Capturing structural changes in French meat and fish demand over the period 1991–2002

1. Introduction

In March 1996, French consumers were informed of the link between Bovine Spongiform Encephalopathy (BSE) and new variant Creutzfeldt-Jacob disease (vCJD). This information caused a strong consumer reaction (Perretti-Watel, 2001) since vCJD in humans is fatal. From March to April 1996, the quantity of beef purchased fell sharply by 22.1 per cent and the unit value of beef (ratio of expenditure to quantity purchased) increased by 6.4 per cent, indicating that households opted for more expensive cuts of beef. At the same time, poultry and fish quantities purchased increased by 9.6 and 14.9 per cent, respectively, whereas the unit value of poultry rose by almost 6 per cent and the unit value of fish price remained stable.¹ In November 2000, a second ‘mad cow’ crisis was triggered when a cow was diagnosed in France with BSE. This incident aroused great public concern, and the French authorities were compelled to take two important decisions in December 2000.² From November to December 2000, the volume of beef purchased fell by 23.3 per cent and the unit value of beef increased by 6 per cent, as in the first crisis, whereas poultry quantities sold rose by 10.7 per cent and fish quantity purchased was unchanged, although the unit values of poultry and fish increased by 2.9 and 2.7 per cent, respectively.³ The common feature of the two crises is that there were sharp and sudden changes (in opposite directions) in beef and poultry demand. The objective of this study is to shed new light on changes over the period 1991–2002 in the structure of French meat and fish demand, of which the BSE-induced swings are the most striking.

Structural changes in food consumption are usually studied using time-varying coefficient (TVC) demand systems.⁴ Using this kind of model rather than models that use some kind of information index as a regressor (Burton and Young, 1996; Burton et al., 1999; Verbeke and Ward, 2001; Piggott and Marsh, 2004) has been recently justified by Mazzocchi (2006) in the context of a prominent and sudden food safety incident. He stressed that TVC demand systems ‘result in a better econometric and forecasting performance’ (p.740). Confining our attention to the almost ideal demand (AID) model, several TVC-AID specifications have been developed such as the dynamic AID model, which allows for a linear trend in the intercept (Burton and Young, 1996), and the switching AID (S-AID) model, which includes a trend effect for all parameters and assumes a flexible definition of the transition path of the structural change between two preference structures (Mangen and Burrell, 2001; Moschini and Meilke, 1989; Rickertsen, 1996). A unique and irreversible change in tastes is traditionally assumed in the S-AIDS.⁵ However, this feature makes the S-AID model inappropriate for analysing food demand dynamics caused by the multiple and resurgent risks associated with food, such as BSE crises, food chain contamination with bacteria like salmonella and listeria or with pollutants like mercury and dioxins, and the resulting recurrent food scares (Beardsworth and Keil, 1996). Deschamps (2003) and Mazzocchi (2003) developed original TVC-AID systems to overcome this inadequacy: Mazzocchi (2003) proposed a demand system based on Harvey's (1989) structural time series approach in which the intercept and the other coefficients are assumed to follow a random walk process with drift, and a random walk, respectively; Deschamps (2003) embedded the AID model in a vector-autoregressive distributed lag model with time-varying intercepts. In this paper, an alternative TVC-AID model that is also able to deal with resurgent crises is illustrated: the Markov switching AID (MS-AID) model. To the best of our knowledge, this paper is the first that has applied a Markov switching approach to demand analysis.

The main feature of the MS-AID model is that the switching mechanism from one structure (state or regime) of preferences to another is controlled by an unobserved variable that follows a Markov process. As such, a preference structure may prevail for a random time period, and it may be replaced by another structure when the switch takes place, without requiring any timing information about the crisis onset. Thus, changes in structures are caused by factors other than the studied series; the structure-shift variable determines in which structure the demand system is for each period. Below, it is assumed that the shift variable follows a two-state Markov dynamic process, i.e. there are two structures of preferences possible. Allowing for more than two preference structures, which is theoretically possible in the MS-AID model, requires more data, especially following a crisis, in order to get reliable estimates. The need for a large dataset in order to allow for more than two preference regimes is a limitation of the Markov switching model. However, in our application, assuming two preference structures makes sense given the work of Setbon et al. (2005). They showed that the strong preference for red meat of French consumers, whose level was well established before the vCJD risk became known, was conducive to the acceptability of this risk and to a return to a consumption pattern close to the one prevailing before the crisis, after a certain length of time, even though beef is still perceived as a risky good. These authors assessed individuals' preference for red meat using a composite index constructed on the basis of their agreement with the following two statements: ‘Red meat is the meat that I prefer’, and ‘Ceasing to eat beef would be a great sacrifice for me’.⁶ They showed that their index is the main variable explaining reduced avoidance of red meat. Indeed, it seems to partly neutralise the perceived risk of BSE. Its high level in France would explain why French beef consumption can return to a level close to its level before the crisis.⁷ However, we must stress that in general, the assumption of just two states in the Markov process could be very restrictive.

The second feature of the MS-AID model is that changes in structure are stochastic and the probability of the occurrence of each structure of preferences for each period is estimated. Therefore, we know with a certain degree of confidence in which preference structure the demand system was and how many periods it stayed in each structure. This is an advantage in comparison to the S-AID model, and the TVC-AID model. Moreover, assuming that the shift variable follows a Markov process enables us to deal with both sudden and sharp changes in tastes, as was the case for the first and the second BSE crisis, as well as for smooth transition periods that may characterise meat and fish demand dynamics between two preference regimes.

Our empirical application uses 4-weekly data on aggregated French household expenditures and purchased quantities of meat and fish over the period January 1991 to December 2002. We find that our model is able to capture shifts in preferences accurately: the demand for meat and fish indeed shifted twice from one preference structure to the other, and the dates of each shift exactly correspond to the start of each BSE crisis. Furthermore, we find that though the model is built on the assumption that the two crises are similar in terms of changes in preferences, it estimates different lengths for each crisis: the 1996 BSE crisis lasted almost three years, whereas the second BSE crisis lasted five 4-week periods only.

The paper is organised as follows. In Section 2, the MS-AID model is presented. In section 3, the estimation method is described, and the data and results are presented in Section 4. Section 5 concludes.

2. MS-AID model

3. Estimation

1) The optimal inference about preference structures and evaluation of the log-likelihood function L(Ξ), given the value of Ξ.

The log-likelihood function L(Ξ) for the observed data Ω_T is then calculated at the value of Ξ that was used to perform the previous iteration and by noting that the density of the observed vector w_t given past observables is p(w_t/ℵ_t;Ξ) = 1′(ξ_{t/t − 1}°η_t).

2) Estimation of Ξ by maximising the observed log-likelihood function L(Ξ), knowing the optimal inference about preference structures.

Knowing the optimal inference about preference structures, a new value of Ξ is obtained by maximising the observed log-likelihood function L(Ξ). The maximisation was performed using the traditional Broyden–Fletcher–Goldfarb–Shanno (BFGS) method developed in the GAUSS library Optnum. To start the algorithm, we used for each preference structure the same parameter values obtained by estimating the AID model, representing the price index by the Stone index,¹⁰ and the transition probability matrix Π is set equal to the identity matrix.

Hamilton (1996) developed several specification tests for Markov-switching time-series models. The Appendix present tests for misspecification of the Markovian dynamics (White test for the violation of the first-order Markov assumption), and omitted variables (Lagrange multiplier test).

4. Data and results

4.1. Data and descriptive statistics

The data were collected for market research purposes by TNS-SECODIP (Taylor Nelson Sofres-Societé d'Etude de la Consommation, Distribution et Publicité), which has been recording all weekly food expenditure and quantities purchased for a sample of around three thousand households since 1989. Households are selected by stratification according to several socioeconomic variables to provide a panel data set representative of the French population. They stay in the panel for 4 years on average. Each week, households are asked to register their expenditures and quantities for each item bought for home consumption. The items of interest in our study are meats (beef, veal, lamb, horse, pork and poultry) and fish.

Household expenditures and quantities between January 1991 and December 2002 were aggregated on a 4-week basis using a weighted average,¹¹ leading to a sample of 156 observations. Meats were combined into the following groups: beef and veal, poultry and ‘other meat’ (comprising lamb, pork and horsemeat).¹² Fish is considered as one group. For each group, SECODIP provides quite detailed information describing the particular cut of meat and fish, the packaging, if it is frozen, canned or fresh item and if it is pre-prepared. Prepared meats and fish are omitted from our database,¹³ and only canned, fresh and frozen meats and fish are retained. Mollusc and shellfish expenditures are also omitted from our data.¹⁴ Particular attention was paid to the time consistency of our data: each group of meats and fish is composed of the same items over time. Specifically, if a good is not recorded for one period or a new good appears in a group during the studied period, it is excluded from our data set.¹⁵ Fortunately, the items excluded from our data set for this reason over the sample period represent on average less than 0.8 per cent of the quantity purchased of the corresponding group of meats and fish.

Table 1 presents summary statistics for aggregate per capita quantity and expenditure in each group before and after the first BSE crisis. Figure 1 shows the observed expenditure shares. On average, the expenditure and quantity of beef fell sharply after the 1996 crisis, whereas poultry and fish expenditures and quantities increased. The expenditure and quantity of ‘other meat’ slightly decreased after the crisis. This is due to a general decrease in lamb purchases in France (pork and horse consumption stays almost constant over the period), and can be attributed to a general shift from red meat towards white meat and fish (Insee Première, 2002).

4.2. Tests on the structure of the MS-AID model

Different MS-AID specifications are tested to determine which model better explains the dynamic of French meat and fish demand. First, we want to select the variables that should be included in the intercept term α_i,st. Second, we examine whether a Markovian switching mechanism has to be applied also to prices and/or per capita total expenditure.

Eight different models for the intercept are tested in conjunction with four different possible options regarding prices and per capita total expenditure. Specifically, the eight-intercept models are characterised by the following specifications of α_i,st

Model 1 contains a Markovian constant only, Model 2 adds a set of 4-week dummies to Model 1; Model 3a (3b) expands Model 2 by including lagged expenditure shares without (with) a Markovian parameter switch, Model 4a (4b) is Model 3a (3b) with the addition of a time trend without a Markovian parameter switch, and Model 4c (4d) represents Model 3a (3b) with a Markovian-switching trend parameter.

Then, for each of these eight models, four different specifications for the parameters of prices and per capita total expenditure are considered: option I is characterised by no Markov effect on prices and total expenditure, option II allows a Markov switch for prices only, option III incorporates Markovian switching parameters for per capita total expenditure but not for prices, and option IV includes Markovian switching parameters for prices and per capita total expenditure.

The first interesting result is that all the specifications considered exactly detect the start of each BSE crisis. However, the estimated duration of each BSE crisis for each option and each model is different: the estimated duration of the effects of the first BSE crisis effects on meat and fish demand ranges between 11 and 38 4-week periods, and the duration of the second BSE crisis effects ranges from 5 to 12 4-week periods.

For each estimated model, a White test for the violation of the first-order Markov assumption was implemented. We used an F(2,T − m) distribution rather than a χ² (2) distribution despite our large sample size (156 periods), where m is the number of estimated parameters, and T the number of observations.¹⁶ Table 2 shows the p-values of the test.

All the models are rejected for options II, III and IV. We conclude that parameters on prices and per capita total expenditure are not affected by structural change. Introducing lagged per capita expenditure shares leads to acceptance of Markovian switching in option I. However, introducing a Markovian-switching parameter for the trend leads to rejection of the Markovian dynamics assumption in option I; therefore, Models 4c and 4d should be rejected.

Then, Lagrange multiplier tests for omission of explanatory variables were used to determine which specification from 3a, 3b, 4a and 4b should be retained. Table 3 reports the Lagrange multiplier test results, performed at the 5 per cent level of significance.¹⁷ First, we tested whether any lagged expenditure shares are needed (with and without Markovian-switching parameters) in the MS-AID model with switching constant terms and seasonal dummies (Models 3a and 3b). The null hypothesis for both tests was strongly rejected. Then, we tested whether the trend variable should be added to Models 3a and 3b. Table 3 (rows 4 and 5) shows that the hypothesis of no trend is also rejected. Finally, two overall Lagrange multiplier tests were used to check whether the previous tests are globally coherent. The two null hypotheses are rejected.

We then examined whether the parameters on the lagged expenditure shares are or are not subject to Markovian switching; in other words, which of Models 4a and 4b should be chosen? At first sight, a traditional Likelihood Ratio test (LR) testing Model 4a against Model 4b looks suitable for this test. However, the asymptotic distribution of the LR test is not standard in Markov switching models.¹⁸ Comparing the two models on the basis of their estimates, we see that Model 4a always provides very similar estimated parameters for expenditure shares between the two preference structures, and switches in tastes are very frequent. By contrast, the MS-AID system characterised by Markovian-switching parameters on lagged expenditure shares (Model 4b) yields quite different estimated parameters on lagged expenditure shares in the two regimes, and more realistic structural switching dynamics. Comparisons of the maximised log likelihood functions and the AIC also lead us to choose Model 4b. The choice of Model 4b is very meaningful, since it highlights, first, that past consumption has an impact on current consumer choice, as it is also found by Adda (2000) and Mazzocchi et al. (2006), and second, that there is a possible adaptation of habit formation between regimes, as was also found by Adda (2000).

4.3. Structural change dynamics and parameter estimation

Figure 2 shows the evolution of the changes in preference structure for meat and fish demand, where each point gives the value of the probability of being in the ‘crisis’ regime of preferences p(s_t = 2/Ω_T; Ξ) for each period t. It provides a precise idea of the nature of the transition between the two structures of preferences. The MS-AID model perfectly detects the start of the first (1996:04) and the second BSE (2000:12) crisis. Interestingly, the effects of the 1996 BSE crisis on beef and poultry demand fully disappeared in February 1999: the estimated probability that meat and fish demand on February 1999 was in the non-crisis regime is equal to one: p(s_t = 1/Ω_T; Ξ) = 1. The estimated effects of the 1996 BSE crisis lasted almost 3 years in France. The effects of the second BSE crisis lasted a shorter time: the probability that French meat and fish demand is in the post-crisis regime is equal to one from the two last 4-week periods of 2000, then, in February 2001 this probability becomes 0.54, and it decreases to zero on April 2001. Thus, the estimated effects of the second crisis fully disappear in five 4-week periods. We also find that the effects of the two crises end abruptly. We would have rather expected to find a smoother transition when meat and fish demand returns to the non-crisis regime. This ‘result’ may reflect the difficulty of the MS-AID model to capture smooth changes. The Markovian dynamics may create a bias towards finding sudden regime switches.

Table 5 reports the estimated parameters for intercepts, trend and own-lagged expenditure shares. We find that the structural switch to the second regime, s_t = 2, reduces the intercept for beef and increases the poultry intercept. Surprisingly, the shift has a negative estimated impact on the intercept of the fish expenditure share. However, as was stressed above, the overall effect of the structural change is nil for fish expenditure share. The coefficients on the trend term are significant, although very small, in the beef and poultry expenditure share equations. Furthermore, it plays a significantly negative role for the beef expenditure share and a positive role for the poultry expenditure share. Moreover, the parameter values of the own-lagged shares are significant for all shares and the two regimes, except for poultry when s_t = 2. These results suggest that habit formation played a key role in determining consumer choice in the context of BSE crisis, as was also found by Adda (2000) and Mazzocchi et al. (2006) in Italy. Interestingly, habits are less persistent for beef and fish demand since the effect of past consumption on beef and fish expenditure shares is significantly higher when s_t = 1 than when s_t = 2, and past consumption of poultry is no longer significant for poultry in the crisis structure. These effects are small but significant, and illustrate the role of food scares in changing habits, as was found by Adda (2000). Significance tests on the set of seasonal dummies did not reject it, and quite a few seasonal effects were found to be significant (not shown here). In particular, we found that beef expenditure is significantly less during summer, and over the two last 4-week periods of the year, and poultry and fish expenditure is significantly higher during the Christmas period.

4.4. Elasticities

All own-price elasticities have the correct sign, and some cross-price elasticities have a negative sign. However, these latter estimates are not significant, and all compensated cross-price elasticities have the expected sign.²⁰ If we compare these estimated values with those obtained in a dynamic AID model (i.e. including 4-week dummies, trend and lagged expenditure shares) without the Markov switching mechanism, we find that we systematically underestimate the effects of own-prices on the expenditure shares of all goods if structural changes are ignored.²¹ If we focus our attention on the MS-AID model, we find that own-price elasticities for poultry, fish and ‘other meats’ are equal in both regimes. Thus, the structural shift does not seem to modify the effect of prices on poultry, fish and ‘other meat’ demand. This result is consistent with the rejection of options II and IV that allow for switching parameters on prices.

5. Conclusion

The objective of this study was to shed new light on change over time in the structure of French meat and fish demand with regard to the two French BSE crises, by applying a Markov switching approach to the AID model. The main advantage of the MS-AID model compared with the latest TVC-AID models is that the start and the end of each preference regime are determined using the estimated probability of occurrence of each regime, for each period. As such, it provides a precise idea of the dynamics of changes in tastes, conditional on the number of preference regimes assumed.²² In our application, we found that the MS-AID model is able to capture accurately very sudden shifts in preferences, and to assess the length of these changes in preferences, without requiring any timing information about the crisis onset: our chosen MS-AID specification perfectly detected the start of the two mad cow crises, the effects of the first BSE crisis were estimated to have lasted almost three years, whereas those of the second crisis lasted only five 4-week periods. This is the most striking result of our study.

For policy-makers and others in the French meat industry concerned with assessing the impacts of the two BSE crises on consumption, this research provides three results. First, it highlights the importance of allowing for structural changes when analysing the evolution of demand. Without this, our model would have over-estimated the effects of total expenditure changes on the beef expenditure share, and under-estimated the effects of own-prices on meat and fish expenditure shares. Second, it shows the strong preferences of French consumers for meat in general. We found that in France, unlike the Netherlands (Mangen and Burrell, 2001) and Italy (Mazzocchi (2003)), the ‘mad cow’ crises did not lead consumers to change their fish consumption pattern. Third, it stresses that past consumption of beef is one of the main determinants of the response French consumers' behaviour. Although tastes change when the crisis occurs, this change is moderated by the habit persistence effect even if, as expected, the concern about BSE reduces the effect of habit persistence when the crisis occurs. Thus, this paper confirms the findings of Adda (2000) and Mazzocchi et al. (2006) regarding the importance of past consumption for explaining consumption behaviour and it highlights the role of food scares in changing habits.

The MS-AID model illustrated in this paper is well adapted to the analysis of demand that is affected by sudden, strong and recurrent shocks. Regarding the multiple and resurgent risks associated with food, and the resulting food scares, the implementation of a more general MS-AID model more than two preference states could be a fruitful development. However, assuming more regimes of preferences implies the need for a large dataset. A comparison with other alternative forms of TVC demand models, which allow smoother transitions between consumption patterns, such as those developed by Deschamps (2003) and Mazzocchi (2003), would also be very instructive in the context of a food scare. In particular, we could then check whether there is a bias towards finding sudden regime-switches with the MS approach.

Acknowledgements

This paper has benefited substantially from constructive recommendations and comments from Jérôme Adda, Christine Boizot-Szantai, Patrice Bertail, Martin Bruegel, Fabrice Etilé, Sébastien Lecocq, three anonymous referees and the editor, Alison Burrell. The usual disclaimer applies.

Appendix

The following appendix presents the specification tests for the MS-AID model first developed by Hamilton (1996). They are based on the implementation of the score, the derivative of the observed log-likelihood with respect to Ξ at period t, denoted below h_t (Ξ). Allais (2007), largely following Hamilton (1996: 133–138), shows how to calculate them in the context of MS-AID model.

A1. Implementing the Newey–Tauchen–White test for dynamic misspecification

A2. Lagrange multiplier test

References