Download figure as PowerPoint slide

the import price function

The determination of the import price (p^m) is analyzed in terms of a two-stage procedure, which has practical as well as expositional advantages. The first step deals with the transition from the import price (more specifically, in the U. S. case, from the import unit value) to the foreign export price expressed in foreign currency. The second stage deals with the specification of the foreign export price in terms of the exchange rate and of domestic prices in both the importing and the exporting country.

(1) Let p^x denote the foreign export price expressed in foreign currency, and let k stand for the exchange rate expressed in units of foreign currency per U. S. dollar.¹³ As before, p^m is the U. S. import price expressed in U. S. dollar terms, and all variables are defined in terms of natural logarithms. If λ denotes the proportion of contracts denominated in U. S. dollars, θ_i the proportion of current imports contracted in period t — i, and the subscript i indicates the delivery lag, the unit value may be expressed as ¹⁴

Rearranging terms and noting that Σθ_i = 1 by definition, equation (5) can be written more compactly as

where ${{\theta }^{\prime }}_0=1-\lambda \left(1-{\theta }_0\right)\ge 0{{\theta }^{\prime }}_i={\mathrm{\lambda \theta }}_i\mathrm{V}i\ne 0\mathrm{and}\underset{i=0}{\overset{n}{\mathrm{\Sigma }}}{{\theta }^{\prime }}_i=1$.

Equation (6) expresses p^m as a linear combination of current and lagged values of foreign export prices and exchange rates. It could be estimated by standard regression techniques if an appropriate weighted average of foreign export prices could be constructed. Since this is not a feasible alternative, it is necessary to go a step further and examine the price-setting behavior of foreign exporters.¹⁵

(2) Given an optimal long-run export price ${\hat{p}}^x$, the problem of short-run price determination can be viewed as an attempt by the exporting firm to achieve the best possible compromise between several competing targets. Obviously the firm will strive to minimize the cost of being out of equilibrium; at the same time it will try to prevent the emergence of a large discrepancy between its export price measured in U. S. dollars and the price charged by its U. S. competitors—one which could lead to a serious and perhaps irreversible loss in its share of the U. S. market; and finally it will attempt to avoid any sharp widening in the gap between actual and desired levels of resource utilization. One simple and yet reasonably realistic solution to this optimization problem is to set p^x so as to minimize the (positive definite) quadratic loss function:

where y^f and ŷ^f are output levels corresponding to actual and desired levels of foreign capacity utilization, respectively.

As an illustration, it may be noted that a positive value for h₁ implies that, faced with an exogenous decrease in k, the foreign exporter will attempt to “absorb” part of the dollar devaluation impact by reducing the local currency value of its export price (p^x).

The foreign producer’s optimal long-run export price (${\hat{p}}^x$) is assumed to be related to its prevailing home market price (p^f) by the simple log-linear relationship ${\hat{p}}^x=\epsilon +p^f$.¹⁶ Then, denoting the demand elasticity of y^f with respect to the export price p^x by η = ∂y^f/∂p^x < 0 and setting ∂L/∂p^x = 0 yields the first-order minimum condition:

where ξ₀ = εh₀/h > 0, ξ₁ = h₀/h > 0, ξ₂ = h₁/h > 0,

and ξ₃ = —ηw′h₂/h > 0

where h = h₀ + h₁ and w′ = ∂w^f/∂y^f > 0.

Substituting for p^x from equation (8) in equation (6) then gives

where ${\xi }_2^{\prime }=-\left(1-{\xi }_2\right)<0$.

reduced form expression for nominal imports

As was pointed out in Section I, the complete import model composed of equations (2) and (9) cannot be estimated for all end-use categories because import prices (even in the deficient form of import unit values) are not available for a sufficiently long period. For some categories—foods, industrial supplies, and materials—it is possible to construct alternative unit value indexes that are fairly adequate in terms of coverage. But this is not feasible in other cases (for example, automotive imports and capital goods). Even then, however, the model presented above in this section can be used to derive an equation which can be estimated, provided there is information concerning prices in the exporting countries.

Suppose, for instance, that an average p^x of foreign export prices in foreign currency is available. Then, taking the value of p^m from equation (6) and substituting for this value in equation (2) yields the expression

It may be noted that the lag length for both p^x and k is equal to (l + n)—that is, to the lag with which the demand for imports adjusts fully to a change in import prices (l) plus the lag with which the import price reacts fully to a change in exchange rates and foreign prices (n). It may also be pointed out that, in the general case, the distribution of the c_is will be humped, even if the lag distributions for a_i and θ_i are monotonically declining.¹⁷

Since $\overline{m}=m-p^m$, adding p^m on both sides of equation (10) gives

Equation (11) requires data on p^x and k, but not on the import price (p^m).

Suppose now that p^x is not available, but that there is information on the domestic prices of major trading partners, which can be used to construct the weighted average foreign price (p^f). Then, taking the value of p^x from equation (8) and substituting it in equation (11) yields

where ζ₀ = α₀ + ξ₀(1 + α₃), ζ₁ = ξ₁(1 + α₃), ζ₂ = α₂ + (1 + α 3)ξ₂

ζ₃ = (1 + α₃)ξ₃ and ${\zeta }_4=\left(1+{\alpha }_3\right){\xi }_2^{\prime }$.

If α₃ < -1 (an assumption for which considerable empirical evidence will be offered in the following sections), ζ₁ and ζ₂ will be unambiguously negative, and ζ₄ unambiguously positive. Since 0 ≤ ξ₂ < 1, a sufficient condition for ζ₂ to be positive is 1 + α₂ > — α₃.

The reduced form (12) is several steps removed from the original equations of the model, and linear least-squares will not produce estimates of all of the original (structural) parameters. If, however, there is no information on import prices, equation (12) provides an operationally attractive specification of the import function, and one which is consistent with the original assumptions of the model. If these assumptions—including the existence of absorption and of import contracts denominated in foreign currency—are correct, then it is clear from (12) that the widespread procedure of collapsing the price and exchange rate variables into a single “relative price variable” [p^d — (p^f — k)] is incorrect. And while this type of misspecification is likely to be rather benign as long as there are no sharp fluctuations in exchange rates, it will have serious consequences if the sample includes a period such as 1971–73.

aggregate import equation

Table 1A summarizes the results obtained from estimating the aggregate import demand equation (2) from the first quarter of 1960 to the fourth quarter of 1973. The dependent variable ($\overline{m}=m-p^m$) was defined as the logarithm of U. S. merchandise imports (census basis), net of fuels and lubricants and automotive imports from Canada, minus the logarithm of the aggregate import unit value adjusted to exclude petroleum prices. The price of import-competing goods (p^d) was approximated by the U. S. wholesale price index, which seemed appropriate since imported goods carry a very small weight in the wholesale price index.¹⁸ All variables were seasonally adjusted, except the unit value p^m for which there was no indication of seasonality.

Table 1.

Import Volume and Import Price Equations for Total Imports, Excepting Fuels and Lubricants and Automotive Imports from Canada

(Based on quarterly data)

Note: The variable p^m is the unit value of U.S. general imports, adjusted to exclude changes in petroleum prices;$\overline{m}$ is the logarithm of U.S. merchandise imports (less fuels, lubricants, and automotive imports from Canada) deflated by p^m. The symbol y^d stands for real personal consumption expenditure in equation (1.1) and for real personal consumption expenditure on goods in equations (1.2) through (1.5). For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.

Table 1.

Import Volume and Import Price Equations for Total Imports, Excepting Fuels and Lubricants and Automotive Imports from Canada

(Based on quarterly data)

A. Import Volume Equations, First Quarter of 1960 to Fourth Quarter of 1973 (Dependent Variable $\overline{m}$)
Import Volume Equation	Constant	yd	$\stackrel{4}{\mathrm{\Sigma }}{p}^m$	$\stackrel{5}{\mathrm{\Sigma }}{p}^d$	W d	D	D -1	D +1	S	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
(1.1)	1.27	1.331	–1.646	3.378	0.126	–0.251	0.140	0.056	–0.031	—	0.993
	(0.78)	(14.77)	(5.64)	(7.42)	(3.36)	(7.45)	(4.10)	(1.64)	(4.43)		[1.28]
(1.2)	2.48	1.511	–1.983	3.363	—	–0.261	0.124	0.051	–0.032	—	0.992
	(1.67)	(25.92)	(7.05)	(8.31)		(7.84)	(3.69)	(1.50)	(4.73)		[1.41]
(1.3)	3.208	1.428	–2.039	3.655	0.047	–0.259	0.128	0.056	–0.032	—	0.993
	(1.98)	(15.06)	(7.15)	(7.59)	(1.11)	(7.76)	(3.78)	(1.63)	(4.73)		[1.44]
(1.4)	3.438	1.331	–1.950	3.807	0.164	–0.261	0.129	0.051	–0.031	—	0.994
	(2.43)	(14.99)	(7.46)	(9.39)	(2.91)	(8.43)	(4.12)	(1.63)	(4.86)		[1.55]
(1.5)	2.332	1.381	–1.929	3.689	0.130	–0.267	0.119	0.047	–0.027	0.211	0.991
	(1.74)	(12.54)	(6.25)	(7.57)	(1.96)	(9.04)	(3.99)	(1.56)	(3.66)	(1.48)	[2.12]

B. Import Price Equations, First quarter of 1959 to Fourth Quarter of 1973 (Dependent Variable pm)
Import Price Equation	Constant	$\stackrel{5}{\mathrm{\Sigma }}{p}^f$	$\stackrel{4}{\mathrm{\Sigma }}k$	$\stackrel{3}{\mathrm{\Sigma }}{p}^d$	$\stackrel{2}{\mathrm{\Sigma }}{W}^f$	t	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
(1.6)	2.34	1.255	–0.692	0.488	0.111	0.003	—	0.996
	(2.10)	(5.71)	(7.37)	(4.92)	(3.98)	(3.81)		[1.38]
(1.7)	1.68	1.189	–0.686	0.534	0.094	0.003	0.356	0.992
	(1.80)	(4.25)	(5.32)	(3.97)	(2.61)	(2.70)	(2.26)	[2.08]

Note: The variable p^m is the unit value of U.S. general imports, adjusted to exclude changes in petroleum prices;$\overline{m}$ is the logarithm of U.S. merchandise imports (less fuels, lubricants, and automotive imports from Canada) deflated by p^m. The symbol y^d stands for real personal consumption expenditure in equation (1.1) and for real personal consumption expenditure on goods in equations (1.2) through (1.5). For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.

View Table

Table 1.

Import Volume and Import Price Equations for Total Imports, Excepting Fuels and Lubricants and Automotive Imports from Canada

(Based on quarterly data)

A. Import Volume Equations, First Quarter of 1960 to Fourth Quarter of 1973 (Dependent Variable $\overline{m}$)
Import Volume Equation	Constant	yd	$\stackrel{4}{\mathrm{\Sigma }}{p}^m$	$\stackrel{5}{\mathrm{\Sigma }}{p}^d$	W d	D	D -1	D +1	S	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
(1.1)	1.27	1.331	–1.646	3.378	0.126	–0.251	0.140	0.056	–0.031	—	0.993
	(0.78)	(14.77)	(5.64)	(7.42)	(3.36)	(7.45)	(4.10)	(1.64)	(4.43)		[1.28]
(1.2)	2.48	1.511	–1.983	3.363	—	–0.261	0.124	0.051	–0.032	—	0.992
	(1.67)	(25.92)	(7.05)	(8.31)		(7.84)	(3.69)	(1.50)	(4.73)		[1.41]
(1.3)	3.208	1.428	–2.039	3.655	0.047	–0.259	0.128	0.056	–0.032	—	0.993
	(1.98)	(15.06)	(7.15)	(7.59)	(1.11)	(7.76)	(3.78)	(1.63)	(4.73)		[1.44]
(1.4)	3.438	1.331	–1.950	3.807	0.164	–0.261	0.129	0.051	–0.031	—	0.994
	(2.43)	(14.99)	(7.46)	(9.39)	(2.91)	(8.43)	(4.12)	(1.63)	(4.86)		[1.55]
(1.5)	2.332	1.381	–1.929	3.689	0.130	–0.267	0.119	0.047	–0.027	0.211	0.991
	(1.74)	(12.54)	(6.25)	(7.57)	(1.96)	(9.04)	(3.99)	(1.56)	(3.66)	(1.48)	[2.12]

B. Import Price Equations, First quarter of 1959 to Fourth Quarter of 1973 (Dependent Variable pm)
Import Price Equation	Constant	$\stackrel{5}{\mathrm{\Sigma }}{p}^f$	$\stackrel{4}{\mathrm{\Sigma }}k$	$\stackrel{3}{\mathrm{\Sigma }}{p}^d$	$\stackrel{2}{\mathrm{\Sigma }}{W}^f$	t	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
(1.6)	2.34	1.255	–0.692	0.488	0.111	0.003	—	0.996
	(2.10)	(5.71)	(7.37)	(4.92)	(3.98)	(3.81)		[1.38]
(1.7)	1.68	1.189	–0.686	0.534	0.094	0.003	0.356	0.992
	(1.80)	(4.25)	(5.32)	(3.97)	(2.61)	(2.70)	(2.26)	[2.08]

Note: The variable p^m is the unit value of U.S. general imports, adjusted to exclude changes in petroleum prices;$\overline{m}$ is the logarithm of U.S. merchandise imports (less fuels, lubricants, and automotive imports from Canada) deflated by p^m. The symbol y^d stands for real personal consumption expenditure in equation (1.1) and for real personal consumption expenditure on goods in equations (1.2) through (1.5). For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.

Columns (1) through (5) in Table 1A give the estimated coefficients of the constant term and the four explanatory variables included in equation (2), while columns (6) through (9) show the coefficients of various strike variables explained below. Column (10) shows the value of the estimated first-order autocorrelation coefficient $\hat{\rho }$ which applies only to the autoregressive equation (1.5). Finally, column (11) gives the ${\overline{R}}^2$ and Durbin-Watson statistics. Figures in parentheses below the coefficients are t-ratios.

In the first equation of Table 1A, y^d is defined as personal consumption expenditures at constant prices. The more narrow concept of personal consumption expenditures on goods (durable plus nondurable) is used in the other four equations. While the coefficients and standard errors of the price variable are not dramatically affected by these changes, the equations using expenditure on goods only have a slight advantage in terms of standard error and freedom from autocorrelation.

The consequences of using alternative versions of the nonprice rationing variable are somewhat more visible. In equation (1.3), W^d is the gap between actual and potential GNP, while in the last two equations this variable was generated according to the formula of equation (4), R being equal to the ratio of actual to potential GNP, and $\hat{R}$ being equal to 0.97. The standard errors associated with this second version of W^d proved to be consistently lower. The value of ψ (estimated through a scanning procedure) was not found to be significantly different from unity.¹⁹ Equations (1.3) and (1.4) performed somewhat better than equation (1.2), which does not include a nonprice rationing variable.

In Table 1, the coefficients for p^m and p^d are sums of lagged coefficients. (This is indicated by the symbol Σ, with the number of lagged terms given above the summation sign.) These price coefficients—which can be interpreted as long-run elasticities—correspond to α₁ and α₂, respectively, in the symbolism of equation (2). They were quite robust with respect to minor changes in specification, and they passed the t-test quite comfortably at the 0.01 level. The individual lagged coefficients, shown in Table 2, were constrained to lie upon a second-degree polynomial of length l and constrained to zero at t - l - 1.²⁰ These are severe constraints, but they are far less rigid than those that would have resulted from using an (infinite) exponentially declining lag structure of the Koyck type.²¹ The length of the polynomial was determined by minimizing the standard error of the sum of lagged coefficients, subject to the constraint that none of the weights (the a’s) should be significantly smaller than zero.²²

Table 2.

Distributed Lag Coefficients for Aggregate Import Volume and Import Price Equations

(t-statistics in parentheses)

¹Less than 0.001.

Table 2.

Distributed Lag Coefficients for Aggregate Import Volume and Import Price Equations

(t-statistics in parentheses)

	Import Volume Equation (1.4)		Unit Value Equation (3.3)
Lag (i)	pm	pd	pf	k	pd	wf
0	–0.966	0.465	–0.073	–0.308	0.320	0.072
	(3.68)	(1.65)	(0.59)	(3.63)	(1.78)	(2.58)
1	–0.583	0.699	0.145	–0.199	0.160	0.023
	(7.62)	(5.73)	(3.36)	(6.19)	(3.98)	(0.57)
2	–0.295	0.808	0.282	–0.113	0.054	1
	(2.75)	(8.89)	(3.88)	(2.56)	(0.52)
3	–0.102	0.793	0.335	–0.052	1	—
	(0.69)	(5.95)	(3.24)	(0.95)
4	–0.004	0.653	0.306	–0.014	—	—
	(0.32)	(4.63)	(2.97)	(0.35)
5	—	0.389	0.194	—	—	—
		(3.99)	(2.83)

¹Less than 0.001.

View Table

Table 2.

Distributed Lag Coefficients for Aggregate Import Volume and Import Price Equations

(t-statistics in parentheses)

	Import Volume Equation (1.4)		Unit Value Equation (3.3)
Lag (i)	pm	pd	pf	k	pd	wf
0	–0.966	0.465	–0.073	–0.308	0.320	0.072
	(3.68)	(1.65)	(0.59)	(3.63)	(1.78)	(2.58)
1	–0.583	0.699	0.145	–0.199	0.160	0.023
	(7.62)	(5.73)	(3.36)	(6.19)	(3.98)	(0.57)
2	–0.295	0.808	0.282	–0.113	0.054	1
	(2.75)	(8.89)	(3.88)	(2.56)	(0.52)
3	–0.102	0.793	0.335	–0.052	1	—
	(0.69)	(5.95)	(3.24)	(0.95)
4	–0.004	0.653	0.306	–0.014	—	—
	(0.32)	(4.63)	(2.97)	(0.35)
5	—	0.389	0.194	—	—	—
		(3.99)	(2.83)

¹Less than 0.001.

The coefficients shown in columns (6), (7), and (8) of Table 1 refer to dummy variables for domestic dock strikes, and those in column (9) to a domestic steel and copper strike variable (S). The dock strike variable D was designed by Takacs (1974) and defined as

where the index π refers to various U. S. ports, N_{π, t} to the number of days port π was on strike in quarter t, and N_π,67/M₆₇ is the proportion of the 1967 value of imports that entered the United States through port π. Following Takacs’ suggestion, D was used with a one-period lead to reflect anticipatory imports and with a one-period lag to account for the makeup of imports following each dock strike.²³ The results presented in Table 1 are consistent with a priori expectations and suggest that, while dock strikes have seriously affected the timing of imports, their impact on the volume of imports has been largely offset on average by anticipatory and compensatory purchases.

The value of the Durbin-Watson statistic for equation (1.3) lies in the intermediate range, where the hypothesis of positive serial correlation cannot be conclusively accepted or rejected. The error term was then assumed to follow a first-order Markov scheme u_t = ρu_t-1 + e_t (with values of e_t assumed to be serially independent).²⁴ The equation was then re-estimated in its autoregressive form using a nonlinear least-squares technique. The results, shown in equation (1.5), Table 1A, indicate an estimated value of ρ which is fairly small and not significantly different from zero at the 0.05 level.

aggregate unit value equation

The estimation results for the import price equation (9) are presented in Table 1B. The dependent variable p^m is defined as the unit value of total U. S. imports adjusted to exclude petroleum import prices. The average foreign price and exchange rate variables were defined as

where the p^v’s and the k^v’s are wholesale price and exchange rate indexes, respectively, for eight of the largest U. S. trading partners.²⁵ The symbol μ_v denotes U. S. imports from country v as a proportion of total imports from the eight-country group, with figures adjusted to exclude petroleum products and automotive trade with Canada. The variable W^f is a foreign capacity utilization variable constructed by Parrish and DiLullo.²⁶ Finally, the unit value p^m is based on Fisher’s formula, while the components of p^f are Laspeyres’ indexes. It was noted earlier that these two types of price indexes describe different rates of change. The linear time trend t was included in the regressions to account for this purely methodological difference.²⁷ All the coefficients shown in Table 1 have the expected sign, and their significance levels are not seriously affected by changes in specification. The constraint that ξ′₂ = — (1 — ξ₂) is not inconsistent with the results. Not surprisingly, the untransformed regression (1.6) is associated with low values of D-W. Adjustment for autocorrelation does not radically alter the magnitude of the coefficients, however, and it does not increase substantially their standard errors.

A domestic cyclical variable (W^d) was also introduced in the regressions to test whether the availability of locally produced goods affected the propensity of foreign exporters to raise prices. The results (not shown in Table 1) were unsatisfactory as the estimated coefficient of W^d had the wrong (negative) sign in most trials.

overview

The end-use breakdown of import data provided by the U. S. Department of Commerce is designed to reflect the different demand forces stemming from various sectors of the economy. It includes six basic categories: (0) foods, feeds, and beverages; (1) industrial supplies and materials; (2) capital goods other than automotive vehicles; (3) automotive vehicles, parts, and engines; (4) consumer goods, excluding foods and automobiles; and (5) other imports. For the purpose of this study, imports of industrial supplies and materials are adjusted to exclude fuels and lubricants, while automotive imports from Canada under the Special Agreement are excluded from category (3). The behavior of these types of imports over the last 15 years is illustrated in Table 3.

Table 3.

Composition of U.S. Imports in Selected Years

(Percentage of total value of imports)

Source: U.S. Department of Commerce, Survey of Current Business, various issues.

Table 3.

Composition of U.S. Imports in Selected Years

(Percentage of total value of imports)

	End-Use Category		1958	1970	1973
(0)	Foods, feeds, and beverages		25.9	15.4	13.1
(1)	Industrial supplies and materials		51.8	37.8	38.4
		Fuels and lubricants	72.2	7.7	12.0
		Other	39.6	30.1	26.4
(2)	Capital goods, excluding automotive vehicles, parts, and engines		3.4	9.6	10.9
(3)	Automotive vehicles, parts, and engines		4.2	14.8	15.7
		From Canada	0.1	8.9	8.5
		From other areas	4.1	5.9	7.2
(4)	Consumer goods, excluding foods and automobiles		8.9	18.9	19.0
(5)	Other		5.9	3.5	2.9

Source: U.S. Department of Commerce, Survey of Current Business, various issues.

View Table

Table 3.

Composition of U.S. Imports in Selected Years

(Percentage of total value of imports)

	End-Use Category		1958	1970	1973
(0)	Foods, feeds, and beverages		25.9	15.4	13.1
(1)	Industrial supplies and materials		51.8	37.8	38.4
		Fuels and lubricants	72.2	7.7	12.0
		Other	39.6	30.1	26.4
(2)	Capital goods, excluding automotive vehicles, parts, and engines		3.4	9.6	10.9
(3)	Automotive vehicles, parts, and engines		4.2	14.8	15.7
		From Canada	0.1	8.9	8.5
		From other areas	4.1	5.9	7.2
(4)	Consumer goods, excluding foods and automobiles		8.9	18.9	19.0
(5)	Other		5.9	3.5	2.9

Source: U.S. Department of Commerce, Survey of Current Business, various issues.

The relative importance in domestic demand of categories (0) and (1)—which together account for more than half the total value of imports—has not shown a noticeable tendency to increase during the past decade. At present, each represents less than 6 per cent of the domestic market.²⁸ By contrast, imports of categories (2), (3), and (4) have increased rapidly in relation to domestic demand; the first two account for some 12 per cent and the last one for roughly 6 per cent of the domestic market.

The analysis of U. S. imports for the various end-use categories was confronted with the various difficulties, discussed earlier, stemming from the unavailability of appropriate import price data. A strategy designed to overcome these difficulties was outlined in Section I and formalized in Section II, providing the basis for the econometric results presented in the rest of this section.

foods, feeds, and beverages

The results reported in Table 4A were obtained by estimating the demand equation (2) for imports of foods, feeds, and beverages expressed in volume terms. A weighted average (p^m) of unit value indexes for crude and manufactured foods was used to deflate the import value series. (In 1970, the proportion of value covered by the sample items was 76.2 per cent for the unit value index of crude foods, and 63.2 per cent for that of manufactured foods. The index p^m is therefore not unsatisfactory in terms of coverage.) The import price used on the right-hand side of the equation was defined as P^m = P^m (1 + τ), where τ is an average tariff variable for imports of foods, feeds, and beverages.²⁹ With regard to the domestic variables, the wholesale price index for processed foods and feeds was used for p^d, and real disposable income was used for y^d. Consumption expenditure on food was also tried as a scale variable, but it was substantially weaker than disposable income. Indeed, the more aggregative concepts of demand—for example, personal consumption expenditures and disposable income—performed consistently better than any sectoral demand variable for all of the end-use categories.

Table 4.

Import Volume and Import Price Equations for Imports of Foods, Feeds, and Beverages

(Based on quarterly data)

Note: The variables p^f₁, p^f₂, and p^f₃ are dollar spot price indexes for coffee, sugar, and cocoa, respectively, in New York; p^f is a weighted average of these three indexes; p^m is a weighted average unit value index for imports of foods, feeds, and beverages; and $\overline{m}$ denotes U.S. imports of foods, feeds, and beverages, deflated by p^m. For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.

Table 4.

Import Volume and Import Price Equations for Imports of Foods, Feeds, and Beverages

(Based on quarterly data)

A. Import Volume Equations, First Quarter of 1959 to Fourth Quarter of 1973 (Dependent Variable $\overline{m}$)
Import Volume Equation	Constant	yd	$\stackrel{4}{\mathrm{\Sigma }}{\tilde{p}}^m$	$\stackrel{4}{\mathrm{\Sigma }}{p}^d$	T	D	D -1	D +1	${\overline{R}}^2$ [D-W]
(4.1)	7.58	0.381	–1.058	1.994	—	–0.369	0.150	0.209	0.883
	(2.48)	(3.72)	(3.45)	(4.48)		(5.64)	(2.28)	(3.18)	[2.09]
(4.2)	6.45	0.428	–0.966	1.829	—	1.078	—	—	0.913
	(2.44)	(4.98)	(3.64)	(4.76)		(8.21)			[1.48]
(4.3)	2.41	0.407	–1.044	1.078	0.008	1.110	—	—	0.927
	(1.80)	(5.17)	(4.29)	(2.60)	(3.41)	(9.23)			[1.75]

B. Import Price Equations, First Quarter of 1959 to Fourth Quarter of 1973 (Dependent Variable pm)
Import Price Equation	Constant	$\stackrel{4}{\mathrm{\Sigma }}{p}^f$	$\stackrel{4}{\mathrm{\Sigma }}{p^f}_1$	$\stackrel{3}{\mathrm{\Sigma }}{p^f}_2$	$\stackrel{3}{\mathrm{\Sigma }}{p^f}_3$	t	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
(4.4)	1.88	0.787	—	—	—	0.381	—	0.982
	(15.79)	(17.41)				(11.46)		[0.39]
(4.5)	1.82	—	0.456	0.251	0.094	0.357	—	0.986
	(16.23)		(17.68)	(5.16)	(7.54)	(9.54)		[0.68]
(4.6)	0.09	—	0.351	0.186	0.094	0.865	0.95	0.802
	(7.32)		(7.04)	(2.67)	(4.52)	(3.32)		[2.01]

Note: The variables p^f₁, p^f₂, and p^f₃ are dollar spot price indexes for coffee, sugar, and cocoa, respectively, in New York; p^f is a weighted average of these three indexes; p^m is a weighted average unit value index for imports of foods, feeds, and beverages; and $\overline{m}$ denotes U.S. imports of foods, feeds, and beverages, deflated by p^m. For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.

View Table

Table 4.

Import Volume and Import Price Equations for Imports of Foods, Feeds, and Beverages

(Based on quarterly data)

A. Import Volume Equations, First Quarter of 1959 to Fourth Quarter of 1973 (Dependent Variable $\overline{m}$)
Import Volume Equation	Constant	yd	$\stackrel{4}{\mathrm{\Sigma }}{\tilde{p}}^m$	$\stackrel{4}{\mathrm{\Sigma }}{p}^d$	T	D	D -1	D +1	${\overline{R}}^2$ [D-W]
(4.1)	7.58	0.381	–1.058	1.994	—	–0.369	0.150	0.209	0.883
	(2.48)	(3.72)	(3.45)	(4.48)		(5.64)	(2.28)	(3.18)	[2.09]
(4.2)	6.45	0.428	–0.966	1.829	—	1.078	—	—	0.913
	(2.44)	(4.98)	(3.64)	(4.76)		(8.21)			[1.48]
(4.3)	2.41	0.407	–1.044	1.078	0.008	1.110	—	—	0.927
	(1.80)	(5.17)	(4.29)	(2.60)	(3.41)	(9.23)			[1.75]

B. Import Price Equations, First Quarter of 1959 to Fourth Quarter of 1973 (Dependent Variable pm)
Import Price Equation	Constant	$\stackrel{4}{\mathrm{\Sigma }}{p}^f$	$\stackrel{4}{\mathrm{\Sigma }}{p^f}_1$	$\stackrel{3}{\mathrm{\Sigma }}{p^f}_2$	$\stackrel{3}{\mathrm{\Sigma }}{p^f}_3$	t	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
(4.4)	1.88	0.787	—	—	—	0.381	—	0.982
	(15.79)	(17.41)				(11.46)		[0.39]
(4.5)	1.82	—	0.456	0.251	0.094	0.357	—	0.986
	(16.23)		(17.68)	(5.16)	(7.54)	(9.54)		[0.68]
(4.6)	0.09	—	0.351	0.186	0.094	0.865	0.95	0.802
	(7.32)		(7.04)	(2.67)	(4.52)	(3.32)		[2.01]

Note: The variables p^f₁, p^f₂, and p^f₃ are dollar spot price indexes for coffee, sugar, and cocoa, respectively, in New York; p^f is a weighted average of these three indexes; p^m is a weighted average unit value index for imports of foods, feeds, and beverages; and $\overline{m}$ denotes U.S. imports of foods, feeds, and beverages, deflated by p^m. For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.

Two types of dock strike variables are used in the equations of Table 4A. The Takacs strike variables—discussed in Section II—are used in equation (4.1), while a strike variable provided by Isard, Lowrey, and Swamy (1974) is used in the other three equations. This latter variable is defined as the difference between the logarithms of actual and normal imports during strike periods;³⁰ the positive coefficient shown in equations (4.2) to (4.4) is therefore consistent with a priori expectations. The regressions using the Isard strike variable have a lower standard error than their counterparts which use the Takacs variables, but they also have a lower value for the Durbin-Watson statistic, which makes it difficult to evaluate the relative performance of these strike variables.

It is sometimes suggested that the rapid expansion in imports of consumer goods since the mid-1960s has resulted not only from the growth of income in the United States but also from a change in tastes induced by increased familiarity with foreign goods. To allow for this possibility, the variable T (equal to zero up to the fourth quarter of 1959 and to a quarterly time trend thereafter) was introduced in equation (4.3).³¹ Its coefficient turns out to be significantly greater than zero at the 0.01 level, but the magnitude of the estimated shift is not very large—the equivalent of an increase of less than 0.1 in the income elasticity of import demand.

The type of import price equation estimated in Section III cannot be reasonably used in the case of foods, feeds, and beverages. A very large share of total imports in this category is accounted for by a small number of agricultural commodities (especially coffee, sugar, and cocoa), and these commodities are typically produced by countries other than those included in the average price and exchange rate variables defined in Section III. Moreover, the export price model of Section II is probably not applicable to agricultural commodities. For these reasons, the import price equations in Table 4B simply relate the unit value index p^m to spot prices of the three principal imported commodities, using distributed lags to capture the delays between contract and delivery.³² In equation (4.4), p^f is a weighted average of coffee, sugar, and cocoa prices, while in equations (4.5) and (4.6), the components of p^f are used separately.³³ The variable p^f₁ is a weighted average of Brazilian, Colombian, and Salvadoran coffee prices; p^f₂ is the New York price for raw sugar (Carribean); and p^f₃ is the New York price for Brazilian cocoa. The estimated coefficients in equations (4.5) and (4.6) are in line with the relative importance of these three commodities in U. S. imports.

industrial supplies and materials

Table 5A summarizes the estimation results for imports of industrial supplies and materials expressed in real terms. The dependent variable in each of three equations excludes fuels and lubricants, and it is deflated by a weighted average of unit value indexes for crude materials and semimanufactures adjusted to exclude petroleum prices.³⁴ Among the explanatory variables, y^d is the aggregate index of industrial production in the United States, and p^d is a U. S. wholesale price index constructed by the authors for nonfood, nonfuel crude, and intermediate materials. As in the case of foods, feeds, and beverages, the import price variable ${\tilde{p}}^m$ is adjusted for changes in tariffs.³⁵

Table 5.

Import Volume and Import Price Equations for Industrial Supplies and Materials

(Based on quarterly data, first quarter of 1959 to fourth quarter of 1973)

Note: The variable p^m is a weighted average of unit value indexes for crude materials and semimanufactures; $\overline{m}$ is the logarithm of U.S. imports of industrial supplies and materials (other than fuels and lubricants) deflated by p^m. For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.

Table 5.

Import Volume and Import Price Equations for Industrial Supplies and Materials

(Based on quarterly data, first quarter of 1959 to fourth quarter of 1973)

A. Import Volume Equations (Dependent Variable $\overline{m}$)
Import Volume Equation	Constant	yd	$\stackrel{4}{\mathrm{\Sigma }}{\tilde{p}}^m$	$\stackrel{4}{\mathrm{\Sigma }}{p}^d$	$\stackrel{4}{\mathrm{\Sigma }}{w^d}_1$	wd 2	D	D -1	D +1	S	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
(5.1)	–10.47	0.493	–1.789	2.968	0.101	0.317	–0.212	0.103	0.011	–0.055	—	0.988
	(9.48)	(6.20)	(5.48)	(9.17)	(4.13)	(5.17)	(5.96)	(2.96)	(0.31)	(8.34)		[1.41]
(5.2)	–10.43	0.472	–1.920	3.104	0.102	0.299	–0.210	0.107	0.012	–0.058	—	0.989
	(10.01)	(5.97)	(6.20)	(9.63)	(4.48)	(5.02)	(6.05)	(3.14)	(0.35)	(8.79)		[1.45]
(5.3)	–7.57	0.458	–1.227	2.908	0.104	0.262	–0.231	0.101	0.012	–0.056	0.274	0.982
	(8.43)	(4.88)	(4.45)	(7.81)	(3.78)	(4.01)	(6.96)	(3.22)	(0.37)	(7.60)	(1.87)	[1.92]

B. Import Price Equations (Dependent Variable pm)
Import Price Equation	Constant	$\stackrel{3}{\mathrm{\Sigma }}{p}^f$	$\stackrel{3}{\mathrm{\Sigma }}k$	$\stackrel{3}{\mathrm{\Sigma }}{w}^f$	W d	t	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
(5.4)	0.345	1.521	–0.527	0.063	0.008	0.005	—	0.987
	(0.24)	(7.28)	(3.97)	(1.71)	(2.64)	(4.63)		[0.84]
(5.5)	–0.487	1.772	–0.357	0.023	0.003	0.006	0.663	0.961
	(0.79)	(7.07)	(1.82)	(0.34)	(1.21)	(4.67)	(6.04)	[2.01]

Note: The variable p^m is a weighted average of unit value indexes for crude materials and semimanufactures; $\overline{m}$ is the logarithm of U.S. imports of industrial supplies and materials (other than fuels and lubricants) deflated by p^m. For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.

View Table

Table 5.

Import Volume and Import Price Equations for Industrial Supplies and Materials

(Based on quarterly data, first quarter of 1959 to fourth quarter of 1973)

A. Import Volume Equations (Dependent Variable $\overline{m}$)
Import Volume Equation	Constant	yd	$\stackrel{4}{\mathrm{\Sigma }}{\tilde{p}}^m$	$\stackrel{4}{\mathrm{\Sigma }}{p}^d$	$\stackrel{4}{\mathrm{\Sigma }}{w^d}_1$	wd 2	D	D -1	D +1	S	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
(5.1)	–10.47	0.493	–1.789	2.968	0.101	0.317	–0.212	0.103	0.011	–0.055	—	0.988
	(9.48)	(6.20)	(5.48)	(9.17)	(4.13)	(5.17)	(5.96)	(2.96)	(0.31)	(8.34)		[1.41]
(5.2)	–10.43	0.472	–1.920	3.104	0.102	0.299	–0.210	0.107	0.012	–0.058	—	0.989
	(10.01)	(5.97)	(6.20)	(9.63)	(4.48)	(5.02)	(6.05)	(3.14)	(0.35)	(8.79)		[1.45]
(5.3)	–7.57	0.458	–1.227	2.908	0.104	0.262	–0.231	0.101	0.012	–0.056	0.274	0.982
	(8.43)	(4.88)	(4.45)	(7.81)	(3.78)	(4.01)	(6.96)	(3.22)	(0.37)	(7.60)	(1.87)	[1.92]

B. Import Price Equations (Dependent Variable pm)
Import Price Equation	Constant	$\stackrel{3}{\mathrm{\Sigma }}{p}^f$	$\stackrel{3}{\mathrm{\Sigma }}k$	$\stackrel{3}{\mathrm{\Sigma }}{w}^f$	W d	t	$\hat{\rho }$	${\overline{R}}^2$ [D-W]
(5.4)	0.345	1.521	–0.527	0.063	0.008	0.005	—	0.987
	(0.24)	(7.28)	(3.97)	(1.71)	(2.64)	(4.63)		[0.84]
(5.5)	–0.487	1.772	–0.357	0.023	0.003	0.006	0.663	0.961
	(0.79)	(7.07)	(1.82)	(0.34)	(1.21)	(4.67)	(6.04)	[2.01]

Note: The variable p^m is a weighted average of unit value indexes for crude materials and semimanufactures; $\overline{m}$ is the logarithm of U.S. imports of industrial supplies and materials (other than fuels and lubricants) deflated by p^m. For definitions of other variables, see the text and Appendix, Table 10. All lower case Latin letters refer to natural logarithms.