Theory and Estimation of the Demand for Imports of Consumer Goods

May 22, 1975

THEORY AND ESTIMATION OF THE DEMAND FOR IMPORTS OF CONSUMER GOODS

by

P. Isard, B. Lowrey and P.A.V.B. Swamy

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgement by a writer that he has had access to unpublished material) should be cleared with the author or authors.

Theory and Estimation of the Demand for Imports of Consumer Goods by * P. Isard, B. Lowrey and P.A.V.B. Swamy

1. Introduction and Summary

Despite the abundance of literature on time-series estimation of import demand relationships, several important theoretical problems have not been treated adequately in major references on the subject, and empirical work in this area remains conceptually deficient. The purpose of this paper is to focus on specification problems that, to our knowledge, have not been adequately recognized, and to attempt to resolve a number of these. We present estimates of quarterly levels of U.S. imports for three types of consumer goods: foods, feeds and beverages from (1959 I through 1972 IV), consumer nondurables, excluding foods (1965 I - 1972 IV), and consumer durables, excluding automative products (1961 I - 1972 IV).

The importance of disaggregating imports by end-use is well-recognized; appropriate specification forms depend on whether we are considering consumer or producer demands, and whether the imports under study are durables or nondurables. This recognition, however, is not yet reflected by empirical work in the field. One purpose of this paper is to estimate the demands for imports of

consumer durables using a stock adjustment model.

*/ This paper represents the views of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or its staff. We are indebted to several of our colleages, and especially to

Daniel Roxon, for general criticism and for particular assistance in understanding the limitations of existing data.

Most empirical specifications of consumer demands for imports are based on utility maximization over a single-period horizon. This paper, in contrast, draws its demand specifications from a multi-period framework. A multi-period framework is capable of sorting out the relative impacts of income trends and income cycles on consumer demand for imports, and provides a clear rationale for incorporating lagged income and price variables into aggregate demand hypotheses--namely, as information used by consumers to form expectations about future incomes and prices. Lagged incomes and prices have no place in the singleperiod utility maximization framework, and although they may be important determinants of import deliveries when lags exist between orders and deliveries, the single-period framework may overlook important prior information about the shape of the lag distribution.

Section 2 presents what we feel to represent an appropriate derivation of aggregate consumer demand equations within a multi-period framework. Subsection 2.1 treats the case of nondurables; subsection 2.2 considers durables. Our models distinguish between imports and domestic products, which are imperfect substitutes at the level of commodity aggregation that we consider. Subsection 2.1 confronts the problem of aggregating over individuals and demonstrates that the existence of a stable aggregate demand function is consistent with a world in which individual consumers have different demand parameters and change over time. In our multi-period framework, the individual's demand for imports is related to his wealth or permanent income, rather than being a direct function of his current income. Current demands for imports also depend on the expected future prices of imports and domestic substitutes, which we express in terms of current prices and expected rates of inflation. For simplicity, we assume that

at any moment the consumer expects the rate of inflation of import prices to

-~3-

remain constant over his planning horizon, although he continuously revises his expectations of the magnitude of this constant rate of price advance. Similar assumptions are made about the expected future prices of domestic substitutes. For imports of nondurable consumer goods, demand thus depends on permanent income, the current prices of imports and domestic substitutes, and the rates of inflation that the prices of imports and domestic substitutes are expected to show. Our proxy for permanent income is a geometricallydecaying, weighted average of current and past incomes; and our proxies for expected inflation factors are geometrically-decaying, weighted averages of current and past inflation factors.

These same variables affect the demand for imports of consumer durables. Since stocks of durables carry over from one period to the next, we formulate the consumers demand as an adjustment of actual to desired stocks, taking account of depreciation. Thus, our model for durables also includes speed-of-adjustment and depreciation parameters.

In Section 3 we define and discuss the inadequacies of our commodity groups and data. Additional information on data construction is provided in the Appendix.

Our most serious data problem, which is conceptual in nature, has received surprisingly little attention in the literature. This is the problem that sales of imported goods to consumers~-the variable which measures the demand for consumer good imports--may, in fact, be quite different from the recorded level of consumer good imports--the only series available for use as a dependent

1/

variable.~ Imports are rarely ordered by consumers themselves; rather, sales

1/ Consequently, the dating of the dependent variable may not correspond to the dating of those income and price terms which it is most appropriate to use as independent variables.

-4-

to consumers equal recorded imports minus changes in the inventories of intermediaries. Unfortunately, adequate data are not- available on intermediaries' inventories of imported goods. One serious consequence of omitting from regression models an explicit treatment of these changes in inventories will be a complicated pattern of autocorrelated disturbances. Simple adjustments for autocorrelation are inadequate when inventory behavior is complex .2/

Subsection 3.1 contains a brief discussion of the influence of import quotas on our dependent variables. Subsection 3.2 is a lengthy discussion of our choice of price data and their inadequacies, and also contains a description of tariff factors. A major shortcoming of the price data is their failure to capture the mark-ups between importers or domestic producers and the consumers whose aggregate demand functions are being estimated. A second shortcoming, particularly in the case of durables, is the fact that recorded prices do not adequately summarize the terms of purchase: they ignore installment and down payment terms, the generosity of trade-ins and other concessions, etc. A third shortcoming, independent of the quality of disaggregated price data, is that the weights used to construct aggregate price indexes may involve serious specification errors.

Subsection 3.3 discusses effective prices and omitted variables. It is argued that Gregory's (1971) formulation of effective price variables is inappropriate. We also note that the relative availability of imports and domestic substitutes is an important non-price attribute which, as an omitted 2/ This problem can be avoided by the complicated approach of explaining

recorded imports as an order function adjusted for delivery lags. See Marston (1971).

-5-

variable, may underlie the high estimated income elasticities of demand for imports of non-food consumer goods since the early 1960's.

During our sample periods, approximately 30 percent of our quarterly import records reflect the influence of major U.S. dock strikes, which have had strong impacts on intermediaries' inventories of imports, although not necessarily on sales to consumers. As an effort to avoid the serious autocorrelation problems discussed above, we have obtained weekly longshore manhours data and have attempted to develop a sophisticated set of dock strike dummy variables. Our treatment of dock strikes is described in subsection 3.4.

Section 4 discusses our numerical estimates of import demand relationships for the three commodity groups, based on a nonlinear estimation procedure. In subsection 4.1 we present our results for foods, feeds and beverages (FFB) and consumer non-food nondurables (CND); in subsection 4.2 we present results for consumer durables (CD). For the FFB case we obtained plausible magnitudes and correct signs on all the important parameters of our multi-period demand model. For the CND case we were unsuccessful at estimating the multi-period model and were led to adopt: a simplified structure, similar to conventional single-period models of import demand, by which standards our parameter estimates seem quite acceptable. For the CD case we were again unsuccessful at estimating a multi-period model. Our results for this case are weak, demonstrating only that plausible prior restrictions on depreciation and speed-of-adjustment parameters lead to plausible estimates of income and own-price elasticities. The existence of heterogeneous products within our commodity-group aggregates is a problem. Although the different commodities within each aggregate may exhibit similar income and price elasticities, for the

case of durables the differences in speed-of-adjustment and depreciation

-6-

parameters make it particularly difficult to estimate a stable and well-fitting

aggregate demand equation.

2. Theoretical Foundations for Aggregate Consumer Demand Equations

In this section we derive aggregate consumer demand equations for imports based on utility maximization over a multi-period horizon. Our multi-period focus leads to an appropriate specification of the sensitivity of demand to income (thus sorting out the relative impacts of income trends and income cycles), and provides a clear rationale for incorporating lagged income and price variables into aggregate demand hypotheses. Subsection 2.1 deals with nondurable commodities and subsection 2.2 with durables. It is important to note in these subsections that the derivation of aggregate demand equations does not require the unrealistic assumptions that individual consumers are similar in

their behavior or unchanging over time.

2.1 Demand for Non-Durable Goods

As in Friedman (1957) and Modigliani and Brumberg (1954), we begin by considering an individual consumer who is concerned with the allocation of his resources among goods for current and future consumption, with resources being his current net worth plus the sum of current and discounted future earnings. We take into account his expected consumption of goods and services in future periods 1, ..., L, L being the expected date of his death. His bequests are represented as goods in period I+l. When at times we refer to the consumer's demand for composite commodities, we are implicitly assuming either that the prices or the quantities of the different commodities within each composite are in fixed proportions, or that "homogeneous separability" obtains. For an excellent account of the types of separability and their implications for two-

stage maximization of utility functions, see Green (1964).

-7-

We first consider the behavior of a consumer under conditions of complete certainty. In this context, the consumer's problem may be formulated as

follows: Maximize (1) uly» Ci> cee Gra] subject to

(2) W.=V,+H

0 0 0 E E 1 L =V +E + ——+...4+———___—_ 0 0 ltr (ltr)... (itr, 4) Cc . >.c. + Fi-l A Pr S41 =0-0 (1+r9) see (ltr)... (itr, ) where

¢. is an mx 1 vector of consumptions in period t, with imported products distinguished from domestically-supplied products,

is a 1 x m vector of the corresponding prices in period t,

r_ is the rate at which the consumer can borrow or lend money between periods t and ttl,

Wy is the consumer's wealth in period 0,

Vo is the consumer's non-human wealth in period 0, i.e., the present value of all non-human assets less the present value of all nonhuman liabilities, and

Ho is the consumer's human wealth, which is measured by his current earnings from work, E,, plus the present value of E > «rey Ey his expected earnings from work in the subsequent périods. L

The utility function in (1) will have certain classical properties enumerated

in Goldberger (1967). Given

Wo»P0> eee, Pr+1> To? eee Ti

-8-

the constrained maximization problem in (1) and (2) may be solved to obtain

the consumer's vector of demands in period 0.

3 Cc, = C.[W PL ait] __ (3) Cy = SolWo»Po> Tig ? °°°? (itrg)-- tz)

Following the work of Friedman, we define permanent income, y’, as that rate of receipts per period which, if maintained at a constant level over one's lifetime, would have a present value equal to that of one's total wealth.

Its value in period 0 is determined by solving the following equation for Yo?

1 1 4 Pri + t..t¢o———] - (4) Yol Itt, (Tit)... Gt, 4)! Wo:

Accordingly, we may rewrite eq. (3) as:

= P (3a) fy = SolOyo> doko» 4yPy> +++ Sa Prsi! where 8 =1+y-+ tt aE) TY ( To)--- Tho dy =1 = i = q 5 oooesS—sfrtor rp = 1, ...., TAl

T (itry)..- (itr 4)

In (1) and (2), all t » 0 represent subjective planning time, and not historical time. Only at t = 0 is the consumption plan given by eq. (3a) actually implemented. The problem in (1) and (2) is handled so as to emphasize

the effect of planning for the future upon present behavior, C

fo: At time t > 0

-9-

the consumer again solves the utility maximization problem in a form analoguous

to (1) and (2) under a forward shift of time subscripts.

= P (3b) Se SLOye> IPe> SyPega> +> Spe aPeste]

It should be emphasized that the only operable Cc. is that decided at time t.

This whole procedure requires the assumption that a complete set of intertemporal preferences exists. On the question of whether this assumption is warranted, we quote Hicks (1946, p. 229):

If we assume the individual to have a complete plan of expenditure, extending over a considerable future period, and complete in every detail, we are falsifying his actual behavior quite absurdly; but if we merely use this assumption not to determine the details of the purchases which may (or may not) be planned to be made in the future, but to determine the details of current expenditure alone, we are not involved in anything which is at all absurd. The determination of current expenditure will proceed just as if there was such a complete plan; if we assume the existence of a complete plan we can proceed to determine current expenditure with the minimum of trouble.

The functional form of the demands at time t depends on the functional form of utility at time t. In the spirit of generality (or ignorance) which characterizes the classical approach, however, it is possible to proceed without specifying a particular functional form for utility, see Paulus (1973). We take a log-linear approximation to (3b) as representative of the demand

behavior which would arise from maximization of utility over the relevant range

of variation of permanent income and expected future prices.

L,t1

5 1 =ey +6" logyP te et. e 1

(5) 08 Cis * Borge + Brige 108 Yat pe Petit Miiky 08 4 Pik the (j = 1,2, ..., m)

where i indexes consumers, j and k index commodities, and L, is the expected

lifespan or planning horizon of the jth consumer at time t. Note that we have

- 10 -

factored the coefficients on the discounted future prices into two components: * . Boi jet and Viger’ If we interpret eqs. (5) as a straight log-linear approx- * imation to (3b), the log @ term would be absorbed in Boje? alternatively, we may interpret (5) as a modified log-linear approximation in which, following * Friedman (1957, pp. 11-14), the income coefficient Brige depends on 9, and hence, on expected future interest rates.

Notice that eqs. (5) allow different individuals to have different expectations regarding future prices. Note also that we do not force the coefficients of eqs. (5) to be identical for all consumers at all points in time; rather, we follow a general approach by allowing the coefficients to vary among individuals and over time. Given that individuals do indeed differ greatly in their behavior and change over time, it is doubtful whether any fixedcoefficient demand models integrated into a specific utility-maximization theory can compete with this variable-coefficient double-log model of demand.

A similar argument is offered by Goldberger (1967, p. 107) while commenting on the Rotterdam School models; we have paraphrased at points: If one is to assess the fruitfulness of eqs. (5), it is important

to recognize that no stigma attaches to their being approximate

rather than exact. With the true utility function being unknown,

there is after all no guarantee that any of the "exact" consumer

demand models will be exact in fact. A formulation of the type

eqs. (5) with varying coefficients, quite possibly, provides an

adequate approximation to utility-maximizing behavior over a range

of conceivably true utility functions; this without being exactly

appropriate for any particular one. Such robustness is naturally

desirable.

Up to this point we have been discussing consumer behavior under conditions

of certainty. However, for a variety of reasons mentioned in Friedman (1957,

pp. 14-17), the effect of uncertainty establishes no presumption against the

-ll-

form assigned to the demand functions in (5). According to Friedman, one way of introducing uncertainty is to include the ratio of nonhuman wealth to permanent income as a variable determining the income coefficient, Baye: We do this implicitly: uncertainty is another reason for variability of coefficients.

One complication associated with the formulation in (5) is that it is uncomfortably rich in parameters when the number of commodities (m) and the consumer's planning horizon (L;) are large. Accordingly, we first simplify the formulation of the system, as in Theil (1971, p. 579), by eliminating most of the cross-price terms under direct additivity assumptions; that is, we assume that most cross-price elasticities of demand are zero. To the extent that our commodities represent broad composites of consumer goods, direct additivity may be a plausible specification, see Goldberger (1967, p. 31). Specifically, we suppose that the utility function in (1) can be written as a sum of functions, each containing as arguments only the current and future imports and domestically-produced quantities of one composite commodity. With this simplification, the consumer's demand for imports of any composite commodity depends only on permanent income and the current and future expected prices of these imports and their domestic substitutes. When all these regressors are deflated by a conventional general price index, the consumer's demand function is also consistent with an alternative procedure of simplification which does not involve the assumption of direct additivity, see Goldberger (1967, pp. 101-4).

We now restrict our attention to the consumer's demand for a particular composite of imports. We let pm and pd, respectively, denote the prices of

these imports and their domestic substitutes, where to allow for generality,

~12-

it is understood that these variables, along with the Yee are deflated by a general price index. The assumptions of the previous paragraph then leave the system as; | L,+1 (6) log G,. = Bore + B1y4 108 viet Boe 0 Mim OBC Pm) L,+1 * i * Base 0 WigrtoB(d pds oy) where Bort now includes any combined effect on the dependent variable of the determining factors which are not introduced explicitly.

In a context of perfect foresight, the th individual's demand for imports depends on known values of future prices. To operationalize eq. (6) ina context of uncertainty, we must replace future values by their optimal forecasts. The implicit assumptions here are: first, individuals react to the forecasts of the future values; second, individuals base their forecasts on the past values of the variable in question, and optimize their forecasts given knowledge of some stochastic specification of the mechanism generating the time series of the causative variable, see Nerlove (1967, 1972).

In order to simplify the nature of the estimation problems, we assume that the stochastic structure generating the incomes and commodity prices is of the simple unobserved-components type suggested by Nerlove (1967). It should be noted, however, that the models which Nerlove (1967) uses for generating his optimal predictions of variables are classified as inconsistent models

by Cyert and DeGroot (1974), since individuals do not know the form

- 13 -

of the process which determines prices, and, in fact, base their decisions

3/

on an incorrect model.=

The prices to be forecast in eq. (6) may be rewritten as

_ e POS ety Come PE (7)

e i,the Codie te) Pd,

pd

where pm, and pd are the current prices faced by all consumers and Pine the and ose tte are the ;-period rates of inflation expected by the yuh consumer. To make the model tractable, we adopt the simplifying assumption that at any point in time (t), each consumer expects constant rates of inflation throughout

the future; specifically

Pmi ste, ~ (trom ,) om,

(7a)

evr. PAs tte ~ (ited; ,) ‘Pd,

_th . : The i” consumer's expectations of future quarter-to-quarter rates of inflation

(pms and ods.) are revised from period to period, however, and therefore

carry a time subscript.

3/ An alternative to our proxies for expected future rates of inflation would be the assumption of rational expectations of future rates of inflation. This rational expectations approach is difficult to implement, however, unless

the relevant economic theory of price determination is known.

- 14 - Combining (6) and (7a) yields:

= Po (8) log Ci. = Bore * By, , 108 Yin + Bozy los Pm. e + Baap log pd + Bait log (1 + pm)

e + B5,, log (1+ pd.)

where 8 includes terms in log ds (for += 0, ..., Ly + 1), and the price-

oit elasticities, Bort and Bases include both the direct impacts of current price changes and the indirect impacts that result as current price changes lead to revised expectations of future prices.

The preceding analysis is microeconomic in nature, and since data on individual consumers are not available, an explicit treatment of the aggregation problem is in order. We proceed as in Zellner (1969), Theil (1971, Section 11.5) and Swamy (1971, pp. 15-16). We assume the following:

(a) The vectors, (Boi ¢? Bist? Boi Baib> Baie Bop with different

i and t subscripts, are random drawings from a six-dimensional distribution with the mean vector (Bos B1> Bo» B3 By» Be) and a finite symmetric variance-covariance matrix,

4

(b) The coefficients are independent of the explanatory variables, +/

which are uniformly bounded. 4/ This assumption is not true unless the indifference surfaces are homothetic with respect to the origin. It can be relaxed by taking each coefficient as an explicit function of economic variables plus an error. However, we make assumption (b) to make the estimation procedure more tractable. The dependence between

the coefficients and the explanatory variables for a finite number of individuals does not hurt our procedure.

-15-

The means. of micro coefficents reflect the "representative" tastes of the population and the deviations of micro coefficients from their means reflect idiosyncracies of individuals in tastes. This interpretation is due to McFadden (1974).

Now aggregate eq. (8) across individuals; this gives

n n 1st = 1 yt P (9) n= 108 C., = By + By p~ = log y;, + By log pm, t i=l t i=l n

+ 8, log pd. + 8 1 st tog (1 + om°)

3 t “400 7. it t i=l 1 ars e * * Bsa 2108 d+ pls. tu te

where B =

git By + Coit (L = 0, 2.6; 5), a, is the population in quarter t,

* Coit = Me + Coie? and

n = yt P (10) ee * {Coit + Cit log Vit + Coit log Pm + Cait log pd,

e d& + Cait log (1 + pm + Csit log (1 + p ipl:

* The u, are regarded as the individual-invariant time effects which are not accounted for by the included explanatory variables in eq. (9).

It is possible to show that under certain general conditions the vector

: . : -1 e= (e,> bey ep) has mean vector 0 and variance-covariance matrix of order n

- 16-

where n is the minimum of ni(t = 1, 2, ..., T), see Welsch and Kuh (1974). Consequently, for large enough n and finite T, the vector converges in probability to 0 and can be eliminated from eq. (9) without introducing any error.

Except for the price terms, each variable in eq. (9) is the arithmetic mean of logarithmic values. Arithmetic means of logarithmic values are logarithms of geometric means. Unfortunately, macroeconomic data represent arithmetic averages of micro observations, not geometric averages. If the logarithms of explained and explanatory variables in eq. (9) follow the normal distribution, however, we have a simple relation between geometric and arithmetic means. For given t, let a, (x) and 8, (x) be the respective arithmetic and geometric means of a variable Xie (for i=l, ..., ni)» and let 02 (x) be the variance of the logarithmic values of Kees The variance on (x) is assumed

to be constant at least over the sample period. We then find

2 (1) a(x) = Gee? 0/2 This means that the geometric means of micro variables show time movements close

to arithmetic means. Using the relation (11), we can write eq. (9) as

(12) log a. (C) = Yo + By log a.(yP) + Bo log pm,

+ B3 log pd. + By log aq. + pm*) + Be log a.( 1+ a)

+ u t

where .

1. 2, 2 2 2 Yo = 8g + glo" CC) - Byo (yP) - Byo (1 + om) - Boo (1 + pd®)].

-17-

n Since our dependent variable is log st Cc,

i=1 we also wish to focus on log(n, +a, (y?)) = log ye as an income variable, we

to log(n +a. (C))= log Ci» and because

transform (12) to

= Pp : (12a) log Cc. = Yo + 8, log Ye + Bo log pm + Bz log pd,

+ 8, log a, (1 + om”) + B, log a,(1 + od) + u,

* where u, =u + (8, - 1) (log n.)-

We must now adopt specific predictors of permanent income and the expected rates of inflation. Let y, denote personal disposable income in period t and » reflect

note that historic price ratios, pm, _,/Pm and pd, _,/pd

t-s-1 t-s-1

historic values of the inflation factors (1 + pm) and (1 + od). We adopt all

the stochastic assumptions which make the quantities

foe} o (1-A,)E Ap logy, _., (1-2,)E 05 log(pm,__/pm

<1) (13) s=0 s=0 tes-1

eo and (1-),)2 3 log (pd, _/Pd._._1) s=0

P

the minimum mean square error predictors of log Yee

log ad + om”) and

log aa + od”), respectively; such stochastic assumptions are given in Nerlove (1967, pp. 142-3). In subsection 4.1 below we substitute (13) into (12a) and manipulate the resulting equation to arrive at our basic hypothesis for estimating imports of nondurable consumer goods.

Several important conclusions may be drawn from the analysis of this sub-

section. First, the existence of a stable aggregate consumer demand equation is

- 18 -

consistent with a world in which the tastes of individual consumers differ

from each other and change over time. Second, consumer demand in any period

is not directly related to the prices or incomes that prevailed in the past; rather, it depends on lagged variables only insofar as consumers use historic information to evaluate their current wealth positions (or permanent incomes)

and to forecast future prices. Third, if we believe that the consumer's budget constraint depends on his wealth or permanent income, and that consumption possibility sets are independent of cyclical income patterns, then consumer demand should be related to permanent income, and we should not expect or attempt

to estimate a stable elasticity of demand with respect to current income.

2.2 Demand for Durable Goods

In analyzing the demand for durable goods it is desirable to allow for the fact that the services of a durable are not consumed entirely during the period in which the durable is purchased, as distinct from the case of nondurables. The value of durable goods held at the end of any period t by the yth consumer, Vie is equal to the value of the stock at the beginning of the period,

Vite plus the excess of purchases in that period, q over the consumption of

it’

the period, din l.e.,

(14) v..=V,.,+4q,.-d4

We may rewrite eq. (14) as

(14a)

~. =V.. - Vv, +d, Fit it it-1 it

As in Stone and Rowe (1960), we assume that

(15) Vie 7 Vaeen > Vie Cie 7 Vited

- 19 -

where 0 < y, < 1 and Vie represents the value of the desired level of stocks. Following Tinsley (1971) we can develop a justification for the adjustment

eq. (15). The basic premise of eq. (15) is the existence of some kind of costs of adjustment which prevents the individual consumer from being always

in “equilibrium”. The optimal target, Vie is a moving convolution of future events anticipated over the planning horizon of the individual and can be shown to be a weighted average of all expected future prices of durable commodities.

The adjustment coefficient, y.

ite is a function of the rate of interest and the

relative curvatures of the indifference curves and cost of adjustment functions.

To complete the theory of consumer demand for durables, it is necessary to combine the theory of demand for net additions to stocks of durables with a specification of the depreciation or consumption terms diy: To satisfy eq. (14), depreciation during any period is properly measured as the sum of the scrappage value of units scrapped during the period plus appropriate reductions during the period in the values of the initial stocks and purchases that are not scrapped.

In theory, stocks of consumer durables, and the depreciation of these stocks, should be valued in terms of the flow of consumer utilities that derive from the services of the durables, rather than original production costs, replacement costs, or accounting conventions; and market prices do not necessarily reflect these utility values. We shall refer to these theoretically appropriate values as "written-down values".

Our model of depreciation begins with the simplifying assumptions that for

.th : : the i consumer in period t:

- 20 -

(i) Wide is the value of units scrapped from new purchases; by will be zero if durable goods are not scrapped in the period in which they are bought, (ii) I£ ry is a vector of mortality rates appropriate to each age group in the ith consumer's stock at the beginning of period t, ty is the : : .th ., : th diagonal matrix whose j diagonal element is equal to the j element

‘ _th ' : of r is a vector whose elements express the i' consumer's written-

=i? Pit

down values of units of different ages, B,, is a diagonal matrix whose

it

.th ,. : _th : j diagonal element is equal to the j element of Bit? and Sip1 is

a vector of numbers in each age group in the opening stock, then Libs Steer gives the written-down value of units of different ages scrapped during period t from the stock held by the yth consumer at the beginning of period t.

(iii) Consumption is a continuous process which uses up the existing stock at a constant proportionate rate. In any period, therefore, deprecia-

(1)'

tion (apart from mortality) will consist of both by (I -

(1)

where 8 is a vector of proportions of the written-down values of

EU Bitsiter?

units of different ages not scrapped, plus a further, generally smaller,

2 fraction, be ) of the new purchases of the period not scrapped.

Assumptions (i) - (iii) imply

. = (2) ' (1) a \14 (16) Sie T Teg Op - ula, + lee + oe GE - BB Seed

This formulation cannot be implemented empirically, however, without detailed

data on initial holdings of consumer durables, new purchases of consumer goods

- 21 and their mortality and depreciation rates--data which are not readily available. Consequently, we resort to the usual, apparently crude, procedures. We approx-

imate eq. (16) by

(16a) di = Sine * Sez eMi eed + Sisedie

We might expect Seat = 0 since there cannot be any services derived from durable

goods if Viel = 0 and Wit = 0. However, (16a) is merely an approximation to a

more complicated function in (16). The approximation may become much closer if we allow ourselves the freedom of one more parameter such as Ssite

* Now let Vet in eq. (15) be distributed independently of Vat and Vieni?

with mean y and constant variance, and let the vectors (8, ) be

ilt? Sion $43

independently of Vitel and qt with mean vector (54> 85> 53) and finite variancecovariance matrix. Then it follows from Theil's (1971, pp. 570-1) convergence theorem that for given t, when the number of consumers is sufficiently large and

the variables Vie Vv and q;, are uniformly bounded, eqs. (15) and (16a)

it-1

aggregate perfectly over individuals to

— ** (17) Ye 7 Venn = VE 7 Ven) and (18) di = 6) + SV, + 83%, where n n n hn - * ve os ES Vir? Ye-1 7 = re hitel, vp = " zr Vier Up = 7 zr qs t i=l t-1 i=1 t i=1 * t i=l and n 1 t q, >— 2 q,,. t ne isl it

Similarly, eq. (14a) can be aggregated as

(18a) q7~y 7

-22-

Substituting eq. (18) into eq. (18a) gives

(19) q, = +t {l- (1 - $5)Blv t 1-3 1-3 t 3 3 where B is the backward shift operator defined as Box =x for any x.

t t-s Lagging eq. (19) by one period and subtracting it from eq. (19), we have

1

(20) Aq, = = [1 - (1 - 5,)Blvy, 1-64 = [1-1 - 5, Blvw, - v,_4) [by eq. (17)] 1-5 v _ * _ 81 -—+ 1 - a - &)Blv, - vaq,_) -— sby ea. (19)]

Associated with the equilibrium level of stocks, Veo there is an equilibrium Ke level of purchases, qd. which is wholly replacement demand and just sufficient to maintain stocks constant at the desired level. From eq. (19), these equilibrium

purchases must satisfy

* 1 - - * (21) gq, ==> ©, + Byv,)- 1-8,

Inserting this back into eq. (20) gives

Je ke *

ety Gq, 7 (lL - 69) > ay

(22) a, = (2 - ya.) + 89

wri!

Eq. (22) is in the form of Zellner's (1970) unobservable-variable model. If we

* interpret q, as the services of durables that would be consumed during period t

- 23 -

in an equilibrium state, we may hypothesize that the demand for this flow

of services has a functional form similar to the demand for a flow of non-

5/

durable goods, as given by (12a) of subsection 2.1. We therefore assume—

* i) e e * = + + (23) de = % + HY, F XPM, t aged, +a,(L + om.) + as(1 + pde) + u, where yp is aggregate permanent income, pm, is the own price of the durable-

good imports on the demand for which we are focusing, pd, is the price of domestic substitutes, ome and pdt are the quarterly rates of inflation expected

in the prices of imports and domestic substitutes, and u, isa disturbance term.

3. Definitions and Inadequacies of Commodity Groups and Data 3.1 Commodity Groups and Data Sources

As indicated in Section 1, the empirical focus of this paper is on three groups of consumer goods: foods, feeds and beverages (FFB); consumer nonfood, nondurables, manufactured and unmanufactured (CND); and consumer durables, except automobiles, manufactured and unmanufactured (CD). Our focus is on quarterly data from 1958 I - 1972 IV for FFB, from 1964 I - 1972 IV for CND,

and from 1960 I - 1972 IV for cp.2/

5/ Because demand for durable imports is the sum of net additions to stocks plus depreciation or replacement, it is difficult to work with logarithmic variables in this case.

6/ These groups correspond to end-use categories O(FFB), 40 plus 420(CND), and 41 plus 421(CD), as classified by the Office of Business Economics. The different sample periods were dictated by the availability of price data that we were willing to use, as discussed in subsection 3.2 below. Because of the lag structures in our regression hypotheses, each of our sample periods begins four quarters after the date cited here.

- 24 -

Both FFB and CND contain major import items that have been restricted by quotas during part or all of our data period, see Mintz (1973). Imports of meats, sugars and dairy products--all subject to quota restrictions-represented roughly 19, 13 and 2 percent, respectively, of total FFB imports in 1972.2/ With respect to CND, cotton textile imports have been subject to mandatory quotas since Late 1961, while noncotton textiles have been subject to mandatory quotas since late 1971 and voluntary quotas since at least 1965. For both categories, however, separate quotas have been imposed on imports from particular countries, without ever imposing global quotas on imports of cotton or noncotton textiles. Country quotas have been imposed sequentially over time, and the data show that as soon as imports from one country were restricted, imports from other countries accelerated, often sharply .2/ Similarly, when quotas were applied to particular textile imports from a given supplying country, imports of other textile items from that country often accelerated. Consequently, we feel that quotas did not have a major influence during our data period on aggregate imports of cotton and noncotton textiles from all sources combined.

Our import data were taken from various publications of the U.S. Department of Commerce and Office of Business Economics. Personal disposable income

was used as the explanatory income variable for all three categories. Both

7/' Data from U.S. Department of Commerce, Bureau of the Census: U.S. Foreign

Trade; Highlights of Exports and Imports, FT 990 publication, December 1972, Table 13.

8/ See U.S. Tariff Commission (1968, Tables 8 and 10).

- 25 -

imports (in current dollars) and income were seasonally adjusted using the standard (default) option of the Census Bureau X-11 seasonal adjustment program. Explanatory price variables and the import price deflators were not seasonally adjusted. While we are not willing to assert that the Census X-11 is the best of all possible seasonally adjustment procedures, we do feel

that it is better than a stable seasonal (or dummy variable) adjustment .2/

3.2 Price Data and Their Inadequacies

Econometric studies of import demands frequently lead to price elasticities that have wrong signs or are of questionable magnitudes. The poor quality of price statistics and misspecifications of the model may be responsible for these results. The first problem that we encountered in seeking price data was the unavailability of satisfactory data on retail prices--the prices that consumers face in choosing between imports, domestic substitutes and other goods. There is no easy way to take consumer price indices corresponding to our end-use groups and subdivide these indices into an import price component and a price index for domestically-produced import substitutes.

In selecting price indices for domestic substitutes, our choice was between

the consumer price indices and the wholesale price indices most closely

9] For a critical evaluation of the Census X-11 technique, see Cleveland (1972). Fishman (1969, p. 69) discusses several informal spectral criteria for judging the adequacy of seasonal adjustment. Grether and Nerlove (1972) point out the inadequacies in spectral criteria for the proper assessment of methods of seasonal adjustment and devise methods of seasonal adjustment based on a minimum mean-square-error criterion of optimality. Cleveland (1972) develops alternative methods of seasonal adjustment which are based on Bayesian criteria of optimality.

-~ 26 -

corresponding to our end-use groups. Because of their smaller coverage of import items, wholesale price indices were chosen. 22/ Data were taken from various issues of the Monthly Labor Review. For FFB and CND we used wholesale price indices for finished consumer goods: in the former case, the "foods" index, in the latter case, the index for "other nondurable goods", We did not use the finished consumer goods index for durables due to its coverage of automobiles, which are excluded from our CD category. Instead, we chose the wholesale price index for "furniture and household durables", listed as industrial commodities group. We made no attempt to purge these indices of their import price components.

In constructing the import price variables, we started with a weighted average of unit value indices for FFB and weighted averages of foreign export price indices (converted into U.S. dollars at spot exchange rates) for CND and CD. These were then multiplied by tariff factors.

Several factors governed our use of these different types of price indices for different categories. In the absence of retail price indices for imports, we would have a strong preference for weighted averages of foreign export prices if such data were available for a fairly complete coverage of major supplying countries. In fact, export price indices are not widely available for commodity groups that might be assumed to correspond roughly to our end-use categories. This deficiency in the coverage of export price 10/- In January 1973, 91 (or 43 percent) of the 210 nonfood commodities covered in the CPI had their CPI prices estimated from samples that included at least one import item. Of these 91, roughly one-third were commodities for which import prices accounted for at least 5 percent of the price quotations collected 6 were commodities for which import prices accounted for at least 25 percent of the quotes collected, and in 4 cases, import quotes provided the majority of the sample. In comparison, the wholesale price index, in which it is possible to identify import items precisely, assigned 1.35 percent of its weight to import

prices in December 1972. See, U.S. Department of Labor, Bureau of Labor Statis-

tics, "The Representation of Imports in the CPI and WPT." Mimeographed note, March 1973.

>

-27 -

statistics has to be balanced against the fact that, for our end-use breakdown, unit value indices are erratic and only available on a quarterly basis since 1967.

For CND and CD, the unit value indices seemed particularly erratic and there was no appealing way to match these end-use groups with other commodity groups for which unit value indices are available quarterly before 1967. On the other hand, imports of these items are somewhat concentrated by source, and we were able to come up with export price series for over 40 percent (1967 value shares) of the items in each of these two end-use groups. These data and our choice of weights are described in Appendix Tables Al and A2.

For FFB, the most appealing option was a weighted average of unit value indices for crude foods and manufactured foods. Both of these series are available quarterly since 1958. We decided against splicing this series with the unit value index for the food group as a whole, available since 1967. The data and our choice of weights is described in Appendix Table A3.

For each end-use category the explanatory import price variable (scaled to 1967=100) was multiplied by an appropriate tariff factor (scaled to 1967=1). For the 1967-1972 period, which involved both the Kennedy Round reductions and the 1971 import surcharge, our tariff factors were based on Wilson's (1973) detailed calculations of average tariff rates for each of our three end-use groups. For the 1958-1967 period we used information provided by Hooper (1974) on percentage changes in the average tariff rate on all U.S. imports, assuming that the same percentage changes applied to each of our three end-use groups. Appendix Table A4 presents our tariff factors and explicitly describes their

construction.

- 28 -

The questionable quality and limited coverage of our price indices are obvious deficiencies. It is particularly important to emphasize three ways in which our price data may be conceptually inadequate. First, as noted above, our prices are measured to exclude the mark-ups between importers, or domestic producers, and consumers. Ideally, our prices should be multiplied by appropriate mark-up factors. It is conceivable that these mark-up factors were relatively stable during the 1960s, but very likely that percentage markups changed significantly during 1971-72, when higher import prices resulting from foreign currency revalyations were partly absorbed by domestic importers, while domestic mark-ups were influenced by price and wage controls.

A second problem, particularly in the case of durables, is that measured price does not adequately summarize the terms of purchase: the demand for relatively expensive durables depends upon down payment and installment terms, the generosity of trade-ins and other concessions, warranty offers, etc. This problem applies equally to both import prices and the prices of domestic substitutes.

A third problem is that our explanatory price variables may involve serious specification error. Theil (1967, pp. 150-1, 208-19) has shown that the true cost of living price index can be closely approximated by a moving-weight index based on moving expenditure shares, but we have not followed this procedure. The statistical insignificance of estimated price elasticities may be due as much to incorrectly ‘specified index numbers as to the poor quality of the data

used to construct these indexes.

- 29 -

3.3 Effective Prices and Omitted Variables

We have noted above that quoted prices do not always summarize the relative attractiveness of imports and domestic substitutes to the consumer. In addition to the actual quoted prices, variables such as relative waiting times, trade credit terms, rebates, discounts, and the general ability of sellers to meet customer requirements influence consumer demands, particularly in the case of durables. Gregory (1971) has coined the term effective price in reference to a multi-dimensional vector which describes those price and non-price attributes of the seller's commodity or services that are relevant to the buyer's decision. Consideration of relative effective prices at home and abroad determines whether the commodity is purchased from domestic or foreign suppliers. The conventional focus on income and relative observed prices as explanatory variables in the demand equation may be quite misleading unless relative observed prices have the same time movements as relative effective prices.

Unfortunately, the applied econometrician lacks data on many important components of the effective price vector. Consequently, Gregory has developed a theory of price dynamics which leads him to replace his effective price vectors with proxy variables for which data are available. Some of the assumptions involved in Gregory's derivation of these proxies are subject to

11/

serious criticism, however, and we have chosen not to imitate his approach.

1l/ For example, Gregory assumes that the supply function for a firm under competitive market conditions depends, among other things, on the quantity demanded, which does not seem appropriate, see Klein (1962, pp. 126-7). Gregory also postulates that market prices change in proportion to excess demand, an assumption which has been criticized for ignoring the behavioral underpinnings of price dynamics. An excellent discussion of the theory of price dynamics in disequilibrium markets is provided by Gordon and Hynes (1970), who argue that the competitive model is completely unsatisfactory as a framework within which to analyze price dynamics. Disequilibrium price dynamics must entail some form of imperfect information introduced through a stochastic demand schedule under quasi-monopolistic conditions, where supply functions are not well (cont. .. )

- 30 -

Nevertheless, we share Gregory's opinion that empirical work should focus more on the non-price attributes which help determine the relative attractiveness of imports and domestic substitutes to the consumer. The rapid growth of CND and CD imports during our sample period was in part due to interrelated rapid changes in the availability of imports relative to domestic substitutes .22/ To the extent that relative availability and income are correlated, this

phenomenon may explain the high apparent income elasticities in many estimates

of the demand for imports of nonfood consumer goods.

3.4 Treatment of Dock Strikes

In theory, dock strikes affect consumer demands for imported goods only indirectly, if at all, through delivery lags and effective price changes. Data limitations, however, have forced us to use recorded imports as our dependent variable, rather than consumer demands for imported goods as reflected in purchases out of the foreign-good inventories of domestic merchants. This choice of dependent variable forces us to account for the direct effects of dock strikes. Since 1958, major dock strike disruptions have affected import volumes significantly in roughly 3 out of every 10 quarters, with imports curtailed during strike periods, stimulated just prior to longshore contract deadlines and Taft-Hartley expiration dates, and typically stimulated during the recovery periods which follow contract settlements. Because of the small defined. Demand equations with random coefficients (such as those hypothesized in eq. (5) of Section 2.1) are appropriate for markets which are out of equilibrium, see Cyert and DeGroot (1974). Statistical analysis of such demand

functions is discussed in Swamy and Mehta (1973).

12/ | This is apparent in the rapid growth of foreign car franchises, cheap import houses, shelf space allotted to imported stereophonic equipment and televisions, etc.

-31-

number of data points that were not affected by strikes, which becomes even smaller when imports are specified to depend upon lagged dependent variables, we prefer the dummy variable approach to the alternative of discarding observations that were affected by strikes.

While it is obvious that dock strikes have had a major impact on quarterly movements of imports during the last two decades, little attention has been devoted to constructing sophisticated dock strike dummies .23/ We were fortunate to obtain data from the New York Shipping Association on weekly longshore manhours worked in the Port of New York, which encouraged us to construct a

new set of dock strike dummies, see Isard (1975). The construction of these

strike dummies is explained in Table A5 of the Appendix.

4. Numerical Results 4.1 Estimated Demand Equations for FFB and CND Imports The specification hypothesis for FFB and CND imports is based on eq.

(12a) and assumptions (13) of Section 2.1. For notational convenience we let

M, = logarithm of the recorded volume (or deflated value) of imports in period t

ve = log yp Y. = log Ye

PM. = log pm. PD. = log pd.

mm = log a, ql + om’) nd = log a. ql + od”)

13/ Hooper (1974), and others have based their strike dummies on "mandays lost" statistics, but much more sophistication is possible.

- 32 -

It should be emphasized here that y, measures personal disposable income in constant dollars, and that pm, and pd. have each been divided by the deflator for personal disposable income, for the reason discussed in Section 2.1. In addition, since recorded imports differ from the demand for imports during periods affected by dock strikes, as discussed in Section 3.4, M. corresponds

to consumption of imported goods, i.e., the dependent variable in eq. (12a), plus

a dock strike adjustment, BgD.- Thus, we rewrite (12a) and (13) as:

= ‘P e e (12b) M. Yo + B,Y, + BoM, + B3PD. + B,,7m + Bend. + B.D. + u, wo Po _ Ss (13a) Ye (1 Apz Aq tees s=0 eo e_ _ s . (13b) mm = (1 ode ho (PM. PM 5-1) s=0 [.-) e = . F s . (13c) md a hg)e Ag (PD. PD 5-1)

s=0

Substitution of (13a-c) into (12b), using the Koyck transformation, then yields:

(24) Me = Yo(1-Aq) (ray) (1-ag) + Cytrytrs M1 - CAJAgTA gh gtAGA IM, oth phohgM,

¥ By CLA DY, 84 L-ag) gthy ¥p_ytBy La Ag g¥,_gtLBotB, (1-25) 1PM, ~ [By OytAgthg +8, L-2y) (LEAL HAS) IPM, _j+1B, (Aaa HRA gH

2 3*)

F By Cnhg) Oy thgth Ag) IPM, _o-[ByAq gh gt8, (1-Ap)A Ag IPM, 5

+ [B3+B5 (1-23) IPD, -183 (AytA5#)#B5 (L-Ag) (4A HR) IPD, |

1 °2 °3 1

F UBG Cy Agthyh gt ghz +85 (1-ag) CAytAytA Ay) IPD,»

7 [Bary ApAgtBs (I-AgAADIPD, _gtBeD,-Bg (Ay HAgtAg)D,_

(cont. . . )

- 33 -

+ Be 4A FA SAgtAAA, )D

gtrargtrgay Argh gD, _gtt-Oytrgths ui iy

t-278641 4243) +-3

AAU

+ Oyrgtrorgtrghy UY, o-AqAgAgui_s

Eq. (24) is "over-identified" with respect to its parameters because there are a total of 19 coefficients which are determined by only 10 basic parameters. Hence, we must estimate the 10 parameters under 9 constraints, and since those constraints are nonlinear, recourse must be made to a nonlinear estimating technique 24/

To avoid dealing with a structure even more complicated than eq. (24), we make the simplifying assumption that the ue follow the third-order autoregressive process,

(25) UE = Cytrytrg uy pCa rgtrgrgtrgay Ju, _stagAghgu,_ste,

where the €, are independently distributed with means 0 and constant variance; that is, we assume that the disturbances of eq. (24) are serially independent. Although we have no evidence to support the plausibility of this assumption,

we likewise have no evidence to support the plausibility of any alternative assumption. Given that we have specified our import demand equation to conform to the structure of a consumer demand equation, whereas the M. in eq. (24) deviate from sales to consumers by any changes in the imported inventories of intermediaries, we have good reason to believe that the ur. will exhibit a complicated pattern of serial correlation which reflects these inventory

fluctuations; but we cannot confidently specify the nature of this serial

correlation.

14/ We have used a nonlinear estimation program which incorporates Marquardt's (1973) iterative procedure.

- 34 -

Before discussing the parameter estimates associated with eq. (24), attention should be given to their economic interpretation in terms of the income and price responses of the theory of consumer demand. A unit logchange in current money income with all absolute prices constant results in a unit log-change in current real income with no change in relative prices. According to eq. (24), the resulting log-change in the quantity demanded is 6, (1 - Ay) in the short-run and By in the long-run. Unlike these income elasticities, however, conventional price elasticities are not simply defined within our model, because our PM. and PD. variables represent the logarithms of prices divided by the deflator for personal disposable income. To the extent that a one percent change in import prices (or prices of domestic substitutes) affects the deflator, the change in PM . (or PD.) will differ from one unit, and Y, and PD, (or PM.) will also change. Approximate expressions for conventional uncompensated (Cournot) own and cross-price elasticities can be derived in terms of average budget shares, see Goldberger and Gamaletsos (1970, pp. 359-60). In contrast, the B, and 8, Parameters in eqs. (12b) and (24) are income-compensated (Slutsky) price elasticities, see Goldberger (1967, p. 103).

The estimated equations for FFB imports are described in Table 1. In Case 1, with no prespecified parameter values, we estimated plausible magnitudes and appropriate signs for all six of the 8 coefficients; but the estimates of ho and hg are implausible. It was apparent that estimates of any one of the three )\ parameters would be highly correlated with estimates of the other two, so that we could not hope to estimate all three precisely. Accordingly, we decided to constrain Ao and Ag» setting both equal to zero in

Case 2. This amounts to an assumption that the future rates of inflation

- 35 -

Table 1; Estimation Results for FFB Imports—

Yo By Bo Bs By Bs 86 Ay ho

Case l: -855 .808 -.810 1.06 -482 -1.37 -927 .814 -.999 no pre- (2.75) (.0724) (.342) (.542) (.600) (1.13) (.156) (.831) (.815) specified parameter values

Case 2; 4.03 .733 -.727 . 389 -496 -.930 972 .75b/ 0 hg™Ag=0 (2.47) (.0616) (.295) (.467) (.440) (.610) ¢.144) (.0299)

Sum of h Squared 3 Errors 925 .182 (.500) 0 . 164

a/ Parameters are defined in eqs. (12b) and (13a-c) at the beginning of this subsection. Numbers in

parentheses are standard errors. Sample period is 1959 I - 1972 IV, 56 observations.

dependent variable is 7.03.

b/ The statistical quality of the Case 2 estimates is highly insensitive to the value of hy within the

range between .5 and 1.0; see text.

The mean of the

Standard Error of Estimate

-0629

-0584

- 36 -

expected as of period t are equal to the actual rates of inflation experienced between periods t-1 and t.

All of the estimated parameters for Case 2 have plausible magnitudes and appropriate signs. Despite its low standard error, the estimate of hy is imprecise, and we have reported the midpoint of a range of values that have approximately equal statistical quality. The estimates and standard errors of all other parameters, as well as the sum-of-squared-error statistic, each varies by less than one percent as hy moves from 1.0 to 0.5, but this insensitivity breaks down once Ay drops below .5. The income elasticity of -733 is significant and consistent with the notion that food is a necessary good; the dock strike parameter, Be» is significant and close to our prior expectation of one (see Appendix Table A5). The positive signs of B, and By confirm that FFB imports in period t are substitutes for similar domestic products in period t and for imports in future periods; and the sign of Bs» about which we have no strong prior information, suggests that current FFB imports and future domestic FFB products are viewed as complements. The Standard error of estimate is less than one percent of the mean of the dependent variable.

The estimated equations for CND imports are described in Table 2. Given ‘our particular data, the program seemed unable to achieve convergence in cases in which either Ay ho or hg was specified as a free parameter. Accordingly,

we again assumed Ao = he

37 0; and we fixed Ay = -75, aS suggested by our FFB

results. The Case 1 estimates, when no additional parameters are constrained, show an incorrect sign for Ba> the elasticity of imports with respect to the price

of domestic substitutes. In view of the high correlation between the import

- 37 -

a/

Table 2: Estimation Results for CND Imports—

hy = .75; ho = 7.3 = 0 in all cases

Sum of Standard Squared Error of By B Bs 86 Ay ho hg Errors Estimate

0 2 4 case =| 21.4 | 2.15 | -.448/-5.85 | -.938 | 1.80 | .295 | .75 .0337 0367

po 5 2)T 259) 34891 (951) (436) (.995)f(.153) |

y By p

po Case 2 }-10.9 | 3.67 [-1.35 | 0 | -.962[ 0 J .0274 [475 To To T0866 T0566 | 2.59)| (.119)| (.487 671 226

po

| -9.09 | 3.61 [-1.66 | O J Oo fT of .t50 7.75 To oT 0932 T0577 po Po pO po po po po eee eee ES NE RN EN SORES OS ONES NY OR (ON (OR SE I ER Nes SRO ON OEE (OR RRR CO (OC EEE

s gre defifed in ehs. (12b) and (IBa-c) at| the beginning of this stbsectioh. Numbprs in parbmeters | erfors. Sgmple pefiod is [965 1 -[1972 Iv} 32 obsprvation. The thean of fhe depefdent varibble is | pO Po Pp eee Pp ee eee Po po po po po

- 38 -

price and the price of domestic substitutes, the domestic price variables were eliminated in Case 2 (by imposing the constraints B5 = 8. = 0). The income elasticity for this case is significant and has the correct sign; its Magnitude exceeds our a priori notions of the true income elasticities for necessity items such as CND, and we suspect that this high value reflects a high correlation between income growth and the rapid growth of the availability of CND imports relative to domestic substitutes during our sample period. 22/ The own-price elasticity, 8» is significant with correct sign and sensible magnitude. The dock strike coefficient is insignificant and differs considerably from the expected magnitude of one (see Appendix Table A5) 20! while By, is insignificant and has an incorrect sign.

In Case 3 we imposed the additional constraint By, = 0, thereby omitting expected future rates of inflation from the determinants of the demand for CND imports. This led to little change in the standard error of estimate and only moderate changes in the other estimated parameters.

Although our equation for Case 3 is similar to conventional import demand equations, by which standards our parameter estimates are quite acceptable, we have, nevertheless, failed to capture what we regard as the true structure of the import demand equation for this commodity group. In contrast to our FFB results, we have not been able to separate the own-price and cross-price elasticity parameters; and we have not met with success in estimating the

sensitivity of import demand to expected future own-prices and cross-prices.

15/ Unfortunately, the omitted "relative availability" variable is difficult to quantify for inclusion in regression equations.

16/ The coefficient on the dock strike dummy for CND was also found to differ considerably from one in separate tests, which indicates that the quality of this dummy is probably lower than the quality of the dummies for the FFB and CD cases. See Isard (1975).

- 39 -

4.2 Estimated Demand Equations for CD Imports

The specification hypothesis for CD imports is based on equations (22) and (23) of Section 2.2., combined with proxy variables for ye fal + omy) and (1 + ody). Substitution of (23) into (22) yields a relationship for consumer purchases of CD imports, dye which we assume to differ from recorded

CD imports, mM,» according to:

Rw (26) m= 4 + aD, + ue

Jets x

where De is a dock strike dummy, ue is a stochastic error term, and we expect the parameter a, to be approximately equal to one, (see discussion, Appendix

Table A5). Because the model is cumbersome, we have chosen to simplify

P

drastically our proxies for Yee

e a4 ql + om’) and (1 + od). Initially, we chose to replace permanent income with current income and to equate expected future

inflation factors to current inflation factors: (27a) ye =y,3 (1 + pm) = pm/pm_ 13 (1 + od°) = pd./pd t t? ome cP e-1? et aon eel

When we were unsuccessful at estimating the coefficients on the expected future . : ss e

inflation factors, however, we eliminated (1 + pms) and (1 + od) from the model and returned to our former proxy for permanent income, assuming:

P = - ~ s . = QT) -¥E= AE MYL gt %

ws = 0 (in eq. (23))

Together, (22), (23), (26) and (27b) imply, after a Koyck transformation and

using the notation n = 1/65:

- 40 -

(28) m. = (1-A)Yoq + (L4A-¥)m,_y - A(L-¥)m,_y + (1-A)¥ nay, - G-Y@-Leoyy,_ + ¥ aloypm, + apd, | - TY 2+ Y(a-L) I Loypm, ytespd,_ 1] + AVL) Laypm,_» + apd, 9] + agD.-Ctl-y)agD, yt AL=Wogd, ot ui Otl-yu, + AC-y)u, where uF v nu,-y(a-L)u, tu As in the nondurables case, we assume (29) ue Qtl-y)u. + A(1-y)u,_, =e

where the €, are independently distributed with means 0 and constant variance,

Our initial attempts to estimate equation (28) ran into two problems. As in the case of CND imports, our estimation program seemed unable to achieve convergence when ) was entered as a free parameter, so we again set , = .75, as suggested by the FFB results. In addition, we were again dealing with high correlations between the import price and the price of domestic substitutes; and because we were unable to estimate correct signs for Uy and Ce simultaneously, we decided to eliminate the cross-price term from our model, setting a = QO.

Table 3 describes several estimated equations under the constraints ) = .75 and W, = 0. It should be noted at the outset that relative to the mean of the dependent variable, the standard errors of estimate for this case are quite large.

For Case 1, all estimated parameters have correct signs, but only the dock strike variable is significant and the estimated speed of adjustment, Y> is implausibly low. The estimate n = 6.00, or 85 = 1/n = -167, is highly plausible and, in fact, corresponds precisely to our best a priori guess about the true

value of 85: To see this let s be the rate of scrappage per quarter, and let

-~ 41 -

%9

Case 1: 58.7 yon free (139.) Case 2: -8.04 y=.25,n=6.0 (2.88) Case 3:_ -9.78 v=.33,n=6.0 (2.48) Case 4: -11.6 v=.50,n=6.0 (2.13) Case 5:_ -12.6 vy=.75,n=6.0 (1.96)

al

4.34

(4.03)

3.74 (209)

Table 3:

Estimation Results for CD Imports—

a/

x = .75;, a3 = Q in all cases

(1.31) (.308)

Numbers in parentheses are standard errors. The mean of the dependent variable is 7.33. Approximated, using mean of current income rather than mean of permanent income. Describes the income-compensated response of imports to a change in own-price.

Sum of Standard

Sample period is 1961 I - 1972 IV, 48 observations.

Long-Run Elasticities at Sample Means Squared Error of

9 6 v n Errors Estimate Incomee/ Own=Price®/ -45.5 708 -0252 6.00 5.77 371 3.14 -6.32 (87.9) (.0860) (.0489) (4.52)

-3.56 -644 25 6.0 9.49 464 2.75 -.495

(1.93) ¢.119)

-2.48 ~612 33 6.0 12.3 529 2.73 ~-.345 (1.66) (.141) -1.37 526 50 6.0 20.9 -690 2.72 -.190 (1.42) (.200) -.734 345 75 6.0 39.8 -951 2.70 -.102

Ske

- 42 -

d be the rate of decline in the written-down value of units that have not been scrapped, so that 55 = 1-(1-d)(1-s). Straightforward computation then shows that the estimate 8,

that (i) the written-down value of durables falls by 30 percent per year

= .167 is consistent with the joint assumptions

Cs. (l-a)4 = .7) and (ii) it takes precisely 8 years (32 quarters) before 95 percent of an initial purchase is scrapped Gt. (ls)? = .05).

Because of the implausibly low ¥ for Case 1, we decided to test the sensitivity of the other parameter estimates and the standard errors of estimates to prior restrictions on ¥- In this testing we discovered that our estimates of n declined monotonically as we increased the prespecified value of ’> and plausible restrictions on v did not lead to plausible estimates of n. Accordingly, we report as Cases 2-5, some estimates associated with a range of plausible v restrictions together with the constraint that n = 6.0.

Because the standard error of estimate is 25 percent greater in Case 2 than in Case 1, we cannot argue that the estimates for Case 2 are as good on statistical grounds as those for Case 1, although it may be noted that in Case 2 the income and own-price terms are more significant, and the own-price elasticity seems more plausible. The results for Cases 2-5 tell us that plausible restrictions on the depreciation and speed-of-adjustment parameters are consistent with plausible estimates of income and own-price parameters, but we cannot argue that any of these cases corresponds to the true structure. The insensitivity of the income elasticity to the prespecified value of ¥ is noteworthy. As in the CND case, we suspect that the high apparent income elasticities overstate the true income elasticity due to a high correlation between income growth and the rapid growth of the availability of CD imports

relative to domestic substitutes during our sample period.

- 43 -

4.3 Some Caveats in Connection with the Numerical Results

In assessing our numerical results, due allowance must be given to the defects of the data, the limitations of our theoretical models, and the fact that nonlinear estimation techniques cannot guarantee convergence to a global minimum. There are serious deficiencies in the time series we have used to represent prices, consumer expenditures on imports, and dock strike impacts. Our data are subject to both systematic and random errors which, as Griliches and Ringstad (1970) remark, may lead to severe distortions in estimates of a nonlinear specification. Moreover, we have noted numerous difficulties encountered in the development of our theoretical models.

It is also certain that our commodity-group aggregates are far from homogeneous. Although the different commodities within each aggregate may exhibit similar income and own-price elasticities, for the case of durables the differences in speed-of-adjustment and depreciation parameters make it particularly difficult to estimate a stable and well-fitting aggregate demand

equation.

- 44 - APPENDIX

Table Al: Description of Import Price Index and Value Deflator for CND

1.) Component Series

PJAPAN = Japanese (fixed-weight) export price index for nondurable consumer goods, from Bank gf Japan publications, converted into dollars@/ and scaled to 1967=100.

PITALY = Wholesale price indexfor women's all leather shoes (with calfskin uppers) in Milan, from Instituto Centrale di Statistica, Bolletino Mensile di

Statistica, various issues. Quarterly averages of

monthly prices, converted into dollars,2/ and

scaled to 1967=100. b/

PKOREA = Export price index for South Korea, all commodities— from International Monetary Fund data bank, corresponding to line 74p in International Financial Statistics, scaled to 1967 = 100.

b/

PCHINA = Export price index for Taiwan, all commodities,— from International Monetary Fund data bank corresponding to line 74p in International Financial Statistics, scaled to 1967=100.

2.) Import Price Index

PMFOB = = .5501+PJAPAN + .1900*PITALY +.2599* POTHER where

POTHER = .5446+PKOREA + .4554+PCHINA

Weights in PMFOB reflect base-year (1967) relative shares in the value of total CND imports of (i) CND imports from Japan (.5501), (ii) CND imports of leather footwear and other leather goods (end-use #4110) from Italy (.1900), and (iii) CND imports from Far East Asia excluding Japan and Hong Kong (.2599). These three categories combined represented 41 percent of total CND imports

in 1967. From Census end-use data.

- 45 -

Table Al: (continued) Weights in POTHER reflect relative magnitudes of 1967 imports from Korea and Taiwan of schedule A commodities 83, 84, 85 and 89, Data from Census, FT 155, 1967 Annual, PMFOB is multiplied by tariff factors (see Table A4) to get the explanatory variable used in our regressions,

3.) Import Value Deflator

DEFLATOR = W, °PJAPAN + Wo*PITALY + W.*POTHER

If VJAPAN, VITALY, and VOTHER denote the current-quarter

values of the three import categories and

VJIAPAN VITALY VOTHER 4 = > q.=-, q, =——— , then PJAPAN 2 PITALY POTHER q. the weights are defined as W, = t for i=1, 2,3. +q + q+ 4, + 45

Values for 1965 I - 1972 II are from Census end-use data. Values for 1964 are quarterly averages for 1965. Note that the W; would be unaffected if the denominators of the q; were all multiplied by the same tariff factors.

4.) Notes

a/ Exchange rates are quarterly averages of the monthly spot rates published in the Federal Reserve Bulletin. Monthly rates are averages of certified noon buying rates in New York for cable transfers,

b/ The export prices for Korea and Taiwan are Paasche (moving-weight) indices. Initial sources are Bank of Korea, Monthly Economic Statistics and Republic of China, Taiwan Financial Statistics Monthly.

- 46 -

Table A2: Description of Import Price Index and Value Deflator for CD

1.) Component Series

PJAPAN = Japanese (fixed-weight) export price index for durable consumer goods, from Bank of Japan

publications, converted into dollars®’ and scaled to 1967=100,

PGERMANY = German (fixed-weight) export price index for all consumer goods and all destinations, from Statistisches Bundesamt Wiesbaden, Preise LUhne Wirtschaftsrechnungen, various issues. Quarterly aver gges of monthly prices, converted into dollars,’ and scaled to 1967=100,

2.) import Price index PMFOB = ~1577PGERMANY + .8423PJAPAN

where weights reflect base-year (1967) relative shares in the value of total CD imports. PMFOB is multiplied by tariff factors (see Table A4) to get the explanatory variable used in our regressions.

3.) Import Value Deflator

DEFLATOR = W-+PGERMANY + (1-W) «PJAPAN

where W is defined from current-quarter import values (VGERMANY and VJAPAN) as

VGERMANY

Woo PCERMANY VGERMANY , VJAPAN PGERMANY PJAPAN

Thus W and 1-W represent current-quarter quantity shares.

For quarters from 1960I to 1964IV, W was estimated from average values of VGERMANY and VJAPAN during 1965. 4.) Note

a/ See note a, Table Al.

- 47 -

Table A3: Description of Import Price Index and Value Deflator for FFB

1.) Component Series

UVMFD = unit value index for the economic class of manufactured foods, converted to 1967=100,

UVCRUDE = unit value index for the economic class of crude foods, converted to 1967=100,

2.) Import Price Index

PMFOB = .4403-UVCRUDE + .5597sUVMFD

Weights are relative shares of crude foods and manufactured foods in the value of total food imports in 1967,

PMFOB is multiplied by tariff factors (see Table A4) to get the explanatory variable used in our regressions, 3.) Import Value Deflator

DEFLATOR = weUVCRUDE + (l-w)+UVMFD

If QCRUDE and QMFD are the Census Bureau quantity indices of imports of crude foods and manufactured foods (converted to 1967=100), then .4403*QCRUDE and .5597*QMFD are indices of the constant-1967dollar values of these imports, and

-4403° QCRUDE

-4403°QCRUDE + .5597° QMFD

Table A4:

time period FFB 1956 II 1.1859 .1956 III - 57 II 1.1764 1957 III - 58 II 1.1669 1958 III - 62 II 1.1574 1962 III - 63 II 1.1420 1963 III - 64 II 1.1266 1964 III - 67 LV 1.1112 1968 1.1080 1969 1.1049 1970 1.1018 1971 I, II 1.0996 1971 r112/ 1.1496 1971 rve/ 1.1885 1972 1.0955 Source: See subsection 3.2.

1

1

1

- 48 -

. ._a/ Tariff Factors Prior to Normalization—

CND

- 3005

2901 22797 - 2693 ~ 2524 - 2355 2186 -2125 - 2064 . 2000 . 1939 » 2439 - 2828

. 1875

cp 1.2527 1.2427 1.2327 1.2227 1.2064 1.1901 1.1738 1.1603 1.1467 1.1332 1.1196 1.1696 1.2085

1.1061

Notes: a/ The correct form of the tariff-inclusive price index is

co

Ww

pm.

J

j pm.

J

tlF t TF o 0

—— where the Wj

are fixed weights, the pm are

f.0o.b. prices and the TF are tariff factors. Thus we multiply

our f.0.b. price indices by TF,_/TFo; or the above factors

deflated by their 1967 base-period values,

Table A4&

- 49 -

(continued)

Notes: b/ A 10 percent surcharge on import values applied from August 15 to

December 20, 1971 -- for half of 1971 III and roughly 8/9ths of

1971 IV. For these quarters we calculated the tariff factors -10 -8) .

as (l+_y += and (1 + > +>) respectively, where r+ denotes

Wilson's estimated tariff rate.

- 50 -

Table A5: Description of Dock Strike Dummies

Our strike dummies are based on estimates of the ratio (R) of actual import volume (M) during any strike-affected quarter to the "normal" import volume that would have prevailed in the absence of a strike. If "normal" imports are explained by some behavioral relationship, £(income, prices, ...), then M=R-f. Since log M = log R+ log f, D = log R is an appropriate strike dummy for use in our FFB and CND equations, and in equation (12b) we expect to estimate a coefficient (Be) on D equal to one. For the CD case, our dependent variable is M, rather than log M, so we construct our strike dummy as D = (R-1)M/R, thereby satisfying M= f+ D. Thus, in equation (26) we expect to estimate a coefficient (ag) on D equal to one.

For strike-affected quarters we use the following values of R, based on

Isard (1975). For all other quarters, R = 1.

FFB CND cD 1959 III 1.0616 - - IV -9358 - - 1962 III 1.0606 - 1.0398 IV 9672 - - 9784 1963 Oo -9201 - 9474 II 1.0084 - 1.0055 1964 III 1.0594 1.0444 1.0391 IV 1.0660 1.0494 1.0434 1965 I - 8094 -8574 -8746 II 1.0272 1.0204 1.0179 1968 III 1.0520 1.0389 1.0342 IV -9718 -9789 -9815 1969 I . 7870 - 8407 -8599 Il 1.1032 1.0772 1.0679 1971 III 1.0041 -9681 -8312 IV -8146 -8951 1.0271 1972 oI 1.1126 1.0743 1.0355

Il -9784 - 9864 -9963

- 51 - REFERENCES

Cleveland, W.P. (1972): Analysis and Forecasting of Seasonal Time Series,

Ph.D. dissertation, Department of Statistics, University of Wisconsin, Madison.

Cyert, R.M. and M.H. DeGroot (1974): "Rational Expectations and Bayesian

Analysis," Journal of Political Economy, 82, pp. 521-36.

Fishman, G.S. (1969): Spectral Methods in Econometrics, Cambridge, Mass.: Harvard University Press.

Friedman, M. (1957): A Theory of the Consumption Function, Princeton:

Princeton University Press.

Griliches, Z. and V. Ringstad (1970): "“Error-in-the-Variables Bias in Nonlinear Contexts," Econometrica, 38, pp. 368-70.

Goldberger, A.S. (1967): ‘Functional Form and Utility: A Review of Consumer Demand Theory," Systems Formulation, Methodology, md Policy Workshop Paper 6703, Social Systems Research Institute, University of Wisconsin.

and T. Gamaletsos (1970): "A Cross-Country Comparison of Consumer Expenditure Patterns," European Economic Review, 1, pp. 357-400.

Gordon, D.F. and A. Hynes (1970): "On the Theory of Price Dynamics,"

pp. 369-93, in E.S. Phelps et al., Employment and Inflation Theory,

New York: W.W. Norton and Company, Inc.

Green, H.A.J. (1964): Aggregation in Economic Analysis, An Introductory

Survey, Princeton: Princeton University Press.

Gregory, R.G. (1971): "United States Imports and Internal Pressure of Demand: 1948-68," American Economic Review, pp. 28-47.

Grether, D.M. and M. Nerlove (1970): "Some Properties of "Optimal" Seasonal Adjustment," Econometrica, 38, pp. 682-703.

Hicks, J.R. (1946): Value and Capital, Oxford: The Clarendon Press. Hooper, P. (1974): An Analysis of Aggregation Error in U.S. Merchandise Trade Equations,1954 I - 1972 IV, Ph.D. dissertation in Economics,

University of Michigan.

Isard, P. (1975): "Dock Strike Adjustment Factors for Major Categories of U.S. Imports and Exports, 1958-1974," mimeo.

Klein, L.R. (1962): An Introduction to Econcmetrics, Englewood Cliffs: Prentice-Hall.

-52-

Marquardt, D.W. (1963): "An Algorithm for Least-Squares Estimation of Nonlinear

Parameters," Journal of the Society for Industrial and Applied Mathematics, 11, pp. 431-4.

Marston, R. (1971): "Income Effects and Delivery Lags in British Import Demand," Journal of International Economics, 1, pp. 375-99.

McFadden, D. (1974): "Conditional Logit Analysis of Qualitative Choice Behavior," Chapter 4 in P. Zarembka, ed., Frontiers in Econometrics, New York: Academic Press.

Mintz, I. (1973): U.S. Import Quotas: Costs and Consequences, Washington:

American Enterprise Institute for Policy Research.

Modigliani, F. and R. Brumberg (1954): "Utility Analysis and the Consumption Function: An Interpretation of Cross-section Data," in K.K. Kurihara, ed., Post-Keynesian Economics, New Brunswick: Rutgers University Press.

Nerlove, M. (1967): "Distributed Lags and Unobserved Components in Economic Time Series," pp. 127-69 in W. Fellner, et al., Ten Economic Studies in the Tradition of Irving Fisher, New York: John Wiley and Sons.

(1972): "Lags in Economic Behavior," Econometrica, 40, pp. 221-52.

Paulus, J.D. (1973): "Demand Analysis and Stochastic Prior Information," Annals of Economic and Social Measurement, forthcoming.

Stone, R. and D.A. Rowe (1960): "The Durability of Consumers" Durable Goods," Econometrica, 28, pp. 407-16.

Swamy, P.A.V.B. (1971): Statistical Inference in Random Coefficient Regression ; Models, Berlin, Heidelberg, New York: Springer-Verlag.

and J.S. Mehta (1973): "Bayesian and Non-Bayesian Analysis of Switching Regressions and Random Coefficient Regression Models," Journal of the American Statistical Association, forthcoming.

Theil, H. (1967): Economics and Information Theory, Chicago: Rand McNally & Co.

(1971): Principles of Econometrics, New York: John Wiley

and Sons.

Tinsley, P. (1971): : "A Variable Adjustment Model of Labor Demand," International Economic Review, 12, pp. 482-509.

U.S. Tariff Commission (1968): Textiles and Apparel, T.C. Publication 226, _ Volume 1, Washington, D.C.

Welsch, R.E. and E. Kuh (1974): "The Variances of Regression Coefficient Estimates Using Aggregate Data," mimeo.

- 53 -

Wilson, J.F. (1973): Yet Another Econometric Model of U.S. Trade, 1958-1971, Disaggregated by Commodity and Region, Ph.D. dissertation in Economics,

University of Pennsylvania.

Zellner, A. (1969): "On the Aggregation Problem: A New Approach to a Troublesome Problem," pp. 365-74 in K.A. Fox, et al. (eds), Economic

Models, Estimation and Risk Programming, Berlin, Heidelberg, New York:

Springer-Verlag.

(1970): "Estimation of Regression Relationships Containing Unobservable Variables," International Economic Review, 11, pp. 441-54.