Changing Pattern of Meat Consumption in Australia

Transcription

1 May 213 Chanin Pattern of Meat Consumption in Australia by Lucille Won, E A Selvanathan and Saroja Selvanathan Griffith Business School Griffith University Nathan, Queensland 4111 AUSTRALIA Abstract: The objective of this paper is to present a systematic analysis of the Australian meat demand usin data for the period 1962 to 211 for 5 types of meat, namely beef, lamb, mutton, chicken and pork, under a system-wide framework usin three demand system, Rotterdam, CBS and AIDS. In 211, Australians consumed around 111k of meat per person divided into 33k of beef, 9k of lamb, 43k of chicken and 25k of pork. Australian consumers allocate about 4 percent of their budet to the purchase of meat. Within their expenditure on meat, they allocate about 44 percent on beef, 12 percent on lamb, 21 percent on chicken and 24 percent on pork with very little or none on mutton. In terms of market share, chicken and pork have increased their share by 3 and 2 times, respectively, in the last 5 years at the expense of beef, lamb and mutton. Mutton share was 13.8 percent in 1962 and has been almost wiped out in 211. The retail prices of all five meat types has steadily increased over the last 5 years with beef, lamb and mutton prices increased at faster rate than the prices increase of chicken and pork. The paper also found support four empirical reularities in consumer demand, namely, quantity variance exceeds price variance; demand curve slopes downwards; income flexibility tends towards -.5; and, budet share of food declines with increasin income. In eneral, the two demand theory hypotheses, demand homoeneity and Slutsky symmetry were found to be acceptable for the meat data. The implied income and price elasticities show that beef is a luxury while mutton, lamb, chicken and pork are necessities. The demand for mutton is price elastic and demand for beef, lamb, chicken and pork are price inelastic. We also found that chicken and pork are pairwise complements while all other pairs are pairwise substitutes. 1

2 1. Introduction Meat consumption plays a major role in consumer s daily food intake. Australian consumers currently allocate about 4 percent of their food expenditure allocation on meat. This also accounts for about 4 percent of their total consumption expenditure on all oods and services. Within the meat roup, Australian consumers currently allocate 44 percent of the meat expenditure on beef, 12 percent on lamb, 2 percent on chicken and 24 percent on pork. Furthermore, over the last 5 years, Australian meat consumption pattern has chaned sinificantly between the meat types due to chane in consumer taste as well as some supply side reulations such as trade restrictions, chane in meat classifications etc. Australian consumers have increased their consumption of chicken and pork at the expense of beef, mutton and lamb. Consequently, an economic analysis on the demand for meat in Australia is crucial to the meat producers, meat sellers as well as meat consumers. This paper attempts to present an empirical analysis on the demand for the different types of meat, namely beef, lamb, mutton, chicken and pork, in Australia over the last five decades spannin over the period 1962 to 211. This study adopts the well-known system-wide approach to achieve this purpose. There are three basic reasons for the selection of system-wide approach in this study. Firstly, the implication of the consumer s budet constraint is that any increase in expenditure on one ood can only arise from a decreased expenditure of at least one other ood. This underlyin 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 arisin from consumption theories that necessitate the utilization of a system of demand equations. The first is that demand equations are homoeneous of deree zero in income and prices, termed demand homoeneity. This property stipulates that an equal proportional increase 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, if the consumer s real income is held constant, the quantity chane in the consumption of a ood, arisin from a one-dollar increase in the price of a different ood, will be 2

3 exactly the same as the chane in the consumption of the first ood brouht about by a one-dollar increase in the price of the latter ood. This is termed Slutsky symmetry and when represented alebraically becomes a cross-equation constraint. As such, it is evident that only a system-wide approach will satisfy the constraints under Slutsky symmetry. Besides, economic theories should not accept the takin of one ood in isolation from the rest; thus, this study hopes to tell a common story for all the five meat types. It is only when we can paint a complete picture of the demand conditions for all the five meat types that we can hope to present a true picture. This study s aim is to present a detailed scientific analysis of meat consumption patterns of Australian consumers considerin specifically the five types of meat, beef, lamb, mutton, chicken and pork. We focus on the impact of two economic variables, income of the consumers and individual prices of beef, lamb, mutton, chicken and pork on the consumption of these five meat types. We also investiate the chane in meat consumers tastes, habits etc and the substitutability or complementarities between different types of meat. In addition, this study will also investiate whether the meat consumption data supports a number of empirical reularities found in other consumption studies, such as (1) quantity variance systematically exceeds price variance; (2) income flexibility is about -.5; (3) the demand curve slopes downwards; and (4) budet share of meat declines with increasin income. The paper is structured in the followin manner. Section 2 presents a literature review of a number of past Australian meat studies and summarizes the reported demand model parameters namely income, own-price and cross-price elasticities. This will be followed, in Section 3, by a brief overview of the basic concepts of consumer demand. Section 4 will present a preliminary analysis of the Australian meat data. In the next section we investiate a number of empirical reularities in consumer demand with Australian meat data. In Section 6, we present the demand systems, the Workin s model, the Almost Ideal Demand System (AIDS) and the Rotterdam Model for estimation and in Section 7 select the preferred model usin the oodness-of-fit measure, the information inaccuracy. In section 8 we tabulate the estimation results for the preferred model and present the implied income and price elasticities. Finally, Section 9 provides the concludin comments. 3

4 2. A Summary of Previous Studies In this section, we present a summary of a number of Australian meat demand studies. These studies vary in terms of the data time period, functional forms, type of meats considered, and the method of estimation used. Consequently, the estimated income and price elasticities also vary dependin on the data, time period and the method of estimation. Table 1 presents the income elasticities and own-price elasticities of the five types of meat. Table 2 presents summary measures of all the income and own-price elasticities for the five meat types across all studies. As can be seen, the averae income elasticities across the studies are.77 for beef,.24 for lamb, -.65 for mutton,.47 for chicken and.48 for pork. Except for mutton, all the averae income elasticities are positive. Althouh the averae for mutton is neative, the value ranes between and The estimated income elasticities for the four meat types are mainly positive; indicatin that, consumption of the beef, lamb, chicken and pork will increase commensurate with an increase in income. With respect to the five meats own-price elasticities, on averae, all the elasticities are neative as they should be; that is the quantity demanded for these oods will fall in response to an increase in their prices. Most of the own-price elasticities for beef, lamb, mutton and pork are reater than 1 indicatin that their demand is elastic. In other words, the chane in quantity demanded of these oods will be more than proportionate to a chane in their respective prices. Chicken, with most of the estimates less than 1, appears to have an inelastic demand; hence chanes in the quantity demanded of chicken will be less than proportionate to chanes in its price. Table 3 presents the correspondin cross-price elasticities for the five meat roups from the Australian meat studies. As can be seen, a majority of the cross-price elasticities are positive indicatin a hih deree of substitutability between the five types of meat. There is also some deree of complementarity noticeable between the mutton, pork and chicken meat subroup. 4

5 Table 1 Summary of previous studies and income and own-price elasticities of 5 meat types Author Data period Model / Estimation Income Elasticity Ow n-price Elasticity Beef Lamb Mutton Chicken Pork Beef Lamb Mutton Chicken Pork Taylor (1961) (A) Double Lo (OLS) Van der Meulen (1961) (A) Double Lo (OLS) Taylor (1963) (A) Double Lo (OLS) Marceau (1967) (Q) Double Lo (OLS) Hill (1967) (A) Double Lo (OLS) -1.2 Gruen et al (1968) (A) Double Lo (OLS) Pender & Erw ood (197) (A) ILS Paton (197) (A) Double Lo (OLS) Papadopoulos (1971) (Q) Double Lo (OLS) Throsby (1972) (Q) 2SLS Throsby (1975) (Q) 2SLS Greenfield (1974) (A) Double Lo (OLS) Main et al (1976) (Q) Double Lo (OLS) Main et al (1976) (Q) SUR (Double Lo) Reynolds (1976) (Q) SUR (Double Lo) Reynolds (1976) (Q) SUR Freebairn & Gruen (1977) (Q) Double Lo (OLS) Fisher (1979) (Q) Double Lo (FIML) Fisher (1979) (Q) Modified Translo (FIML) Griffith & Vere (1981) (Q) Linear (OLS) Murray (1984) (A) AIDS (SUR) Murray (1984) (A) Translo (SUR) Murray (1984) (A) Indirect Addilo (SUR) Shaw et al (1983) (A) Lo Chane (OLS) Dew bre et al (1985) Double Lo (OLS) Martin & Porter (1985) (Q) Double Lo (OLS) Alston & Chalfant (1987) (Q) Double Lo (OLS) Alston & Chalfant (1987) (Q) AIDS (Modified Translo) Vere & Griffith (1988) (Q) Double Lo (OLS) Cashin (1991) (Q) LA-AIDS (SUR) Cashin (1991) (Q) LA-AIDS (SUR) Harris & Shaw (1992) (A) LA-AIDS (SUR) Piot et al (1996) (Q) Double Lo (OLS) Vere et al (2) (Q) Linear (2LS) Ulubasolu et al (211) LA-AIDS (OLS) Nhun et al (211) AIDS (OLS) Mounter et al (212) (Q) LA-AIDS AIDS Rotterdam Table 2: Summary income and own-price elasticities across all studies Summary Income elasticites Own-price elasticities statistic Beef Lamb Mutton Chicken Pork Beef Lamb Mutton Chicken Pork Mean Standard Error Median Minimum Maximum Count

6 6

7 3. Basics of Consumer Demand Systems We bein this section by definin basic concepts in consumer demand such as income, budet shares, marinal shares, elasticities, etc. Let p i and q i be the price and per capita consumption of commodity i. Then the total expenditure on all n oods (or income for short), M, and on a roup of oods S, M, are iven by M = n p i q i1 i ; M = i i (1) is p q The unconditional (conditional) budet shares of ood i, the proportion of income (roup expenditure) allocated to a commodity, i, can be defined as: w i p q M i i, i = 1,,n, pq w i i i, i S. (2) M Budet shares are obviously positive; and followin from (1) and (2), they have a unit sum, where n wi i1 1, w 1 (3) i is When income increases by $1, the additional amount spent on commodity i can be measured as ( piqi) i i = 1,,n (4a) M which is referred to as the i-th (unconditional) marinal share. Similarly, when the roup expenditure increases by $1, the additional amount spent on commodity i in roup S can be measured as ( pq i i) i, M is (4b) which is referred to as the i-th conditional marinal share. From (1) and (4), one can easily see that the marinal shares also add up to 1. That is n = 1, i = 1 (5) i i1 is 7

8 Unlike the budet shares, marinal shares need not always be positive; if i is an inferior ood, then i (or i ) will be neative. In other words, for an inferior ood, as income (or roup expenditure) rises, demand for that ood will decrease. The unconditional (conditional) income elasticity of commodity i, i or i, is the percentae chane in consumption of commodity i when income (or roup expenditure) increases by 1 percent. That is qi / qi (lo qi) i, M / M (lo M) i = 1,,n, qi / qi (lo qi) i, is. M / M (lo M) (6) From (2), (4) and (6), it follows that unconditional and conditional elasticities can be written as i, i = 1,,n i w i i i w i, i S (7) If the income elasticity is reater than zero, the ood is classified as a normal ood; implyin that as income (or roup expenditure) rises, quantity demanded of the ood rises. Goods with income elasticities reater than unity are called luxuries; where quantity demanded of these oods increases by a reater proportion than the increase in income (or roup expenditure). Goods with neative income elasticity are inferior oods because income (or roup expenditure) increases lead to decreasin consumption of said ood. On the other hand, the oods with income elasticity less than one are called necessities, where the quantity demanded of these oods increase by a lesser proportion than the increase in income (or roup expenditure). Food is a ood example of a necessity. The price elasticity, ij, is the percentae chane in the consumption of ood i when the price of ood j increases by 1 per cent. That is ij (lo qi ) i, j = 1,,n (8) (lo p ) j Accordin to the Law of Demand for i = j, the own-price elasticity should be neative. If the absolute value of the own-price elasticities of ood i ( ii ) is less than one, that is the consumption 8

9 of ood i increases less than proportionate to its price increase, the demand for ood i is price inelastic. On the other hand, if the absolute value of ii is reater than one (ii >1), then the demand for ood i is price elastic. For i j, the coefficient ij in (8) is the cross-price elasticity of commodity i in reards to commodity j; or the elasticity of demand for i with respect to the price of j. If ij is positive, oods i and j are called ross substitutes; that is the demand for ood i rises with increases in the price of ood j. Accordinly, if ij is neative, then the two oods are ross complementary; that is any increases in the price of ood j will lead to decreases in the demand for ood i. 4. Preliminary Data Analysis In this section, we present the Australian meat consumption data and use them to present a preliminary data analysis on the demand for meat in Australia. We also investiate a number of empirical reularities in consumption patterns with Australian meat data. The Data We consider five types of meat, namely, beef, lamb, mutton, chicken and pork. The per capita consumption and price data for the period are from Roberts (199) and for are from various issues of publications of the Meat and Livestock Australia and the Australian Bureau of Aricultural and Resource Economics and Sciences (ABARES). The consumer price index data ( Consumer Price Index, Australia), the total private final consumption expenditure data ( Australian National Accounts: National Income, Expenditure and Product) and Australian population data (311. Australian Demoraphic Statistics) are all from various issues of Australian Bureau of Statistics publications. Consumption and Prices Table 4 presents the basic data for consumption and prices for five meat types for selected years. Fiure 1 displays the per capita consumption of the five types of meat durin 1962 and 211. As can be seen, in eneral, consumption of pork and chicken have increased steadily and that of beef, 9

10 Table 4 Consumption, prices, expenditure and budet shares for five types of meat, selected years, Year Beef Lamb Mutton Chicken Pork Total meat (1) (2) (3) (4) (5) (6) Per capita consumption (k) Prices ($/k) Price index (1962=1) Expenditure on meat ($/person) Unconditional budet shares (w it ) Conditional budet shares (w it )

11 Per capita consumption (k) Beef Lamb Mutton Chicken Pork Fiure 1 Per capita consumption of meat in Australia, Five meat types, lamb and mutton have fallen steadily. Australian per capita consumption of beef has fallen from 45.3 k in 1962 to 38.6 k in 1969 and then steadily increased to 7.4ks in 1977 and then has aain fallen steadily to 32.8k in 211. This fall in local consumption in the early seventies was due to stron world demand. Hih world price for beef has lead to lower supply of beef to the local Australian market. This situation has chaned in the mid to late seventies due to the increased trade restrictions placed on the Australian major export markets resultin in increased supply of beef in the local Australian market. In the early seventies, improvement in wool prices and the introduction of uaranteed floor price of wool has lead to reduced supply of lamb and mutton to the local Australian meat market as lamb stocks were withheld from slauhter. Lamb consumption has increased from 19.3k in 1962 to 23.6k in 197 and then steadily fell to less than half of what it was in 196 s to 9.2k in 211. Australians consumed more mutton than lamb in the 6 s, but have reduced mutton intake over the years, with 25.2ks per person in 1962 to a very low level of.3k per person in 211. In 211, the per capita consumption of mutton and lamb combined has fallen to almost one-fifth of what they were in the early 6 s. The fall in beef, lamb and mutton consumption have been mostly captured by the increase in the consumption of chicken and pork. Per capita chicken consumption has increased 7 times, increasin from 4.4k in 1962 to 43.3ks in 211. Pork consumption has also increased 3 times, where it has increased from 8.8ks in 1962 to 25.ks in 211. While chicken consumption has increased steadily over the years, pork consumption has fallen slihtly in the mid 198 s and increased steadily from then onwards. 11

12 Part of Table 4 presents the retail prices and their indices for selected years and Fiure 2 displays the retail prices in index form with base 1962=1 durin 1962 to 211. Considerin the prices for the five types of meat for selected years presented in Table 4, we can see that the retail price of beef has increased steadily over the years from $.94/k in 1962 to $15.46/k in 211. Over the same period, lamb price has increased from $.76 to $14.62/k, mutton price from $.46 to $9.45/k and pork price from $1.9/k to $1.91/k. The chicken price has increased from $1.19/k in 1962 to $3.2/k in Before 1987, only frozen chicken were supplied for consumption and from 1987 it was mostly replaced by fresh chicken. The price of fresh chicken has increased steadily from $1.51 in 1988 to $5.49 in 211. As can be seen from Fiure 2, prices of beef, lamb and mutton have increased at a faster rate than the prices of chicken and pork. 25 Price index (1962=1) Beef Lamb Mutton Chicken Pork Fiure 2 Price indices (1962=1) of meat in Australia, Five meat types, The retail price indices (with base 1962=1) toether with per capita consumption data for each meat type durin 1962 to 211 is presented in Fiure 3. As can be seen prices and consumption has moved in the opposite direction for beef, lamb and mutton; while they have moved in the same direction for chicken and pork. Prices of beef, lamb and mutton have increased at a much faster rate than chicken and pork. This may have moved consumption from beef, lamb and mutton towards chicken and pork. 12

13 Beef Lamb Price index (2=1) Consumption (k) Price index (2=1) Consumption (k) Price Quantity Price Quantity Price index (2=1) Mutton Consumption (k) Price index (2=1) Chicken Consumption (k) Price Quantity Price Quantity Pork Price index (2=1) Consumption (k) Price Quantity Fiure 3 Price indices and per capita consumption in Australia, Five meat types, It would be rational, accordin to economic theories, to conclude that the consumption for beef will fall commensurate with the increase in the price of beef; and that the hihest fall in consumption for lamb would result from lamb havin the hihest percentae increase in price. Also in the initial period the consumption of chicken and pork decreases as their price increase, however, in the later years their consumption increase while their price also increase due to the substitution of chicken and pork in place of beef and lamb due to their price increase. 13

14 Budet shares The lower section of Table 4 presents, for selected years, the expenditure on each meat type, the unconditional and conditional budet shares for the five meat types and the budet share for meat as a whole. Fiures 4 and 5 present these budet share series in raphical form. In eneral, the proportion of total income spent on beef, lamb, mutton and pork have been declinin and that of chicken has increased slihtly durin the sample period. Within the meat roup, clearly, chicken and pork have captured the fallin market shares of beef, lamb and mutton. As can be seen, for example in 211, Australians allocate about 1.5% of their income on beef,.4% on lamb,.1% on mutton,.7% on chicken,.8% on pork, ivin a total of 3.4% of their income on meat. Within the meat roup, Australian consumers allocate 44 percent of their meat expenditure on beef, 12 percent on lamb,.3 percent on mutton, 2% on chicken and the remainin 24% of their meat expenditure on pork. Over the years, the consumer s income allocation on beef has fallen from 4.3% in 1962 to 1.5% in 211, on lamb has fallen from 1.5% to.4%, mutton from 1.2% to.1%, pork from 1.% to.8% and chicken has increased from.5% to.7%. For meat as a whole, the allocation of income has more than halved from 8.5 percent in 1962 to 3.7 percent in 211. Clearly, in recent years there is not much demand for mutton and demand for beef and lamb are competin aainst chicken and pork. Budet share (percentae) Budet share(percentae) Total meat Beef Lamb Mutton Chicken Pork Fiure 4 Expenditure share of total meat and the unconditional budet shares of five meat types,

15 Budet share(percentae) Beef Lamb Mutton Chicken Pork Fiure 5 Conditional budet shares of the five meat types, Divisia Moments Now we summarize the data in the form of Divisia index numbers. We define the price and quantity lo-chanes, respectively, as Dpit ln( pit ) ln( pit 1 ) and Dqit ln( qit ) ln( qit 1 ) where p it and q it are the price and consumption of ood i at time t. When these lo-chanes are multiplied by 1, they can be interpreted as percentae chanes or percentae rowth rates from year t-1 to year t. Here and elsewhere, ln refers to the natural loarithm. The overall rowth in prices and consumption of the meat roup can be measured by the Divisia price and quantity indices which are defined as DP t = 5 5 witdp it and DQ t = witdqit (9) i1 i1 where w it = ½ ( wit wit 1) is the arithmetic averae of the conditional budet shares in periods t and t-1. 15

16 Columns 2 and 3 of Table 5 presents the averae absolute ( Dp i and Dq i ) and columns 4 and 5 present the relative price and consumption rowth rates ( Dpi DP and Dqi DQ) for the five meat types, averaed over the sample period. As can be seen, on averae, consumption of beef, lamb and mutton has fallen at a rate of.7, 1.5 and 9. per cent per annum while chicken and pork consumption have increased at a rate of 4.7% and 2.1% per annum, respectively. On averae, the prices have all increased at a rate of 5.7%, 6.%, 6.2%, 3.1% and 4.7%, per annum, respectively. While rowth rates in consumption of beef, lamb and mutton relative to the meat roup are neative, their relative rowth rates in prices are positive. The relative rowth in the consumption of chicken and pork are positive while their relative price rowth rates are neative. Table 5 Averae rowth rates in consumption and prices ( ) Meat type Growth rate Relative Consumption Price Consumption Price (1) (2) (3) (4) (5) Beef Lamb Mutton Chicken Pork Empirical Reularities in Consumption Patterns Various consumption studies have observed a number of empirical reularities in the consumption patterns of consumers in a number of countries (see, for example, Selvanathan, S., 1993; Selvanathan and Clements, 1995; Chen, 21). The four such important empirical reularities we investiate in this paper are, namely: Empirical Reularity 1: Empirical Reularity 2: Empirical Reularity 3: Empirical Reularity 4: Quantity variance exceeds price variance; Demand curve slopes downwards; Income flexibility tends towards -.5; and, Budet share of food declines with increasin income. Below, we investiate whether these reularities are supported by the Australian meat data. 16

17 Empirical Reularity 1: Quantity Variances Exceeds Price Variances To measure the variation in prices and consumption, we use the second-order Divisia moments. The correspondin Divisia second-order moments, Divisia price and quantity variances defined as t = 5 i1 2 it[ it t ] w Dp DP and K t = 5 i1 2 it[ it t ] w Dq DQ The co-movement of prices and quantities is measured by the Divisia price-quantity correlation where t = t t =, 5 i1 t t it it t it t w [ Dp DP ][ Dq DQ ] is the price-quantity covariance. Table 6 presents the Divisia quantity and price indices, for the meat data for the period As can be seen from the mean row of the first two columns, on averae, meat as a whole its consumption hasn t rown that much, whilst meat prices have rown at a much larer rate of 5.8 percent per annum over the same study period. A comparison of the quantity variances (K t ) in column (5) with the correspondin price variances ( t ) in column (4) reveals that, in most years, quantity variance systematically exceeds the price variance. In Fiure 6, we plot the standard deviations, K t aainst t, for t=1,.., T, toether with the 45 o line, which shows that most of the points lie above the 45 o line; indicatin that, on averae, the quantity variance does exceed the price variance. The above findins arees well with the results of Clements (1982, 1983), Meisner (1979), Selvanathan, S. (1993), Selvanathan and Selvanathan (1993, 1994), Selvanathan and Clements (1995), Theil and Suhm (1981), and Suhm (1979), Selvanathan and Selvanathan (23). 17

18 Table 6 Divisia Moments for meat: Australia

19 Price Quantity Price Quantity Price quantity Price quantity Year index DP t index DQ t variance t variance K t covariance t correlation t (1) (2) (3) (4) (5) (6) (7) Mean

20 25 2 y = x Quantity SD Price SD Fiure 6 Quantity vs Price standard deviation, meat roup, A point also worth notin is the unusually hih values of both the price and quantity variances durin the years 1973, 1974, 1979 and As stated before, the hih variances could be due to (i) the hih export demand resultin in hiher prices and lower local consumption of beef in the Australian meat market; (ii) reduced supply of lamb and mutton due to better wool prices resultin in shortae of lamb and mutton for local consumption; (iii) increased trade restrictions in the Australian major export markets durin the 197s; (iv) events such as the introduction of fresh chicken instead of frozen chicken into the Australian meat market; and (v) the introduction of pimeat imports into the Australian meat market durin the late 198s. We shall revisit this later the paper. Empirical Reularity 2: Demand Curves Slope Downwards Last column of Table 6 presents the Divisia price-quantity correlations. As can be seen, almost all the price-quantity correlations presented in Table 6 are neative, with an averae value of -.4, indicatin that there is a neative relationship between price and consumption supportin the Law of Demand. To investiate this further, In Fiure 7, we plot the relative consumption (Dq it DQ t ) aainst the relative price (Dp it DP t ), t = 1,,T, for each meat type for Australia. As can be seen, in all scatter plots, most points are scattered around a neatively sloped line. This aain ives supports to the law of demand that the demand curve slopes downwards. 2

21 Empirical Reularity 3: Income flexibility is about -.5 Fiure 7 plots the relative consumption (Dq it DQ t ) aainst the relative price (Dp it DP t ), t = 1,,T, for the five meat types and for total meat for the period 1962 to 211. The slope of the estimated trend line can be interpreted as an estimate of the reciprocal of the income flexibility (the income elasticity of the marinal utility of income) for each of the meat type. Table 7 collects the slope estimates of each plot, which are estimates of income flexibility. The last row of the tables, ives the averae of the 6 estimates, which is = These findin ive support to a number of previous econometric findins that income flexibility is an international constant and is about -.5 (e.., see Theil and Suhm, 1981; Theil and Clements, 1987; Selvanathan, 1993; and Selvanathan and Selvanathan, 25) Beef y =.4665x R² = y =.9554x R² = Mutton Pork y =.5178x R² = Lamb y =.5181x R² = Chicken y =.2594x R² = Total Meat y =.4975x 4.57 R² =.7116 Fiure 7 Relative quantity vs relative price, five meat types and total meat,

22 Table 7 Estimates of income flexibility* Meat type Income flexibility Beef.47 Lamb.52 Mutton.96 Chicken.26 Pork.52 Total meat.5 Mean.54 * Based on Fiure 7. Empirical Reularity 4: Budet share of food declines with increasin income. An averae Australian s budet share of meat, in relation to total private expenditure as evidenced in Table 4, shows a continuous decline except for 25 and 26, from about 8.4 percent to 3.4 percent for the period 1962 to 211. One of the most important empirical reularity in consumption economics, Enel s Law, states that the budet share of food falls with increasin income. We investiate whether Enel s Law holds for different types of food items individually as well, in particular for the five meat types. Fiure 8 presents the plot of budet share of the five meat types and total meat aainst the loarithmic of the per capita expenditure for Australia. As can be seen, the points are scattered around a neatively slopin straiht line. In other words, when income increases, the share of expenditure on the various meat types falls. 6 The Demand Models In terms of differential demand systems, the three most popularly utilised in applied demand analysis have been the Rotterdam demand system (Barten, 1964; Theil, 1965); the Workin 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, 198). In this section, we introduce the three demand systems to be used for estimation and then test the demand theory hypotheses. We then select the preferred model amon the three and present the estimation results and implied income and price elasticities for the five meat types based on the preferred model. 22

23 Beef Lamb Budet share (%) y =.722x R² = Budet share (%) y =.336x R² = Lo(Income) Lo(Income) Mutton Chicken Budet share (%) y =.2221x R² = Lo(Income) 1 12 Budet share (%) y =.1695x R² = Lo(Income) Pork Total meat Budet share (%) y =.951x R² = Budet share (%) y = x R² = Lo(Income) Lo(Income) Fiure 8 Budet shares of meat roups vs lo of income, five meat types and total meat, Rotterdam Model The basic specification of the Rotterdam model for ood is, in differentials, takes the form (see, for example, Theil, 198; Selvanathan, 1993; Selvanathan and Clements, 1995) it it i i t ij jt it, is (1) js wdq DQ Dp 23

24 where it w, Dq, it Dp it and DQ t are defined as before; and i is the constant term of the i th demand equation satisfyin. is i The use of the constant terms in the demand equations is to take into account any trend-like chanes in tastes etc. The marinal share, i, answers the question if roup expenditure increases by one dollar, how much of this increase will be allocated to commodity i? and also satisfies 1. i S i If i wit, then the commodity i is classified as a necessity; if it is otherwise, then it will be classified as a luxury. The coefficient ij is the (i,j) th Slutsky price coefficient which satisfies is ij. These coefficients also satisfy js ij. (11) Constraint (11) reflects the homoeneity property of the demand system that postulates that a proportionate chane in all prices has no effect on the demand for any ood under the condition that real income is constant. Accordinly, it is known as demand homoeneity. The Slutsky coefficients are symmetric in i and j, that is ij ji, i,js, (12) which is known as Slutsky symmetry. In other words, when real income 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 interchaned, the substitution effects are symmetric in i and j. As well, the Slutsky matrix, ij, is symmetric neative semi-definite with rank (n -1), where n is the number of oods in roup S. 24

25 The term it is the disturbance term of the i th equation. It is assumed that the disturbance terms, it, i=1,,n, are serially independent and normally distributed with zero means with a contemporaneous covariance matrix. Equation (1) for i=1,,n, is a fairly eneral 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 (1) over i=1,,n, we obtain i it =, for t=1, T. Therefore, the ε it s are linearly dependent and one of the equations becomes redundant and can be deleted (Barten, 1969). We delete the n -th equation. It can be shown that the best linear unbiased estimators of the parameters for the system of equations (1) for i=1,,n will be the same as those obtained by estimatin each equation separately by least squares (LS). See Theil (1971) for details. CBS Model The basic specification of the second differential demand system, the CBS model, for ood i in differentials takes the form (see, for example, Barten et al, 1989; Selvanathan, 1993; Selvanathan and Clements, 1995) it ( it t ) i i t ij jt it, (13) js w Dq DQ DQ Dp where i is the constant term of the i th demand equation satisfyin. is i As above, the use of the constant terms in the demand equations is to take into account any trend-like chanes in tastes and the like. The income coefficient i satisfies is i.. If i is neative (positive), then the commodity is classified as a necessity (luxury). As before, the coefficient ij is the (i,j) th Slutsky price coefficient; here as well, these coefficients satisfy the demand homoeneity and Slutsky symmetry properties. 25

26 AIDS In differential form, Deaton and Muellbauer s (198) AIDS takes the form it i i t ij jt it, is (14) js dw DQ Dp v where it it it 1. The riht-hand side of the AIDS is very similar to the CBS model, but dw w w the left-hand side dependent variable is not it ( it t ), but the chane in budet share, w Dq DQ dw it. The properties of the i and ij are similar to those of the CBS model. Testin Demand theory hypotheses We use the Demand Analysis Packae, DAP2 (Yan et al, 2) and DEMMOD-3 (Barten et al, 1989) proram to estimate the three demand systems iven by (1), (13) and (14). In the models, we have included two dummy variables, one to take into account of the chane in the type of chicken meat from frozen to fresh as well as the introduction of pi-meat imports (from 1988 onwards); and the other is to cater for the chanes in trade restrictions as well as the hih price of wool durin the 197s. Testin Demand Homoeneity As discussed above, demand homoeneity postulates that a proportionate chane in all prices has no effect on the demand for any ood when real income is held constant. We now test the demand homoeneity based on the estimation results of the three demand systems usin the Australian meat data. For testin homoeneity, there are two tests available. The Wald test which is an asymptotic 2 test with n -1 derees of freedom and the other is a finite-sample test introduced by Laitinen (1978) based on Hotellin s T 2 distribution which is also a constant [(n -1)(T-n -1)/(T-2n +1)] multiple of the F distribution with n -1 and T-2n -1 derees of freedom. The results for the Australian meat data with n =5 meat types (and T=5) are presented in Table 8. 26

27 Table 8 Testin for demand homoeneity, Australian meat data, Wald Test Laitinens Test Model Test Critical value Decision Test Critical value Decision statistic 2 (.5,4) 2 (.1,4) 5% level 1% level statistic F (.5,4,37) F (.1,4,37) 5% level 1% level Rotterdam Reject Do not reject Reject Do not reject CBS Reject Reject Reject Do not reject AIDS Reject Do not reject Reject Do not reject As can be seen from Table 8, the homoeneity hypothesis is rejected for all three models at the 5 percent level and not rejected for two models at the 1 percent level by the Wald test. This result is not surprisin 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, while homoeneity is rejected at the 5 percent level, it is acceptable at the 1 percent level for all three models. Slutsky Symmetry For testin symmetry, we use asymptotic χ 2 test with q = ½(n -1)(n -2) derees of freedom (see Theil, 1971, for details). The results for the Australian meat data are presented in Table 9. As can be seen, symmetry is acceptable for all three models at the 1 percent level of sinificance. Takin homoeneity as iven, the symmetry hypothesis is acceptable for all three models at the 5 percent level. Thus, overall, we conclude that homoeneity and symmetry hypotheses are enerally acceptable by all the three models; and, in the remainin sections of the paper, we consider models with homoeneity and symmetry imposed. Table 9 Testin for Slutsky symmetry, Australian meat data, Symmetry Symmetry iven Homoeneity Model Test Critical value Decision Test Critical value Decision statistic 2 (.5,1) 2 (.1,1) 5% level 1% level statistic 2 (.5,6) Rotterdam Reject Do not reject Do not reject CBS Reject Do not reject Do not reject AIDS Do not eject Do not reject Do not reject 27

28 6. The preferred demand model We select the preferred model amon the three demand systems, Rotterdam, CBS and AIDS, by calculatin the predicted budet shares from each model and then use them to calculate the oodness-of-fit measure, information inaccuracy, for each meat type and for meat as a whole. Let w 1t,, w ntbe the observed budet shares of n commodities in period t, and w ˆ1 t,, nt ˆ w be the predicted budet shares implied by the demand model. The information inaccuracies for the predictions by meat type (i) is iven by wit it it ˆ it wit 1 w I w lo (1 w )lo, 1 wˆ it it is, (15) and the overall information inaccuracy for the predictions is iven by I t it it w wit lo. is wˆ (16) The information inaccuracies measure the extent to which the predicted budet shares ( ) differ from the correspondin observed budet shares ( w it ). Both I it and I t are non-neative and the larer their observed value, the poorer is the quality of the predicted budet shares w ˆ1 t,, w ˆnt. A naïve model of no-chane extrapolation is one in which the current period prediction of w it is specified as wit 1. That is, wˆ it wit 1. Table 1 presents the information inaccuracies for the three models and for the no-chane model, for the five meat types and for the total meat roup. As can be seen, at the individual meat type level as well as the total meat, in most cases AIDS model performs better than the other two. Based on the oodness-of-fit measure, information inaccuracy, we conclude that the preferred model for modellin meat demand is AIDS. 28

29 Table 1 Information Inaccuracies I it and I t (x 1 2 ) Demand model Meat type Rotterdam CBS AIDS No Chane Best fit Beef AIDS Lamb AIDS Mutton AIDS Chicken CBS Pork AIDS Total meat AIDS Estimates and implied elasticities Next we present the estimation results usin the Australian meat data for the preferred model, AIDS with homoeneity and symmetry imposed, and then use the estimates to obtain the implied income and price elasticities. Table 11 presents the estimation results for AIDS with homoeneity and symmetry imposed usin the Australian meat data. As can be seen, a majority of the coefficient estimates are statistically sinificant at the 5 percent level of sinificance. The estimated constant terms for beef, lamb and mutton are neative and for chicken and pork are positive, indicatin that there is an autonomous trend out of beef, lamb and mutton into pork. The income coefficient for beef is positive, indicatin that it is a luxury, while for lamb, mutton, chicken and pork are neative, indicatin that they are necessities. Table 11 Parameter estimates AIDS, Australian meat data, * Constant Income Beef Lamb Mutton Chicken Pork I 1 I 2 Beef (.2) (.523) (.18) (.35) (.41) (.97) (.4) (.133) (.147) Lamb (.11) (.295) (.35) (.51) (.23) (.71) (.4) (.77) (.83) Mutton (.1) (.265) (.41) (.23) (.46) (.74) (.56) (.71) (.75) Chicken (.9) (.239) (.97) (.71) (.74) (.14) (.129) (.78) (.68) Pork (.12) (.35) (.4) (.4) (.56) (.129) (.13) (.89) (.85) * Standard error are in parentheses. 29

30 Based on AIDS, the income elasticity for ood i will be iven by i 1 i w i and the own and cross price elasticites are iven by ii 1 ii w i i and ij w ij i / wi j wj. Table 12 presents the implied income and price elasticities calculated at sample means toether with the estimates presented in Table 11. Table 11 Implied income and price elasticities Income Price elasticities Meat type elasticity Beef Lamb Mutton Chicken Pork (1) (2) (3) (4) (5) (6) (7) Beef Lamb Mutton Chicken Pork As can be seen from Table 12, the income elasticity for beef is 1.54 ( > 1), lamb.56 (< 1), mutton.45 ( < 1), chicken.22 ( < 1) and pork.44 (< 1). This means that amon the 5 meat types, beef is a luxury and lamb, mutton, chicken and pork are necessities. All the own-price elasticities are neative as they should be. The values are beef (-.41), lamb (-.71), mutton (-1.19), chicken (-.28) and pork (-.53). As the manitude of muttons own price elasticity is larer than one, demand for mutton is price inelastic and the absolute vales of the own-price elasticity of all other four meats are less than one indicatin that the demand for beef, lamb, chicken and pork are price inelastic. 3

31 Amon the cross-price elasticities (except for pork-chicken), all are positive indicatin that pork and chicken are complements and all other combinations are pairwise substitutes. 7. Concludin Comments In this paper, we have presented a systematic analysis of Australian meat demand usin data from 1962 to 211 for the 5 meat types, namely beef, lamb, mutton, chicken and pork. Accordin to the statistics published for 211, Australians consume about 111 ks of meat per person divided into 33k of beef, 9k of lamb, 43k of chicken and 25k of pork. In recent years, Australian consumers allocate about 4 percent of their budet to the purchase of meat. Within their expenditure on meat, they allocate about 44 percent on beef, 12 percent on lamb, 21 percent on chicken and 24 percent on pork with very little or none on mutton. In terms of market share, chicken and pork have increased their share by 3 and 2 times, respectively, in the last 5 years at the expense of beef, lamb and mutton. Mutton share was 13.8 percent in 1962 and has been almost wiped out in 211. The retail prices of all five meat types has steadily increased over the last 5 years with beef, lamb and mutton prices increased at faster rate than the prices increase of chicken and pork. In this paper, we also investiated the followin four empirical reularities in consumer demand and find stron support for all of them usin the Australian meat data, (1) the quantity variance exceeds the price variance; (2) demand curve slopes downwards; (3) income flexibility tends towards -.5; and, budet share of food declines with increasin income. To model the data, we used three well-known and popular demand systems, namely, Rotterdam, CBS and AIDS and tested the two demand theory hypotheses, demand homoeneity and Sltusky symmetry. In enereal, both hypotheses were acceptable for all three models usin the meat data. We then used the oodness of fit measure, information inaccuracy to select the preferred model amon the three and found that AIDS performed better than Rotterdam and CBS for the Australian meat data. 31