THE IMPLICATIONS OF SPATIAL AGGRE~fiIUR1_ TO FOOD EXPENDITURE

Transcription

1 WP THE MPLCATONS OF SPATAL AGGRE~fiUR_ TO FOOD EXPENDTURE by James C. O. Nyankori*

2 WP July 984 THE MPLCATONS OF SPATAL AGGREGATON TO FOOD EXPENDTURE PROJECTONS by James C. o. Nyankori*.. _: ~ -=.:...::=<:::.. a:_ -= ~ -==~~.~~ Working Papers are not subject to internal review wi thin the Department,--::-, ~-; of Agricultural Economics and Rural Sociology, Clemson University.. _ ~ ::. *Associate Professor, Department of Agricultural Economics and Rural Sociology, Clemson University, Clemson, South Carolina.

3 THE MPLCATONS OF SPATAL AGGREGATON TO FOOD EXPENDTURE PROJECTONS ntroduction Empirical studies of food consumption using Engel analysis show that household income has a significant influence on household total food ependitures (Blanchiforti et al., 98; Seauer, 979; Smal l wood and Blaylock, 98). The influence of income on food ependitures has also been shown to vary~cross income groups. This suggests that changes in income distribution of households have considerable impact on total food ependitures and, consequently, bear important implications for producers, marketing and public food policy decision makers. n practice, strategic food marketing and policy adjustments to changing household income distribution require nationwide projections of household total food ependitures. However, given the regional differences in the structures of the food ependiture relationship there arises a question of the relative merit of regional versus national projections. n this paper, the results from projections of food ependitures using aggregate (national) and subaggregate (regional) data are compared. n the former, a model of U.S. household food ependitures is estimated and used to make national projections and in the latter, the U.S. projections are obtained by aggregating projections from regional models. Aggregation problems have received considerable treatment in theoretical and empirical studies. n a fo~al way, Theil developed

4 2 conditions under which bias can be introduced in aggregating from microeconomic to macroeconomc relations. Green, in a survey of earlier works on aggregation reiterates that the problem of the appropriate type and degree of aggregation belongs to the field of statistical decision theory. n practice, the purpose of the investigator is paramount but ought to be weighed against likely errors from a high degree of aggregation and the cost of using disaggregated model. Yet the resolution of the problem is compounded by the specification argument (Grunfeld and Griliches, 960); the loss of information argument (Edwards and Or~utt, 969; Orcutt, Watts and Edwards, 968), and the measurement argument (Aigner and Goldfeld, 973). Changes in the u.s. Household ncome Distribution Since 970, there have been noticeable annual variations in the income distributions of U.S. households. Generally, there have been increases in the percentage of households in the lowes~~wo and the top income groups and decreases in the third and fourth income groups between 970 and 980. At the same time, the number of households grew at a steady annual rate. However, the national ~nd regional income distribution patterns and the annual rates of growth in the number of households differ markedly. Furthermore, there are interregional differences in the magnitude L i.. and direction of changes in the income distributions and number of households. Given that the food ependiture-income response structures are specific to income groups, clearly the national total food bill will vary with the number and income distributions of households.

5 3 But the intranational and interregional differences in the ependiture response structure, income distributions and the total number of households raise the still unanswered question regarding aggregation and projections and suggests, for practical purposes, a comparison of total food ependiture projections from national and regional models. Accurate projections are important to a number of food marketing and public policy decisions. Public decisions regarding the allocation of funds to food programs at the national and regional levels are not independent. Projections at the national level are needed to determine the gross program cost~ yet regional level information is needed for a more equitable interregional allocation of the program budget. Similarly, in the private sector, national and regional projections are needed to determine gross capital requirements and the allocations to regional processing and distribution capacity development, respectively. Data and the Models nformation on the income, total food ependitures and demographic characteristics of U.S. households are from the Consumer Ependitures Survey, of the Bureau of Labor Statistics This is a nationwide survey of a sample of approimately 20,000 U.S. households and contains, J information used to update the Consumer Price nde! - - Suppose the household food ependitures -re-ationship _ is characterized by the Engel function of the form, ~... ;--- E. = a + ~ where E. (i = household, Y. by.,2,...,n) is the is the the annual term, a, and income coeffici~~t, b. 7'~: _ ~-=---:-':;:=:~~:~~~::::.~~ ~._- total food~~~enditures ~for~the ith~~- -. ~,:=~~.:;~:.:.~~_-:..::-:.;.:;;ii'.-' _--- constant ~_ household =~ncome -with - the -~- :.:~.:::~ -.::~..:. -.::. ~.~~.::... ~ ~ -;-:~. ()

6 ', _--' ~-,-.. 4 /.. : To eplicitly introduce food ependiture-income relationships at different income ranges in relationship (), household income, Y, is tarnsformed as Yli = Y. Yki = Y. = 0 Y k if Y i > Y k if Y i ~ k =,2,...,K Y k The specific values of Y k are eogenously given and correspond to (2).t'.. ; / the upper limit income values of the kth fifth (k =,2,3,4) of the per-, centage share of aggregate income received by households in 980. The transformed variables in (2) are used to reformulate the Engel '. relationship () as (3) where a is the constant term and ~ is the marginal propensity to spend. The change in the marginal propensity to spend is ~k (k > ) at household income Y i = Y k (k = 2,3,...,5), and u i is the error term..... ' ~,' '.,~ r': '! ' ',. l,\ Equation (3) is estimated with the logarithm of E. as the dependent variable. The set of income 'values Y k : Y < Y 2 < Y 3 < Y 4 defines five income groups and for each income group so defined, the mean total food ependiture, E, is computed as g E = a + Yg l ~k' g k=l r (r, g =,2,.., K) where Yg is the sample mean household income for the gth income group and the term in parentheses is the ependiture-income coefficient for -. the 8th. income group. _' -~ (4)

7 5 therefore, The total household food ependiture for the gth income group is, E = nw E g =,2,.,k g g g k w = g g= j ' ; where w is the proportion of households in the gth income group and g n is the total number of households. The total household food ependiture for all income groups is, consequently, the sum of all income group ependitures k E = L g= E g g =,2,...,k. Suppose the original (980) vector of household income distribution is characterized by the vector, W, o (5 ) Because of the numerous possibilities of income distributi on outcomes, alternative income distribution vectors are generated f r om (4), for the purposes of projections, using a cumulative distribution factor, 0 <! < 00, such that the resulting percentage households in the gth income group is w g h = (w / L w )! ~ g < h og g=. og G (w / L w ) * (00-t) h ~ g < G. (6) og g=h og the values of t, and h, several household income distriwere generated for the U.S. and each of the four regions: North Central,- South and West. total national _ fo~d e~enditure projections, En' were computed from the esti~f~d p~a~~t ~ rs.~ -: ::-Z:... 4:-: - ~ =-... ~ ;.~ - -- of t he U.s. model, the generated r -

8 6 income distribution vectors and the data on U.S. mean ependitures for each income group. The aggregated projections, E, were similarly a obtained but using the estimated parameters of of the regional models and the regional group mean ependitures and income distribution vectors, and finally summing across regions E a = 4 l: i= E. (i =,2,3,4). Since the effect of aggregation is not known a priori, the two sets of projections were compared for equality on the basis of a significance test. f it could be,established that there were no significant differences between national projections, E, and the aggregated projections, n E, then the problem of spatial aggregation would be considered to be of a no empirical consequences in this case. f, however, there were significant differences between the two sets of projections some conclusions that have important implications to the analysis of household food ependiture for policy and marketing decisions could be drawn. Therefore, the national and the aggregated ependiture projections were compared using the test that the two vectors of projections, E and n E, are simultaneously equal a Ho: (E - E ) = 0, a n (7a) (7b) Model Results.. 0..,, -.. ~ The estimated model parameters are presented in table. The main effect of income on household total food ependitures (3.) is sign;fi- -=- cant and positive in all the regional and U.S. models~ There are, how- - ever, differences in the magnitudes of the estimated main income effect ranging from 0 ~ in the West to ::::=- ---

9 -- ::: Table. Estimated ncome Coefficients of Household Food Ependitures in the U.S. and in the Northeast, North Central, South and West Regions of the United States Coefficient Estimates United States Northeast North Central South West..,!...., - '. ' Ci (89.) (35.9) (39.9) (50.6) (32.2) (7.2) (7.3) (. 3) (2.) (. 34) ) (. 8) (-2.3) (. 8) (. 6) (2.7) (-3.4) (-0.5) (-0.5) (-.6) (-2. 7) (-0.8) (0.5) (-2.7) (-0.3) (0.6) ,.', (-3.6) (-3.) (-0.4) (-.6) (-2.5) ,.,. Notes: ~ is the main income coefficient; ~ is the change in the income effect at $7,999; ~3 is the c~ange in income effect at $2,4999; ~4 is the change in income effect at $20,000; ~5 is the change ~n income effect at $34,999. The dollar values refer ~ to the annual household income levels and the numbers in parentheses are the t-values. : '-

10 8 The changes in the effect of income on total household food ependitures at household income $7,9999 (P2)' were significant and positive in all ecept the Northeast and varied in magnitude from (Northeast) to (West). At household income $2,499, there were no significant changes in the effect of income on total food ependiture '0' ;, \, ~ ependitures (P3) in the Northeast and North Central but there were negative changes in the South, West and U.S. n all but the North Central, there are no significant changes in the effect of income, (P 4 ), on total food ependitures at household income $9,999. Finally, at household income $34,999 there was a decrease in the effect of income (P s ) on total food ependitures in all but North Central. The estimated income coefficients shown in table were used to generate two sets of U.S. food ependiture projections: the national model projections and the aggregated projections. The ratios of the national projections epressed as percentage of the aggregated regional projections are shown in figure. Clearly the national projections are lower than aggregated projections in all income distribution scenarios. On the basis of the test of significance, the hypothesis that there, ~,\ is no difference between the national and aggregated projections is rejected. Projections using the national model of U.S. households were invariably lower than the those computed by aggregating projections from regional models of households. Summary and Conclusions n this paper, the problem of aggregation was discussed within the specific framework of total food ependiture projections using household - food epend'itures data aggregated at national. 8nd _ re~ional ~ le~e~~~~~i~~_. ~. --'- ~ ~--: - ~,,' ~!;.-t~:~~~- ~~~--Zi:- ~ ~!.r =-~. -- -

11 H '! i : : \.!.,.', +,... j, +./ ~.,. t.. ' + J., ~. + ',. [ X.\, ; +.'., : ,'./ '. + ~ ' ' NCOME DSTRBUTON SCENAROS, Figure. The rations of national to aggregated regional food ependiture projections (Percentages)

12 -. \ 0 Regression estimates of the food ependiture responses across prespecified income groups were generated for U.S. households and for households in the Northeast, North Central, South and West. These, together with J national and regional income data were used to make household total food ependiture projections under alternative income distribution scenarios. A comparison of the national projections using the estimated national ependiture parameters and aggregated regional projections showed that the former were invariably lower than the national projections. Furthermore, a significance test led to the rejection of the null hypothesis that the national and aggregated projections were equal. The general conclusion is that there are significant differences in food ependiture projections from aggregated and subaggregated data. Since subaggregate data contains additional information inevitably lost in aggregation, aggregated projections are preferred, especially in situations where underestimation is more costly than overestimation.

13 References. '. ~. ~ Aigner, D. J. and S. H. Goldfeld, Simulation and Aggregation: A Reconsideration. Rev. Econ. Stat. 55(973):4-8. Blanchiforti, L., R. Green, and S. lane. ncome and Ependiture for Relatively Hore Nutritious Versus Relatively Less Nutritious Foods Over the Life Cycle. lamer. J. Agr. Econ. 63(98): Dunn, D. H., W. H. Williams, and T. L. DeChaine, Aggregate Versus Subaggregate Hodels in Local Area Forecasting. J. Amer. Stat. Assoc. 7(976):68-7. Edwards, John B. and Guy H. Orcutt, Should Aggregation Prior to Estimation be the Rule? Rev. Econ. Stat. 5(969): J Green, John H. A., Aggregation in Economic Analysis, An ntroductory Survey, Princeton, New Jersey: Princeton University Press, 970. Grunfeld, Yehuda and Zvi Grilliches, s Aggregation Necessarily Bad? The Review of Economics and Statistics, 42(960):-3. Orcutt, Guy, H., Harold W. Watts and John B. Edwards, Data Aggregation and nformation Loss. Amer. Econ. Rev. 58(968):773-87, Seauer, B. The Efect of Demographic Shifts and Changes in the ncome Distribution on Food-Away-From-Home Ependitures. Amer. J. Agr. Econ. 6(979): Smallwood, D., and J. Blaylock. mpact of Household Size and ncome on Food Spending Pattern. ESCS Tech. Bull Theil, Henri, Principles of Econometrics, New York: John Wiley Sons, nc., 97. i -

14 SOUTH CAROLNA AGRCULTURAL EXPERMENT STATON, CLEMSON UNVERSTY, CLEMSON, SOUTH CAROLNA W. C. GODLEY, ASSOCATE DEAN AND DRECTOR S. C. EXPERMENT STATON LUTHER P. ANDERSON, DEAN, COLLEGE OF AGRCULTURAL SCENCES The South Carolina Agricultural Eperiment Station s a cooperative program financed from federal and state funds. t is the policy of the Eperiment Station to comply fully with the regulations of Title V. the Civil Rights Act of 964. Complaints may be filed wilh the Director. S. C. Agricultural Eperiment Slallon, Clemson University. Clemson. S. C