Modelling the meat consumption patterns in Australia

Economic Modelling 49 (2015) 1–10

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Modelling the meat consumption patterns in Australia☆ Lucille Wong, Eliyathamby A. Selvanathan, Saroja Selvanathan ⁎ Griffith Business School, Griffith University, Nathan, Queensland 4111, Australia

a r t i c l e

i n f o

Article history: Accepted 2 March 2015 Available online xxxx Keywords: Consumption patterns Meat group Demand theory hypotheses Elasticities Information inaccuracy

a b s t r a c t Meat plays an important role in Australia's food intake as Australians currently allocate 40% of their food expenditure on meat. This paper attempts to model the demand for the various types of meat in Australia using data from 1962 to 2011 and the system-wide approach to modelling. The paper considers a number of alternate models, verifies the validity of the demand model hypotheses and selects a preferred model using the information inaccuracy criterion. The paper then uses the preferred model to forecast meat demand in Australia under various economic policy scenarios. The results show that between 1962 and 2011, meat budget share has more than halved and that consumer taste plays a significant role in shifting the meat consumption in Australia to chicken and pork at the expense of beef and lamb. Beef is a luxury, while mutton, lamb, chicken and pork are necessities. Demand for mutton is price elastic and, beef, lamb, chicken and pork is price inelastic. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Meat consumption plays a major role in consumers' daily food intake. Australian consumers currently allocate about 10% of their income on food and 40% of their food expenditure on meat. This accounts for about 4% of their total consumption expenditure on all goods and services. Within the meat group, Australian consumers currently allocate 44% of the meat expenditure on beef, 12% on lamb, 20% on chicken, 24% on pork and very little on mutton. Furthermore, over the last 50 years, the Australian meat consumption pattern has changed significantly between the meat types due to changes in consumer taste as well as some supply-side regulations such as trade restrictions, change in meat classifications, etcetera. Australian consumers have increased their consumption of chicken and pork at the expense of beef, mutton and lamb. Therefore, an economic analysis using more recent data on the demand for meat in Australia to explain such changes in the consumption patterns is crucial to the meat producers, meat sellers, as well as meat consumers. This paper attempts to model the demand for the different types of meat, namely beef, lamb, mutton, chicken and pork, in Australia over the last five decades spanning the period 1962 to 2011. This study adopts the well-known system-wide approach (Theil and Clements, 1987) to achieve this purpose. Several publications that have appeared in the literature analyse the demand for meat in Australia, for example, see Alston and Chalfant (1991), Fisher (1979), Martin and Porter (1985), Cashin (1991), Piggott et. al. (1996) and, Hyde and Perloff (1998). Our study differs ☆ The authors would like to thank the editor of this journal and Professor Ken Clements of the University of Western Australia for their valuable comments on an earlier version of this paper. ⁎ Corresponding author. E-mail address: s.selvanathan@griffith.edu.au (S. Selvanathan).

http://dx.doi.org/10.1016/j.econmod.2015.03.002 0264-9993/© 2015 Elsevier B.V. All rights reserved.

from most of these studies in a number of ways: (1) The current study focuses on modelling the demand for meat by considering the systemwide approach and a number of alternate models; (2) time series properties of all variables used in the models are investigated before estimation; (3) tests various demand theory hypotheses for each model considered; (4) uses the most recent available data; and (5) uses simulations to predict what could happen to meat consumption in Australia under different policy scenarios. There are three basic reasons for the selection of a system-wide approach in this study. Firstly, the implication of the consumer's budget constraint is that any increase in expenditure on one good can only arise from a decreased expenditure of at least one other good. This underlying interrelationship between the consumption of the different types of meat can only be studied when the demand equations for all meat types are considered simultaneously. Secondly, there are certain constraints arising from consumption theories that necessitate the utilisation of a system of demand equations. The first is that demand equations are homogeneous of degree zero in income and prices, termed demand homogeneity. This property stipulates that an equal proportional change in a consumer's income and prices of the different meat types should have no effect on the quantities consumed; this translates to the assumption that the consumer is not subject to money illusion. The next is that, when the consumer's real income is held constant, the quantity change in the consumption of a good, arising from a onedollar increase in the price of a different good, will be exactly the same as the change in the consumption of the first good brought about by a one-dollar increase in the price of the latter good. This is termed Slutsky symmetry and when represented algebraically becomes a cross-equation constraint. As such, it is evident that only a systemwide approach will satisfy the constraints under Slutsky symmetry.

2

L. Wong et al. / Economic Modelling 49 (2015) 1–10

Besides, economic theories should not accept the taking of one good in isolation from the rest; thus, this study hopes to tell a common story for the five types of meat. It is only then that we can paint a complete picture of the demand conditions for all the five meat types. This study's aim is to model and present a detailed economic analysis of meat consumption patterns of Australian consumers. This paper is structured in the following manner. In Section 2, we present the data source and a preliminary analysis of the Australian meat data. In Section 3, under the system-wide framework, we use three popular demand systems, the Rotterdam Model, the Working's model and the Almost Ideal Demand System (AIDS) to model the meat consumption patterns in Australia. In Section 4, we select the preferred demand model among the three, using the goodness-of-fit measure, the information inaccuracy; and model consistency with the demand theory hypotheses. Section 5 presents the estimation results and the implied income and price elasticities from the preferred model. Using the estimated results from Section 5, we analyse the change in consumption patterns of the five meat types and show how these results can be used in policy related issues in Section 6. Finally, Section 7 provides the concluding comments. 2. Preliminary data analysis In this section, we present the sources for the Australian meat consumption data together with a preliminary data analysis. In the next section, we investigate a number of empirical regularities in Australian meat consumption patterns. 2.1. The data We use annual data for the five types of meat, namely, beef, lamb, mutton, chicken and pork, for the period 1962–2011. For the period, 1962–1977, the per capita consumption and price data are from Roberts (1990) and, for 1978–20111, from various issues of publications of the Meat and Livestock Australia and the Australian Bureau of Agricultural and Resource Economics and Sciences (ABARES). The continuity of the two data sets was checked and found to be consistent. Data for the consumer price index (6401.0 — Consumer Price Index, Australia), the total private final consumption expenditure (5206.0 — Australian National Accounts: National Income, Expenditure and Product) and Australian population (3101.0 Australian Demographic Statistics) are all from various issues of the Australian Bureau of Statistics publications. 2.2. Consumption and prices Table 1 presents the basic data for per capita consumption (qit) and prices (pit) for the five meat types for arbitrarily selected years. The left graph in Fig. 1 displays the per capita consumption of the five types of meat for the period 1962 to 2011. As can be seen, in general, overall meat consumption has increased over the period under study; consumption of pork and chicken have increased steadily and that of beef, lamb and mutton have fallen steadily. Australian per capita consumption of beef fell from 45.3 kg in 1962 to 38.6 kg in 1969; steadily increased to 70.4 kg in 1977; and then has again fallen steadily to 32.8 kg in 2011. This fall in domestic consumption in the sixties was due to strong world demand resulting in a high world price for beef which led to increased export; hence reducing the supply of beef to the domestic Australian market. This situation was reversed in the mid to late seventies due to the increased trade restrictions enacted by Australia's major export markets; resulting in increased supply of beef to the domestic Australian market. 1 Disaggregate price data for beef, lamb, mutton, chicken and pork are available only up to 2011.

Table 1 Consumption, prices, expenditure and budget shares for five types of meat, selected years, 1962–2011. Year

Beef

Lamb

Mutton

Chicken

Pork

Total meat

(1)

(2)

(3)

(4)

(5)

(6)

25.21 15.95 2.71 9.60 5.12 0.30

4.44 11.10 20.20 23.10 30.90 43.30

8.80 13.80 15.30 18.40 18.80 25.00

103 104 102 104 101 111

0.46 0.64 2.29 3.54 5.33 9.45

1.19 0.98 2.63 4.80 4.97 5.49

1.09 1.48 4.39 6.51 8.35 10.91

1.16 0.58 0.10 0.24 0.12 0.01

0.53 0.62 0.87 0.79 0.70 0.69

0.96 1.17 1.10 0.85 0.71 0.79

13.81 8.13 1.39 4.73 3.20 0.25

6.32 8.69 11.92 15.42 17.98 20.59

11.46 16.35 15.10 16.67 18.38 23.62

Per capita consumption (kg) 1962 45.30 19.30 1971 40.30 23.14 1981 47.60 16.49 1991 39.50 13.20 2001 34.50 11.75 2011 32.80 9.20 Prices ($/kg) 1962 0.94 1971 1.52 1981 5.42 1991 9.73 2001 12.25 2011 15.46

0.76 0.96 3.68 5.28 7.95 14.62

Unconditional budget shares (wit) 1962 4.27 1.48 1971 3.51 1.27 1981 4.23 0.99 1991 2.73 0.49 2001 1.92 0.42 2011 1.47 0.39 Conditional budget shares (w'it) 1962 50.78 17.63 1971 49.05 17.78 1981 57.96 13.64 1991 53.48 9.70 2001 49.51 10.93 2011 43.90 11.65

8.41 7.16 7.29 5.10 3.87 3.35

Per capita lamb consumption increased from 19.3 kg in 1962 to 23.6 kg in 1970 and then steadily declined to 9.2 kg in 2011, less than half of what it was in the 1960s. In the early 1970s, improvement in wool prices and the introduction of guaranteed floor price for wool, lead to reduced supply of lamb and mutton to the local Australian meat market as lamb stocks were withheld from slaughter. Australians consumed more mutton than lamb in the 1960s, but have reduced mutton intake over the years, falling from 25.2 kg per person, in 1962, to a low of 0.3 kg per person in 2011. In 2011, the per capita consumption of mutton and lamb combined has fallen to almost onefifth of what they were in the early 1960s. The fall in beef, lamb and mutton consumption has been mostly captured by chicken and pork. Per capita chicken consumption has increased by almost 10 times, from 4.4 kg in 1962 to 43.3 kg in 2011. Per capita pork consumption has also increased by about 3 times, from 8.8 kg in 1962 to 25.0 kg in 2011. While chicken consumption has increased steadily over the years, pork consumption has fallen slightly in the mid-1980s and increased steadily from then onwards. The graph on the right-hand side in Fig. 1 displays the retail prices in index form with base 1962 = 100 for 1962 to 2011. From the second half of Table 1, which presents the prices for the five types of meat, we can see that the retail price of beef has increased steadily over the years from $0.94/kg in 1962 to $15.46/kg in 2011. Over the same period, lamb price has increased from $0.76/kg to $14.62/kg, mutton price from $0.46 to $9.45/kg and pork price from $1.09/kg to $10.91/kg. Similarly, chicken price has increased from $1.19/kg in 1962 to $3.02/kg in 1987. Before 1987, only frozen chicken was supplied for consumption but from 1987 it was mostly replaced by fresh chicken. The price of fresh chicken has increased steadily from $4.80/kg in 1991 to $5.49/kg in 2011. Another point worth noting is that, prices of beef, lamb and mutton have increased at a faster rate than the prices of chicken and pork. The increase in the price of chicken is only moderate compared to all other types of meat.

L. Wong et al. / Economic Modelling 49 (2015) 1–10

80

2500

Per capita consumption

3

Price Indices (1962=100)

2000

60

Price index

Consumption (kg)

70

50 40 30 20

1500 1000 500

10 0 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010

1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010

0

Beef

Lamb

Chicken

Pork

Mutton

Beef

Lamb

Chicken

Pork

Mutton

Fig. 1. Per capita consumption and price indices (1962 = 100) of meat in Australia, five meat types, 1962–2011.

  and consumption growth rates Dpi −DP g and Dqi −DQ g for the five

2.3. Budget shares The lower two sections of Table 1 present the proportion of total expenditure and meat expenditure allocated to each meat type, namely, the unconditional and conditional budget shares, p q wit ¼ Xn it it ; p q j¼1 jt jt

i ¼ 1; …; n;

0

wit ¼ X

pit qit j∈Sg

p jt q jt

;

i∈Sg ¼ Meat group;

respectively, for the five meat types and the budget share for meat as a whole. As can be seen, consumer expenditure allocation on meat as a whole is on the decline; falling from 8.4% in 1962 to 3.4% in 2011. The proportion of total income spent on beef, lamb, mutton and pork (unconditional budget shares) has been declining while that of chicken has increased slightly during the sample period. This is evidenced in beef's share falling from 4.3% in 1962 to 1.5% in 2011; lamb from 1.5% to 0.4%; mutton from 1.2% to 0.01%; pork from 1.0% to 0.8%; in contrast, chicken's share rose from 0.5% to 0.7%. For meat, as a whole, the allocation of income has more than halved between 1962 and 2011. Within the meat group (conditional budget shares), in 2011, Australian consumers spent 44% of their meat expenditure on beef, 12% on lamb, 0.3% on mutton, 20.6% on chicken and the remaining 23.6% of their meat expenditure on pork. Clearly, within this group, chicken and pork have captured the falling market shares of beef, lamb and mutton. In recent years, there has been hardly any demand for mutton and, the demand for beef and lamb are competing against that for chicken and pork. 2.4. Divisia moments We summarize the price and quantity data in the form of Divisia index numbers and use them later in the estimation of the demand systems. The overall growth in prices and consumption of the meat group can be measured by the Divisia price and quantity indices which are defined as DP gt ¼

5 X i¼1

0

wit Dpit and DQ gt ¼

5 X

0

wit Dqit

meat types, averaged over the sample period. As can be seen, consumption per annum of beef, lamb and mutton has fallen at a rate of 0.7%, 1.5% and 9.0%, respectively, while that of chicken and pork have increased at a rate of 4.7% and 2.1%, respectively. The prices have all increased at a rate of 5.7%, 6.0%, 6.2%, 3.1% and 4.7%, respectively, per annum. While relative growth rates in consumption of beef, lamb and mutton are negative, their relative growth rates in prices are positive. The relative growth in the consumption of chicken and pork is positive while their relative price growth rates are negative.

3. The demand models In terms of differential demand systems, under the system-wide approach, the three most popularly utilised demand systems in applied demand analysis have been the Rotterdam demand system (Barten, 1964; Theil, 1965); the Working's (1943) parameterisation of the Rotterdam model, also termed the CBS demand system (Keller and van Driel, 1985) and the Almost Ideal Demand System, AIDS (Deaton and Muelbauer, 1980). In this section, we introduce the three demand systems to model Australian meat consumption and then test the demand theory hypotheses of homogeneity and symmetry. In the following section, we select, from the three, the preferred model. In Section 5, we present the estimation results and implied income and price elasticities for the five meat types from the preferred model. To cater for the impact of the events that occurred in the 1970s and 1980s discussed in Section 2, we include a dummy variable in each equation of the demand models.

Table 2 Average growth rates in consumption and prices, 1962–2011. Meat type

i¼1

where Dpit = ln(pit) − ln(pit − 1) and Dqit = ln(qit) − ln(qit − 1) are the  0  0 0
it ¼ ð1=2Þ wit þ wit−1 is the arprice and quantity log-changes, and w ithmetic average of the conditional budget shares in periods t and t − 1. Columns 2 and 3 of Table 2 present the average absolute price and consumption ðDpi and Dqi Þ and columns 4 and 5 present the relative price

Absolute

Relative

Consumption

Price

Consumption

Price

(1)

(2)

(3)

(4)

(5)

Beef Lamb Mutton Chicken Pork

−0.66 −1.51 −9.04 4.65 2.13

5.72 6.02 6.18 3.12 4.70

−0.70 −1.55 −9.08 4.61 2.09

0.40 0.70 0.86 −2.20 −0.62

4

L. Wong et al. / Economic Modelling 49 (2015) 1–10

3.1. Rotterdam model

3.2. CBS model

The basic specification of the Rotterdam model for good i∈Sg, in differentials, takes the form (see, for example, Theil, 1980; Selvanathan and Selvanathan, 1993; Selvanathan and Clements, 1995) 0

0

wit Dqit ¼ α i þ θi DQ gt þ

X j∈Sg

0

π i j Dp jt þ εit ; i∈Sg

ð1Þ

The basic specification of the CBS model, for good i is a re0

0

0

wit ðDqit −DQ gt Þ ¼ α i þ βi DQ gt þ

0

where wit ; Dqit ; Dpit and DQ gt are defined as before; and ai is the constant term of the ith demand equation satisfying ∑iαi = 0. The use of the constant terms in the demand equations is to take into account any trend-like changes in tastes, etcetera. The marginal share, θ'i, answers the question ‘if the meat group expenditure increases by one dollar, how much of this increase will be allocated to meat type i?’ and also 0

0

satisfies ∑iθ'i = 1. If θi bwit (or equivalently, income elasticity b 1), then meat type i will be classified as a necessity; otherwise it will be classified as a luxury. The coefficient π'ij is the (i,j)th Slutsky price coefficient which satisfies the adding-up restrictions X

0

i∈Sg

πi j ¼ 0;

0

j∈Sg

πi j ¼ 0;

i∈Sg :

X

0

πi j Dp jt þ εit ; i∈Sg ;

ð5Þ

j∈Sg

where ai is the constant term of the ith demand equation satisfying ∑i αi = 0. As above, the use of the constant terms in the demand equations is to take into account any trend-like changes in tastes and the like. The income coefficient β'i satisfies ∑i β'i = 0. As before, the coefficient π'ij is the (i,j)th Slutsky price coefficient; here as well, these coefficients satisfy the demand homogeneity and Slutsky symmetry properties given by Eqs. (2) and (3), respectively. The income and price elasticities implied by the demand system in Eq. (5) are given by 0

0

0 πi j β ηit ¼ 1 þ 0i and ηi jt ¼ 0 : wit wit

j∈Sg

0

and demand homogeneity X

0

0

parameterization of the Rotterdam model with θi ¼ βi þ wit , and in differentials takes the form (see, for example, Barten et al, 1989; Selvanathan and Selvanathan, 1993; and Selvanathan and Clements, 1995)

ð2Þ

ð6Þ

If β'i is negative (positive), then the commodity is classified as a necessity (luxury). 3.3. AIDS

Constraint (2) reflects the demand homogeneity property of the demand system that postulates that an equiproportionate change in all prices has no effect on the demand for any good under the condition that total meat consumption is held constant. The Slutsky coefficients are symmetric in i and j, that is 0

0

In differential form, Deaton and Muellbauer's (1980) AIDS takes the form 0

0

0

dwit ¼ α i þ βi DQ gt þ ∑ j∈Sg γ i j Dp jt þ vit ;

ð7Þ

i∈Sg

ð3Þ

where dw'it = w'it − w'it − 1. The right-hand side of the AIDS is very similar to the CBS model, but the left-hand side dependent variable,

which is known as Slutsky symmetry. In other words, when total meat consumption is held constant, the effect of an increase in the price of commodity j on the demand for commodity i is equal to the effect of a price increase of i on the demand for j. In other words, as the commodity subscripts can be interchanged, the substitution effects are symmetric in i and j. As well, the Slutsky matrix, [π'ij], is symmetric negative semidefinite with rank (ng − 1), where ng is the number of goods in group Sg. The term εit is the disturbance term of the ith equation. It is assumed that the disturbance terms, εit, i = 1, …, ng, are serially independent and normally distributed with zero means with a contemporaneous covariance matrix. Eq. (1) for i = 1, …, ng, is a fairly general demand system in the sense that it can be considered as a first-order approximation of the true demand equations. If we sum both sides of Eq. (1) over i = 1, …, ng, we obtain ∑i εit ¼ 0; for t ¼ 1; …T. Therefore, the εit values are linearly dependent and one of the equations becomes redundant and can be deleted (Barten, 1969). We delete the ng-th equation. It can be shown that the best linear unbiased estimators of the parameters for the system of Eq. (1) for i = 1, …, ng will be the same as those obtained by estimating each equation separately by least squares (LS). See Theil (1971) for details. The income and price elasticities implied by the demand system in Eq. (1) are given by

wit ðDqit −DQ gt Þgt ; is now the change in budget share, dw'it. The properties of αi and γ'ij are similar to those of the CBS model. Based on the AIDS given in Eq. (7), the income and price elasticities are given by

π i j ¼ π ji ;

0

ηit ¼

0

i; j∈Sg ;

0

πi j θi and ηi jt ¼ 0 : 0 wit wit 0

ð4Þ

If the income elasticity of good i is less (greater) than 1, then good i is classified as a necessity (luxury).

0

0

ηit ¼ 1 þ

0

βi 0 ; wit

0

ηiit ¼ −1 þ

0

0

0 γii 0 −β i wit

and

0

ηi jt ¼

γi j 0

w jt

0

−

0

βi =wit ; 0 w jt

i≠j : ð8Þ

3.4. Stationarity of the time series variables in the models As the variables we use to estimate the demand system are time series variables, before estimation, it is desirable to investigate whether the variables to be used in the demand system estimation are stationary. We use the Augmented Dicky–Fuller unit root test (Dickey and Fuller, 1979, 1981) for this purpose. The test results are presented in Table 3. As all p-values are close to 0, we can safely assume that all the variables to be used in the demand system are stationary. 3.5. Testing demand theory hypotheses We use the Demand Analysis Package, DAP2000 (Yang et al, 2000) and DEMMOD-3 (Barten et al, 1989) program to estimate the three demand systems given by Eqs. (1), (5) and (7). In the models, we have included a dummy variable, to take into account any impacts on consumption due to changes in trade restrictions; the high price of wool; the change from ‘frozen’ to fresh’ chicken meat; and the introduction of pig-meat imports from early to late 1980s.

L. Wong et al. / Economic Modelling 49 (2015) 1–10

5

Table 3 Testing for the stationarity of the demand system variables. τ-statistic

p-value

Stationarity (5% level)

0

−3.26

0

Yes

0

−6.42

0

Yes

0

−6.74

0

Yes

0

−8.55

0

Yes

0

−7.27

0

Yes

0

−5.5

0

0

−6.48

0

−7.06

0 0

Variable Dw1 Dw2 Dw3 Dw4 Dw5 w1 Dq1 w2 Dq2 w3 Dq3 w4 Dq4 w5 Dq5

τ-statistic

p-value

Stationarity (5% level)

−4.71

0

Yes

−5.67

0

Yes

−6.54

0

Yes

−6.13

0

Yes

−6.71

0

Yes

−4.00

0

Yes

Dp2

−5.01

0

Yes

Dp3

−5.57

0

Yes

Yes

Dp4

−4.73

0

Yes

Yes

Dp5

−3.88

0

Yes

DQg

−6.98

0

Yes

Yes

Variable  0  w1 Dq1 −DQ g  0  w2 Dq2 −DQ g  0  w3 Dq3 −DQ g  0  w4 Dq4 −DQ g  0  w5 Dq5 −DQ g Dp1

0

Yes

0

Yes

−4.98

0

−7.37

0

Testing demand homogeneity We now test the demand homogeneity hypothesis based on the estimation results of the three demand systems using the Australian meat data. For testing homogeneity, there are two tests available. The Wald test which is an asymptotic χ2 test with ng − 1 degrees of freedom and the other is a finite-sample test introduced by Laitinen (1978) based on Hotelling's T 2 distribution which is also a constant [(ng − 1)(T − ng − 2)/(T − 2ng )] multiple of the F distribution with ng − 1 and T − 2ng degrees of freedom. The results for the Australian meat data with ng = 5 meat types (and T = 49) are presented in Table 4. As can be seen from the table, based on the Wald test, the homogeneity hypothesis is acceptable for the Rotterdam model and the AIDS at the 5% level, and acceptable for all three models at the 1% level. The result for the CBS at the 5% level is not surprising as the asymptotic test has been found to be biased towards rejection of the null hypothesis (see, for example, Barten, 1977). When we apply Laitinen's finite sample test, homogeneity is acceptable at the 5% level for all three models.

the predicted budget shares from each model and then use them to calculate the goodness-of-fit measure, information inaccuracy, for each meat type and for meat as a whole. 0 0 Let w1t ; …; wng t be the observed budget shares of ng commodities in 0

0

^ 1t ; …; w ^ ng t be the predicted budget shares implied by the period t, and w demand model. The information inaccuracies for the predictions by meat type (i) is given by 0

wit I it ¼ wit log 0 ^ it w 0

!

0 !  0  1−wit þ 1−wit log ; i∈Sg ; 0 ^ it 1−w

ð9Þ

and the overall information inaccuracy for the predictions is given by It ¼

X i∈Sg

0 ! wit : wit log 0 ^ it w 0

ð10Þ

For testing symmetry, we use the asymptotic χ 2 test with q = (1/2)(ng − 1)(ng − 2) degrees of freedom (see Theil, 1971, for details). The results for the Australian meat data are presented in Table 5. As can be seen, symmetry is acceptable for all three models at the 5% level of significance. Therefore, we conclude that the homogeneity and symmetry hypotheses are both generally acceptable by all the three models; and, in the remaining sections of the paper, we consider models with homogeneity and symmetry imposed.

The information inaccuracies measure the extent to which the predicted budget shares (ŵ'it) differ from the corresponding observed budget shares (w'it). Both Iit and It are non-negative and the larger their observed value, the poorer is the quality of the predicted budget shares ŵ'1t, …, ŵ'nt. A naïve model of no-change extrapolation is one in which the current period prediction of w'it is specified as w'it − 1. That is, ŵ'it = w'it − 1. Table 6 presents the information inaccuracies, based on the three models and the no-change model, for the five meat types and total meat group. As can be seen, at the individual meat type level, looking at the best-fit column, CBS and AIDS perform equally. Considering the best-fit, CBS performs better than the other two models. Therefore, based on the goodness-of-fit measure, information inaccuracy, we conclude that the preferred model for modelling meat demand is CBS.

4. The preferred demand model

5. Estimates and implied elasticities

We select the preferred model among the three demand systems, Rotterdam in Eq. (1), CBS in Eq. (5) and AIDS in Eq. (7), by calculating

Table 7 presents the estimation results of the CBS model in Eq. (5) with homogeneity and symmetry imposed, and Table 8 gives the

Testing Slutsky symmetry

Table 4 Testing for demand homogeneity, Australian meat data, 1962–2011. Model

Wald test Test statistic

Rotterdam CBS AIDS

8.40 9.72 8.67

Laitinen's test Critical value

Decision

χ2(0.05,4)

χ2(0.01,4)

5% level

1% level

9.49 9.49 9.49

13.28 13.28 13.28

Do not reject Reject Do not reject

Do not reject Do not reject Do not reject

Test statistic

Critical

Decision

F(0.05,4,39)

5% level

1.95 2.25 2.01

2.61 2.61 2.61

Do not reject Do not reject Do not reject

6

L. Wong et al. / Economic Modelling 49 (2015) 1–10

Table 5 Testing for Slutsky symmetry given homogeneity, Australian meat data, 1962–2011. Model

Rotterdam CBS AIDS

Test statistic

8.69 11.09 9.56

Critical value

Decision

χ2(0.05,6)

5% level

12.6 12.6 12.6

Do not reject Do not reject Do not reject

implied income and price elasticities. As can be seen from Table 7, a majority of the coefficient estimates are statistically significant.2 The estimated constant terms for beef, lamb and mutton are negative but for chicken and pork are positive, indicating that there is an autonomous trend out of beef, lamb and mutton into chicken and pork.3 The dummy variable is positive and significant for beef, negative and significant for lamb and mutton but insignificant for both chicken and pork, indicating that export trade restriction on beef has increased local beef available for consumption and high wool prices have led to a reduction in lamb and mutton consumption. Changes in the availability of frozen/ fresh chicken and imported pork meat have made no significant difference in the consumption of chicken and pork. The income coefficient for beef is positive, indicating that it is a luxury, and the negative signs for the other meat types indicate that lamb, mutton, chicken and pork are necessities. Considering the implied income elasticities presented in Table 8, we can see that the income elasticity for beef is about 1.6 (N1), lamb 0.5 (b1), mutton 0.5 (b1), chicken 0.2 (b1) and pork 0.4 (b 1). Hence, among the 5 meat types, beef is a luxury and lamb, mutton, chicken and pork are necessities. All the own-price elasticities are negative as they should be; with beef about − 0.33, lamb − 0.79, mutton − 1.02, chicken − 0.23 and pork − 0.42. As the magnitude of mutton's own price elasticity is larger than one, demand for mutton appears to be price elastic and the absolute values of the own-price elasticity of all the other four meat types are less than one indicating that the demand for beef, lamb, chicken and pork is price inelastic. Among the cross-price elasticities (except for chicken–mutton, lamb–pork and chicken–pork), all are positive indicating that pork and chicken, lamb and pork, and mutton and chicken are pairwise complements and all other combinations are pairwise substitutes.

Table 6 Information inaccuracies Iit and It (×102)*. Meat type

Beef Lamb Mutton Chicken Pork Total meat

Rotterdam

CBS

AIDS

No-change

263 170 511 125 243 1080

249 166 515 109 249 1063

254 151 545 141 240 1102

563 266 614 379 332 1684

Best-fit

Second best-fit

CBS AIDS Rotterdam CBS AIDS CBS

AIDS CBS CBS Rotterdam Rotterdam Rotterdam

beef, lamb and mutton has fallen, from 45.3 kg to 32.8 kg, from 19.3 kg to 9.2 kg, and from 25.2 kg to 0.3 kg, respectively. During the same period, we also found that the conditional budget share of chicken has more than tripled (from 6.3% to 20.5%), pork has more than doubled (from 11.5% to 23.6%) while beef's share fell from 50.8% to 43.9%, lamb from 17.6% to 11.7% and mutton from 13.8% to 0.3%. In this section, we use the estimated results presented in Section 5 to analyse the change in consumption patterns of beef, lamb, mutton, chicken and pork and show how these results can be used in policy related issues. Here, we present three applications that we will utilise for the analysis. The first application shows how to decompose the growth in beef, lamb, mutton, chicken and pork consumption in terms of autonomous trend, income, own-price and cross-prices. The second application demonstrates how the change in budget shares of beef, lamb, mutton, chicken and pork can be decomposed in terms of autonomous trend, income, own-price and cross-prices. The third application shows how the consumption of beef, lamb, mutton, chicken and pork can be simulated under various economic policy scenarios. To perform these applications, we use the coefficient estimates presented in Tables 7 and 8 together with the consumption and price data. 6.1. Growth in meat consumption and its components Now we divide both sides of the demand system in Eq. (5) by the 0

budget share wit to give 

6. Impact of various policy scenarios on meat consumption

Demand model

0

0

Dqit ¼ α it þ ηi DQ gt þ ηii Dpit þ

4 X

0



ηi j Dp jt þ εit ; i ¼ 1; …; 5; t ¼ 1; …; T:

jð≠iÞ¼1

ð11Þ In Section 2, we noted that between 1962 and 2011, Australian per capita consumption of both chicken and pork has increased, from 4.4 kg to 43.3 kg and from 8.8 kg to 25 kg, respectively; while that for 2 To check the quality of our estimates and the stability of the model, as discussed in Theil et al (1983) and Theil and Clements (1987), we have used the bootstrap simulation technique developed by Efron (1979). We resample the residuals using the bootstrap technique and use them together with the observed values of the independent variables to generate pseudo values for the dependent variables. We then assume the “CBS” model as the true model and re-estimate the model with the pseudo values of the dependent variables together with the observed values of independent variables. We repeat this simulation process for 1000 trials and calculated the average of the 1000 simulated estimates and their bias and RMSEs. For the simulated estimates we also calculated the corresponding implied income and price elasticities over the sample period. We have used DAP2000 (Yang et al, 2000) for this purpose. We then compared the results presented in Tables 7 and 8 with the simulation results. The results show that the simulation estimates and the corresponding implied income and price elasticities are very close to the data-based estimates and income and price elasticities presented in Tables 7 and 8. This gives assurance on the quality and stability of the model estimates. 3 In addition to the income and price variables, in all demand systems, we have included a dummy variable to take into account the impact of trade restrictions on the consumption of different meat products. In addition, a constant term is added to each equation to take into account any trend-like changes in taste etc. The change in taste could be due to various reasons; one of them could be due to changes in the national economic conditions such as economic expansion or recession. The results show that there is an autonomous trend out of beef, lamb and mutton (which are the expensive meat types throughout the sample period) into chicken and pork (which are the cheap meat types throughout the sample period).

0

where α it ¼ α i =wit is the autonomous trend in consumption of item i and η'i and η'ij are income and price elasticities. Therefore, growth in consumption of item i (Dqit) in each year can be decomposed into the following five components, namely, (1) Autonomous trend component (αit⁎); (2) Income component (η'iDQgt); (3) Own-price component (η'iiDpit); (4) Cross-price component (∑5j(≠i) = 1η'ijDpjt); and (5) Residual component (εit⁎). Table 9 presents the decomposition of Dqit into the five components at sample means for beef, lamb, mutton, chicken and pork. Row 1 of the table reveals that, on average, the total growth in beef consumption has declined at a rate of 0.7% per annum. This total growth is made up of the following: (1) autonomous trend, − 0.68%; (2) dummy, 0.23%; (3) income component, 0.06%; (4) own-price component − 1.89%; (5) cross-price component, 1.68%; and the (6) residual component, − 0.06%. The two components, those of the own- and cross-prices almost cancel each other out, leaving the autonomous trend as the dominant component resulting in a negative growth in beef consumption. The same outcome can be seen with both lamb and mutton. Changes in consumer preferences have negatively affected beef, lamb and mutton consumption. The positive consumption growth for chicken and pork can be attributed mostly to changes in consumer preferences together with the increased prices of beef, lamb and mutton.

L. Wong et al. / Economic Modelling 49 (2015) 1–10

7

Table 7 Estimation results, CBS model, Australian meat data, 1962–2011. (Standard errors are in parentheses). Meat type

Constant

Dummy

Income coefficient

(1)

(2)

Beef

−0.004⁎(0.002)

0.058⁎ (0.012)

0.290⁎ (0.048)

Lamb Mutton Chicken Pork

−0.001 (0.001) −0.003⁎(0.001) 0.004⁎(0.001) 0.002⁎(0.001)

−0.037⁎ (0.008) −0.027⁎ (0.009) −0.0009 (0.0060) 0.006 (0.010)

−0.068⁎ (0.027) −0.023 (0.027) −0.102⁎ (0.0215) −0.098⁎ (0.027)

(3)

(4)

Price coefficients Beef

Lamb

Mutton

Chicken

Pork

(5)

(6)

(7)

(8)

(9)

−0.173⁎ (0.033)

0.062⁎ (0.0189) −0.102⁎ (0.036)

0.008 (0.018)

0.036⁎ (0.013)

0.067⁎ (0.022)

0.034 (0.033) −0.046 (0.036)

0.009 (0.010) −0.008 (0.011) −0.031⁎ (0.010)

−0.002 (0.017) 0.01 (0.017) −0.007 (0.011) −0.070⁎ (0.02)

⁎ Statistically significant at the 5% level.

6.2. Decomposition in the change in the budget shares In finite changes, the budget share, w'it = pitqit/Mgt, can be expressed as (see Clements and Johnson, 1983) 0

0

0

0

Δwit ¼ wit Dqit þ wit ðDpit −DPgtÞ−wit DQ gt þ o3 ;

i ¼ 1; …; 5; t ¼ 1; …; T

ð12Þ where Δw'it = (w'it − w'i,t − 1); DQgt + DPgt = DMgt and o3 is a remainder term of the third degree (see Theil, 1975/76, pp 37–40 and 215). If we 0

substitute wit Dqit from Eq. (1), Eq. (12) becomes 5  0 X 0 0  0 0 Δwit ¼ α i þ θi −wit DQ gt þ πi j Dp jt þ wit ðDpit −DPgt Þ

ð13Þ

j¼1

þ o3 þ ε it ;

i ¼ 1; …; 5; t ¼ 1; …; T:

Eq. (13) shows that The change in budget share of item i ¼ autonomous trend component; ai  0 0  þ income component; θi −wit DQ gt 0

þ own−price components; πii Dpit þ cross−price component; X5 0 π Dp jt jð≠iÞ¼1 i j

ð14Þ

prices have affected negatively on their shares, while cross-price substitution has helped to offset the negative impacts on their budget shares. For chicken and pork, the change in consumer preference and crosssubstitution favoured greatly while some negative contribution was a result of the change in their own prices. Why has chicken consumption grown while lamb consumption declined? Now we simulate beef, lamb, mutton, chicken and pork consumption under different scenarios to isolate the key factors that are responsible for the growth in chicken and pork consumption and the decline in beef, lamb and mutton consumption in Australia. It is an interesting policy issue to investigate what happens to the consumption of beef, lamb, mutton, chicken and pork, for example, (a) if consumer preferences didn't change (that is, each constant term in the demand equation is equal to 0); (b) if total meat consumption does not grow (that is, DQsgt = 0 for any period t); and (c) if total meat consumption grew at a rate of 0.5% per annum instead of the actual observed average growth rate of DQ g ¼ 0:04% (that is, DQsgt = 0.5 % for any period t). What if consumer preferences did not change? 0

If we divide both sides of demand Eq. (1) by the budget share, wit ; the demand equation takes the form 0



Dqit ¼ α it þ ηi DQ gt þ

5 X

0



ηi j Dp jt þ εit ;

i ¼ 1; …; 5; t ¼ 1; …; T: ð15Þ

j¼1

þ direct relative price component; 0

If the simulated consumption log-change corresponding to scenario (a) that there is no change in consumer preference is Dqsit, then

wit ðDpit −DPgt Þ þ the residual component:

The estimated values of these components at sample means are presented in Table 10. Looking at the first row of the table, on average, the budget share of beef has declined by 0.14 percentage points per annum. The major contributors for this fall are the shift in consumer preferences against beef (− 0.357%) and increase in its own price (− 0.991%). Even though income (0.119%) and cross price effects (0.379 + 0.065 + 0.115 + 0.321 = 0.88%) had a positive influence on the change in its budget share, the negatives had an upper hand. For lamb and mutton, changes in consumer preferences, income and own-

0

5 X

0



ηi j Dp jt þ εit ; i ¼ 1; …; 5; t ¼ 1; …; T:

ð16Þ

j¼1

Therefore, from Eqs. (15) and (16), we get s



Dqit ¼ Dqit −α it

i ¼ 1; …; 5; t ¼ 1; …; T:

ð17Þ

Next, using Eq. (17), we calculate the simulated consumption by converting changes to levels  s s s s qit ¼ qit−1 exp Dqit with qi;1962 ¼ qi;1962 ;

Table 8 Implied income and price elasticities, CBS model. Meat type

s

Dqit ¼ 0 þ ηi DQ gt þ

i ¼ 1; …; 5; t ¼ 1; …; T: ð18Þ

Income elasticity

Price elasticities Beef

Lamb

Mutton

Chicken

Pork

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Beef Lamb Mutton Chicken Pork

1.55 0.48 0.49 0.23 0.42

−0.33 0.47 0.18 0.27 0.40

0.12 −0.79 0.75 0.07 −0.01

0.02 0.26 −1.02 −0.06 0.07

0.07 0.07 −0.17 −0.23 −0.04

0.13 −0.02 0.26 −0.05 −0.42

The simulated consumptions for beef, lamb, mutton, chicken and pork, using Eqs. (17) and (18) together with the estimates of the αi ' s from Table 7 are presented in columns (7)–(11) of Table 11. For comparison, the actual consumption is also presented in columns (2)–(6) of the same table. Looking at columns (7)–(11) of the table, it can be seen that the simulated per capita consumption of beef, lamb, mutton, chicken and pork for the year 2011 is 45.79 kg, 12.23 kg, 5.11 kg, 8.07 kg and 12.75 kg, respectively. Accordingly, in 2011, the

8

L. Wong et al. / Economic Modelling 49 (2015) 1–10

Table 9 Decomposition of change in consumption of beef, lamb, mutton, chicken and pork. Australia, 1962–2011 (at sample means). Item, i

Total growth (Dqi)

Components of growth in the consumption of item i Autonomous trend

Dummy

Income

Own-price

Cross-price

Residual

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Beef Lamb Mutton Chicken Pork

−0.660 −1.510 −9.040 4.650 2.130

−0.681 −0.536 −5.783 3.429 1.373

0.226 −0.580 −1.215 −0.013 0.077

0.062 0.019 0.020 0.009 0.017

−1.888 −4.756 −6.304 −0.718 −1.974

1.675 4.420 6.236 1.360 2.536

−0.055 −0.077 −1.994 0.582 0.101

shift in consumer preferences resulted in beef consumption being about (45.79 − 32.80)/45.79 = 28.4% lower than otherwise; lamb to be (12.23 − 9.20)/12.23 = 24.8% lower than otherwise; mutton to be (5.11 − 0.03)/5.11 = 94.1% lower than otherwise; chicken to be (8.07 − 43.30)/8.07 = 437% higher than otherwise; and pork to be (12.75 − 25.0)/12.75 = 96% higher than otherwise. What if total meat consumption does not grow? If the simulated consumption log-change corresponded to the scenario (b) of no change in total meat consumption (that is, DQsgt = 0) is Dqsit, then s



Dqit ¼ α it þ 0 þ

5 X

0



ηi j Dp jt þ εit ;

i ¼ 1; …; 5; t ¼ 1; …; T:

ð19Þ

j¼1

Therefore, from Eqs. (15) and (19) we get 0

s

Dqit ¼ Dqit −ηi DQ gt



0

ð22Þ

We evaluate the simulated consumption as before using Eqs. (18) and (22). Columns (17)–(21) of Table 11 present the simulated consumption. As can be seen, the simulated per capita consumption of beef, lamb, mutton, chicken and pork for the year 2011 is 46.6 kg, 10.25 kg, 0.34 kg, 45.64 g and 27.5 kg, respectively. Accordingly, in 2011, a 0.5% growth in the total meat consumption would have caused beef consumption to be about (46.62 − 32.80)/32.80 = 42.1% higher than otherwise; lamb to be (10.25 − 9.20)/9.20 = 11.4% higher than otherwise; mutton to be (0.34 − 0.30)/0.30 = 13.3% higher than otherwise; chicken to be (45.64 − 43.30)/43.30 = 5.4% higher than otherwise; and pork to be (27.50 − 25.00)/25.00 = 10.0% higher than otherwise. 7. Concluding comments

We evaluate the simulated consumption as before, using Eqs. (18) and (20). Columns (12)–(16) of Table 11 present the simulated consumption. As can be seen, the simulated per capita consumption of beef, lamb, mutton, chicken and pork for the year 2011 is 31.89 kg, 9.12 kg, 0.298 kg, 43.14 kg and 24.89 kg, respectively. Accordingly, zero growth in the total meat consumption would have caused beef consumption to be about (31.89 − 32.80)/32.80 = 2.8% lower than otherwise; lamb to be (9.12 − 9.20)/9.20 = 0.9% lower than otherwise; mutton to be (0.298 − 0.30)/0.30 = 0.7% lower than otherwise; chicken to be (43.14 − 43.30)/43.30 = 0.4% lower than otherwise; and pork to be (24.89 − 25.00)/25.00 = 0.4% lower than otherwise. What if total meat consumption grew at a rate of 0.5% per annum? If the simulated consumption log-change corresponded to scenario (c) of a growth rate in total consumption of the meat group of 0.5% per annum (that is, DQsgt = 0.5) is Dqsit, then s

 0 s Dqit ¼ Dqit þ ηi 0:5−DQ gt ; i ¼ 1; …; 5; t ¼ 1; …; T:

ð20Þ

i ¼ 1; …; 5; t ¼ 1; …; T:

Dqit ¼ α it þ ηi ð−0:5Þ þ

Therefore, from Eqs. (15) and (21), we get

5 X

0



ηi j Dp jt þ εit ;

i ¼ 1; …; 5; t ¼ 1; …; T:

j¼1

ð21Þ

In this paper, we have modelled Australian meat demand under a system-wide framework, using data from 1962 to 2011 for the 5 meat types, beef, lamb, mutton, chicken and pork. According to the statistics published for 2011, Australians consume about 111 kg of meat per person composed of 33 kg of beef, 9 kg of lamb, 43 kg of chicken and 25 kg of pork. In recent years, Australian consumers allocated about 4% of their budget to the purchase of meat. Within their expenditure on meat, they allocate about 44% on beef, 12% on lamb, 21% on chicken and 24% on pork with very little or none on mutton. In the last 50 years, in terms of market share, chicken and pork have increased their share by 3 and 2 times, respectively, at the expense of beef, lamb and mutton. Mutton share was 13.8% in 1962 and has been almost eradicated by 2011. The retail prices of all five meat types have steadily increased over the last 50 years with beef, lamb and mutton prices increasing at a faster rate than that of chicken and pork. We used three well-known demand systems under system-wide framework, namely, the Rotterdam model, the CBS model and the AIDS to model the demand for meat in Australia and tested the two demand theory hypotheses, demand homogeneity and Slutsky symmetry.

Table 10 Decomposition of changes in budget shares of beef, lamb, mutton, chicken and pork Australia, 1962–2011 (at sample means). Item, i

Change in the budget share Δwi × 100

Components of Δwi × 100 Trend

Dummy

Income

Price substitution Beef

Lamb

Mutton

Chicken

Pork

Direct relative price

Residuals

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Beef Lamb Mutton Chicken Pork

−0.140 −0.122 −0.277 0.291 0.248

−0.357 −0.070 −0.259 0.454 0.231

0.119 −0.075 −0.054 −0.002 0.013

0.012 −0.003 −0.001 −0.004 −0.004

−0.991 0.349 0.046 0.205 0.385

0.379 −0.617 0.202 0.056 −0.010

0.065 0.209 −0.282 −0.049 0.073

0.115 0.028 −0.024 −0.095 −0.021

0.321 −0.012 0.055 −0.031 −0.332

0.210 0.091 0.038 −0.292 −0.104

−0.012 −0.022 0.002 0.049 0.018

Table 11 Actual and simulated consumption of beef, lamb, mutton, chicken and pork, Australia, 1962–2011. Year

Actual consumption

Simulated consumption with no preference

Simulated consumption with meat group growth rate = 0% per annum

Simulated consumption with meat group growth rate = 0.5% per annum

Lamb

Mutton

Chicken

Pork

Beef

Lamb

Mutton

Chicken

Pork

Beef

Lamb

Mutton

Chicken

Pork

Beef

Lamb

Mutton

Chicken

Pork

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Mean

45.30 47.50 45.00 42.00 38.60 40.70 41.30 38.60 39.60 40.30 40.40 43.60 55.00 62.00 66.37 70.35 65.87 50.44 45.30 47.60 49.30 42.30 44.30 40.10 41.40 39.90 41.20 43.20 40.10 39.50 37.20 37.00 38.80 35.00 39.30 41.30 38.30 37.90 37.70 34.50 36.90 37.70 37.60 36.70 37.80 37.00 33.80 33.80 34.90 32.80 42.46

19.30 18.97 18.49 16.30 18.67 19.44 21.88 22.47 23.56 23.14 22.63 16.88 17.19 16.33 15.59 15.57 15.77 15.77 15.98 16.49 16.41 17.15 17.27 17.12 15.27 15.14 15.13 14.97 14.33 13.20 12.37 11.68 12.14 11.48 10.96 11.01 11.37 11.50 12.62 11.75 11.29 10.43 10.38 10.05 10.81 11.56 10.63 10.46 9.64 9.20 14.95

25.21 23.39 20.49 20.13 17.44 17.48 17.15 16.21 13.73 15.95 13.99 7.49 8.77 8.34 5.90 4.02 3.92 3.92 3.82 2.71 4.29 3.75 5.23 7.58 7.64 8.16 6.47 7.73 8.47 9.60 8.13 7.72 7.45 5.73 5.83 6.03 6.03 6.08 5.70 5.12 4.04 3.18 3.13 2.98 3.09 2.64 1.81 1.30 0.58 0.30 8.12

4.44 4.43 5.20 6.20 7.40 8.40 9.00 10.50 10.40 11.10 12.30 13.00 13.40 13.40 14.40 15.60 16.60 18.70 20.10 20.20 19.40 20.20 19.80 21.60 22.80 23.20 21.70 21.90 22.40 23.10 23.50 25.30 25.90 25.40 25.70 27.00 28.90 29.40 31.10 30.90 34.40 33.10 34.80 35.70 37.40 37.00 35.80 36.20 40.80 43.30 21.85

8.80 8.50 8.80 9.50 9.80 10.10 10.80 11.30 13.60 13.80 14.60 16.00 13.10 11.70 12.10 13.00 13.30 13.50 15.50 15.30 14.80 15.90 16.40 16.70 17.20 17.30 17.50 17.70 18.30 18.40 19.30 19.00 20.00 19.80 18.40 18.80 19.30 19.20 19.80 18.80 20.70 22.10 22.30 23.80 23.30 25.60 24.30 25.10 25.80 25.00 16.87

45.30 47.82 45.61 42.86 39.66 42.10 43.02 40.48 41.82 42.84 43.25 46.99 59.68 67.74 73.00 77.92 73.45 56.63 51.21 54.18 56.50 48.81 51.46 46.90 48.75 47.31 49.18 51.92 48.52 48.12 45.63 45.69 48.24 43.82 49.54 52.41 48.94 48.76 48.83 44.99 48.45 49.84 50.05 49.18 51.00 50.26 46.23 46.55 48.39 45.79 49.91

19.30 19.49 19.10 16.93 19.49 20.41 23.10 23.84 25.13 24.82 24.40 18.30 18.74 17.89 17.17 17.24 17.57 17.66 17.99 18.66 18.67 19.62 19.86 19.79 17.74 17.69 17.77 17.68 17.01 15.76 14.85 14.09 14.73 14.00 13.44 13.57 14.09 14.33 15.81 14.80 14.30 13.28 13.29 12.93 13.99 15.04 13.90 13.75 12.74 12.23 17.16

25.21 24.76 22.99 23.93 21.97 23.32 24.25 24.30 21.79 26.82 24.93 14.15 17.54 17.68 13.25 9.56 9.89 10.47 10.82 8.12 13.64 12.62 18.64 28.67 30.58 34.60 29.09 36.82 42.75 51.34 46.08 46.35 47.40 38.62 41.63 45.63 48.35 51.65 51.30 48.83 40.81 34.05 35.50 35.81 39.34 35.62 25.87 19.69 9.31 5.11 28.43

4.44 4.28 4.86 5.60 6.45 7.08 7.33 8.27 7.91 8.16 8.73 8.92 8.88 8.59 8.91 9.33 9.60 10.44 10.85 10.53 9.78 9.84 9.32 9.82 10.02 9.85 8.90 8.68 8.58 8.55 8.40 8.74 8.65 8.20 8.01 8.13 8.41 8.27 8.45 8.12 8.73 8.12 8.25 8.17 8.27 7.91 7.40 7.23 7.87 8.07 8.32

8.80 8.38 8.56 9.12 9.27 9.42 9.94 10.26 12.18 12.19 12.72 13.76 11.11 9.79 9.98 10.58 10.67 10.69 12.10 11.78 11.24 11.91 12.12 12.17 12.37 12.27 12.24 12.21 12.46 12.35 12.78 12.41 12.89 12.58 11.53 11.62 11.77 11.55 11.75 11.00 11.95 12.58 12.52 13.18 12.73 13.80 12.92 13.16 13.34 12.75 11.63

45.30 46.96 46.94 46.42 43.83 42.93 40.83 39.05 37.92 37.14 36.89 41.55 44.35 46.71 47.32 46.80 45.86 43.92 41.64 42.04 42.35 40.30 39.87 37.85 38.19 37.66 38.85 38.67 37.75 37.48 37.21 37.10 36.55 36.95 38.74 38.27 36.52 36.23 34.90 35.36 34.48 35.07 34.54 33.68 33.28 32.00 32.88 32.69 32.32 31.89 39.08

19.30 18.90 18.72 16.80 19.41 19.75 21.80 22.54 23.23 22.55 21.99 16.63 16.08 14.95 14.03 13.72 14.10 15.10 15.56 15.86 15.65 16.89 16.71 16.80 14.88 14.87 14.85 14.46 14.06 12.98 12.36 11.68 11.91 11.67 10.91 10.75 11.20 11.34 12.32 11.83 11.05 10.19 10.11 9.78 10.39 11.05 10.53 10.35 9.41 9.12 14.62

25.21 23.29 20.76 20.77 18.15 17.76 17.08 16.27 13.53 15.53 13.59 7.38 8.19 7.62 5.30 3.53 3.50 3.75 3.72 2.60 4.09 3.69 5.05 7.45 7.44 8.00 6.35 7.46 8.31 9.44 8.13 7.72 7.31 5.83 5.80 5.88 5.94 5.99 5.56 5.16 3.95 3.11 3.05 2.90 2.97 2.52 1.79 1.29 0.57 0.30 8.01

4.44 4.42 5.23 6.30 7.54 8.48 8.99 10.53 10.33 10.97 12.14 12.91 12.99 12.86 13.70 14.69 15.74 18.33 19.86 19.84 18.98 20.07 19.50 21.43 22.54 23.02 21.52 21.56 22.21 22.93 23.51 25.32 25.68 25.62 25.66 26.71 28.71 29.22 30.76 31.03 34.07 32.76 34.38 35.27 36.72 36.23 35.67 36.04 40.36 43.14 21.62

8.80 8.48 8.86 9.64 9.98 10.17 10.78 11.32 13.51 13.63 14.40 15.89 12.69 11.22 11.50 12.24 12.60 13.23 15.30 15.02 14.47 15.78 16.14 16.55 16.99 17.15 17.35 17.41 18.14 18.26 19.30 19.01 19.82 19.96 18.36 18.59 19.16 19.07 19.57 18.87 20.49 21.86 22.02 23.50 22.86 25.05 24.20 24.97 25.50 24.89 16.69

45.30 47.33 47.68 47.51 45.21 44.63 42.78 41.22 40.35 39.82 39.86 45.25 48.68 51.66 52.74 52.57 51.92 50.11 47.87 48.71 49.45 47.42 47.29 45.24 45.99 45.71 47.52 47.67 46.90 46.92 46.95 47.17 46.84 47.72 50.42 50.20 48.28 48.27 46.85 47.84 47.02 48.19 47.83 47.00 46.80 45.35 46.97 47.06 46.89 46.62 47.03

19.30 18.94 18.81 16.93 19.60 19.99 22.11 22.92 23.68 23.04 22.53 17.07 16.54 15.43 14.51 14.22 14.65 15.73 16.25 16.60 16.42 17.76 17.62 17.76 15.76 15.78 15.81 15.42 15.03 13.91 13.29 12.59 12.86 12.63 11.83 11.69 12.21 12.39 13.49 12.99 12.16 11.25 11.18 10.85 11.54 12.31 11.76 11.58 10.56 10.25 15.39

25.21 23.35 20.86 20.92 18.33 17.98 17.34 16.55 13.80 15.88 13.92 7.58 8.43 7.87 5.48 3.66 3.64 3.91 3.89 2.73 4.29 3.88 5.33 7.88 7.89 8.51 6.77 7.97 8.90 10.13 8.75 8.33 7.91 6.32 6.31 6.41 6.49 6.56 6.10 5.68 4.36 3.44 3.38 3.22 3.30 2.82 2.01 1.44 0.64 0.34 8.33

4.44 4.43 5.25 6.32 7.57 8.53 9.05 10.61 10.43 11.09 12.28 13.08 13.17 13.05 13.92 14.95 16.03 18.69 20.27 20.28 19.42 20.56 20.00 22.00 23.17 23.69 22.18 22.23 22.94 23.71 24.34 26.24 26.65 26.61 26.68 27.81 29.93 30.49 32.14 32.45 35.68 34.35 36.08 37.05 38.62 38.15 37.61 38.04 42.65 45.64 22.41

8.80 8.49 8.94 9.82 10.23 10.35 10.90 11.50 13.67 13.75 14.54 16.16 12.67 11.13 11.37 12.01 12.47 13.48 15.73 15.39 14.81 16.40 16.69 17.25 17.69 17.95 18.19 18.18 19.09 19.28 20.56 20.29 21.05 21.53 19.68 19.82 20.55 20.50 21.00 20.54 22.10 23.62 23.80 25.45 24.69 27.05 26.56 27.45 27.95 27.50 17.57

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Beef (1)

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In general, both hypotheses were acceptable by all three models. We then used the goodness of fit measure, information inaccuracy, to select the preferred model and found that the CBS model performed better than the Rotterdam model and the AIDS. We also presented the CBS model estimates and the implied income and price elasticities. The results showed that beef is a luxury while mutton, lamb, chicken and pork are necessities. The demand for mutton is price elastic and that for beef, lamb, chicken and pork is price inelastic. We also found that chicken and pork, lamb and pork, and chicken and mutton are pairwise complements while all other pairs are pairwise substitutes. Using the income and price elasticity estimates, we also simulated per capita consumption of beef, lamb, mutton, chicken and pork under various policy scenarios. Simulation results show that change in consumer taste has played a significant role in Australian meat consumption where consumers shifted their preferences mostly from beef, lamb and mutton to chicken and pork during the last fifty years. References Alston, J.M., Chalfant, J.A., 1991. Can we take the con out of meat demand studies? Western Journal of Agricultural Economics 16 (1), 36–48. Barten, A.P., 1964. Consumer demand functions under conditions of almost addictive preferences. Econometrica 32, 1–38. Barten, A.P., 1969. Maximum likelihood estimation of a complete system of demand equations. Eur. Econ. Rev. 1, 7–73. Barten, A.P., 1977. The systems of consumer demand functions approach: a review. Econometrica 45, 23–51. Barten, A.P., Bettendorf, L., Meyermans, E., Zonderman, P., 1989. Users' Guide to DEMMOD-3. Kathlieke Universiteit Leuven, Belgium. Cashin, P., 1991. A Model of the Disaggregated Demand for Meat in Australia. Australian Journal of Agricultural Economics 35 (3), 263–283. Clements, K.W., Johnson, L.W., 1983. The demand for beer, wine and spirits: a systemwide analysis. J. Bus. 56, 273–304. Reprinted in. Coyne, T.J. (Ed.), 1985. Reading in Managerial Economics, 4th ed. Business Publications, Inc., Plano, Texas, pp. 127–155.

Deaton, A.S., Muellbauer, J., 1980. Economics and Consumer Behaviour. Cambridge University Press, Cambridge, USA. Dickey, D., Fuller, W.A., 1979. Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc. 74, 427–431. Dickey, D., Fuller, W.A., 1981. Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, 1057–1072. Efron, B., 1979. Bootstrap methods: another look at the jackknife. Ann. Stat. 7, 1–26. Fisher, B.S., 1979. The Demand for Meat - an Example of an Incomplete Commodity Demand System. Australian Journal of Agricultural Economics 23 (3), 220–230. Hyde, C.E., Perloff, J.M., 1998. Multimarket market Power Estimation: The Australian Retail Meat Sector. Applied Economics 30 (9), 1169–1176. Keller, W.J., van Driel, J., 1985. Differential consumer demand systems. Eur. Econ. Rev. 27, 375–390. Laitinen, K., 1978. Why is demand homogeneity so often rejected? Econ. Lett. 1, 187–191. Martin, W., Porter, D., 1985. Testing for Changes in the Structure of the Demand for Meat in Australia. Australian Journal of Agricultural Economics 29 (1), 16–31. Piggott, N.E., Chalfant, J.A., Alston, J.A., Griffith, G.R., 1996. Demand Response to Advertising in the Australian Meat Industry. American Journal of Agricultural Economics 78 (2), 268–279. Roberts, J., 1990. The Demand for Meat, Discussion Paper No.90-11. Department of Economics, The University of Western Australia. Selvanathan, E.A., Clements, K.W., 1995. Recent Developments in Applied Demand Analysis. Springer-Verlag, Berlin, Germany. Selvanathan, S., Selvanathan, E.A., 1993. A cross-country analysis of consumption patterns. Appl. Econ. 25, 1245–1259. Theil, H., 1965. The information approach to demand analysis. Econometrica 33, 67–87. Theil, H., 1971. Principles of Econometrics. John Wiley and Sons, New York, USA. Theil, H., 1975/76. Theory and Measurement of Consumer Demand. Two volumes. NorthHolland Publishing Company, Amsterdam. Theil, H., 1980. The System-wide Approach to Microeconomics. The University of Chicago Press, Chicago, USA. Theil, H., Clements, K.W., 1987. Applied Demand Analysis: Results from System-Wide Approaches. Ballinger Publishing Company, Cambridge, Massachusetts. Theil, H., Finke, R., Rosalsky, M.C., 1983. Verifying a demand system by simulation. Econ. Lett. 13, 15–18. Working, H., 1943. Statistical laws of family expenditure. J. Am. Stat. Assoc. 38, 43–56. Yang, W., Clements, K.W., Chen, D., 2000. The demand analysis package. In: Selvanathan, E.A., Selvanathan, S. (Eds.), International Counsumption Comparisons: OECD versus LDC. World Scientific, pp. 295–320.