engel curves for meat consumption in australia

ENGEL CURVES FOR MEAT CONSUMPTION IN AUSTRALIA*

D. L. RYAN, T. J. WALES and A. D. WOODLAND

University of British Columbia

I. INTRODUCTION

In view of the high levels of domestic per capita meat consumption and production in Australia, it is of considerable interest to analyse the resulting patterns of household meat consumption. In this paper we use cross-section micro data for the years 1964-65 and I967 to investigate how the allocation of meat expenditures among the three broad aggregates of beef, lamb and other meats is affected by changes in total expenditure on these groups, and by changes in demographic variables.' Our study differs from most in the literature in two major respects. First, we pay particular attention to the behavioural assumptions underlying meat purchases; in particular we assume that these purchases are the result of a utility maximisation process by households. Second, in the empirical work we recognise the fact that many households purchased only one or two of the meat categories during the survey period (one week). Thus, for example, there are a significant number of households for whom consumption of beef is zero. Such a consumption pattern (with a large number of observations at zero) makes the appropriate estimation of income responses much more difficult. Our estimation technique takes this difficulty into account.

11. THE ECONOMETRIC MODEL OF MEAT DEMAND

We begin by specifying and discussing the model of behaviour underlying the empirical work reported in Section 111. This model is based upon the principle of utility maximisation subject to a budget constraint, allows for differences in preferences among households, deals explicitly with the occurrence of corner solutions which are given positive probabilities, and is operational.'

Utility muzcimisution It is assumed that individual households have preferences described by a utility

function in which three meat types form a separable group. That is, the utility function

*We wish to thank the Bureau of Agricultural Economics, Canberra, for making the data available on magnetic tape, and the referee for his comments on the paper. Woodland gratefully acknowledges financial support from the Reserve Bank of Australia.

Although these surveys were taken some time ago they do not appear to have been analysed in detail, except by the Bureau of Agricultural Economics. There is a similar survey [8] undertaken in 1972 in Brisbane, but we only became aware of it after completion of this paper. The model is sketched here. For further details see Wales and Woodland [l 11.

106

1982 ENGEL CURVES FOR MEAT CONSUMPTION 107

is ofthe form 14 = U ( . . .. G(s) , . . .) wheres = (s1,xZ,x3) is thevector ofconsumptions of the three meat types, namely beef, lamb and “other”. I t is further assumed that the expenditure on meat, m, is determined in the first stage of a two-stage utility maximisation p r o c e d ~ r e . ~ The second stage, consisting of the allocation of 171 among the three meat types to maximise G ( s ) , can be written as

(1)

where v = ( v l , v , , v , ) ~ > O is the vector of normalised prices v, = p l / i n . I f G ( s ) is a continuously differentiable, quasi-concave, increasing function the Kuhn-Tucker conditions (necessary and sufficient) for a solution to ( 1 ) are

niax {G(s): v?x < 1, .Y 3 01

where L is the Lagrange multiplier associated with the budget constraint and G, (.u) = dG(.x)/?x, denotes the ifli partial derivative?

A convention used here is that whenever double inequalities are written as in (2) it is implied that the two terms which have inequality constraints have zero as their product. Since G ( s ) is increasing, all ofm will be spent and thus at least one good will be consumed. Taking this to be the first good without loss of generality, conditions (2) may be rewritten as

I ~ ~ G ; (x) - V ; G,(x) 6 0 <s,

1’ x = 1 i = 2 , 3

T (3)

These conditions simply state that if x , > O then vi/v1 = Gl(.x)/G1(.y) meaning that the indifference curve is tangent to the budget plane in ( x , , . ~ , ) space. Also, if xi = 0 then v j / v 1 2 G; (.y)/G1 (.u) meaning that the slope of the indifference curve may be less than the slope of the budget plane. This is the familiar condition for a corner solution.

To make the model operational we assume that G ( s ) is a quadratic utility function given by

which is a “flexible functional form”. Several parameter normalisations are made. Firstly, since the utility function can only be identified by the data up to a factor of proportionality, we obtain complete identification by imposing the arbitrary normalisation

2

2 UjO = 1 i= I

( 5 )

An alternative procedure would be to assume that m is endogenously determined in the model and that income is predetermined or exogenous. Unfortunately, the data set used here does not contain accurate income information, and thus this alternative is ruled out.

Also, it would be desirable to take account of household purchases of meats in the period prior to. or of the stocks of meats held at the beginning of. the survey week since meat is storable. However. this information was not available. See. for example. Arrow and Enthoven [I] .

108 AUSTRALIAN ECONOMIC PAPERS JUNE

A second normalisation arises from the fact that our data are from cross-sectional surveys. Since each sample was taken in a single city over a relatively short period of time we assume that all households face the same prices for meats and without loss of generality set them at unity. Thus xi is interpreted as both the quantity of, and expenditure on, meat type i. Clearly, without price variation we can only estimate the effect of changes in total meat expenditure m upon x . Thus, not all parameters are identified, and further normalisations are required. We choose to impose the normalisations aij = 0 ( i # j ; i, j = 1,2,3) and a33 = - 1. Under these normalisations the utility function takes the form

where (5) holds and a33 = - 1. It should be emphasised that the simple structure of the utility function in (6) is due to identifying normalisations, and not restrictions on preferences.

Given utility function (6) and the assumption that all of m is spent, the Kuhn- Tucker conditions (2) may be solved for x in terms of m for every possible expenditure pattern5 Since prices are all unity the binding first order conditions become

a, + aiixi = A Z xi = m

id

i d

(7)

where I is the set of subscripts i for those goods that have positive expenditure. The solution to (7) for the xis in terms of m yields the Engel curves

ie I

where si = l/aii/ Z l / a j is the marginal budget share for good i. Clearly, if $I then JEI xi = 0.

The Engel curves are linear in m for each expenditure pattern. Such curves are consistent with any set of preferences which have a Gorman polar form. For example, the Stone-Geary utility function yields Engel curves which are linear in m. Thus the quadratic utility function provides one way of obtaining the estimating equations, and our results may be reinterpreted within the context of any utility function which has a Gorman polar form.

Variations in preferences among households Differences in preferences are taken into account by assuming that the ajo

parameters of the utility function are themselves linear functions of a vector of household characteristics and a random term. That is,

It is evident that the quadratic utility function cannot be quasi-concave and increasing in m for all s>O unless it takes the trivial linear form. That is. there will exist a “bliss point” beyond which not all of m will be spent. However. from a practical viewpoint all that is required is that this bliss point be beyond the set of observed sample points. This condition was verified in our empirical work.


where =, is thej'"characteristicj = 1 , . . ., 5, the cs are parameters to be estimated and u,

is a random variable. Because of the restriction that c uf0 = 1, the c parameters have the constraints

3

f = I

while u = (ul , u2, 143) must satisfy

3

i= I c uj = 0.

According to this specification there are two sources of differences in preferences among households. Non-random differences are captured by the household characteristics variables which are specified in the following section. In addition our specification assumes that preferences are randomly distributed over the population. Thus, each household with a particular vector of characteristics, z, will have different preferences. but each is independently drawn from the same distribution. I t is assumed that

U"(0, C), (12)

that is, u is normally distributed with mean 0 and covariance matrix C. This implies that the coefficients, uio, of the xis in the utility function are normally distributed over

the population with mean arO = c jo+,~; j j z j . The aim of our study i s to use observa-

tions on s, L and In for a sample of households to estimate the parameters of the mean utility function and the covariance matrix C.

5

Estirnution procedure Using a sample drawn from the population the aim is to use observations on the

expenditure vector x, household characteristics vector I and total meat expenditure m to estimate the non-random parameters of the utility function and the means and covariances of the random parameters. Since G(x) is random (from the analyst's viewpoint, but not the household's) so are the marginal utilities G , ( s ) , and alsox, since it satisfies the Kuhn-Tucker conditions (3). Thus the density function for .Y may be calculated, the likelihood function for the sample formed, and maximum likelihood estimates of the parameters obtained.

For the quadratic utility function (6) the Kuhn-Tucker conditions corresponding to

-.Ti < 0 < X i i =2 ,3 (13)

(3) may be written in the form


i,j = 2,3 (14)

and x1 has been eliminated using the budget constraint.

The derivation of the density function for x, and xg from (1 3) is provided in Wales and Woodland [ 1 1].6 Here we simply note some of its features. First, if (x2 ,x3) >O then the LHS of (13) holds with equality. Thus (x, ,x3) corresponds to a unique ( ~ 2 , ~ 3 ) and therefore has density with no probability mass. Indeed since (yz, y 3 ) is normally distributed so is (x,,x~). However, if (x,,x3) = 0 then inequalities prevail and the density for (x,,x3) = 0 is obtained by integrating over all (y2,y3) such that yi<yi. This event therefore has a probability mass obtained by integrating under the bivariate normal density function. Ifx, = 0 but xg >O then the density is obtained by integrating over y, <lyz only, yielding a “pile-up’’ of density for this event.

The Kuhn-Tucker conditions (3) and (1 3) have been written for the case where the first meat type has positive expenditure. Clearly, the choice of good 1 for this role is arbitrary and other cases can be dealt with by a rearrangement of subscripts.

The parameter estimates are obtained by maximising the sample likelihood function, and they are asymptotically normally distributed about the true parameter values under the assumptions of the model. It is noted that the adding-up condition (1 1) implies that 1% = 0, and hence that the distribution for u is degenerate. Consequently, the complete covariance matrix can be defined by just three parameters which we take to be c1 and c,, the standard deviations for u, and u,, and their correlation coefficient, p,,. In total there are seventeen free parameters to be estimated, namely gl, g2, p,,, c10,c20, a,,, a,,, cll, . . ., c15, czl, . . ., ~ 2 5 . The parameters c3j, j = 0, . . ., 5 can be obtained in terms of the free parameters using (10). Hence, by setting u = 0, we can obtain estimates of the Engel curves defined by (8) for a household with characteristics z and mean preferences.

Summary In summary, the random preferences model yields a positive probability for the

event that two meat types are not consumed and a pile-up of density for the event that one meat type is not consumed. In the samples used in our empirical work there are a significant number of households which are observed not to consume one or two meat types during the interview period. The model developed here is designed to permit the estimation of preferences for meat using these samples, paying particular attention to the significant occurrences of zeros and to the budget constraint.

Note that the budget constraint forces the joint density for x = (x,, x2, x3) to be degenerate

1982 ENGEL CURVES FOR MEAT CONSUMPTlON 111

111. DATA AND RESULTS

Data In this section we discuss an application of the econometric model outlined above

using two surveys of household meat consumption carried out by the Bureau of Agricultural Economics in Australia [ 2 ] , [3]. Each survey contains information on the purchases of various types of meat by each household in the sample, together with information on the characteristics of the household members. The first survey, undertaken in Sydney in late 1964-early 1965, contains information collected over one week using the recall method and over a second week using the diary method. In the second survey, undertaken in Melbourne in 1967, the expenditure information is based upon the recall method only and covers a one week period. Because of the short survey period there are categories of meat expenditures involving no purchases, even when the data are aggregated into three broad groups-beef, lamb and other meats. Although the percentage of households for which meat expenditure is positive for all three meat groups ranges between 66 per cent and 72 per cent in the three samples. the econometric model developed in the previous section allows estimation of an economic model of meat consumption using all observations in the samples.

summary statistics. The Appendix contains further details regarding the sample data. including some

Effects oj demograpliic variables After eliminating some households due to lack of complete information, the three

samples-Melbourne, Sydney Recall and Sydney Diary -consisted of 789. 478. and 437 households, respectively.

The following five characteristics are hypothesised to affect household preferences for meat:

z1 = number of individuals in household, 13 years or older. z2 = number of individuals in household, younger than 13 years. z3 = 1 if the household head is a Roman Catholic.

0 otherwise. z4 = 1 if the household head was not born in Australia or New Zealand.

0 otherwise. z5 = l / ( R + 1 ) if 2, = 1 , where R is the number of years of residence in Australia.

0 if z4 = 0.

Variables z1 and zz are intended to reflect the influence of family size and age composition upon the pattern of household meat consumption. Variables z4 and zs are introduced to take account of possible differences in tastes between Australian born families and others. Variable z, allows for a permanent difference in tastes while z5 allows for the possibility that the taste patterns of non-Australians may alter over time.

For each sample, we test the significance of the demographic variables using the likelihood ratio statistic formed from the maximum likelihood estimates based on all the observations in that particular sample. Separate tests of the null hypothesis that a


group of variables do not affect the shares of meat expenditure were carried out for the following groups: (a) family size and age composition (zl, z2), (b) Religion (z3) and (c) country of birth and length of residence (z4, z5). For the Melbourne sample, the null hypothesis of no effect was rejected at the 1 per cent level of significance for each group of variables. For the Sydney Recall sample, the null hypothesis could not be rejected for the religion variable, z,, For the Sydney Diary sample, unambiguous results of this hypothesis testing procedure were not obtained. Although the hypothesis of no effect was rejected at the 1 per cent level both for the first group of variables and for all variables taken together, it could be rejected only at the 10 per cent and 15 per cent levels respectively for the religion variable and the residence group of variables. However, the hypothesis that these two groups of variables together have no effect was rejected at the 2.5 per cent significance level.

The effects of the demographic variables upon the consumption of beef, lamb and other meats for each consumption pattern in which more than one meat type is consumed are presented for each sample in Tables 1-111. These demographic variables do not appear to have a very large effect upon the consumption of the three meat types. For example, the estimates for the Melbourne sample in Table I reveal that when all three meat types are consumed an increase in the number of household members thirteen years and older, zl, increases beef consumption by 3.6 cents, lamb consumption by 7.6 cents and consequently reduces the consumption of other meats by 1 1.2 cents. A somewhat surprising result is that Catholics (z3 = 1) on average spend 35.1 cents more on the consumption of beef, 25.4 cents less on lamb, and 9.7 cents less on other meats (which includes fish) than do others ( z , = O).’

Variable z4 allows households with Australian born heads to have different expenditure patterns than other households, while variable z5 permits an adjustment over time of expenditure patterns of households with non-Australian born heads.8 If dxi/dz, = 0 then differences in the expenditure patterns of these two groups persist over time, whereas, if dxi/az4 = 0 the initial differences decrease (asymptotically) as years of residence increase. To interpret the results, we consider first the case of a household whose head is non-Australian and who resided in Australia less than one year. With years of residence equal to zero, z, = 1 and so axi/az4 + axi/dzs is the difference in the expenditure for category i between Australian and non-Australian headed households. Again examining the estimates for the Melbourne sample contained in Table I, the results indicate that, when all three meat types are consumed, non-Australians have an estimated expenditure for beef which is $1.40 lower than Australians, $0.99 lower for lamb, and $2.39 higher for other meats. As years of residence increase, z5 declines towards zero so that axi/dz4 is the limiting difference between the expenditures for households with Australian born heads and others for category i. The dxi/dz4 estimates for beef, lamb and other meats are 0.375, -0.525, and 0.150, respectively. This means that immigrants reduce their expenditure on other meats and increase their

For the Melbourne sample, approximately 20 per cent of the expenditure on other meats category consists of expenditure on seafood.

* Recall that z5 = 0 for a household with an Australian born head and z5 = 1/( 1 + R) for other households where R is years of residence in Australia of the household head.


expenditure on beef and lamb as years of residence increase, and eventually spend more on beef but still less on lamb than do households with Australian born heads.

Estimates of the effects of the various demographic variables on the consumption of meats for the different consumption patterns involving two meat types are also presented in Tables 1-111. These estimates can be interpreted in the same manner as for the case where all three meat types are consumed. Of course, when just one meat type is consumed the demographic variables have no effect upon consumption, since no reallocation of expenditure is possible.

Although not discussed in detail here, the results for the two Sydney samples may be analysed in an analogous manner, and differences between these results and those for the Melbourne sample may be studied.

Engel curves In addition to the demographic effects described above, Tables 1-111 also include

estimates of the marginal budget shares for each of four consumption patterns. For each sample, we have calculated the Engel curves relating expenditure on each meat type to total meat expenditure for both the “average Australian born household” and the “average non-Australian born household”, that is, with the 2,s set equal to the sample means for each respective group of households and with the parameters of the utility function equal to the maximum likelihood estimates. In order to better represent the characteristics of the “average non-Australian born household”, the mean of thk residence variable, z5, for this group is replaced in the calculations by l / ( f i + I ) , where R is the average length of residence in Australia for a non-Australian born household.’

The Engel curves for the Melbourne sample are presented in Figure 1. We observe that for nz less than $0.67, lamb (good 2) is the only meat type consumed by the average Australian born household, so that its marginal budget share is unity. For nz greater than $0.67 but less than $1.34, both beef and lamb are consumed by this household, with marginal budget shares estimated to be 0.686 and 0.314, respectively. If nz exceeds $1.34, this household will consume all three meat types with marginal budget shares of 0.409, 0.188 and 0.403. For a non-Australian born household in the Melbourne sample, only beef (good 1 ) will be consumed for 172 less than $0.14, while both beef and lamb will be consumed for nz between $0.14 and $0.83. For total meat expenditure exceeding $0.83. such a household will consume all three meat types.

Similar patterns of meat consumption for both types of average household are found in the two Sydney samples. In all cases, meat consumption of the “average Australian born household” consists only of lamb up to some threshold meat expenditure level ($0.51 for Sydney Recall and $0.23 for Sydney Diary), then beef and lamb up to a higher expenditure level ($1.44 and $1.77, respectively), after which all three meat types will be consumed. For the “average non-Australian born household”, meat consumption consists entirely of beef at low meat expenditure levels, then beef

-

The averages of the i’s for the two household types are presented in the Appendix


TABLE I Marginal Budget Shares and Demographic Effects-Melbourne

a x p n ax,jazl ax,jaz, ax,jaz3 ax,laz, axtjaz,

xl, x2, xj positive

X1 0.409 0.036 0.052 0.351 0.375 - 1.770 (0.018) (0.053) (0.044) (0.123) (0.139) (0.797)

(0.010) (0.038) (0.033) (0.092) (0.105) (0.619)

(0.013) (0.044) (0.037) (0.106) (0.1 19) (0.674)

.y2 0.188 0.076 0.096 -0.254 -0.525 -0.465

x3 0.403 -0.112 -0.148 -0.097 0.150 2.235

xi, xt positive

X1 0.686 -0.040 -0.049 0.285 0.478 -0.238 x2 0.314 0.040 0.049 -0.285 -0.478 0.238

(0.019) (0.039) (0.033) (0.090) (0.103) (0.605)

xlr xg positive

x1 0.504 0.074 0.100 0.223 0.111 -2.005 -‘13 0.496 -0.074 -0.100 -0.223 -0.111 2.005

(0.018) (0,044) (0.037) (0.105) (0.1 19) (0.669)

x2, x3 positive

x2 0.318 0.087 0.112 -0.143 -0.406 -1.027 -y3 0.683 -0.087 -0.112 0.143 0.406 1.027

(0.013) (0.031) (0.027) (0.078) (0.089) (0.518)

Notes: The x, s and m are measured in dollars per week. Standard errors are contained in parentheses. Since marginal budget shares sum to unity and demographic effects sum to zero, when only two meat types are consumed the standard errors on these shares and effects are the same for both meat types.

and lamb and finally all three meat types. In interpreting these results it should be noted that the Engel curves in Figure 1 (and the corresponding ones (not shown) for the two Sydney samples) refer to “average” households, and that individual households with different values for their utility function parameters and their zi variables will have different Engel curves, involving a different sequence of consumption patterns as m increases, and with the switches from one pattern to another occurring at different levels of m.

Recall versus diary methods An interesting aspect of the Sydney survey is that data were collected using both the

recall and diary method (in different weeks) for most households in the sample. As can be seen from Tables I1 and 111, differences appear to exist between these two samples in terms of both the demographic effects and the Engel curves. To formally test the

1982 ENGEL CURVES FOR MEAT CONSUMPTION

TABLE I1 Marginal Budget Shares and Demographic Ef”ects-Sj.dnej. Recnll

.vl, x2. s3 positive

s 0.383 0.115 0.013 0.497 - 1.472 (0.024) (0.059) (0.048) (0.205) ( I ,842)

(0.015) (0.045) (0.038) (0.164) ( I ,468) .x3 0.401 -0.187 - 0.130 - 0.262 2.738

(0.021) (0.048) (0.039) (0.173) ( 1.535)

.Y, .v2 positive

x z 0.216 0.072 0.117 -0.235 - 1.265

z , 0.639 -0.005 -0.070 I 0.330 0.278 x2 0.361 0.005 0.070 -0.330 --0.278

(0.027) (0.047) (0.038) (0.160) ( 1.434)

x , . x3 positive

x I 0.489 0.150 0.070 0.382 - 2.09 1

(0.027) (0.048) (0.039) (0. I 7 3 ( 1.534) d3 0.511 -0.150 -0.070 -0.382 2.091

.v2, x3 positive

.x-2 0.351 0.112 0.121 -0.061 - 1.781

.y3 0.650 -0.112 -0.121 0.061 1.781 (0.021) (0.036) (0.031) (0.136) (1.207)

115

note.^: The .v,s and Standard errors are contained in parentheses. Since marginal budget shares sum to unity and demographic effects sum to zero, when only two meat types are consumed the standard errors on these shares and effects are the same for both meat types.

are measured in dollars per week.

hypothesis that the diary and recall methods are equivalent methods of recording meat consumption behaviour. we proceed by assuming that our model is correct and that (as seems plausible) tastes did not change from one week to the next. The null hypothesis then is that the parameters ofthe model generating the recall and the diary data sets are the same. Estimating the parameters of the preferred model after pooling the two data sets, we form the likelihood ratio statistic for this hypothesis as minus twice the difference between the log of the likelihood obtained using the pooled data set and the sum of the logs of the likelihoods obtained from the recall and diary data sets. Since the religion variable is significant for the Sydney Diary sample, although not for Sydney Recall, the likelihoods used in forming the likelihood ratio statistic are those obtained when all variables are included. The observed value of this statistic is 33.27 while the critical chi-square value at the 1 per cent level of significance (with 17 degrees of freedom) is 33.41, and at the 5 per cent level of significance is 27.59. From these results

116

xi

3 -

AUSTRALIAN ECONOMIC PAPERS JUNE

FIGURE 1 (a) Engel curves: Australian headed households

A

.88

.67 .46 I

FIGURE 1 (b) Engel curves: non-Australian headed households

s, 1

1

1982 ENGEL CURVES FOR MEAT CONSUMPTION 1 I7

TABLE I11 Morgiiial Budget Shares and Deiiiogrup/iic Ejfects--S)diiq~ Diurj’

x , , x2, x3 positive

XI 0.307 0.163 0.036 0.245 0.005 2.308 (0.019) (0.062) (0.050) (0.135) (0.222) (1.967)

(0.015) (0.048) (0.039) (0.106) (0.168) (1.495)

(0.016) (0.055) (0.047) (0.128) (0.214) (1.924)

-Y2 0.203 0.070 0.119 -0.213 -0.172 -1.026

.Y3 0.490 -0.234 -0.155 -0.032 0.167 -1.282

.rl. sz positive

.Y 0.601 0.023 -0.057 0.216 0.106 1.537 1 - 2 0.399 -0.023 0.057 -0.226 -0.106 -1.537

(0.029) (0.050) (0.039) (0.100) (0.160) (1.41 1 )

xl. x3 positive

I, 0.385 0.190 0.082 0.163 -0.061 1.913 sj 0.615 -0.190 -0.082 -0.163 0.061 -1.913

(0.021) (0.054) (0.044) (0.122) (0.203) (1.808)

x2 . x3 positive

sz 0.293 0.118 0.130 -0.141 -0.171 -0.349 .Y3 0.707 -0.118 -0.130 0.141 0.171 0.349

(0.018) (0.040) (0.035) (0.094) (0.152) (1.369)

Notes: The .I-, s and i n are measured in dollars per week. Standard errors are contained in parentheses. Since marginal budget shares sum to unity and demographic effects sum to zero, when only two meat types are consumed the standard errors on these shares and effects are the same for both meat types.

we conclude that there is a significant difference in the recall and diary methods of collecting the data: the probability of being incorrect in our conclusion only marginally exceeds 1 per cent. It is interesting to note that in this respect we differ from the Bureau of Agricultural Economics who based their decision to use only the recall method for the Melbourne sample on the conclusion that for the Sydney survey, “differences in the information supplied using the two methods were not significant”.”

IV. COMPARISON WITH OTHER STUDIES

It is of considerable interest to compare the results obtained with our model to those of other published studies of meat consumption. The only studies, of which we are

See Bureau of Agricultural Economics 13. p. 71. Presumably this decision was based upon a comparison of summary tables from the two methods. However. no formal test of the hypothesis is included in their reports.


aware, that use micro survey data are those conducted by the Australian Bureau of Agricultural Economics (B.A.E.) [2], [3]. In addition to various tabulations and summaries of the data obtained in the respective surveys, these studies also present estimates of elasticities of expenditure on various meat categories, including total meat consumed, with respect to income. Although none of these elasticities are directly comparable with any we are able to calculate for our study, an elasticity which can be compared across studies is obtainable from the B.A.E. results by dividing the income elasticities of expenditure on the various meat categories by the income elasticity of total expenditure on meat. The resulting values are elasticities for expenditure on the various meat categories with respect to total expenditure on meat. These elasticities, evaluated at sample means are presented in Table IV.

TABLE IV

Expenditure Elasririties from B.A.E. Studies

Combined Sydney Meat Category Melbourne Samples

Beef and Veal 1.105 1.080 Mutton and Lamb 0.421 0.600 Pork and Small Goods - Poultry and Game 0’632}1.369 0.737 -

In our model, it is easy to verify that the elasticity for expenditure on meat type i with respect to total expenditure on meat is given by the ratio of the marginal budget share for meat type i to the average share of meat type i in the total meat budget. In Table V, estimates of these elasticities are presented for those households in each sample that consume all three meat types. These elasticities are evaluated at the average share of each meat type in the meat budget for these households. For the three samples, these elasticities for the lamb category range from 0.64 to 0.67 while for beef they range from 0.84 to 1.08. Elasticities for the “other” meat category all exceed unity, ranging from 1.23 to 1.48.

In comparing the elasticities for the two studies, as presented in Tables IV and V, two important qualifications should be noted. First, the meat categories in the two studies do not exactly correspond. Second, the elasticities derived from the B.A.E. results refer to expenditure per effective person, while those in Table V refer to expenditures per household. Despite these qualifications, there are similarities between the two sets of elasticities. In particular, the elasticities in the Sydney samples for both the beef category and the lamb category are of approximately the same magnitude in the two studies. For the Melbourne sample, the beef elasticity is similar in both studies but our estimate of the elasticity for lamb is greater than that in the B.A.E. study while our elasticity for other meats (1.232) is less than that for pork and poultry combined (1.369) in the B.A.E. study.

1982 ENGEL CURVES FOR MEAT CONSUMPTION I19

TABLE V Estimates of Espendititre Elasticities froiii Curreiit Stutdi.

Meat Category Melbourne Sydney Recall Sydney Diary

Beef and Veal (Category 1 ) 1.077 0.990 0.836

Lamb and Mutton (Category 2) 0.641 0.673 0.674

Other (Category 3) 1.132 1.37 I 1.478

(0.047) (0.062) (0.052)

(0.034) (0.047) (0.050)

(0.040) (0.072) (0.048) ~

Note. Standard errors are contained in parenthesea.

At the aggregate level, there are a number of studies ofper capita meat consumption in Australia, including Fisher [4], Reynolds [7], McShane [5], Taylor [9] and van der Meulen [lo]. Unfortunately none of these studies present elasticities with respect to total meat expenditure. Using quarterly data from 1962 to 1977, Fisher presents elasticities with respect to income for five meat types using alternative functional forms for the meat consumption equations. Tn a similar vein Reynolds presents estimates of income elasticities of demand for the same five meat types based upon monthly, quarterly, and annual data sets.

Fisher’s “modified translog” estimates of the income elasticities of demand are 0.54, -0.81,0.09,0.04 and 0.20 for beef, mutton, lamb, pork and chicken respectively. If the elasticity of total expenditure on meat with respect to income is 0.58, an estimate obtained by Podder [6] using cross-sectional data, then the corresponding elasticities with respect to meat expenditure are 0.93, - 1.40, 0.16, 0.07 and 0.34. These may be cautiously compared with our results in Table V. The beef elasticities are not dissimilar, but those for lamb and mutton, and for other meats bear little resemblance to our estimates.

In other studies, McShane presents income elasticity estimates based on the B.A.E. surveys, while Taylor, using annual data from 1949 to 1959. reports that consumption of beef is unaffected by income. Finally. van der Meulen also uses annual data from 1949 to 1960 and presents elasticities with respect to income. However, since he claims that a 1 per cent increase in income results in a 1 per cent increase in consumption of meat”, these elasticities which are 0.400 for beef and 0.225 for lamb can be regarded as elasticities with respect to total meat expenditure. These are substantially below our estimates.

V. CONCLUSION

In this paper we analyse patterns of meat consumption in Australia using cross- section micro data for the years 1964-65 and 1967. We present estimated Engel curves which relate expenditure on each of our three broad meat aggregates to total expenditure on these aggregates and to various demographic characteristics. Most of

I ’ van der Meulen [lo. p. 371.

1 20 AUSTRALIAN ECONOMIC PAPERS JUNE

the implied expenditure elasticities are similar to those in the existing literature on cross-sectional studies, when calculated for households consuming all three types of meat. The demographic variables, reflecting religion, nationality and length of residence in Australia, and family composition all significantly affect consumption patterns, although the magnitudes of these effects are generally small. For the Sydney sample we formally test the hypothesis that the recall and diary methods of collecting information are equivalent, and conclude that they are not; the probability of being incorrect in this conclusion only slightly exceeds 1 per cent.

Our analysis differs from that in the literature in two important respects. First, we assume that the decisions about meat purchases made by households are the outcome of a utility maximisation process by these households. Second, we explicitly take into account the fact that many households did not purchase all three meat categories during the survey week by considering corner solutions to the utility maximisation problem. Such a consumption pattern, with a large number of observations at zero, makes the appropriate estimation much more difficult. Our estimation technique takes this difficulty into account and maintains the adding-up condition on the Engel curves.


APPENDIX In this appendix, we present details of the three samples of households analysed in this study. Table A1 presents the means and standard deviations for the demographic variables and for the shares of each meat type in the household's total meat budget. In each case. values are presented for Australian born households, non-Australian born households, and all households. Table A2 reveals the number of households having each type of meat expenditure pattern in the three samples.

TABLE A 1 Summary Statistics for Variables Used iii Ti7is Study

MELBOURNE SYDNEY RECALL SYDNEY DIARY

Non- Non- Non- Variable Aust. Aust. Total Aust. Aust. Total Aust. Aust. Total

No. of obs. 526 263 789 364 114 478 330 107 437 m 5.32 6.27 5.64 4.57 5.05 4.69 5.34 6.16 5.54

(2.94) (3.55) (3.18) (2.48) (2.98) (2.62) (3.05) (4.30) (3.42) S, 0.434 0.437 0.435 0.431 0.490 0.445 0.417 0.395 0.411

(0.216) (0.220) (0.217) (0.210) (0.238) (0.219) (0.198) (0.214) (0.203) S, 0.367 0.299 0.347 0.377 0.356 0.373 0.331 0.325 0.330

(0.216) (0.206) (0.215) (0.208) (0.215) (0.209) (0.183) (0.185) [O.l84) S, 0.335 0.417 0.364 0.314 0.367 0.326 0.343 0.458 0.371

(0.189) (0.199) (0.197) (0.189) (0.217) (0.197) (0.179) (0.210) (0.193) z1 2.59 2.76 2.64 2.62 2.56 2.61 2.64 2.55 2.62

(1.12) (1.12) (1.12) (1.11) (0.956) (1.08) (1.13) (0.940) (1.09) zZ 0.835 0.989 0.886 0.753 0.798 0.764 0.764 0.804 0.774

(1.26) (1.14) (1.22) (1.23) (1.04) (1.19) (1.23) (1.05) (1.19) z3 0.200 0.384 0.261 0.228 0.404 0.270 0.224 0.421 0.272

(0.400) (0.486) (0.439) (0.420) (0.491) (0.444) (0.417) (0.494) (0.445) -4 0 1 0.333 0 1 0.239 0 1 0.245

(0.47 1) (0.426) (0.430) R - 18.8 - - 19.5 18.9 ~ ~ -

(15.8) (14.3) (14.1)

Notes: Values presented in the table refer to the sample means. Standard deviations are contained in parentheses.

'For any household S , is defined as expenditure on the i"' meat category divided by m. the total expenditure on meat. The mean and standard deviation for any S, value is calculated after excluding observations for which expenditure on that S, value is zero. Hence. the sum of the average meat shares over the three categories is not equal to one. For the Sydney surveys, information was not available on actual years of residence ( R ) for household heads not born in Australia. Since information was available on years of residence grouped into three categories. we used the Melbourne averages for these categories in place of R. The averages are 4.57 years for the category 0-9 years. 14.16 for the category 10-19 years. and 39.72 for the category 20 years and over.


I . 2.

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TABLE A2 Number of Households in Each Expenditure Pattern

Positive Expenditures on Goods 1,2,3 2,3 1,3 1,2 1 2 3 Total

Melbourne 519 53 115 63 18 14 7 789 Sydney Recall 316 13 64 57 15 7 6 478 Sydney Diary 314 18 61 29 1 1 1 3 437

Notes: The indices 1,2,3 refer to three meat categories; beef, lamb, and “other” respectively. The beef category (1) comprises beef, veal, and beef sausage. In terms of the B.A.E. codes it

is defined as: 101-1 15, 201-209, and 603. The lamb category (2) comprises lamb and mutton. In terms of the B.A.E. codes it is

defined as: 301-313, and 401413. The other category (3) comprises pork, ham, bacon, poultry, game, seafood, offal, small

goods (e .g . , frankfurters), sausage (except beef sausage). In terms of the B.A.E. codes it is defined as: 501-509.801-806, 1101-1107, 1109, 1 1 10, 1201-1204, 1208, 121 I-1215,701-709, 901-903, 601, 602. and 604.

The items in these three meat categories include fresh, frozen and ready-to-eat (cooked) meat products only, all canned products are excluded. (Also, pet food is excluded as a meat product.)

REFERENCES K. J. Arrow and A. C. Enthoven, “Quasi-concave programming”, Econometrica, vol. 29, 1961. Bureau of Agricultural Economics, Household meat consumption in Sydney, Beef Research Report No. 3, December 1967, Canberra, A.C.T. Bureau of Agricultural Economics, Household meat consumption in Melbourne, Beef Research Report No. 8, July 1970, Canberra, A.C.T. B. S. Fisher, “The demand for meat-an example of an incomplete commodity demand system”, Australian Journal of Agricultural Economics, vol. 23, 1979. R. W. McShane, “Report on Australian meat industry”, mimeo., University of Newcastle, 1973. N. Podder. “Household consumption of food in Australia”, Australian Journal of Statistics, vol. 14, 1972. R. G. Reynolds, Retail demandfor meats in Australia: a study of the theory and application of consumer demand, M.Ec. Thesis, University of New England, 1978. C. W. Roberts and P. J. Neville. A survey of household meat consumption in Brisbane, Queensland Department of Primary Industries, June 1974. G. W. Taylor. “Beef consumption in Australia”. Quarter!,> Review of Agricultural Economics, vol. 14. 1961. J. van der Meulen, “Some quantitative relationships in meat marketing”, Review of Marketing and Agricultural Economics, vol. 29. 1961. T. J. Wales and A. D. Woodland, “A random preferences model for the estimation of consumer demand systems with binding non-negativity constraints”, Economics Department Discussion Paper No. 79-32, University of British Columbia, September 1979.

engel curves for meat consumption in australia

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