structural change in canadian meat demand

Structural Change in Canadian Meat Demand

Anderson Reynolds and Ellen Goddard Respectively, postdoctoral fellow and

associate professor, Department of Agricultural Economics and Business, University of Guelph,

GueEph, Ontario, NIG 2 WI

Received 24 April I990, accepted 18 March 1991

Results derived from a time-varying parameterization of the AIDS model provide evidence of a structural change in Canadian meat demand (beef, pork, chicken). The structural change was accompanied with significant changes in some of the parameters of the model, and was biased in favor of chicken at the expense of beef.

Les rtsultats d'une pararnttrisation du modkle AIDS variant dans le temps indiquent une modification structurelle de la demande de viande (boeuf, porc, poulet) au Canada. Cette modification structurelle a ttC accompagnte par des changements importants i certains paramktres du modkle et semble favoriser le poulet aux dCpens du boeuf.

INTRODUCTION Due to unobservability or insufficient data, many variables characterizing the economic environment of interest are excluded from econometric models. However, changes in the economic environment brought about by these excluded variables represent a potential source of structural change. Paradoxically, however, many of the same econometric models assume parameter constancy, with the unintended implication that the presence of changing structural parameters results in misleading parameter estimates, which situation in turn has serious implications for policy decisions and forecast accuracy.

One such change occurring in the mid-1970s in the economic environment surrounding food demand was the evolution of North American preferences (taste) away from a diet high in cholesterol and other saturated fats. This phenomenon has been hypothesized to constitute a structural change in meat demand as reflected in the observed shift' (beginning in the late 1970s) in meat consumption from red meat to white meat (Figure 1). While a number of studies (Braschler 1983; Chalfant and Alston 1988; Chavas 1983; Dahlgran 1987; Eales and Unnevehr 1988; Moschini and Meilke 1984; Nyankori and Miller 1982; Thurman 1987; Wohlgenant 1985; and Moschini and Meilke 1989) investigate the hypothesis of a structural change in U.S. meat demand, studies by Young (1987) and Atkins, Kerr and McGivern (1989) are among the few that attempt to analyze the changing structure of Canadian meat demand. Both of these latter studies, however, assume

Canadian Journal of Agricultural Economics 39 (1991) 21 1-222 211

2 12

20

CANADIAN JOURNAL OF AGRICULTURAL, ECONOMICS

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Pnk A*_ .** - b- .A* -*6 -*- .*-4-

........*.......~..~.... C~

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Figure 1 . Per capita meat disappearance, 1968-87

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that the change from one regime to the other was abrupt. Given that taste and preferences may change slowly over time, excluding the possibility of a gradual change seems inappropriate.

Potential structural change in Canadian meat demand is an important con- cern because such changes may necessitate corresponding changes in the meat industry. The advent of national beef and pork advertising campaigns in the 1980s was one such industry response to declining red meat consumption. For best results, however, such industry responses should be based on sound economic modeling and economic forecasts. Models that do not explicitly account for the changing nature of meat demand may be inappropriate, and thus may suggest industry changes that are inconsistent with economic reality. For example, advertising elasticities obtained from studies that wrongly assume parameter constancy are likely to be incorrect, thus providing misleading indications of the effective- ness of advertising.

When structural change is defined as a change in one or more of the parameters of the model in question, the econometric problem becomes one of identifying the points in time (join points separating the regression into different regimes) at which the parametric change occurred, characterizing the speed of transition from the old to the new regime (whether the transition is abrupt or gradual), and drawing inferences about the parameters of the model before and after the structural change.

In this study. a time-varying version of the almost ideal demand system (AIDS) model, which assumes unknown join points (points in time associated with the beginning and ending of transition periods between regimes) and accommodates a gradual transition to a new regime, is employed to test the hypothesis of no structural change in Canadian meat demand. Following the structural change test, the impact of structural change on the estimated parameters of the model and

STRUCTURAL CHANGE IN CANADIAN MEAT DEMAND 213

on the pattern of meat consumption is examined. Since previous studies addressing the meat demand structural change issue have focused on beef, pork and chicken, to allow a comparison with such studies, these three meat items comprise the demand system under study.

GRADUAL SWITCHING AIDS MODEL

The gradual switching AIDS model employed by Moschini and Meilke (1989) and adopted for the present study is specified in first-difference form as (see Moschini and Meilke for further elaboration):

where wi = the budget share of the ith good (beef, pork, chicken), p j = the log of the nominal price of the jth good, Sk = seasonal dummies for the first three quarters of the year (k = 1,2,3), y = ln(Y/P), with Y being total expenditure and P a price index approxi-

t n = a transition function expressing the transition or time path from one mated by Stones price index (In P = C i wi pi) and

regime to the other, defined as:

tn, = 0 fo r t = 1, . . . , t l

in, = (t - t l ) / ( t 2 - t l ) fo r t = t , + 1 , . . . , t 2 - 1 ( 2 )

tn, = 1 for t = t 2 , . . ., T

t l I T - m / ( n - l ) , t2 1 m / ( n - l), t l < t2

where t l = the end point of the first regime, t2 = the start point of the second regime, n = the number of equations in the demand system, and m = total number of free parameters to be estimated. According to Eq. 2 , at time t = t l , the parameters O1 = (0, P i j , Pi, a+)

of Eq. 1 begin to gradually switch along a linear time path to O2 = (yi, P i j + 6,, Pi + 6i, aik + - y i k ) . At t = t2, the switch is complete; hence t2 signifies the beginning of the second regime. Note that if t2 = t l + 1 , the shift in regime is abrupt. Note also that with yi = 6 , = 6i = (Yjk = -yik = 0, Eq. 1 reduces to the basic AIDS model developed by Deaton and Muellbauer. After the joint

214 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

estimation of 8, t , and t 2 , a test for structural change can be constructed as a test of the hypothesis that O2 - 8, = 0.

By construction. the demand system represented by Eq. 1 should satisfy the adding up restriction; hence the following are implied:

The homogeneity and symmetry conditions implied by demand theory are satis- fied, respectively. by the following restrictions:

A change in the price and expenditure parameters of the model suggests that the way in which consumers respond to changes in price and income has changed. A comparison of price and expenditure elasticities, before and after the structural change, may indicate the nature of this behavioral change. Marshallian elasticities under the assumption of structural change and conditional on meat expenditures are expressed as:

where \v ,~, = the mean of the ith good share after structural change. To obtain elasticities prior to the structural change, the 6 parameters in Eq. 6 are set to zero and wi(l is replaced by M ' , ~ , the mean of the ith budget share before structural change.

Notwithstanding the impact of structural change on the price and income parameters, the intercept term and the seasonality parameters may also exhibit structural shifts. In fact, structural shifts in these parameters, in abstraction of prices and expenditures, as manifested in changes in budget shares, provide an indication of the bias of structural change. Following Moschini and Meilke (1989), a measure of the bias of structural change (0, = w,, - wIb) can be obtained by evaluating the good share at the mean of the data, such that pi = x' = 0 and SL = 0.25. Accordingly, the bias of structural change can be estimated as p, =

Yi + 0.25Gn r ,n) .


DATA The meat demand system to be estimated is on a per-capita basis and includes the goods beef, pork and chicken. The study uses quarterly data from 1968 to 1987. Meat disappearance data are obtained from Agriculture Canada and Statistics Canada, while price and price index data are obtained from Statistics Canada (consumer prices and price indexes). Obtaining price data that span the time period under study proves illusive. Therefore, recognizing that the price index data obtained have 1981 as base year, 1981 prices are employed to convert the price index series into price data. The conversion for a given series is obained by dividing the price index series by the 1981 price index datum of that series and then mul- tiplying the result by the 1981 price. The 1981 beef and pork prices are weighted average prices of the various cuts of meat that comprise each carcass. Both the price and expenditure variables are divided by their sample means before the loga- rithmic transformation. The data will be made available by the authors upon request.

ESTIMATION AND RESULTS Maximum likelihood estimates of the gradual switching AIDS model specified in Eq. 1 , with the homogeneity and symmetry restrictions imposed, are obtained using the LSQ option in TSP. Since Eq. 1 has discontinuous derivatives with respect to tl and t2 , the estimation strategy followed entails searching over all possible pairs of tl and t2 (such that tl I 1984, 4 4 , t2 L 1971, Q1 and tl < t2) for the pair that maximizes the log likelihood function. The search yields an optimum value o f t , = 1975, Q1 and t2 = 1984, Q1.

The maximum likelihood estimates, conditional on the optimum value of tl and t2 , are given in Table 1 along with some summary statistics. Standard errors of estimated parameters are in parentheses. The R2 values indicate that the fit of the model is satisfactory, while the D-W test statistics indicate that tests for autocorrelation are inconclusive.

Over 70% of the non-varying parameters in Table 1 are more than twice the size of their standard errors. All expenditure parameters are significant at the 95 % level. The seasonality parameters associated with the second and third quarters in each equation are similarly significant. Price effects in the chicken equation are all significant. Also significant are the beef own-price effect and the cross-price effect between beef and chicken and between pork and chicken. In contrast to the non-varying parameters, only seven of the 24 time-varying parameters are at least twice the size of their standard errors. Four of these significant parameters are associated with the seasonality variables, while the remaining three correspond to the pork expenditure term and cross-price effects between beef and pork.

Likelihood ratio test statistics distributed as chi-square are computed to test the hypothesis of no structural change. These computed values along with

2 16 C A N A D I A N J O U R N A L OF A G R I C U L T U R A L E C O N O M I C S

Table 1 . Gradual switching AIDS model of meat demand ____

__

Equations

Variable Beef Pork Chicken

Non-varying P I

P2

P3

Y

s1

S2

S 3

Time-varying 7-17 c TnP I

TnP 2

TnP 3

Tn Y

TIIS 1

TnS 2

TnS 3

Summary statistics Budget share D ' W ( I ) K 2 Log I~kelihood

0.0552 (0.0260)

(0.0229)

(0.01 16) 0.1475

(0.041 1 ) 0.0020

(0.0025) 0.0094

(0.002 9) 0.0171

(0.0024)

-0.0059

- 0.0494

-0.0761 (0.0489) 0.1137

(0.0589) -0.1043 (0.05 12)

-0.0094 (0.0249)

(0.0702)

(0.0042) 0.0085

(0.0057) 0.0083

(0.0043)

- 0.0784

-0.0069

-0.0059 (0.0229) 0.0372

(0.0234) -0.0315 (0 01 12)

-0.0834 (0.0387)

(0.0023)

(0.0027)

-0.0009

-0.0159

-0.0246 (0.0023)

0.0384 (0.0460)

(0.05 12) 0.0929

(0.05 I I ) 0.01 14

(0.02 15) 0.1320

(0.0659) -0.0022 (0.0039) - 0.0 1 6 I (0.0052)

(0.0040)

-0.1043

-0.0108

-0.0494 (0.01 16)

-0.0315 (0.01 12) 0.0809

(0.0 137) - 0.0640 (0 .O 16.5)

-0.001 1 (0.OOlO) 0.0065

(0.00 12) 0.0075

(0.00 10)

0.0377 (0.0196)

(0.0249) 0.01 14

(0.0215) -0.0020 (0.0236) -0.0536 (0.0284) 0.0091

(0.0017) 0.0076

(0.0023) 0.0025

(0.00 18)

-0.0094

0.5425 0.3419 0.1156 2.37 2.32 2.44 0.82 0.87 0.79

615.39 Sample 1968, QI to 1987, Q4 -


Table 2. Testing for structural change

Hypothesis of no Likelihood ratio structural change test statistic

All parameters 65.70 Intercept parameters 4.48 Price and expenditure

parameters 11.38 Seasonality parameters 37.86 Smooth structural change 6.00

Degrees of 2 freedom X i " 1 x o 05

I I 27.69 22.35 2 9.2 1 5.99

3 11.34 7.81 6 16.81 12.59 2 9.21 5.99

associated degrees of freedom and critical values at the 0.01 and 0.05 probability levels are given in Table 2. The hypothesis of no structural change in all parameters, in the price and expenditure parameters and in the seasonality parameters are all rejected at the 0.01 probability level.

The above tests provide strong indications of structural change in Canadian meat demand, and the estimated join points suggest that the change began during the first quarter of 1975 and was completed in the first quarter of 1984 - a transition period of almost 10 years - implying a very gradual structural change adjustment. The structural change path represented by the estimated join points and the adopted transition path does not necessarily rule out other structural change paths. For example, while the hypothesis of a smooth structural change path, t / T, associated with a chi-square test statistic of 6.00 with two degrees of freedom, is rejected at the 95% level, it cannot be rejected at the 99% level. A transition path that allows a non-linear structural change path represents yet another possible structural change path that is not accommodated in the model specification.

Since, with the exclusion of fish, this study includes the same goods and uses the same methodology as Moschini and Meilke (1989), a comparison between the results obtained for Canada and those obtained for the U.S. is feasible. In conformity with the results for Canada, Moschini and Meilke suggest that the structure of meat demand in the U.S . also changed and that this change started in the later part of 1975. However, in contrast with the results for Canada, they report a transition period of only one year, suggesting that the structural change was much more rapid in the U.S. than in Canada.

Atkins et a1 (1989), using a single-equation approach and the assumption that structural change occurred during the fourth quarter of 1977, reject the hypothesis of no structural change in Canadian beef demand, but find no such evidence of structural change in Canadian demand for pork and chicken. Structural change in beef demand is attributed to declining disposable income. Young (1987), on the other hand, with the same single-equation approach, finds evidence of structural change in Canadian demand for pork, chicken and turkey, but finds no such evidence for beef. The estimated structural change break point for pork is the first quarter


Table 3. Bias of structural change

Mean share

Meat group Bias 1968, Q1 to 1975. Q1 1984, Q1 to 1987. Q4

Beef - 0.0736 0.5561 0.5072

Pork 0.0312 0.3455 0.3490

Chicken 0.0425 0.0984 0.1439

(0.0488)

(0.0459)

(0.0 195) - ~ _ _

of 1974, for chicken the second quarter of 1978 and for turkey the third quarter of 1978. As alluded to above. both of these studies preclude the possibility of a gradual switch in regimes.

BIAS OF STRUCTURAL CHANGE The results concerning bias of structural change are presented in Table 3. According to the signs and significance level of the estimates of structural change bias, the structural change appears to be biased away from beef consumption and toward the consumption of chicken, while pork consumption appears to be neu- tral. To test the hypothesis of no bias of structural change, a Wald test statistic with two degrees of freedom is computed at 5.41. Comparison with a corresponding critical value of 4.61 at the 0.10 probability level suggests the rejec- tion of such a hypothesis. The results obtained by Moschini and Meilke for the U.S . also suggest that the structural change was biased away from beef toward white meat (chicken and fish).

IMPACT OF STRUCTURAL CHANGE ON DEMAND ELASTICITIES

In estimating Marshallian elasticities, the study follows two different approaches. In the first approach. the mean of the budget shares after and before structural change are taken to represent W,,, and W,b, respectively. The second approach follows that of Moschini and Meilke, and allows the mean of the budget shares over the entire sample to represent W,, , while W,, is obtained by subtracting the average bias measure shown in Table 3 from W,(,. This second approach allows the evaluation of elasticities at the same level of the exogenous variables.

With regard to Marshallian elasticities estimated in accordance with the first approach (Table 4), all the expenditure elasticities associated with the period before structural change are at least twice the size of their standard errors. Beef is por- trayed as a luxury good while pork and chicken are characterized as necessities. Own-price elasticities are of the expected signs, but only the own-price elasticities of beef and pork are significant. Among the cross-price elasticities, only


Table 4. Marshallian elasticities (evaluated at mean of budget shares before and after structural change)

Price of

Elasticity of Beef Pork Chicken Expenditure

Before structural change: Beef - 1.0482 -0.1020 -0.1 I50 1.2652

(0.0599) (0.0497) (0.0226) (0.0740)

Pork 0.1176 -0.8088 -0.0673 0.7585 (0.0881) (0.0793) (0.0347) (0.11 19)

Chicken -0.1406 -0.0948 -0.1139 0.3493 (0.1406) (0.1254) (0.1423) (0.1673)

After structural change: Beef -0.7359 - 0.2646 -0.1356 1.1361

(0.0981) (0.0877) (0.0420) (0.0995)

(0.1288) (0.1243) (0.0529) (0.1356)

Chicken 0.0055 0.1459 -0.3342 0.1829 (0.1366) (0.1211) (0.1272) (0.1442)

Pork - 0.3 860 -0.6756 - 0.0774 1.1391

the price elasticity of substitution between beef and chicken, and between beef and pork, are significant at the 95% level. The signs of these cross-price elasticities suggest complementary relationships. In fact, as in the case of the results of Moschini and Meilke (1989), most of the cross-price elasticities (both before and after structural change) suggest complementary relationships. This contrasts with some previous Canadian studies (Curtin et al 1987; Hassan and Johnson 1976) that in general find the three meat items to be substitutes for each other.

With regard to the Marshallian elasticities corresponding to the period after structural change, eight of 12 elasticities are at least twice the size of their standard errors. More importantly, several of the elasticities have changed consider- ably from the elasticities obtained before structural change. Though still classi- fied as a luxury good, beef is now less elastic and, with an expenditure elasticity of 1.15, pork has changed from a necessity to a luxury good. The expenditure elasticity of demand for chicken has decreased from 0.35 to 0.18 but is now insignificant. The cross-price elasticity between pork and beef is now negative and significant. The own-price chicken elasticity has also changed to being significant. Along with changes in signs and levels of significance, some of the price elasticities have also changed in magnitude. For example, while beef and pork have become less price elastic, the size of the own-price elasticity of chicken has about tripled in absolute value.


Table 5. Marshallian elasticities”

Price of

Elasticity of Beef Pork Chic ken Expenditure

Before structural change: Reef - 1.0578

(0.0567)

Pork 0.1368 (0.1030)

Chicken -0.1367 (0. I97 1 )

After structural change: Beef -0.7576

(0.0932)

Pork -0.3991 (0.1339)

Chicken 0.0427 (0.1723,

-0.0838 (0.0436)

(0.0860)

(0.1657)

-0.7963

-0.1581

-0.2465 (0.08 17)

- 0.6679 (0.1265)

0. I744 (0.1503)

-0.0977 (0.0198)

(0.0376)

0.1706 (0.1901)

-0.0816

-0. 1232 (0.0381)

-0.0750 (0.0522)

-0.1999 (0.1561)

1.2393 (0.0668)

0.7315 (0.1245)

0.1241 (0.2252)

1.1273 (0.0930)

1. I420 (0.1384)

-0.0172 (0.1796)

“Computed wlith the mean of the buget share over the entire sample representing W,,, , while the result of subtracting the bias measure reported in Table 3 from WJ(, is used to represent W,,, .

The expenditure elasticities reported above appear to be of larger magnitude than those of some previous studies. For example, based on 1950-75 data, Hassan and Johnson (1976) report income elasticities of 0.51, 0.13 and 0.15 for beef. pork and chicken, respectively. Using more recent data (1973-85). Curtin et a1 report income elasticities (0.18. 0.07 and 0.08) of even smaller magnitude. However. while the expenditure elasticities computed here are conditional on total group expenditures. the estimated elasticities of both of these studies are based on total income. In contrast to the expenditure elasticities. the own-price elasticities are within range of results reported by these studies.

To test the importance of the estimated changes in Marshallian elasticities that have taken place, the standard errors of the difference between before structural change elasticities and after structural change elasticities are computed. These standard errors reveal that the change associated with pork expenditure elasticity. beef own-price elasticity and cross-price elasticity between pork and beef are significant at the 95% level. Moreover, based on a Wald test with five degrees of freedom. the hypothesis of no change in Marshallian elasticities as a group is rejected at the 0.02 probability level. This test suggests that changes in

STRUCTURAL CHANGE IN CANADIAN MEAT DEMAND 22 1

consumer preferences have interacted with meat prices and/or expenditures to the extent of changing the pattern of consumer response to changes in these variables.

Estimated Marshallian elasticities computed in accordance with the second approach are presented in Table 5 . Beef and pork expenditure and own-price elasticities are comparable with the results of the previous method. But regarding the chicken expenditure and own-price elasticity, there are significant differences. For example, in contrast to the first approach, the before structural change chicken expenditure elasticity is insignificant, while the chicken own-price elasticity is of the wrong sign and is insignificant. Similarly, the chicken after structural change expenditure elasticity is negative and insignificant.

SUMMARY The study strongly rejects the hypothesis of no structural change in Canadian meat demand. Instead, results suggest that a gradual change, starting in 1975 and completed in 1984, took place in the structure of Canadian meat demand. The structural change is found to have had a significant impact on some of the estimated parameters of the model. Furthermore, estimates of bias of structural change suggest that the structural change was biased in favor of chicken to the disadvantage of beef. The time coincidence of structural change with the shift in consumer preference away from fatty foods suggests that this dietary change may have con- tributed in part to structural change in meat demand. Accordingly, a suggested industry response would be to focus attention on the production of lean meat and at the same time engage in promotional programs designed to change negative attitudes toward meat.

NOTE

'Other possible causes of the observed shift from red meat to white meat consumption include changes in such factors as relative prices, real income, demographics and lifestyles. Changes in the pattern of meat consumption resulting from income and price movements, however, are not construed as structural change because price and income changes are not expected to effect changes in structural parameters.

REFERENCES

Atkins, F. J. , W. A. Kerr and D. B. McGivern. 1989. A note on structural change in Canadian beef demand. Canadian Journal of Agricultural Economics 37: 513-24. Braschler, C. 1983. The changing demand structure for pork and beef in the 1970s: Impli- cations for the 1980s. Southern Journal of Agricultural Economics 15: 105-10. Chalfant, J. A. and J. M. Alston. 1988. Accounting for changes in tastes. Journal of Political Economy 96: 391-410. Chavas, J. P. 1983. Structural change in the demand for meat. Amrricun Journal of Agricultural Economics 6.5: 148-53.

222 CANADIAN JOURNAL. OF AGRICULTURAL ECONOMlCS

Dahlgran, R . A. 1987. Complete flexibility systems and the stationarity of U.S. meat demand. Wc.stern Joirrnul of Agricirlturul Economics 12: I 52-63. Deaton, A. and J . Muellbauer. 1980. An almost ideal demand system. Anwrican Eco- nomic Rwicw. 70: 3 12-26. Eales, J . S. and L. C'nnevehr. 1988. Demand for beef and chicken: Separability and structural change. Atncv%xni Joicrriul of Agriciclrurul Ecoriornics 70: 52 1-32. Hassan, Z. A. and S. R . Johnson. 1976. Consumer demand for major foods in Canada. Economics Branch Report 76/2. Ottawa Agriculture Canada. Curtin, L., D. 'ThkorOt and M. Zafiriou. Demand for foods in Canada: Recent estimates. Policy Branch. Working Paper 13/87. Ottawa: Agriculture Canada. Moschini. G . and K. D. Meilke. 1984. Parameter stability and the U.S. demand for beef. Wcmwi Joi~rnc11 of Agriciilrurul Econornicx 9: 27 1-82. Moschini, G . and K. D. Meilke. 1989. Modeling the pattern of structural change in U S . meat demand. AmcJrrcutr J o u r n d of Agricu/tirruI Economics 7 I : 253-6 1 . Nyankori, J. C. 0. and G. H. Miller. 1982. Some evidence and implications of structural change in retail demand for meats. Souflwrn Journnl ufAgriculturu1 Eiwiornic~.s 14:

Thurman, W. N. 1987. The poultry market: Demand stability and industry structure. American Joirrniil of Agricrrlturd Ecoinottiit:~ 69: 30-37. Uohlgenant, M. K. 1985. Estimating cross elasticities of demand for beef. Western Journal o j Agriciilturid Ecorioniic.s 10: 322-29. Young, L. J. 1987. Canadian meat demand. Policy Branch Working Paper 10187. Ottawa: Agriculture Canada. June.

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