Cdn. J. of Agric. Economics REVIEW ARTICLE

32 (March 1984)

Consumer Demand Analysis at Agriculture Canada - Past and Future

Zuhair A. Hassan* and S. R. Johnson**

This paper traces the development of consumer demand analysis at Agriculture Canada for the period I972 lo 1982 and ident9es areas forfuture work. The objectives of this exercise are threefold: ( I ) to assess existing empirical resulls, emphasizing problems in specfiing. estimaiing and evaluating allernative models; (2) to make the benefit of the Canadian experience available to applied researcher.7 in Canada and other countries who are investigaling the struclure of consumer demand; and (3) lo provide perspective for future ana!yses of consumer demand.

Keyword.7: Agriculture Canada. alternate Mois-clefs: Agriculiure Canada, methodes statistical meihods, consumer statistiqurs ul[ernutives. analssr demand analysis. Engel analysts, de lu demande du policy ana!ysis consommaieur. ana!sse d'Engel.

analyse agricole de la poliiique

Cet article retrace le developpement de l'analyse de la demande des consommateurs de I972 u I982 a Agriculture Cunada et etablit les champs d'interPt du iravail a venir. Le but de ceile mise en perspective se divise en trois: (1 ) evaleur les rexultats empiriques deja obtenus en mettant l'accent sur la sp6c@iation, l'estimation er I'ivaluution de modeles de remplacement. (2) rendre les avantages de l'experience canadienne di.sponible aux specialistes de la recherche appliquee du Canada el de I'etranger qui etudient la structure de la demande de consommalion et. (3) fournir des perspectives pour d'iventuelles analyses de la demande des consomma- teurs.

Before 1972, consumer demand analysis and demand parameters used for policy in Canada were largely those from partial-equilibrium, highly specialized statistical models. Estimation methods did not reflect simultaneity in price determination processes, and specifications did not incorporate fully the prior information from the theory. As a consequence, there was little progress in developing information on the structure of consumer demand in Canada. Estimates of elasticities were widely differing, and based on different and not generally accessible data bases. Moreover, these estimates frequently changed substantially from one analysis to another as new data became avail- able. * Marketing and Economics Branch. Agriculture Canada, Ottawa

** Department of Economics and Agricultural Economics. University of Missouri-Columbia The authors thank 8. Huff, R. Lopez. 8. Davey. 0. Al-Zand and K. Wilde for helpful comments on an earlier draft of this paper.

@Copyright 1984, Canadian Agricultural Economics and Farm Management Society

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The impetus to improve consumer demand parameters available for policy analysis and to develop a better understanding of the structure of consumer demand in Canada came from four areas. First, studies in the United States by Brandow, by George and King, and by Ferber showed the value of the theory for applied work and the potential for exploiting existing time series and cross-sectional data bases more systematically. Second, Statistics Canada had similar time-series and survey data bases which were not evaluated for the information they contained about basic demand parameters and influences of socio-economic factors on consumption patterns. Third, theory and estimation methods developed to the point that undertaking estimation of more complete sets of demand parameters was feasible - and in fact imperative - for enlightened food-production and food-consumption policies. Fourth, the availability of advanced computer software packages made feasible the handling of large data bases in complex estimation problems.

The Past: 1972-83 Past work on consumer demand at Agriculture Canada can be viewed as

having been done in the following four areas: (1) commodity demand functions, (2) Engel analysis, (3) food demand matrix. and (4) complete demand systems.

Commodity Demand Functions Early estimates of demand elasticities for major food commodities in

Canada were based upon different functional forms, data sources and estimation methods. As a consequence, the literature contained conflicting and sometimes even counter-intuitive consumer demand parameter estimates. In view of the extensive use of demand parameters for policy, it was decided that a consistent and complete set of these parameters should be estimated for Canada. The following objectives were established: (i) to provide estimates of consumer demand parameters for major food groups in Canada, (ii) to evaluate alternative statistical methods for estimating demand parameters and (iii) to compare the resulting estimates to those already available for policy analysis.

Simple specifications were used to estimate price and income elasticities for major food groups. In particular, the per-capita disappearance of each food was assumed to be a function of its own price, the price(s) of selected other foods and per-capita personal disposable income. A double logarithmic function was hypothesized. That is, the assumed functional form was:

ki lnqi = ai + niInrn + Ze,lnp, + ui for i = 1, 2, . . ., n

where qi is the per-capita quantity demanded of the ilh commodity, m is the per-capita money income,p, is the price of thej* commodity, ni is the income elasticity of demand, e, is the price elasticity of the

(1) J

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commodity i with respect to thej 'h price, In is the natural logarithm operator, uj is the scale parameter, and ui is the disturbance term

Three methods were used to estimate the demand parameters (1) for the n commodities: ordinary least squares (OLS), seemingly unrelated regressions (SUR) and full-information, maximum-likelihood (FIML) techniques. If the disturbances (uts) are identically, independently and log-normally distributed and there are no contemporaneous correlations between disturbances for different commodities, the OLS method yields unbiased, consistent and efficient estimators. However, if the disturbances are contemporaneously correlated and the sets of explanatory variables are not identical for all equations, SUR and FIML yield estimators asymptotically more efficient than those from OLS. Moreover, for selected commodities, serial correlation in the disturbances was evident. This problem was accommodated by first trans- forming the equations appropriately for the systems estimation methods (Parks).

To estimate the price and income parameters, annual time-series data (1958-72) on per-capita disappearance of various foods, retail food prices and per-capita disposable income were used. Data actually utilized in estimating the demand parameters are contained in the Handbook of Food Expenditures, Prices and Consumption (Agriculture Canada 1973), and were derived from basic sources supplied by Statistics Canada. Specific references to these sources are given in the Handbook.

Estimates of own-price, of some cross-price and of income elasticities were computed for twenty-seven food items. In general, the estimated parameters were statistically significant and had signs consistent with the theory and magnitudes that appeared reasonable. Parameters estimated by SUR and FIML had similar relative magnitudes. The FIML parameter estimates had slightly smaller estimated standard errors (Table I ) .

Although these results represented newly available information on food demand in Canada, they were not without important limitations. Identifying these limitations will perhaps give an added appreciation for the advantages and disadvantages of the empirical results. Important problems encountered in obtaining these results related to functional form, prices, income measures and econometric considerations.

The double logarithmic system used is ad hoc in two respects. First, it is not consistent, except in special and implausible circumstances, with the restric- tions implied by the theory of consumer behavior (Johnson, Hassan and Green). Secondly, and more importantly, the equation-specific limit of summation ki in equation ( I ) shows that the parameter restrictions were not the same for all the demand functions. Although the included set of prices always contained own price, a more elaborate rule for exclusion restrictions was not used. Instead, the specifications were based on previous empirical

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Table 1: Estimated Direct-Price and Income Elasticities for Selected Food Commodities

Estimated E l a s t i c i t i e s

Direct-Price In-

-tY SUR FlML OLS SUR FlML OLS

Beef -0.72 -0.76 (0.07) (0.06)

Pork -0.93 -0.95 (0.09) (0.09)

Chicken -0.53 -0.56 (0.08) (0.06)

0.48 0.55 (0.08) (0.08)

0.25 0.26 (0.09) (0.09)

0.70 0.73 (0.04) (0.04)

B u t t e r -0.83 -0.83 -0. R4 0.25 0.28 0.26 (0.09) (0.08) (0.10) (0.10) (0.11) (0.13)

Cheese -0.86 (0.19)

-0.90 0.98 (0.21) (0.15)

1.00 (0.17)

Margarine -0.64 -0.66 -0.72 0.11 0.10 0.12

Shortening -0.68 -0.67 -0.70 0.78 0.76 0.91

(0.18) (0.16) (0.20) (0.07) (0.06) (0.07)

(0.32) (0.26) (0.39) (0.12) (0.10) (0.13)

sugar -0.08 (0.02)

0.11 (0.02)

Coffee -0.37 0.12 (0.10) (0.05)

Notes: SUR = seemingly unrelated regressions: FlML = full-informalion. maximum-likelihood: OLS = ordinary least squares. Estimated standard e'rrors are in parentheses.

studies, results of preliminary tests, and judgement. Judgement was governed by economic principles, intuitional knowledge and observed demand patterns, but it remains important in limiting the results.

Food prices and income were explanatory variables in the demand equation, but prices and quantities are determined simultaneously in competitive markets. It was assumed that the locus of observed equilibrium points identified the demand functions. This assumption was rationalized on the basis of the importance of supply management programs in setting food prices and the influence of the larger U.S. and international markets on prices of food commodities in Canada.

Finally, estimation of income and price elasticities from time-series data posed many statistical problems (e.g., highly interrelated values for prices, income and persistent consumption) that made it difficult to separate statistically the effects of prices, income and tastes and preferences. A related problem was that the available time-series data could not support estimation of demand functions with large numbers of explanatory variables. Thus, the

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results were highly dependent upon judgements made in addressing these practical estimation problems. In retrospect, principal components or ridge regression methods might have been used to make these arbitrary judgements more systematically.

Engel Analysis Income parameters can be estimated from cross-section data on households,

family budgets or both. Estimation of income parameters from family-budget surveys is appealing because of the experimental control of price effects and the socio-economic information available for specializing the relationships. Data from family-budget studies are typically more disaggregated and results can be more specialized to socio-economic features of the population than can those from time-series. The objectives of studies by Hassan and Johnson ( 1 976; 1977) were (i) to analyze food expenditure patterns of urban families in Canada using the 1974 Urban Family Food Expenditure Survey, and-(ii) to evaluate effects of socio-economic characteristics on food expenditure patterns in Canada.

A semi-logarithmic function was hypothesized for the Engel analysis. The semi-logarithmic function implies that the income elasticity varies inversely with the level of consumption. Reasons for choosing this algebraic specifica- tion were characteristics of the survey data, the types of commodities studied and expected magnitudes for the income elasticities (Prais and Houthakker). Both expenditures on food and quantities of food consumed were used as dependent variables in estimating relationships with income and household sue. The semi-log models were:

(2) f j h = aoj + al;h Yh + a2;h Nh + Y;h

(3) qjh = ba + bliln Y,+ + b2;In N,+ + uih where ri is the expenditure on the iIh commodity; q, is the quantity consumed

of the i'h commodity; Y is household income; N is household size: v, and ui are the disturbance terms; aoi, ali , boi, azi , bIi, and bzi are the parameters; and the subscript h denotes the sample observation unity or h Ih surveyed household

The data used were from the 1974 Urban Family Food Expenditure Survey (Statistics Canada). The survey was designed to provide information on families and unattached individuals living in private households in fourteen major cities. Families and unattached individuals for different monthly periods throughout 1974 (January-December) were asked to keep records of food consumption and purchases for two consecutive weeks. The respondents were instructed to record the quantity of each item purchased, their expenditure on the item and where the item was purchased.

Estimates of Engel relationships for 122 food items were obtained by

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applying the ordinary least squares to the sample data for equations (2) and (3). The sample size for each food item was 4,934. In addition, the sample was partitioned by income class and city. Three income classes were defined under $6,000, $6,000 to $14,999, and $15,000 or more. The city partitioning was for eight major urban centers. Estimated parameters by city were more reliable than those by income class. The income partitioning limited variation in the income variable and reduced the sample size. Also, expenditure elasticity estimates for the middle income class were most consistent across foods. There were smaller numbers of observations and more limited variation in income within the two extreme groups. Representative food-expenditure elasticities are given in Tables 2 and 3. Problems encountered in estimating the Engel curves related to the income variable, family size, functional form, treatment of zero observations and grouped data. Table 2: Estimated Food Expenditure Elasticities, by Family Income Class

E s t h t e d Fxpnditure Elasticities

All Under $6,000- $15,000 Families $6,000 $14,999 6. Over

0.0922 0.0859 0 -1656 0.0711 (0.0140) (0.0545) (0.0471) (0.0490)

0.8310 0.4265 1.0546 0.8592 (0.0354) (0.1717) . (0.1093) (0.1060)

Total food 0.2364 0.1421 0.3234 0.2438 (0.0130) (0.0510) (0.0426) (0.0457)

Note: Estimated standard errors are in parentheses.

Table 3: Estimated Food Expenditure Elasticities, by City C i t y

-tY St. Jchn’s Halifax mntreal Toronto Winnipq €dunton Vancouvei

0 1637 0.0679 0.0375 0.0472 0.0479 0.1157 0.1170 Food at hcm (0:0494) (0.0542) (0.0320) (0.0395) (0.0469) (0.0697) (0.0538)

Fmd conswed 0.7990 0.9064 0.9450 0.8130 0.8793 0.7623 0.6936 away fran hare (0.1621) (0.1679) (0.0931) (0.0998) (0.1272) (0.1251) (0.1007)

Total fmd 0.2274 0.2218 0.2296 0.2153 0.2702 0.2489 0.2606

Note: Standard errors are in parentheses.

(0.04701 (0.0510) (0.0309) (0.0371) (0.0438) (0.0629) (0.0461)

Income as reported in the household survey had several deficiencies. Actual or nominal income is not the variable required by the theory for Engel curve estimation. Instead, “normal” or “perceived” income of the household is required. Limitations of using total expenditures as a surrogate for income were shown by Summers. Engel parameter estimates are biased even for large

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samples if this approach is used. The argument against the direct use of household income was formalized by Friedman, who showed that estimators based on nominal income as a measure of unobservable “true” or permanent income are biased and inconsistent. It was Leviatan who showed that, with nominal income as an instrument for permanent income (Sargan), the problems identified by Friedman and by Summers were overcome for large samples.’

Three approaches have been used to estimate family size effects. The first is to stratify the sample according to number and type of persons in the household (Forsyth). This approach is least popular, because it can result in many estimated relationships and few observations within the sample partitions. A second approach is to standardize the consumption unit (Brown and Deaton). Various age-sex scales have been used for this purpose (Stone). The third approach is a variant of the second. The number of persons in the family is used directly in the Engel equation. This last approach is the most popular, largely because of its simplicity (Houthakker 1957; Leviatan) and the problems of admitting analysis of economies of size (Brown and Deaton, p. 1178).*

The third problem for estimating parameters of Engel curves has received considerable attention. Although less subtle, functional form remains impor- tant for reconciling empirical results. Generally, choices of functional form have been guided by one of two themes. On one hand, functions consistent with the theory can be specified. The approach is to formulate a demand model, dependent upon a separability assumption, and deduce the implied form of the Engel curve. Because such demand functions limit price effects, this process is not complicated (Houthakker 1960; Leser). Alternatively, functions of a simple form can be specified arbitrarily (Thomas).’ Since Engel curves are conditional on the relative prices and other features of the population, efforts to obtain estimates totally consistent with demand theory were presumed not warranted (Brown and Deaton; Prais and Houthakker; Thomas).

Fourth, the zero consumption observations were due to: (i) families not purchasing products because of market prices above a threshold (e.g., luxury goods); (ii) families not purchasing products irrespective of price (Muslim and Jewish families do not consume pork); and (iii) families failing to purchase products (although normally consumed) during the short time span of the

I In another study (Hassan and Johnson 1976). both the Friedman and Leviatan approaches were applied to estimate Engel curves for major goods and services. That is, both income and total expenditures were used as instrumental variables. Results obtained using the instrument-variable approach were superior statistically to those obtained from the ordinary least squares procedures (Tables 21 and 22. Hassan and Johnson 1976). For a study this extensive, an ambitious procedure for adjusting estimates to family size was not feas- ible. As already indicated. the semi-logarithmic function was hypothesized as the functional form for the Engel curves.

2

3

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observation period, or products not being available. In each case, the zero observations should be in~luded.~ Functional forms that permit zero observa- tions and estimation procedures that reflect probabilities of zeros in the sample data (Tobin) are required. If reasons for zero observations are known, the sample can be partitioned for purchasing and non-purchasing families. For reason (iii), deletion of non-purchasing families from the analysis leads to biased and inconsistent estimates (Thomas; Heckman; Amemiya) due to sample-selection bias.

Finally, if the generalized least-squares method is applied to grouped data, unbiased estimates of the regression coefficients are obtained, but these sampling-variance estimates may be unduly large compared with those from ordinary least-squares and ungrouped data (Prais and Aitchison). However, this result is specific to linear functions. Comparable applications of generalized least-squares for non-linear Engel curves requires geometric and harmonic means. If arithmetic means are used as proxies for geometric and harmonic means, estimates of parameters for non-linear Engel curves will be biased (Kakwani). Another consequence of grouping observations is that it tends to inflate explanatory power.s

Food Demand Matrix The third phase of the Agriculture Canada demand analysis work was

concerned with the use of the individually estimated parameters, as described in the previous two sections, in the construction of a full demand matrix. A complete set of demand parameters including own-price, cross-price and income elasticities was derived for twenty-seven foods. Construction of the full demand system used the Slutsky conditions (Hassan and Johnson 1976). With these restrictions, the food demand system was internally consistent with the theory of utility maximization. Also, the estimates for the food commodities were constrained to be consistent with a more highly aggregated system for a food/non-food grouping of commodities (Hassan and Johnson 1977).

The full demand matrix provided a consistent set of food-price and income-elasticity estimates. Although directly related to the theory, the demand matrix was constructed in an ad hoc fashion. Externally estimated parameter values and expenditure proportions were used to construct the demand matrix. Homogeneity, symmetry, Cournot or Engel aggregation and a value for money flexibility were used. The construction procedure for the demand matrix was as follows:

1. An income elasticity for total food was calculated as a weighted average of the income elasticities for the twenty-seven individual food commodities. The weights were expenditure proportions. 4 5

In the reported study. zero observations were included in the analysis. Data used in this study were for individual families and unattached individuals (micro data) rather than groups or aggregates of families and unattached individuals.

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2. The income elasticity for total non-food was derived from the Engel aggregation condition.

3. Direct- and cross-price elasticities for total food and total non-food were calculated using direct additivity assumption and a money flexibility estimate of -0.86 (Brandow, p. 21).

4. Cross-price elasticities between individual food commodities and total non-food price were calculated using block additivity.

5. Cross-price elasticities for the food commodity block were calculated by using symmetry relationships.

6. Cross-price elasticities for individual commodities within the food group were calculated by commodity: (a) the sum of the food cross-elasticities in each row was calculated by applying the homogeneity condition, and the sum was denoted by Si (for i = 1,2, ... , 27); (b) the column vector of cross-elasticities was calculated by the Cournot aggregation and assuming the individual cross-elas- ticities were proportional to S,; (c) given a column vector of cross-elasticities, the corresponding row vector was calculated by the symmetry relation; (d) by repetition of rules (b) and (c) this component was completed.

Although the parameters used for constructing the matrix were estimated from different data sources and estimation methods, once specified, rules ( 1 ) to (5) fixed all of the demand-matrix elasticities except those determined by rule (6). Here there was considerable latitude. for judgement. Individual cross-elas- ticities can be pre-specified without violating (6). If strong prior information existed on the cross-elasticities, they were pre-specified.

Major limitations of this full demand matrix are the estimation procedure, derivation of the cross-price elasticities and the separability assumption. Estimates of the parameters were obtained without introducing the restrictions used in construction of the full system. That is, the demand matrix was not ,estimated jointly from the sample and prior information. Losses in efficiency and possibilities for statistical evaluations of the restrictions were a result. Also, the procedure for deriving most cross-price elasticities within the food group was arbitrary. The problem is that the restrictions (6) were not sufficient to uniquely determine parameter values.

Finally, strong separability was used to calculate the price elasticities for the total food and total non-food commodity groups and cross-price elasticities between individual food commodities and total non-food. This assumption is highly restrictive. For example, it rules out the possibility of specific substitution effects, inferior goods and complementary goods.

Complete Demand Systems The preceding demand analysis work was a prelude to direct estimation of

full demand systems. Full demand systems can be estimated directly by imposing sufficiently strong behavioral restrictions. The structure of consumer

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demand in Canada was examined by using several complete systems: three static (linear expenditure, Rotterdam and indirect addilog) and two dynamic (state adjustment and a dynamic version of the linear expenditure). All five systems were estimated for four aggregate commodity groups. Selected static systems were also estimated for nine commodity groups.

Time series (1947-72) data on personal consumption expenditures and prices were used in estimating the parameters of the demand systems. The personal-consumption expenditure data for major commodity groups and services were from Statistics Canada. These annual estimates of personal consumption have been available continuously since 1926 and provide consumer expenditures in considerable detail. The other required data were implicit price indexes ( 1 97 1 = 100) for the commodity groups, and came from the same source. Price indexes were implicit deflators derived by dividing expenditure in current dollars by expenditures in constant dollars (weights for composite commodities shifted with their changing compositions). Finally, the population data used for the per-capita variables were for mid-year (June I ) , and came from Statistics Canada as well.

Generally, there was substantial similarity among the parameter estimates for the alternative demand systems. The static models produced estimates with similar policy implications. Of the two dynamic models, the linear expenditure system performed better on the basis of simulations within and outside the sample period. Finally, a comparison of the estimated static and dynamic systems indicated that the habit, adjustment and inventory hypotheses of dynamic models gave more plausible representations of the structure of consumer demand (Tables 4 and 5). However, characterizations of persistence in static models with vector-valued autoregressive processes for the distur- bances produced similar results (Green, Hassan and Johnson, 1978 and 1980).

Although the results from this analysis were generally consistent with a priori expectations, they were not without limitations. For example, separabi- lity was applied in estimating the complete demand systems. As indicated already, separability is highly restrictive, behaviorally. In the dynamic models,

Table 4: Estimated Elasticities from Parameters of Static Demand Systems In- Elasticity D i r e c t - P r i c e Elasticity

Linear Linear Expen- Indirect m- Indirect

COrmDaity Grow IIDtterdam diture Addilcq I IDtterdam diture naailog

Durable gooas 1.69 1.34 1.40 -1.23 -0.96 -0.86

Semi-durable qmds 0.84 0.58 0.59 -0.69 -0.44 -0.17

Non-durable gocds 0.66 0.68 0.73 -0.62 -0.59 -0.45

Services 1.11 1.32 1.25 -0.91 -0.96 -0.80

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Table 5: Estimated Elasticities from Parameters of the Dynamic Demand Systems

Incans Elasticity Direct-Price Elasticity

cormodi ty State Linear State L i n e K r-uP Adjustrrent Expenitwe A d j u s m t Epditure

~

Durable goods SR 3.30 LR 1.43

Semi-durable SR 1.19 gooas LR 0.73

Non-durable SR 0.42 gooas LR 0.74

Services SR 0.52

LR 1.19

3.13

1.09

1.11 0.71

0.53

0.71

0.60 1.33

-1.31 -0.57

-0.35 -0.21

-0.43 -0.76

-0.13 -0.31

-1.44 -0.89

-0 -67 -0.63

-0.41 -0.62

-0.49 -0 -97

Note: SR = short run: LR = long run

current expenditures were assumed to be influenced by past consumption, but the effects of current expenditures on future choice were ignored. Finally, the demand systems were estimated without recognizing differences in supply conditions that prevailed during the sample period.

Lessons and Applications Despite the many limitations, the consumer demand analysis at Agriculture

Canada has provided an improved empirical basis for policy in the food and agricultural industries. Selected examples of areas where these results were used for policy analysis and forecasting include:

Cost of Living. Estimates from complete demand systems were used to calculate cost-of-living indexes that were employed to measure effects of rising food prices on low-income families. The question was, do lower-income consumers bear a heavier burden from food-price increases than higher-in- come coasumers, and if so, to what extent (Roberts 1982)?

Consumer Surplus. Demand elasticities for pork were used to derive estimates of benefits to consumers from lower pork prices for the period April, 1979, to March, 1980 (Hassan 1980).

Subsidy Program. In the fall of 1973, the Canadian government introduced consumer subsidies on skim-milk powder, fluid milk and wheat for domestic use. These programs ended or were modified by 1978. Demand parameters were used to evaluate re-introducing these subsidies on food consumption and market prices (Hassan 1979).

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Long-Term. Income elasticities from the demand studies were used for long-term analysis of demand for major food commodities (Barewal). Also, the retail demand matrix was used as a main component for a study by Denton and Spencer. Results from this study were used in 1981 to generate a 25-year projection for personal disposable income, consumer expenditures for food and non-food, and per-capita consumption of major food groups in “Challenge for Growth: An Agri-Food Strategy for Canada” (Agriculture Canada 198 I).

Short-Term. Demand elasticity estimates for supply-managed commodities (chicken, eggs, turkey and dairy products) have been used widely to estimate annual domestic consumption at prescribed prices.

From the empirical applications and evaluations of the demand models and the use of the parameter estimates in forecasting and policy analysis, a number of general observations can be made. These observations reflect lessons from the experience and illustrate types of useful insights that can be generated from a sustained program emphasizing application and use of a systematic body of economic theory.

1. In time-series data, it is difficult to separate statistically the effects of income and trend and to obtain plausible estimates of income elasticities and persistence parameters. Estimates of income elasticities from cross-section data have performed better than those from time-series-based demand systems for projecting food consumption behavior.

2. Results from the Engel analyses indicated that an understanding of consumption patterns for socio-economic groups within the population was important for forecasting domestic food requirements. Results were improved by introducing parameters to reflect the different food-consumption patterns of various socio-economic groups.

3. Attempts to estimate direct-price elasticities from the price variation observed in cross-section data proved useful. This suggests the possibility of pooling sets of cross-section data to estimate price elasticities, since aggregated time-series data are limited for estimating detailed demand systems.

4. Results from transformation-of-variable analysis showed that estimated demand equations had a variety of functional forms. Elasticities calculated from “appropriate” forms were, at times, markedly different from those from more conventional specifications.

5 . Results for the food-demand matrix indicated differences between consumption patterns in Canada and the United States. These differences have had important implications for policy analysis.

6. For complete demand systems, the alternative static models that were evaluated produced estimates with similar implications. Results from the dynamic models indicated the existence of persistence in consumption patterns was important.

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7. Persistence in consumption patterns was introduced with autoregressive processes in the disturbances and by direct structural hypotheses. Discrimina- tion between the two persistence hypotheses proved difficult.

8. Complete demand systems were difficult to estimate at the levels of commodity disaggregation necessary for analyzing food-policy questions and for use in commodity forcasting. Separability arbitrarily limited the estimated cross-price effects. Improved approaches that do not impose separability in obtaining demand-parameter estimates are required if the theory is to be applied more directly.

The Future Future work on demand analysis is likely to address problem areas

identified by previous studies and to generate more practical empirical results. This will be accomplished by extending the analysis of consumer demand in Canada in three directions. First, the cross-section data will be pooled to provide estimates of own- and cross-price elasticities. Second, joint estimation of demand and supply relationships will be attempted. Third, more fully dynamic demand systems will be applied to the aggregate time-series data.

Price Elasticity Estimates f r o m Budget Data There are two approaches in which cross-section data can be used to

estimate price effects, in addition to income or expenditure elasticities and translation or scaling impacts of socio-economic factors. The first approach is empirical and was applied in a 1977 study of urban food-consumption patterns (Hassan and Johnson 1977). Available price variations observed during the survey period were used to estimate price elasticities. The advantage of the approach was, of course, simplicity. A disadvantage was that without the a priori information from a complete demand model, the price variations were not large enough to permit estimation of more than own-price elasticities. Thus, the elasticity estimates included specialized restrictions following from ad hoc assumptions that were implied by the exclusion of all but own-prices and income from the demand functions. These, and questions of whether price variations were true or a result of quality change (Wold and Jureen), cause results from such empirical studies to be viewed as exploratory.

Another approach was to employ more structured demand models in analyzing the cross-section data. This approach includes two major lines of inquiry. First, price effects were estimated with data from a single cross-section using models from which price impacts could be deduced without observing price variation. Howe; Powell; Green, Hassan and Johnson (1979); and Chisholm and Tyers have estimated price elasticities from cross-section data using versions of the extended linear expenditure system.

Second, cross-section data from different surveys can be pooled. Current expenditures can be obtained from survey data, while corresponding price data

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or proxies are available in published consumer-price indexes. Pollak and Wales estimated two complete demand systems, the linear and the quadratic expenditures system, using U.K. household budget data from two periods, and price indexes from National Income and Expenditure accounts. Ray estimated the almost-ideal demand system using household expenditure surveys for India, with price indexes constructed from wholesale price data.

Joint Estimation of Demand and Supply Relationships All demand systems that can be reconciled with the theory have been

applied without recognizing changing supply and market conditions. It is well known that unless very specialized supply conditions prevail or the variance in supply is large relative to demand, estimated parameters reflect the supply structure. Thus, in principal, the demand-system parameters estimated could be improved by specifying a supply structure.

Dynamic Demand Systems A major difficulty with existing estimates of the consumer demand

structures is that the theoretical models motivating the analyses are static. This problem has been to an extent addressed at Agriculture Canada (Hassan, Johnson and Green 1977). Two demand models that feature inventory adjustment and habit formation were estimated. Results from this application were encouraging; they are consistent with the theory, intuitively plausible and reconcilable with the static estimates.

More fully dynamic models of consumer behavior have been proposed by Philips, by Lluch, and by Klijn. Results from application of these systems are limited. However, those available indicate that the more dynamic models can contribute valuable information to that available from static and quasi- dynamic models. Moreover, these models highlight a crucial problem for understanding fully persistencies in the data. That is, do these persistencies exist because preferences are dynamic or because of data and structure, e.g., lumpiness in availability of consumer goods, changes in expectations (McCallum), temporal and commodity aggregation, organization of house- holds (Becker), etc.?

Concluding Remarks In summary, the primary objectives of future work in demand analysis at

Agriculture Canada will be (i) to refine and update the existing estimates of food demand parameters, (ii) to quantify effects of changes in the economic, social and demographic factors on food expenditure and consumption patterns using more general household models, (iii) to explain persistence in consumption patterns for food commodities, and (iv) to generate more practical research results for use in policy analysis.

The need for continuing research on consumption behavior and demand is

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clear. Changes in economic, social and demographic environments occur continually; relative prices, new products, rates of growth of personal disposable income, age/sex distribution of the population, household organi- zation, family size, participation in the labor force, and habits and tastes. These changes call for continual revision and specialization of theory and estimation methods, and effective use of existing information bases, if policies and decisions of government and of the private sector are to have desired or intended outcomes and if the accuracy of consumption forecasts is to im- prove.

[Received July, 1983; Revisions accepted November, 19831

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