Mandatory labels, taxes and market forces: An empirical evaluation of fat policies

Mandatory labels, taxes and market forces: An empirical evaluation of fat policies

Journal of Health Economics 43 (2015) 27–44 Contents lists available at ScienceDirect Journal of Health Economics journal homepage:

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Journal of Health Economics 43 (2015) 27–44

Contents lists available at ScienceDirect

Journal of Health Economics journal homepage:

Mandatory labels, taxes and market forces: An empirical evaluation of fat policies Olivier Allais a,∗ , Fabrice Etilé a,b , Sébastien Lecocq a a b

INRA, UR1303 ALISS, F-94205 Ivry-sur-Seine Cedex, France Paris School of Economics, F-75600 Paris, France

a r t i c l e

i n f o

Article history: Received 26 June 2014 Received in revised form 8 June 2015 Accepted 10 June 2015 Available online 25 June 2015 JEL classification: H32 I18 L13 Keywords: Mandatory fat-content label Ad valorem tax Quasi-natural experiment Firm strategic pricing Differentiated products

a b s t r a c t The public-health community views mandatory Front-of-Pack (FOP) nutrition labels and nutritional taxes as promising tools to control the growth of food-related chronic diseases. This paper uses household scanner data to propose an ex-ante evaluation and comparison of these two policy options for the fromage blanc and dessert yogurt market. In most markets, labelling is voluntary and firms display fat labels only on the FOP of low-fat products to target consumers who do not want to eat fat. We here separately identify consumer preferences for fat and for FOP fat labels by exploiting an exogenous difference in legal labelling requirements between these two product categories. Estimates of demand curves are combined with a supply model of oligopolistic price competition to simulate policies. We find that a feasible ad valorem fat tax dominates a mandatory FOP-label policy from an economic perspective, but both are equally effective in reducing average fat purchases. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In the context of a worldwide rise in overweight and obesity, mandatory labelling and tax policies have attracted a great deal of interest from policy makers and public health advocates. We here provide an empirical evaluation of these policies, focusing for heuristic purposes on a segment of the yogurt market. Using a structural econometric approach, we estimate the impact of Frontof-Pack (FOP) fat labels on key market and health outcomes, such as the equilibrium prices, market shares, firm profits, consumer welfare, fiscal revenues and fat purchases. We show that mandatory labelling reduces average fat purchases, despite market forces – consumer valuation of (and reaction to) information and prices, and firm pricing strategies – that may defeat such a well-intended public health policy. However, a feasible ad valorem fat tax policy is found to be as effective in terms of public health, and more effective in terms of economic surplus.

∗ Corresponding author at: INRA, UR1303 ALISS, 65, bd de Brandebourg, 94205 Ivry-sur-Seine Cedex, France. Tel.: +33 149596931. E-mail addresses: [email protected] (O. Allais), [email protected] (F. Etilé), [email protected] (S. Lecocq). 0167-6296/© 2015 Elsevier B.V. All rights reserved.

Fat in calories available for human diet represents between 40 and 45% of total daily calorie intake in most OECD countries, as against 20–30% one century ago. This trend has been related to cardiovascular and cancer risks and to the spectacular growth in obesity and overweight, which has reached epidemic proportions globally, with more than 1 billion adults being overweight worldwide in 2010 (see OECD, 2010; Etilé, 2011, for example). In this context, the OECD has called for the implementation of tax policies on food items with high fat or sugar contents (Cecchini et al., 2010).1 Nutritional taxes on unhealthy food are attractive for two reasons. A first standard reason is that they may compensate various externalities such as the healthcare overspendings generated by the growth of diet-related diseases.2 Second, they may help reduce the lack of self-control that people have over their food

1 In 2009-2010, additional taxes on sugary drinks were proposed in at least 17 U.S. States; Denmark introduced a 25% tax increase on ice cream, chocolate, sweets and soft-drinks in January 2010 (Danish Ministry of Taxation, 2009), and a tax on fat in October 2011, which was withdrawn in November 2012; in Hungary, a tax on various processed products was imposed in 2011; in France, a tax on soft-drinks was introduced in January 2012. 2 Finkelstein et al. (2009) estimate that, for the U.S. in 2006, obesity and overweight alone are associated with $86 billion of medical spending, representing about 10% of national medical expenditures. The total cost of obesity and overweight for


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choices. Marketing studies have shown that individual perceptions of product characteristics are naturally biased, which is used by the food marketing to influence consumer choices (Chandon and Wansink, 2011). A separate public policy proposed by the European Parliament is the mandatory labelling of the nutrients content on FOPs: this is more salient and easier to use than the back-of-pack nutritional facts panel, which is already mandatory.3 To date, FOP nutritional labelling has been voluntary for almost all food products. FOP labels may a priori help consumers move from high to low fat-content products (Wansink et al., 2004; Grunert and Wills, 2007). Whether FOP fat labels are effective at decreasing fat purchases and increasing consumer welfare, and whether they should remain voluntary or become mandatory are important research questions. One key element of the debate is that voluntary FOP labelling does not only play an informational role; it also contributes to differentiation and market segmentation. When labelling is voluntary, firms are more likely to display fat labels on the FOP of low-fat products to target consumers who do not want to eat fat. This has two consequences. First, a firm decision to introduce a FOP label may depend on unobserved consumer tastes, rendering this product attribute endogenous in the demand function. Second, it is not obvious that making FOP labels mandatory will yield significant and important welfare gains for consumers. Given that the absence of a label can currently be used to infer that the product is not low in fat, mandatory fat labels will essentially help them to better discriminate varieties within the range of products with moderate to high fat levels. We here exploit an exogenous source of variation in legal labelling requirements in the French market for yogurts to identify the causal impact of fat-content labels on consumer choice. This market includes three broad categories of products: standard yogurts, fromages blancs and dessert yogurts.4 The French labelling legislation requires firms to signal the percentage of fat contained in fromages blancs by a fat-content label displayed on the front of the packaging, while fat-content FOP labelling is not mandatory for yogurts. The observation of households purchasing patterns reveal that households tend to substitute between fromages blancs and dessert yogurts, but not between fromages blancs and standard yogurts. We thus restrict the analysis to the relevant market for fromages blancs, which include dessert yogurts but not standard yogurts. The products fall into three fat categories: skimmed, semiskimmed and full-fat. Firms never put FOP fat-content labels on full-fat dessert yogurts, while 50 percent of semi-skimmed dessert yogurts have one. They are required to do so for all fromages blancs, whatever their fat content. Combining this exogenous variation with firm labelling strategies for dessert yogurts, and using the variations in market shares between dessert yogurts and fromages blancs and between products with different fat contents, we can disentangle the consumer preferences for fat-content labels from their preferences for fat. In the empirical application, we use

the French public health insurance is estimated at 4.2 billion euros (in 2003), i.e. 4.5% of annual public health expenditures (Emery et al., 2007). In the U.K., the total medical cost of obesity and overweight was estimated at 1.5 billion pounds in 2002, which represents 3.7% of total net National Health Service expenditures (McCormick and Stone, 2007). Using an instrumental variable approach, Cawley and Meyerhoefer (2012) suggest that these estimates tend to underestimate the actual medical costs, as unobserved heterogeneity (e.g. a strong preference for the present) may be positively correlated with Body Mass Index and negatively correlated with access to healthcares. 3 See EUFIC (2012). 4 The fromage blanc is a creamy, soft, fresh, white cheese made with whole, semiskimmed or skimmed milk. In this paper, following the French legislation, we include in the fromage blanc category the faisselles, which have similar culinary uses. Dessert yogurts include products such as strained/Greek style yogurts and fromages blancs or yogurts mixed with cream or other animal fats.

scanner data from a representative panel of French households, with information on their monthly purchase decisions in 2007, as well as on product and on household characteristics. We apply a three-steps structural econometric strategy that has been recently used by Bonnet and Réquillart (2013) to analyse softdrink taxes. In a first step, we use scanner data, disaggregated at both the household and product levels, to estimate a discrete choice model of demand allowing for substitutions both between varieties of fromages blancs or dessert yogurts and towards an outside option. We represent consumer preferences using a Mixed Multinomial Logit model, controlling for the (usual) endogeneity of prices, but also for the endogeneity of fat-content labels on dessert yogurts. We do so by constructing a control function based on the exogenous source of variation in labelling requirements that has been described above. This estimation approach identifies householdspecific preference parameters and the demand curves for the varieties on the market. In a second step, we model the supply side as an oligopoly proposing differentiated products and competing à la Nash in a Bertrand game, in the spirit of Berry et al. (1995), Nevo (2001). We use the estimated demand curves to identify the price-cost margins for each product and the unit costs of production for firms. Knowing all parameters of firm pricing strategies and consumer purchasing behaviours, we are eventually able to simulate in a third step the new market equilibrium implied by each policy. We compare the mandatory labelling policy to a fat tax policy based on ad valorem tax variations that are compatible with the Value Added Tax (VAT) framework that has been implemented in France in January, 2014: a VAT of 5% is applied to skimmed products, 10% to semi-skimmed products, and 20% to full-fat products. As the VAT rate for yogurts and fromages blancs was at 5.5% in 2007, the simulated fat tax amounts to increasing VAT by 14.5 percentage points (pp) and 4.5 pp for full-fat and semi-skimmed products, respectively, and decreasing VAT by 0.5pp for skimmed products. We find that the mandatory labelling and fat tax policies reduce household fat purchases by −8% and −7 % , respectively. Although quantitatively similar, the impacts of these two policies differ according to the Body Mass Index (BMI) of the household main shopper. The fat tax policy yields higher reductions in fat purchases when the BMI is above 27, while the mandatory labelling policy achieves larger effects for BMIs under 27. We also find that firm price responses are much stronger in the case of the mandatory labelling policy. This is made possible by the sizeable initial margins on dessert yogurts, and high price elasticities just after the policy shock. The fall in margins is partially offset by the recovery of large market shares, which limits profit losses. However, only the market leader, which ex-ante has 30% of the market, can neutralize the fall in profit. A back-of-the-enveloppe analysis also reveals that the fat tax would yield aggregate economic benefits, because it generates high revenues for public finance. By comparison, the mandatory labelling generates large economic costs due to a fall in firm profits that is offset neither by an increase in consumer welfare nor by any additional fiscal revenues. This research contributes to the flourishing literature on market-based public health policies targeting food-related chronic diseases. While food taxes have been extensively studied (see inter alia, Chouinard et al., 2007; Allais et al., 2010; Fletcher et al., 2010; Finkelstein et al., 2013), empirical econometric evidence on the impact of food labels and mandatory labelling policies on natural purchasing behaviour is much more scarce. The major obstacles are the difficulty of finding exogenous sources of variations in firm labelling decisions and credible control groups. Some marketlevel analysis has exploited quasi-natural experiments, such as changes in labelling legislation due to the enactment of the Nutrition Labelling and Education Act (Mathios, 2000; Variyam, 2008), or

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the lifting of a regulatory ban against advertising the health benefits of ready-to-eat cereal (Ippolito and Mathios, 1990). Other works have used field experiments in supermarkets (Teisl et al., 2001; Berning et al., 2010; Kiesel and Villas-Boas, 2013). They have provided mixed results. For instance, Variyam (2008) finds that the U.S. Nutrition Labelling and Education Act (NLEA) has had little impact on the nutrient intake of those individuals who already read the labels prior to the NLEA. Mathios (2000) analyzes the salad dressing market and uncover evidence of a significant decline in the shares of products with the highest fat content. Using scanner data from a field experiment in supermarkets, Teisl et al. (2001) find a positive impact of fat labels on the market share of healthy products for milk and cream cheese. Kiesel and Villas-Boas (2013) also uncover empirical evidence from a similar field experiment. They find that implementing low-fat shelf labels for microwave popcorn decreases sales. However, they cannot evaluate the substitutions within this product category. An additional issue in these papers is that they all have focused on back-of-pack or shelf labels, and have not explored any firm strategic reaction to mandatory labelling. We here complement this research through the combination of a quasi-natural experimental design and the structural modelling of the market. The rest of the paper is organized as follows. Section 2 presents the data and discusses the boundaries of the market. Section 3 outlines the empirical model and the estimation strategy. The estimation results are then discussed in Section 4 and the simulations in Section 5. The last section concludes.

2. Data We use household panel home-scanner data from Kantar WorldPanel (KWP) for the 2007 calendar year. The advantage of scanner data over the experimental or hypothetical choice approaches is that observations are based on actual purchases in a natural shopping environment. Consumer preferences and firm strategies can thus be identified in a realistic setting. There are 13,380 households in the initial sample, which is nationally representative of the French population. The data record, on a weekly basis, all purchases of yogurts and fromages blancs for home consumption made by the household over the year. The Universal Product Code (UPC) of each purchase, the quantity purchased and the expenditure are registered using a handheld scanner. KWP does not directly provide UPCs, but a large set of product attributes. We choose to divide the year into 13 periods of four weeks (the time unit t in the next section). We thus focus on representative purchasing behaviours in each four-week period, i.e. the choices that are the most frequently observed in a sense that will be defined below.5 2.1. The relevant market There are three broad categories of yogurts and fromages blancs: standard yogurts; standard fromages blancs; and dessert yogurts. This market was chosen for three reasons. First, it accounts for a quite substantial share of total household fat purchases (2.75%). Second, a large variety of products are offered, which allows consumers to easily switch from one brand to another. Last, the fact that labelling is mandatory in France for fromages blancs but not

5 Others authors dealing with the same kind of data have made a different choice. For instance, Griffith et al. (2010) choose one unique random shopping trip during the calendar year. In our view, considering the household purchasing behaviour over several four-week periods provides a more representative picture of household preferences. In addition, this reduces concerns about choices being driven by stockpiling motives.


for yogurts makes it easier to identify consumer preferences for labelling and for fat separately. We restrict our analysis to unflavored products, which represent 43% of all purchases of yogurts and fromages blancs. Flavored varieties are complements rather than substitutes to unflavored varieties. They also contain sugar additives, which give firms additional degrees of freedom for reacting to public policies. As such, fat-content labels may be less salient for consumers, and less relevant from a nutritional point of view.6 We also eliminate products that are not made from cow milk (4.5% of purchases), as well as drinking yogurts and yogurts with cereals, which account for less than 1.5% of purchases. In the remaining sample, 46.3% of the households consuming fromages blancs over a four-week period also purchased standard yogurts, while only 5.4% purchased dessert yogurts. These statistics suggest that fromages blancs and standard yogurts are probably not substitutes competing on the same market, which is the case for fromages blancs and dessert yogurts. Following the guidelines of the European Union, the relevant market for a product A comprises all of the products that a significant fraction of consumers consider as substitutes to A in terms of characteristics, prices and intended use.7 A formal test comes from analyzing household yearly budget choices between standard yogurts, dessert yogurts and fromages blancs, in a classic demand-system setting. Household expenditures on these three categories are aggregated over the year, and local price indices are computed for each category, as in Lecocq and Robin (2006). A Quadratic Almost Ideal Demand System is then estimated and the uncompensated cross-price elasticities are derived (Banks et al., 1997; Deaton and Muellbauer, 1980). We find only one significant cross-price elasticity, indicating that fromages blancs are substitutes for dessert yogurts (the elasticity is +0.406). An increase in the price of dessert yogurts or fromages blancs does not significantly impact the consumption of standard yogurts (see the additional results in Appendix A.1). The analysis will hence focus on the relevant market for plain fromages blancs, which includes plain dessert yogurts but not standard yogurts.8 We remove occasional shoppers, defined as those consuming less than 10 weeks over the year, because they are not the target population of the policies we consider. Such a selection leads to underestimate the preferences for the outside option (which may lead to overestimate margins), but it has the advantage of not making inferences from noisy choices and better identifies consumer preferences. This leaves us with data on 1,785 households.

2.2. Product attributes The data contain information on the fat content of all dessert yogurts and fromages blancs, as well as their texture, brand, pack size, type of milk used, whether it is organic or not, and whether probiotics (bifidus) have been added or not. These attributes can be used to describe the alternatives available on the French market in 2007.

6 In addition, the French yogurt and fromage blanc market is characterized by a huge variety of flavors (249 different identified flavors in our dataset), and considering all of these, or even grouping some flavors together, would have rendered the estimation of the model infeasible. 7 See summaries/competition/firms/l26073 en.htm. 8 This result is in line with the professional practice in marketing of considering that dessert yogurts and fromages blancs compete on the market of fromages frais, while yogurts form another market: see for instance the trade publication Linéaires, No. 173 (September 2002), p. 98, No. 187 (December 2003), p. 110, and No. 190 (March 2004), p. 74. A last argument supporting this view is that fromages blancs and dessert yogurts often have the same culinary use: they are both served as desserts, with sugar, jam, honey or fruit frequently being added.


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2.2.1. Fat content and fat-content labels We sort the products into three fat-content categories: fullfat (more than 6% fat), semi-skimmed (between 3% and 6%), and skimmed (less than 3%).9 Fat-content labels are mandatory for all fromage blanc products.10 However, the data do not provide any information about the presence of fat-content labels on dessert yogurts. We have therefore collected additional data from a number of information sources. Our main information source is Mintel’s Global New Products Database (GNPD), which shows high-resolution color images of the packaging of 80% of the products in our dataset, and their changes over time. We have also exploited information from the monthly French professional magazine Linéaires, which provides detailed descriptions and pictures of a number of new food products launched in France every month. Last, we also visited the popular website, which proposes more than 4 billion images, the French consumer network website, and, for a small number of products, TV advertisements broadcasted in 2007 from the on-line audiovisual archives of the Institut National de l’Audiovisuel. 2.2.2. Other characteristics We control for a number of other product characteristics, which were selected because they were significant in preliminary regressions. Differences in hedonic characteristics are captured by a set of discrete variables indicating whether the product is a fromage blanc or a dessert yogurt, and whether it has a traditional or smooth texture. Health characteristics other than the fat content are captured by a dummy variable indicating whether the product is organic or has probiotics added. Another binary variable shows whether the product is sold in individual portions (200 g or less). Last, there are 15 dummy variables that control for firm heterogeneity. The fourteen biggest existing firms are separately considered, including the main producers of national brands (Yoplait, Danone, Triballat, etc.) and the big retailers having their own brands (Carrefour, Leclerc, Intermarché, etc.). The small national producers are grouped together, along with the small retailers. As most firms offer multiple brands, we also control for three levels of brand quality (low-, medium- and high-quality brands). The low-quality category includes hard-discount and first-price retailer brands. The national and high-quality retailer brands form the high-quality category. All these variables are used to describe a set of 279 distinct varieties of dessert yogurts and fromages blancs. To avoid having too much noise in the estimation process, we exclude products that were purchased less than 10 times in a period. This leaves us with 224 different products. 2.3. Household choice set, choice and prices These 224 varieties are distributed through a number of stores, supermarkets and hypermarkets. To simplify the analysis, we define 14 homogenous categories of distribution channels, according to criteria such as the company name (for supermarkets and hypermarkets) and the store format (hard-discount, hyper and supermarkets, grocery stores).11 We retain these two criteria because they are significant determinants of quality positioning

9 This corresponds closely to the division adopted in food marketing; see for instance the professional review Linéaires, No. 187 (December 2003), p. 110. 10 See the décret 88-1206 in the Journal Officiel de la République Franc¸aise, 31/12/1988. 11 The 14 distribution channels are: independent hard discount such as Lidl and Aldi; hard discount Ed; hard discount Leader Price-Franprix; hyper and supermarket Intermarché; hypermarket Carrefour; hypermarket Casino; hypermarket and supermarket Cora; hypermarket Auchan; hypermarket Leclerc; hypermarket and supermarket U; supermarket Carrefour (Stock, Shopi, and Proxi); supermarket Casino (Monoprix, EcoService, PetitCasino, Spar, and Maxicoop); supermarket

and pricing strategies. For each distribution channel, we assume that the set of products that is available in each four-week period is the set of products that is observed in the yearly purchase data for this channel. We know the distribution channels that were visited by each household in each period. We define each household choice set as the set of all products available in these channels. Choice sets therefore vary both from one period to another for the same households, and across households in the same period, if they visited different distribution channels. The empirical analysis is thus made conditional on the predetermined household choice of the distributions channels that are visited in the period. We assume that variations in the prices or labelling of fromages blancs and dessert yogurts do not determine household choice over distribution channels. In addition, any potential selection bias is controlled in the estimates by dummy variables indicating at each period all the distribution channels that were visited by the household and that proposed the variety. If the household did not make any purchases or purchased a single product, then defining choice is not a problem. However, when more than one product was purchased, we have to choose the product that is the most representative of household preferences. In order to avoid arbitrary choices, we select this at random with selection probabilities being proportional to the share of each product in the household annual purchases.12 The price of each product in the household-choice set is constructed in two steps. We first calculate the mean unit price for this product by distribution channel and period; we then average these mean unit prices over the distribution channels that were visited by the household during the period. Prices thus vary over time and between households according to the distribution channels that were visited. 2.4. Market and household characteristics Table 1 presents the summary statistics of the product characteristics, in the universal choice set containing all products and in the union of all household choice sets. Note that there are far fewer low- and medium-quality products in the latter than in the former, simply because many of these are private labels that can be found in only one distribution channel. The main market characteristics are described in Table 2. The final sample contains 8,975 observations on the choices of 1,795 households over five periods. 12 out of the 24 semi-skimmed dessert yogurts have fat-content labels, while none of the full-fat dessert yogurts (20 products) do. Fromages blancs account for 70.8% of choices, dessert yogurts for 23.9%, and the outside alternative of consuming none of these products over a four-week period for 5.4%. More than 54% of the purchased fromages blancs are semi-skimmed, about 23% are skimmed, and as many are full-fat. By way of contrast, 72% of the purchased dessert yogurts are full-fat. On average, full-fat products are more expensive than the others, with smaller variations in prices for dessert yogurts than for fromages blancs.13 Our empirical specification also includes household characteristics: income quartiles, household size, and three dummy variables indicating whether the head of the household is aged over 65, whether the main shopper is classified as being risky overweight (BMI > 27), and whether the main shopper is a man. Table 3 shows the average and standard deviation of these variables in the estimation

Auchan (Atac, and Maximarché); and other distribution channels such as cheesemongers, and grocery stores. 12 For instance, if there are two goods, and the household purchased a quantity Q1 of good 1 and a quantity Q2 of good 2 over the year, then the probability of selecting good 1 in a four-week period where both goods were purchased is Q1/(Q1 + Q2). 13 The fromage blanc is a traditional food product. As such, some product varieties are prestigious and expensive.

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Table 1 Mean values of product characteristics. Variable name Price (std. dev.) Products with a label Skimmed Semi-skimmed Full-fat Fromage blanc Texture Small pack size Organic or bifidus products Low-quality retailer and hard-discount brands Medium-quality retailer brands High-quality retailer and national brands


Smooth Portion < 200 g Organic/bifidus Low-quality Medium-quality Reference

In the universal product set

In the household choice set

2.44 (1.09) 85% 24% 38% 37% 80% 75% 54% 4% 20% 39% 40%

2.71 (1.22) 81% 22% 35% 43% 78% 73% 59% 8% 9% 23% 68%

Notes: Column 2 refers to the variable names in Table 4 below; column 3 refers to the means over 224 products, that is in the hypothetical situation where all households would face all 224 products; column 4 refers to the means over 8,497 observed purchases, that is in the actual situation where each household only faces a subset of the 224 products, those displayed in the visited distribution channels.

Table 2 Market characteristics. Outside option

Number of products (number with a label) Mean prices (std. dev.) in euros Market shares inc. the outside option Market shares exc. the outside option

0 5.4%

Fromages blancs

Dessert yogurts






54 (54) 1.99 (0.88) 16.2% 17.1%

63 (63) 1.98 (0.78) 38.9% 41.1%

63 (63) 2.95 (1.14) 15.7% 16.6%

24 (12) 2.88 (1.36) 6.7% 7.1%

20 (0) 3.09 (0.39) 17.2% 18.2%

Notes: The mean prices are calculated over the universal product set; using the household choice set yields fairly similar results.

Table 3 Household characteristics (N = 1,785).

Monthly household income (D ) Household size Male main shopper Single household Couple without children Couple with children Aged over 65 Body Mass Index (BMI) Main shopper overweight: BMI ≥ 25 Main shopper risky-overweight: BMI ≥ 27 Main shopper obese: BMI ≥ 30 Education = primary Education = high school Education = Baccalauréat Education > Baccalauréat


French population (2007)

2,696 (1,435) 2.6 (1.33) 4% 8% 23% 39% 31% 24.77 (4.23) 40% 26% 12% 25% 33 % 26 % 16 %

3,000 2.31 32.9% 25.8% 29.3% 20.6% 25 43.7% 30.6% 13.1% 28.9% 27.6% 13.1% 19.3%

Notes: Mean over the 1,785 households in our sample; main shopper’s body mass index (BMI) is based on self-reported measures of height and weight; French statistics are from INSEE (2014) and, for BMI, Eschwege et al. (2012).

sample, and in the whole French population in 2007. It is worth noting that the prevalences of overweight and obesity in our sample are very close to the prevalences observed in the population. These variables are interacted with product attributes in our estimation of the demand curves to account for the effect of observable characteristics on preferences. 3. Empirical modelling Following the empirical industrial organization literature, the market is modelled by combining a flexible discrete choice model of demand for differentiated products with a linear pricing model of supply. Discrete choice demand models are particularly appropriate to evaluate accurately policy impacts on specific markets. As food markets are highly segmented, a fat tax or a fat label is more likely to make consumers of a high fat-content variety first exit the market or switch to the nearest low fat-content counterparts in

the same market segment, rather than substitute for a product in another food category. Demand systems for the continuous choice of quantities consumed are better tailored for modelling substitutions between aggregate food categories in the whole diet, but they ignore substitutions within market segment, which results in low cross-price elasticities (see, for an example, Allais et al., 2010). This section describes our analytical framework, together with the estimation strategy and the simulation of each policy option.

3.1. Structural model for the demand side Consumer preferences are modelled in a random utility framework, via a Mixed Multinomial Logit model (MMNL) (Berry et al., 1995; McFadden and Train, 2000). Preferences over product characteristics are specified in a flexible manner, as this allows for both observed and unobserved heterogeneity in the intercept and slopes of the utility function. Household heterogeneity in the Willingness-To-Pay (WTP) for fat-content labels is thus more precisely identified. The MMNL also relaxes the “Independence of Irrelevant Alternatives” constraint imposed by the standard Conditional (or Multinomial) Logit model, which is unlikely to hold at the aggregate level as the choice set varies from one household to another. The identification of the heterogeneity in WTP takes advantage of the panel structure of our data. The intuition is that, in a set of observationally identical consumers choosing the same product, price variations make some consumers switch to another product and some not. Given that the estimation procedure is time-consuming, we first reduce the dataset to an extent by randomly selecting five periods out of 13 for each household. Then, we model the five-choice sequence and estimate the parameters maximizing the probability of observing this sequence (and not five independent choices). This, together with variations in the choice set between households and between periods, makes easier the empirical identification of household heterogeneity in WTP (see Cherchi and Ortúzar, 2008).


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3.1.1. The random utility model Each household i = 1, . . ., N faces a set of Jit products in a choice situation t = 1, . . ., T.14 Each product j ∈ Jit is described as a bundle of characteristics. A number of product characteristics are observable (or can be known by careful inspection or consumption) by the consumers but some of them are unobserved by the econometrician. Examples of the observable characteristics are package size, brand, nutritional facts, etc; the unobserved characteristics include the position of the product within the range of products sold under the same brand or the way it is displayed and advertised on shelves in a particular distribution channel. Formally, denote by pijt the price of good j faced by household i in period t, and lj the binary variable indicating whether a fat-content label is displayed on the packaging of j. Furthermore, let xj denote the vector of observed exogenous attributes of j and let j = 0 be the outside (or no purchase) option, whose characteristics are all set to zero. Considering that each household buys only one product at a time, the utility that household i obtains from the consumption of one unit of good j in period t can be written as p

uijt = vijt + εijt = vi (pijt , lj , xj ; ˛i , ˛li , ˇi ) + εijt ,


where vijt is the deterministic part of utility, depending on the p observed attributes of j, ˛i , ˛li and ˇi are parameters representing the preferences of household i over pijt , lj and xj , respectively, and εijt is unobserved utility. The latter captures the consumer valuation of the unobserved product characteristics. 3.1.2. Endogenous prices and fat-content labels There is empirical evidence that some of the observed and unobserved characteristics are correlated, producing endogeneity problems (Berry, 1994). For instance, promoted products are often moved to the front of the shelf, advertised and sold at a lower price at the same time. The estimated impact of observed prices on demand will then capture both a true price effect and the effect of unobserved marketing efforts. Prices may also be endogenous if some unobserved characteristics are positively valued by consumers, who are thus ready to pay a premium for them. This may be taken into account by firms in setting their prices. In both cases, / 0. we have E(εijt | pijt ) = Following Berry et al. (1995), we instrument the price of product j in period t for household i by the average price of all products (excluding j) available in period t in the distribution channels visited by i. The identifying assumption is that, controlling for firms, distribution channels and demographic factors, the individual valuation of the product-specific unobserved characteristics, εijt , is independent across products. Given this assumption, the valuation of a particular product will be independent of the average price of its rivals. At the same time, common market structures, and production and/or distribution costs imply that the price of a product within a distribution channel will be correlated with the average price of competitors, which can therefore be used as a valid Instrumental Variable (IV). Most papers dealing with endogeneity in MMNL models have focused on price endogeneity, assuming the exogeneity of all other observed characteristics. We here relax this assumption for the fatcontent label. The variable indicating the presence of a fat-content label on the package is endogenous when the firm decision to place the label is based (at least partly) on unobserved determinants of demand, that is when E(εijt | lj = 1) = / E(εijt | lj = 0). This may happen for a number of reasons: for example, because marketing studies

14 In the empirical section below, a choice situation is defined as a four-week period; the set of products is indexed by i as households visit different distribution channels and therefore face different choice sets (see Section 2).

show that a significant group of consumers, characterized by factors which are unobserved to us, are ready to pay for the label; or because the label is correlated with elements of packaging (colors, shapes, etc.), which are also unobserved to us but valued by consumers. It is reasonable to argue that the decision by a firm to put a label on a product is taken once and for all when introducing the product on the market, and that changes in unobserved factors over time, in customer services or in the perception of the product for example, have little to do with it (Ackerberg et al., 2007). If t0 were the date of introduction of the good, we might assume that εijt = εijt 0 + eijt , where εijt 0 denotes the initial unobserved factors that conditioned the decision and eijt is mean independant of the label variable. Then, even if lj cannot be modified by firms after t0 , it is endogenous (in the econometric sense). An IV for fat-content labels can be constructed by exploiting the exogenous variation in labelling rules between fromages blancs and dessert yogurts. Considering the absence of a label as a treatment, we know that the probability of being treated is zero for fromages blancs, regardless their fat content (since labelling is mandatory), and more or less positive for dessert yogurts, depending on their fat content. The interaction between the dessert yogurt and the full-fat (or semi-skimmed) dummy variables is a good predictor of the firm labelling decision: the fatter the dessert yogurt, the less likely the firm is to signal this to consumers. In our data set, full-fat dessert yogurts are indeed never labelled. This interaction dummy variable is our IV and respects the monotonicity condition required for identification. The marginal value of a fat-content label is then implicitly identified from the difference-in-differences in the empirical market shares of fromages blancs and dessert yogurts with different fat contents. The identifying assumption is that the differences in stable unobserved taste factors between fromages blancs and dessert yogurts consumers are the same for full-fat and semi-skimmed products. This assumption and the resulting exclusion restriction hold if consumers of fromages blancs value similarly a fat increase as consumers of dessert yogurts do (see Appendix A.2 for more details). 3.2. Empirical estimation of the demand functions 3.2.1. A control function approach to endogeneity To correct for price and fat-content label endogeneity, decompose εijt as εijt =  εijt +  εlijt +  εijt , p


εijt is the error component related to the price,  where  εlijt the error p

εijt is an i.i.d. component related to the presence of a label, and  extreme-value term. We then apply a control function approach, as proposed by Petrin and Train (2010) for discrete choice models. p Consider the following orthogonal decompositions for  εijt and  εlijt

εpijt = p pijt +  p pijt and εlijt = l lijt +  l lijt , p



where ijt and lijt are jointly normal, and ijt and lijt are i.i.d. standard normal (whose standard deviations  p and  l are estimated). p In this equation, ijt and lijt represent the variations in prices and fat-content labels that are explained neither by the other observed variables nor by the instruments, and which may affect utility (if p or l = / 0). There is endogeneity when these unobserved factors are correlated with prices or fat-content labels. The control funcp tion approach explicitly takes into account the effect of ijt and lijt on utility, by introducing proxy measures of these variables into the estimations. These proxy measures are constructed in a first

O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

stage, as the residuals from the regressions of the price and fatcontent label variables on the vector of all exogenous variables and instruments, zijt p

pijt = ıp zijt + ijt


lj = ıl zijt + lijt ,


where ıp and ıl are vectors of parameters. The estimated residuals, p  ˆ ijt and  ˆ lijt , are called the control functions. Their introduction, as additional explanatory variables, in the regressions solves the endogeneity problem. Examining whether their coefficients, p and l , are significantly different from 0 provides a direct test of endogeneity. 3.2.2. Parameterisation of the utility function Combining (1) to (3), and assuming a linear specification for the deterministic part of the utility function vi (•), we have uijt = vijt + ϕijt +  εijt , where

vijt = −˛pi pijt + ˛li lj + ˇi xj and p


p  ˆ ijt



 ˆ lijt

p +  p ijt


+  l lijt . p

The tastes for observed product characteristics, ˛i , ˛li and ˇi , are modelled as a function of observable household characteristics. As we are primarily interested in the heterogeneity of consumer p preferences for fat-content labels, we further allow ˛i and ˛li to depend on unobservable household characteristics. Formally, denote respectively si and i the vectors of observed and unobp served attributes of household i, and let ˛i = (−˛i , ˛li ). Then ˛i = ˛ ¯ + i + Asi

¯ + Bsi , and ˇi = ˇ

where ˛ ¯ = (−˛ ¯ p, ˛ ¯ l ) is the vector of the average tastes for the price and the label in the population, and A, B and are respectively two matrices and a symmetric matrix of parameters (specifically, is the Cholesky decomposition of the covariance matrix of i ). Under this specification, the elements of ˛ ¯ + i correspond to the ranp dom coefficients of the price and label variables; we assume that ˛i

follows a log-normal distribution and ˛li a normal distribution. The two distributions are correlated (the off-diagonal element of is non-zero). We hence end up with a MMNL model with mixing over the error components and random coefficients for the endogenous variables. The choice probabilities can then be obtained by summing the choices implied by the utility model over the distribution of the unobserved attributes of households in the population of interest, i and  εijt , as well as over the distribution of the error components, p ijt and lijt . Their expression, the likelihood and the estimation procedure are detailed in Appendix A.3. 3.3. Structural model for the supply side Firms are likely to adjust to exogenous shocks, and ignoring their strategic behaviour may lead to biased estimates of the effect of public policies (Griffith et al., 2010; Bonnet and Réquillart, 2013). The simulation of the effects of policy shocks on the market equilibrium therefore requires a structural model of the supply side. In the demand model, two variables result from firm strategic decisions: price and label. In the case of a mandatory labelling policy, labelling is strictly exogenous and only price strategies can be implemented. In the case of a fat tax policy, it seems reasonable, as explained above, to suppose that the labelling decision is taken once and for all when introducing the product on the market. This is also justified by the fact that firms often prefer to introduce new food products


rather than modify the characteristics of existing ones. We thus focus on the price as the only strategic variable for firms. We assume that firms set prices and compete à la Nash-Bertrand to maximise their profit conditional on the demand parameters and the prices of other firms, holding the set of supplied products and every other observed and unobserved characteristics constant, as in Berry et al. (1995) and Nevo (2001). We determine the average price strategy implied by the implementation of the two policies. Specifically, we assume that the marginal costs cj are constant for each product over the year. We also assume that consumers now face a single and constant price for each product pj = (1 + )p , where j pj denotes the average, over periods and distribution channels, of the mean unit prices computed in Section 2.3, pj the producer price, and the value added tax indistinctly imposed on all fromages blancs and dessert yogurts in France 2007. Once the marginal costs are computed (see Appendix A.4), and assuming that the marginal costs, all demand parameters and consumer choice sets are fixed throughout the simulation, we can simulate counterfactual equilibria that result from the mandatory labelling of all dessert yogurts or from an ad valorem fat tax proportional to the fat content of the product. Appendix A.4 provides additional details on the simulation algorithms. 4. Estimation results This section presents the MMNL estimates obtained using the control function approach described in Section 3 to correct for the endogeneity of price and label variables.15 The variances of the estimators are corrected by standard formulae for two-step estimators, given the additional variation due to the introduction of the residuals from the first-step instrumental regressions (Murphy and Topel, 1985). 4.1. Utility functions Table 4 shows the estimated coefficients of the MMNL model: these can be interpreted directly in terms of marginal utilities. As outlined in the previous section, the marginal utilities of price and FOP fat label have both deterministic and random components. The first column shows the mean marginal utility of each product characteristic for a reference main shopper who is a woman aged under 65, with a BMI under 27, living in a household in the top income quartile. The second column shows the estimated standard deviation of each random component. Both are significant at the 1% level, indicating that the marginal utilities of price and label do vary with unobservable household characteristics. The remaining columns list the coefficients for a number of interactions between the product characteristics, listed in the first column, and the household characteristics, in the first row (household income quartiles, household size, whether the main shopper is risky overweight, a man, and aged over 65). For instance, the difference in the mean marginal utility of price between the reference shopper and one in the first income quartile (first line, fourth column) is −0.280 utility units. The bottom part of Table 4 provides the estimates of the price and label control functions and the standard deviations of the associated error components. As expected, the probability of choosing an alternative falls with its price. The marginal utility of price is the inverse of the marginal utility of income. Its mean is negative (−2.19), and larger for households below median income, which is consistent with poorer households having a higher marginal utility of income. The standard deviation of the random effect on price is fairly high


First-step estimates are reported in Appendix A.3.


O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

Table 4 Estimated coefficients. Mean

Price Label Semi-skimmed Full-fat Fromage blanc Low-quality Medium-quality Below 200g Smooth

−2.187*** (0.105) 0.363 (0.271) 0.308*** (0.065) 0.469*** (0.091) 1.212*** (0.168) -2.253*** (0.216) -0.902*** (0.174) 1.720*** (0.091) −1.096*** (0.102)

Std. dev.

1.655 *** (0.071) 3.741 *** (0.130)

Income First quartile

Second quartile

Third quartile

−0.280 *** (0.070) 0.389 (0.331) 0.663*** (0.086) 0.415*** (0.107) −0.041 (0.199) 0.379*** (0.121) 0.355*** (0.085)

−0.209 *** (0.065) 0.838 * (0.311) 0.401*** (0.083) 0.170* (0.103) −0.779*** (0.174) 0.194* (0.112) 0.441*** (0.078)

−0.076 (0.066) 0.377 (0.323) 0.358*** (0.089) 0.255** (0.106) −0.675*** (0.184) 0.219* (0.119) 0.435*** (0.079)



Household size

Over 65

−0.190 (0.117) −0.013 (0.597) 0.746* (0.178) 1.001*** (0.208) 0.317 (0.381)

−0.071 (0.054) 0.340 (0.255) −0.206* (0.070) 0.020 (0.087) −0.263* (0.137)

−0.034 * (0.020)

0.190 *** (0.056) −0.373 (0.247) 0.186*** (0.071) 0.246*** (0.084) −0.123 (0.135)

0.165*** (0.032) 0.061*** (0.023) −0.396*** (0.153)

Terms to correct for endogeneity 1.143*** Residuals, price (0.110) 0.830*** Residuals, label (0.131) −0.242*** Err. compnt, price (0.083) −0.028 Err. compnt, label (0.096) Notes: Standard errors are in parentheses; the column “Std. dev.” shows the standard deviation of the random coefficients; the random coefficients are distributed according to the opposite of a lognormal law for price, and to a normal law for the label; their coefficient of correlation is 0.741*** ; the other control variables are the fixed effects for the 14 distribution channels and the 15 firms or groups of firms (results available from the authors upon request); these results are obtained with D = 500 draws; the reference individual is a female main shopper in the top income quartile, aged under 65, whose BMI is under 27. *** Significance at the 1% level. ** Significance at the 5% level. * Significance at the 10% level.

(1.66), implying that the marginal utility of income is very heterogeneous, beyond the effect of the observed socio-demographic attributes. This may be due to households who systematically take advantages of price promotions, and who are therefore very sensitive to price variations. FOP fat-content labels have, on average, a positive value (0.36 for the reference individual), but once again the standard deviation is large relative to the mean effect (3.74) and highly significant: there is a considerable unobserved heterogeneity in household preferences over these labels. We also get a hump-shaped income effect peaking in the second income quartile. The marginal utility of labels is not significantly higher when the main shopper is risky overweight (BMI > 27). The random utilities of price and label are positively and significantly correlated, with a coefficient of 0.74 (see notes in Table 4). A strong taste for labels is thus associated with a lower marginal disutility of price. In other words, the less sensitive to prices, the more sensitive to labels. The coefficients on the control functions, at the bottom of Table 4, are both positive and significant. Ignoring the label endogeneity leads to overestimate the marginal utility of labels: when labelling is not mandatory, firms display labels according to the consumer positive valuation of some unobserved product characteristics (e.g. a brand name or a packaging colour associated to feelings of healthiness). The marginal disutility of price is underestimated when the presence of unobserved product characteristics is ignored: higher prices correspond to unobserved characteristics that are positively valued by consumers. Households tend to prefer semi-skimmed and full-fat products to skimmed ones. This taste for fat is more developed in low-income households, and when the main shopper is a man or elderly. Table 4 also reveals that low- and medium-quality products are much less popular than high-quality ones for high-income households,

while they have more success in low-income and large households. Female main shoppers are more likely to prefer products sold in small portions. Last, the bifidus/organic characteristic has a significant effect on utility (not reported), and smooth textures are associated with a utility loss, which is consistent with the fact that non-smooth varieties (especially faisselles and fromages blancs de campagne) are considered as luxuries and part of French culinary culture. A household-specific Willingness-To-Pay (WTP) can be calculated from the estimates, conditional on household-specific information (observed choices, product and household characteristics), from Eq. (A.7) in Appendix A.5. The WTP for a label is defined as the change in price (here expressed in D ) that keeps utility unchanged when a fat-content label is added on the front of the pack. Our key finding, reported in Table 5, is that a non negligible

Table 5 Descriptive statistics of the WTP for fat-content labels. WTP ≤ 0 (%)*

Median (D )




Income First quartile Second quartile Third quartile Fourth quartile

38.63 43.88 43.68 48.08

0.42 0.67 0.28 0.12

Main shopper BMI BMI≤27 BMI>27

42.82 46.19

0.44 0.22


Proportion of households with negative WTP.

O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

fraction of households (44%) have WTP less than or equal to zero.16 This proportion increases with income (from 39% for the first quartile to 48% for the fourth quartile), and according to whether the main shopper has a BMI above or under 27 (43% vs. 46%). 4.2. Robustness We tested the robustness of our estimations using different sets of instruments for the price and fat-content label. Let us start with the IV for prices. First, compared to our instrument (based on Berry et al., 1995), using input costs (a wage index, price indices for milk, plastic, gasoline, and their interaction with a dummy variable indicating whether the product is from a retailer brand or not) as IVs gives very similar estimation results. We further tried to construct IV assuming independence across geographical areas. Following Zhen et al. (2014), we calculated the prices for each distribution channel in 8 geographical areas and each four-week period. Unfortunately, the number of household purchases in each area and each four-week period is not very large, so that we could only identify between 105 and 177 distinct products purchased per area/period. As a consequence, we were not able to construct a price for our 224 items in each area and period. Using yearly averages instead of four-week period averages induces a loss of time variability in prices which is key for the identification of the price effect.17 When the model is estimated without instrumenting the label, ¯ l , are the results, and in particular the mean impact of the label ˛ very similar. Note that this does not mean that instrumenting the label has no effect on predictions and policy simulations since the control function l is strongly significant. Had ˛ ¯ l estimates been sizeably different when not instrumenting the label, we would have suspected an issue with our exclusion restriction. But this is not the case. We also constructed four additional IVs for the label: the proportion of labelled products other than j in the distribution channels either visited by the household (a) or not visited by the household (b), and the proportion of labelled products other than j in the portfolio of, either the firm producing j (c) or the firms not producing j (d). Unfortunately, all instruments except (c) are too strongly collinear with the exogenous variables to be introduced in the reduced form equations. Regarding (c), the correlations are comparable to those obtained with our IV. As it is significant in the reduced form equation for the label (F-statistic= 325.30), we estimated the full model using (c) as an IV for the label. We found that the control function l was not significant, which indicates that the exogeneity of the label cannot be rejected and, therefore, that the label does not have to be instrumented. In addition, meaningful household-specific WTP for the label could not be obtained from these estimates: (1) 73% of households have a negative WTP, (2) the average (median) WTP among households choosing at least one semi-skimmed dessert yogurt is −3.81 (−3.38) euros, whereas the observed average price difference between a semi-skimmed dessert yogurt with and without label is only −0.57 euros.18 4.3. Price-cost margins


deviation), as well as the associated average price-cost margins, are then computed for each product. The top panel of Table 7 shows the initial market share, producer price, marginal cost and margin for the five categories of products (skimmed, semi-skimmed and fullfat fromages blancs, and semi-skimmed and full-fat dessert yogurts). On average, the marginal costs and price-cost margins are equal to D 1.59 (with a standard deviation of D 0.87) and 34% (with a standard deviation of 0.1), respectively.19 The differences in marginal costs across the product categories are consistent with technological factors. In fact, the price of raw milk was around D 0.30 per litre in 2007, and about 2, 3.2, and 4 litres of milk are required to produce one kilogram of skimmed, semi-skimmed and full-fat fromages blancs, respectively. Our estimates of average marginal costs are almost equal for skimmed and semi-skimmed fromages blancs (D 1.26 and D 1.27, respectively). A possible explanation is that higher advertising and packaging costs may help sell less tasty, skimmed varieties. The marginal costs of dessert yogurts are on average higher than those of fromages blancs for semi-skimmed products (1.81 vs. 1.27). It is the opposite for full-fat products (1.83 vs. 2.03). In the case of semi-skimmed products, the higher relative cost of dessert yogurts can be explained by the addition of costlier ingredients that can give the texture of fat without fats, as well as higher R&D and advertising costs. For full-fat products, the average marginal cost hides heterogeneity, as illustrated by the quite high standard deviation found for full-fat fromages blancs (0.96). In particular, marginal costs are higher for full-fat national and highquality retailer brands of dessert yogurts, but lower for small and medium national brands that produce very high-quality full-fat fromages blancs. Unsurprisingly, the unit costs are lower for the main retailer brands (between D 0.93 and D 1.47) than for the main national brands (between D 1.65 and D 2.29). However, the pricecost margins for the main retailer brands are higher (from 30% to 44%) than for the main national brands (from 27% to 31%). The margins of dessert yogurts and fromages blancs are quite similar (36% and 33 % , respectively). Although we do not have precise information on the actual margins of the industry for this specific market, governmental studies on prices and margins find that the raw margin of the food industry accounts for 54% of the retailer price in 2007 (FranceAgriMer, 2013). Moreover, the margins were close to 60% in 2007 for the standard yogurts, which is not far from our estimates.20 This suggests that the model correctly fits the industry for this specific market. 5. Ex-ante policy evaluation In this section, the methodology described in Section 3.3 is applied to the estimated demand functions in order to ex-ante evaluate two fat policies: (i) a mandatory labelling policy requiring a fat-content label on the FOP of all products; and (ii) an ad valorem fat tax policy. We consider a feasible tax based upon the reform of the VAT rates that took effect from the 1st of January, 2014: the reduced VAT of 5% is applied to skimmed products to subsidize their purchases, a 10% VAT is applied to semi-skimmed products,

The marginal costs are recovered for each product by using the procedure described in Appendix A.4. Their mean (and standard 19

Marginal costs cannot be listed in detail here for confidentiality reasons. The “Observatoire de la Formation des Prix et des Marges” (OFPM) [Observatory of prices and margins formation] provides information on the prices along the food chain for nature yogurts sold under private labels and national brands in 2007. Then, following Nevo (2001), we can construct marginal costs from accounting data, as the sum of the cost of milk (using OFPM data), and the marginal costs of the industry and the retailers. These marginal costs are crudely estimated using data on the margins of retailers (GMS) and accounting data for the dairy industry. One problem is that a number of accounting items aggregate together fixed and average variable costs, whilst only the latter matter in our model. The figure of 63% emerges as an upper – conservative – bound, and the lower bound is 22%. Details are available upon request. 20

16 Note that, when we constrain the marginal utility of information to be positive by assuming a log-normal distribution for all random coefficients, the estimation does not converge. 17 Enlarging the area to the adjacent ones (1) does not solve the problem completely and (2) makes impossible the use of the price instrument proposed by Zhen et al. (2014). Note that these authors can exploit very large geographical variations: in many cases the size of a single market equals the size of France, meaning that we should instrument the price in France by, say, the price in Germany. 18 All robustness results are available upon request from the authors.


O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

Table 6 Variations in average household annual fat purchases (in grams). Base fat

Mandatory labelling

Fat tax

No producer response

Producer response

No producer response

Producer response


718 (430)

−79 (54)

−55 (40)

−58 (26)

−49 (22)

Income First quartile Second quartile Third quartile Fourth quartile

733 (482) 712 (434) 731 (422) 698 (380)

−68 (52) −69 (44) −85 (56) −94 (59)

−51 (39) −39 (28) −56 (37) −72 (46)

−57 (27) −57 (26) −57 (25) −62 (27)

−48 (23) −48 (22) −47 (20) −52 (23)

Main shopper BMI BMI≤27 BMI>27

710 (439) 740 (405)

−79 (56) −80 (51)

−57 (41) −49 (35)

−57 (25) −63 (30)

−48 (21) −53 (25)

Notes: Standard deviations are in parentheses; household annual fat purchases are calculated using the predicted choice probabilities and the household purchase frequencies in 2007; under mandatory labelling all products have a fat-content label; the ad valorem tax is increased by 14.5 pp and 4.5 pp for full-fat and semi-skimmed products, respectively, and decreased by 0.5 pp for skimmed products.

and a 20% VAT is applied to full-fat products, as it became effective for sweets, margarine, vegetable fats, alcohol and certain kinds of chocolate (milk, hazelnut, and white). Let cat,j be the variation in the tax rate for product j in the fat-content category cat . Given that the French VAT rate for the fromage blanc and yogurt market is currently = 5.5%, we set the following variations: skimmed,j =−0.5 %, semi-skimmed,j =+4.5 % and full-fat,j =+14.5 %. The policies are simulated both with and without firm strategic price responses, to compare their effectiveness in reducing the quantity of fat purchased, and their impact on market shares, prices and consumer surplus. We first present the results in terms of fat purchases and body weight variations. We then discuss in detail the key market outcomes.

5.1. Impact on fat purchases How effective are these policies at achieving the public health goal of reducing fat consumption? Table 6 lists the mean variations (and their standard deviation) of household annual fat purchases in grams, by demographic group, with and without firm price reactions. For each household, annual fat purchases are calculated by multiplying the household purchase frequency observed in 2007 by a weighted average of the fat content (in grams) of each product, where the weights are the predicted household purchase probabilities. Pre-policy, 718 g of fat were purchased on average by the households in the sample. Ignoring firm price responses, both policies produce falls in fat purchases that are similar in magnitude: −79 g (−11%) for the mandatory labelling policy and −55 g (−8%) for the fat tax policy. When we allow for firm price responses, fat purchases still fall but to a lesser extent, and the two policies have almost the same impact: −58 g (−8%) for the mandatory labelling policy and −49 g (−7%) for the fat tax policy. When we extrapolate these variations to the entire French population using the Kantar WorldPanel sample weights, 1,87 tons of fat are initially purchased by households via the fromages blancs and dessert yogurts. The mandatory labelling and fat tax policies lead to a change of −7.8% and −7.0%, respectively. The fat tax affects all demographic groups similarly (with a fall ranging between −6.5% and −7.4%). However, the households whose main shopper has a BMI higher than 27 and those in the fourth income quartile (−7.2% and −7.4%, respectively) are the most affected. The effects of mandatory labelling show more variations between demographic groups (between −5.5% and −10.3%). Specifically, the households in the fourth income quartile (−10.3%) and those whose main shopper has a BMI lower than 27 (−8.0%) have the highest reductions in fat purchases. Overall, the fat tax policy is found to be slightly more effective than the mandatory labelling

policy in reducing fat purchases for those who would need to switch from high- to low-fat products. This overall result can be translated in terms of body weight variations. Using the dynamic simulation model proposed by Hall et al. (2011), we can convert the predicted reduction in fat purchases into kilograms of weight loss.21 The weight loss per household consumption unit at the end of the first year would be 24 g (45 g after ten years) for the mandatory labelling policy, and 20 g (39 g after ten years) for the fat tax policy. The variations are similar across income and BMI groups for the mandatory labelling policy (around 40 g loss in all groups after ten years). However, the households with BMI higher than 27 are more affected by the fat tax policy than those with a BMI lower than 27: −52 g vs. −33 g on average after ten years. 5.2. Impact on market equilibrium The effects of both policies on market shares, prices, costs and margins are summarized in Table 7 for the outside option and the five product categories (skimmed, semi-skimmed, full-fat fromages blancs and semi-skimmed and full-fat dessert yogurts). The middle and bottom panels present the changes in shares, prices and margins following the mandatory labelling policy and the fat tax policy, respectively, the top panel describing the initial situation. For each policy, the first line presents the average changes (and their standard deviation) in market shares, in percentage points (pp), when only household responses are taken into account; the three remaining lines show the average changes (and their standard deviation) in shares (in pp), prices (in D ) and margins (in pp) after firm price responses. The tax pass-through is also reported in the table. 5.2.1. Mandatory labelling policy When we ignore firm price responses, the mandatory labelling policy is as efficient as the fat tax in reducing the demand for full-fat products (−7.5 pp). The fall in the market share of full-fat dessert yogurts, from 18.2% to 6.0% (−12.2 pp), following the introduction of a label is far from being offset by the rise in the market share of (cheaper) full-fat fromages blancs (+4.7 pp). These effects are explained by the variations of the WTP for the label across consumers selected in different segments of the market before the implementation of the policy. Table 8 shows the median WTP for the label according to whether the household never chose or chose at least once one of the six options listed in the first column. The

21 The predicted daily energy variations are calculated by dividing the predicted variation in household annual fat purchases by the number of household consumption units times the number of days in 2007, and multiplying the result by the average calorie content of one gram of fat (8.9 kcal).

O. Allais et al. / Journal of Health Economics 43 (2015) 27–44


Table 7 Variations in market shares and prices produced by the fat tax and mandatory labelling, by product category. Outside option

Initial market shares (%) Initial consumer prices (D /kilo) Initial marginal costs (%) Initial margins (%) Mandatory labelling Share variation with no firm response (pp) Share variation with firm response (pp) Consumer price change (D /kilo) Producer price change (D /kilo) Margin change (pp) Fat tax Share change with no firm response (pp) Share change with firm response (pp) Consumer price change (D /kilo) Producer price change (D /kilo) Pass through (%) Margin change (pp)

Fromages blancs

Dessert yogurts






15.69 (0.04) 1.98 (0.88) 1.26 (0.74) 35.98 (0.10)

38.35 (0.09) 1.97 (0.80) 1.27 (0.67) 34.69 (0.10)

15.41 (0.04) 2.95 (1.12) 2.03 (0.96) 29.26 (0.08)

6.67 (0.04) 2.87 (1.35) 1.81 (1.06) 36.42 (0.11)

18.16 (0.10) 3.06 (0.43) 1.83 (0.32) 36.97 (0.05)

4.48 3.94

1.70 (0.01) 1.04 (0.01) −0.02 (0.03) −0.02 (0.03) −1.11 (0.73)

2.97 (0.02) 1.25 (0.02) −0.02 (0.02) −0.02 (0.02) −1.14 (0.62)

4.71 (0.02) 3.05 (0.02) 0.00 (0.06) 0.00 (0.06) -0.56 (1.01)

−1.67 (0.02) −1.31 (0.02) −0.18 (0.23) −0.17 (0.22) −5.52 (5.30)

−12.20 (0.05) −7.97 (0.05) −0.38 (0.16) −0.36 (0.15) −8.97 (2.83)

0.76 1.18

4.25 (0.01) 3.83 (0.01) −0.03 (0.03) −0.02 (0.03)

1.49 (0.01) 0.46 (0.01) 0.06 (0.01) −0.02 (0.03) 76.27 (21.76) −0.39 (0.26)

−5.12 (0.01) −4.43 (0.01) 0.30 (0.10) −0.08 (0.05) 76.84 (5.62) −0.32 (0.26)

0.56 (0.00) 0.59 (0.00) 0.03 (0.04) −0.08 (0.07) 30.31 (27.84) −0.38 (0.26)

−2.36 (0.00) −1.21 (0.00) 0.23 (0.04) −0.16 (0.04) 55.99 (6.89) −0.36 (0.35)

−0.40 (0.25)


Notes: Standard deviations are in parentheses; mandatory labelling requires all products to display a fat-content label; under the fat tax, the ad valorem tax is increased by 14.5 pp and 4.5 pp for full-fat and semi-skimmed products, respectively, and decreased by 0.5 pp for skimmed products; the abbreviation pp stands for percentage point; price and margin changes are averages by product category, weighted by product market shares; margins are given by (price-mc)/price, where mc denotes the marginal cost; price and margin changes include firm strategic price responses; pass-through is the equilibrium consumer price minus the initial consumer price divided by the consumer price with no firm price response minus the initial consumer price.

Table 8 Household product choice and median WTP for a fat-content label.

Outside option Skimmed fromages blancs Semi-skimmed fromages blancs Full-fat fromages blancs Semi-skimmed dessert yogurts Full-fat dessert yogurts

Median WTP (D )

Equality test


At least once


0.69 0.17 −0.24 0.56 0.53 0.76

−0.38 0.65 0.62 0.09 −1.06 −2.33

0.000 0.000 0.000 0.000 0.000 0.000

Notes: The columns “never” and “once” refer to households that never chose or chose at least once one of the six options listed in the first column, respectively; the final column shows the P-value for the hypothesis that the two medians are equal.

final column shows the P-value for the hypothesis that the two medians are equal. Before the implementation of the policy, all consumers of full-fat dessert yogurts have a negative WTP for the label. Hence, introducing a fat label push these consumers to purchase more fromages blancs. Allowing for firm price responses leads to a weaker fall in the market share of dessert yogurts (−8.0 pp for full-fat dessert yogurts), but the decline in demand for full-fat items is now slightly smaller than for the fat tax policy (−5.0 pp for mandatory labelling vs. −5.6 pp for fat tax). This can be explained by the fall in the prices of dessert yogurts: semi-skimmed and full-fat dessert yogurts exhibit average consumer price falls of about D 0.17 and D 0.36, respectively. It leads to a reduction of the margins for all categories within a range of 28.7–34.9% vs. 29.3–37.0% before the implementation of the labelling policy.22 Firms can afford price cuts on dessert yogurts for two key reasons: the initial margins; the elasticity and concavity of the demand curves. The initial price-cost margin is 36.9% for full-fat dessert yogurts on average, as opposed to a smaller 29.3% for full-fat fromages blancs. In addition, the estimated own-price elasticity of

22 Some additional computations also show that the largest falls in purchases of full-fat dessert yogurts occur in the fourth income quartile, while the smallest reductions are for households whose main shopper has a BMI above 27: −11.3 pp and −6.1 pp, respectively, compared to −8.0 pp on average.

demand for full-fat dessert yogurts is −6.1 in the absence of a price response. Firms can therefore expect to win back market shares via price cuts. This is particularly true for unlabelled full-fat dessert yogurts, which both show the largest margins and the largest ownprice elasticities. By contrast, the estimated demand elasticity for full-fat fromages blancs is −5.0 in the absence of a price response. The firm price strategies are also constrained by two factors. First, the demand becomes less and less elastic as price falls: the elasticity of full-fat dessert yogurts is −5.0 after the price response. Profit maximisation entails a trade-off between lower margins and larger market shares, which is partly determined by the concavity of the demand function, i.e. the change in elasticity (see Stern, 1987, and Delipalla and Keen, 1992, for the case of taxation under imperfect competition). Second, each firm faces the price response of all other producers and must in addition optimise its own response over a portfolio of products. Some firms supplying only fromages blancs have a means of countering the price cuts on dessert yogurts, but their reactions are limited by lower initial margins. Most firms produce both fromages blancs and dessert yogurts, which explains why the prices of fromages blancs do not vary much on average. These firms will defend the market shares of those of their products that have the highest initial margins. A good illustration of this is given by the leader of the market, who reduces the prices of its unlabelled full-fat dessert yogurts by 17–20% while the prices of its fromages blancs and labelled dessert yogurts remain constant (with an absolute variation of less than 1%). 5.2.2. Fat tax policy In the absence of firm price responses, the impact of the fat tax on market shares is substantially different from that of the mandatory labelling. The market shares of full-fat products decrease, and this is mainly due to the full-fat fromages blancs (−5.1 pp), to the benefit of skimmed (+4.2 pp) and semi-skimmed fromages blancs (+1.5 pp). These effects remain qualitatively similar with firm price responses, but smaller. The market shares are reduced by 4.4 pp and 1.2 pp for the full-fat fromages blancs and full-fat dessert yogurts, respectively, which still benefits to the skimmed (+3.8 pp) and semi-skimmed (+1.0 pp) items but to a lesser extent. Households move away from the fatter fromages blancs, but not from the fatter dessert yogurts. Firms are willing to absorb most of


O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

Table 9 Economic impacts of the mandatory labelling and fat tax policies (in million of euros). Base

Consumer expenditures


Firm costs


Firm profits


Tax revenues Variation in consumer surplus Economic costs/benefits: Variations in firm profit, tax revenues, and surplus


Mandatory labelling

Fat tax

No producer response

Producer response

No producer response

Producer response

119.42 −6.89% 75.75 −4.23% 37.45 −11.84% 6.23 −6.89% −0.53 −7.63%

117.45 −8.43% 75.98 −3.93% 35.34 −16.80% 6.12 −8.43% −0.46 −4.23%

131.84 2.79% 75.76 −4.34% 34.37 −19.09% 14.74 120.40% −0.29 −10.10%

130.59 1.82% 76.83 −2.86% 39.03 −8.13% 14.75 120.45% −0.10 −3.38%





Notes: All aggregate effects are calculated using the household demographic weights provided by Kantar WorldPanel; firm costs are computed as the sum across products of the marginal cost multiplied by the market share and the market size; tax revenues are calculated as the sum across products of the applicable tax rate multiplied by the producer price, the market share and the market size.

the intended policy shock on consumer prices for full-fat dessert yogurts, much more than for full-fat fromages blancs. We find that the pass-through rate is equal to 56.0% for the former category vs. 76.8% for the latter category, for which margins are much smaller (see penultimate line of Table 7).23 We also find that the fat tax induces substitutions from full-fat to skimmed fromages blancs and semi-skimmed dessert yogurts for all households, especially those in the fourth income quartile and those whose main shopper has a BMI above 27 (not reported). However, the effect is mainly achieved through the large decrease in the purchases of full-fat fromages blancs. 5.3. Welfare analysis The global impact of the policies depends on the variations in firm profit, consumer welfare, tax revenues and health. While it is difficult to evaluate the latter component, we can compute an economic cost of the fat purchase reduction generated by each policy. Table 9 reports the aggregate impacts of each policy for the whole French population. All are calculated using the predicted choice probabilities and the observed household purchase frequencies for fromages blancs and dessert yogurts over the year for the households in the estimation sample, and extrapolated to the French population using the sampling weights provided by Kantar WorldPanel. The table shows the pre- and post-policy levels (and their variations) of total consumer expenditures, total firm costs, total profits, tax revenues and consumer surplus.24 These extrapolations are reported in columns 3 and 4 for the mandatory labelling policy, and in columns 5 and 6 for the fat tax policy, without and with firm price response. As expected, the mandatory labelling generates a decrease in total consumer expenditures (−8.4%), as prices fall for all products and the market shares of the most expensive ones (dessert yogurts) decrease. Conversely, there is a small increase under the fat tax (+1.8%), which can be explained by the rather moderate pass-through rates chosen by the firms. Tax revenues decrease with the mandatory labelling policy (−8.4% with price response), as consumer expenditures fall, while they considerably increase with the fat tax policy (+120% with price

23 The final increase in consumer price with a 100% pass-through would be D 0.61 (3.06 times the tax of 20%) for the full-fat dessert yogurts, whereas it is only D 0.38 with a price response. 24 The formulae for these welfare calculations appear in Appendix A.6. These are short-term welfare effects, since the welfare impact of health changes is not included.

response). Both policies reduce firm annual profits, but only firm price responses implemented after the fat tax policy help minimize the fall in aggregate profit: from −19.1% to −8.1%. In the case of the mandatory labelling, the price responses lead to an additional fall in aggregate profit: from −11.8% to −16.8%. This surprising result is due to a composite effect. For the market leader, which has almost 30% of market shares and is also the most impacted by the labelling policy, the optimal price response neutralizes the fall in profit; but its price response worsens the situation of the other firms, especially the retailers producing their own brands, which explains the aggregate fall in profit.25 Table 9 eventually reports the economic costs/benefits of each policy. The mandatory labelling policy would cost D 8.2 millions as firm profits and tax revenues decrease. In spite of the drop in both firm profit and consumer welfare implied by the fat tax policy, the high level of tax revenues lead to a policy benefit of almost D 4.5 millions. These differences suggest that the fat tax policy dominates the mandatory labelling policy from a public economic perspective.

6. Conclusion This paper has developed an ex-ante evaluation of the market impact of a fat tax and a policy making FOP fat labels mandatory. This evaluation requires the separate identification of consumer preferences for fat and for fat-content labels. This is possible by focusing on the specific French market for fromages blancs and dessert yogurts, where an exogenous variation in legal FOP fatcontent labelling requirements can be exploited. We do so within the framework of a structural econometric model, combining a flexible discrete choice model of demand, estimated on scanner data (disaggregated at both the household and product levels), with a linear-pricing supply model. Having estimated the parameters of the demand curves (consumer preferences) and the supply curves (firm price-cost margins), we are able to simulate the impact of a fat tax policy and the mandatory implementation of FOP fat labels on the market equilibrium. In terms of reduction in fat purchases, the fat tax and mandatory labelling policies produce similar effects (only attenuated by firm price responses). However, the fat tax policy has a larger impact on the overweight population. The fat tax also dominates the mandatory labelling policy from a public economic perspective,

25 The changes in profits and market shares are not shown here in detail due to legal restrictions imposed by the Kantar WorldPanel Company.

O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

as it generates high tax revenues and has a much lower impact on firm profits. The key policy message of our research is twofold. First, firm strategic price response to policies should be integrated in the evaluation of labelling policies, and more generally any public health policy targeting consumer markets. Indeed, it may happen that, for particular shapes of the demand curves and ex-ante cost structures and technologies, firm reactions neutralize the intended effect of a policy. Second, nutritional taxes may eventually be more efficient for achieving public health objectives – the overweight would react more to the tax – while the mandatory labelling policy would rather favor the non-overweight individuals (usually rich and welleducated). A tax yields additional economic benefits due to the revenues that are generated, which is not the case for labelling policies. These revenues can be reallocated to offset any unfair loss in welfare. While this paper is, to the best of our knowledge, the first to compare a nutritional tax and a labelling policy in a structural econometric framework, there are some restrictive assumptions that had to be made. First, all of the simulation results are based on a supply model without explicit modelling of the vertical relationships between retailers and producers. A recent literature enriches this setup, by taking such relationships into consideration (see Villas-Boas, 2007; Bonnet and Dubois, 2010; Bonnet et al., 2013). Although we obtain qualitatively similar results when we model them as a two-part tariff contract with resale price maintenance (where wholesale prices are such that the retailer’s price-cost margins are zero), it would be interesting to check whether other types of vertical relationships have significant consequences for the market equilibrium. Second, the set of products is supposed to be fixed, so that firms can only use pricing strategies. However, new products may enter the market, some products may exit and/or be reformulated. Third, our analysis is limited to households with stable preferences who are currently in the market. However, a labelling policy may encourage individuals to enter the market if the label indicates that these products are less healthy than they may have otherwise thought. Fourth, the hypothesis of capacity constraints is maintained, which means that our results will pertain to the short-term equilibrium effects of policies. Fifth, as all papers using instrumental variable techniques, the identification is only local. We have implicitly assumed that the estimated distribution of the WTP can be extrapolated to the population. Last, the demand model does not take into account, in a structural way, the health effects of fat consumption. As such, it is difficult to evaluate the long-run welfare effects of each policy, and to rank the various options according to health. While the short- and long-run welfare effects are probably only little different for a single product, this would certainly not be the case if a larger range of products were targeted. We leave these questions for future research.

Acknowledgements The authors thank Armelle Champenois for bibliographic research, Christine Boizot for data assistance and two anonymous referees for their comments and suggestions, Céline Bonnet for providing us input costs. This paper benefited from discussions by Eric Delattre, Paul Frijters, Laura Grant and Maarten Lindeboom, and comments by seminar participants at the 1st joint EAAE/AEAA conference (Freising, Germany), Imperial College, the York Seminar in Health Econometrics, the University of Paris 1, the ERS Conference on scanner data and food policy, the IRDES workshop on health policy evaluation, the Paris School of Economics, the Journées Louis-André Gérard-Varet, the European Workshop on Health Economics and Econometrics, the INRA-SMART seminar and the AFSE Conference, the Melbourne Institute of Applied


Economic and Social Research, the Centre for Health Economics at Monash University, the University of Queensland. Financial support from the ANR-French National Research Agency, projects ANR-07-PRNA-018 ALIMINFO, ANR-011-ALID-002-02 OCAD, and INRA-Metaprogram DIDIT is gratefully acknowledged. Appendix A. A.1. Defining the relevant market In this paper, we want to exploit the difference in labelling rules between fromages blancs and yogurts. Hence the set of alternatives must necessarily include all of the fromages blancs. We have to determine whether both standard and dessert yogurts should be included in the definition of the relevant market for fromages blancs. The purpose of any relevant market test is to measure the degree of competition exerted over a given product from other products. In its guidelines for the assessment of relevant markets, the European Commission (1997) defines the three main factors determining competition: substitution on the demand side, substitution on the supply side generated by the strategic responses of competitors to the firm decision, and the entry of new competitors on the market.26 We here only check for demand substitution, which represents the most immediate competitive constraint for firms. For each decision regarding product ingredients and marketing-mix, firms have to bear in mind that customers can switch from one variety to another. Demand substitution is analyzed via the estimation of a Quadratic Almost Ideal Demand System (Banks et al., 1997; Deaton and Muellbauer, 1980). The latter relates the yearly budget share sij of products j = 1, . . , J for household i = 1, . . ., N to log total expenditure xi for unflavored standard yogurts, dessert yogurts and fromages blancs, and the log price J-vector pi , through the following equation 2

sij = ˛j + j pi + ˇj (xi − a(pi , )) + j

(xi − a(pi , )) + uij , b(pi , )

with the following non-linear price aggregators a(pi , ) = ˛0 + ˛ pi + b(pi , ) = exp(ˇ pi ),

1  p p , 2 i i

where ˛ = (˛1 , . . ., ˛J ) , ˇ = (ˇ1 , . . ., ˇJ ) ,  = ( 1 , . . ., J ) ,  is the set of all parameters, and uij is an error term.27 Household heterogeneity enters the demand system through the ˛’s, which are modelled as linear combinations of a set of socio-demographic variables zi observed in the data: ˛i = Azi , where A = (˛j ). Here zi includes the number of household members, position in the lifecycle, socio-economic status, gender and education of the main shopper, whether the main shopper has a body mass index over 27, and the region and type of residential area. Following Lecocq and Robin (2006), product-level prices are computed as the average prices of all purchases made in the same region and area, and we control for the endogeneity of log total expenditure via a control function approach using the log of household income as an instrument. The estimation is performed using the aidsills Stata command (see Lecocq and Robin, 2015). The first row of Table A.1 presents the uncompensated elasticities for fromages blancs with respect to the price of fromages

26 Also see summaries/competition/firms/l26073 en. htm. 27 Parameter ˛0 in the first price aggregator is unidentified and can be set to 0 or to any other fixed value.


O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

Table A.1 Uncompensated price elasticities.

Fromages blancs Dessert yogurts Standard yogurts

Fromages blancs

Dessert yogurts

Standard yogurts

−0.972*** (0.214) −0.230 (0.517) 0.029 (0.202)

0.406* (0.209) −1.124* (0.580) −0.321 (0.214)

0.259 (0.221) −0.261 (0.517) −1.163*** (0.207)

Notes: Standard errors are in parentheses; *** Significance at the 1% level. ** Significance at the 5% level. * Significance at the 10% level.

A.1. Identifying labelling preferences.

blancs, dessert yogurts and standard yogurts.28 The second and third rows display the same elasticities for dessert and standard yogurts, respectively. We can see that there is a significant increase in the purchases of fromages blancs as the price of dessert yogurts increases. A similar but insignificant effect is found for the price of standard yogurts. This shows that dessert yogurts should necessarily be included in the relevant market for fromages blancs, but not standard yogurts. The other cross-price elasticities are insignificant. We draw a similar conclusion from using Allais et al. (2010)’s cohort-based demand system method and extending the market test to six additional product categories: flavored fromages blancs; flavored dessert yogurts; flavored standard yogurts; dairy desserts (flans, etc.); other nature yogurt-style products (like drinkable yogurts, yogurts from goat milk, etc.); other flavored yogurt-style products. These additional results are available upon request. A.2. Identifying tastes for fat-content labels Under the assumption that the parametric distribution of the coefficient for the label does not vary systematically between consumers choosing different product categories, we are able to identify the preferences for the fat-content label as an average treatment effect. Specifically, consider the Fig. A.1. Black and white circles represent the sets of products with and without a label, respectively, the size of each circle indicating the market share of each set. Firms never put fat-content labels on full-fat dessert yogurts, while 50 percent of semi-skimmed dessert yogurts have one. They are required to do so for all fromages blancs, whatever their fat content. Combining this exogenous variation in legal labelling requirements with firm labelling strategies for dessert yogurts, we can disentangle the consumer preferences for fat-content labels from their preferences for fat, using the variations in market shares between dessert yogurts and fromages blancs and between products with different fat contents. Identification of the mean

28 Results based on a sample of 9,867 observations (i.e. households). Details are available upon request.

Formally, denote sjt the market share of product j in market t and lj the variable indicating the presence of a fat-content label on the package of j. Consider the following linear model for the market shares sjt = ˛lj + ˇ1 hj + ˇ2 fj + yj + ujt , where hj equals 1 if j is semi-skimmed (and 0 otherwise), fj equals 1 if j is full-fat (and 0 otherwise), yj equals 1 if j is a dessert yogurt (and 0 otherwise); ujt is an error term, and ˛, ˇ1 , ˇ2 and are parameters. In this model, lj is endogenous if the producer decision to display a fat-content label on j is based (at least partly) on some unobserved / E(ujt | lj = 0). determinants of the demand sjt , i.e. when E(ujt | lj = 1) = Consider the absence of a label (lj = 0) as a treatment. The marginal value of a fat-content label is identified from the difference-in-differences in the empirical market shares of fromages blancs and dessert yogurts with different fat contents. We know that the probability of being treated is zero for the fromages blancs, regardless their fat content (since labelling is mandatory), and more or less positive for dessert yogurts, depending on their fat content. Then, we can write E(sjt E(sjt E(sjt E(sjt

| | | |

yj yj yj yj

= 1, fj = 1) = ˛E(lj | yj = 1, fj = 1) + ˇ2 + + E(ujt | yj = 1, fj = 1), = 1, hj = 1) = ˛E(lj | yj = 1, hj = 1) + ˇ1 + + E(ujt | yj = 1, hj = 1), = 0, fj = 1) = ˇ2 + E(ujt | yj = 0, fj = 1), = 0, hj = 1) = ˇ1 + E(ujt | yj = 0, hj = 1).

Applying the difference-in-differences estimator to market shares identifies ˛ as Diff 1 − Diff 2 , E(lj | yj = 1, fj = 1) − E(lj | yj = 1, hj = 1) where Diff 1 = E(sjt | yj = 1, fj = 1) − E(sjt | yj = 0, fj = 1), Diff 2 = E(sjt | yj = 1, hj = 1) − E(sjt | yj = 0, hj = 1), and under the assumption that E(ujt | yj = 1, fj = 1) − E(ujt | yj = 0, fj = 1) = E(ujt | yj = 1, hj = 1) − E(ujt | yj = 0, hj = 1). Hence, assuming that, every other individual and household characteristics being equal, the differences in unobservable factors between fromages blancs and dessert yogurts consumers are the same for full-fat and semi-skimmed products, the taste for the fatcontent label is given by the difference between the market shares of full-fat dessert yogurts and fromages blancs minus the difference between the market shares of semi-skimmed dessert yogurts and fromages blancs, divided by the difference between the proportions of unlabelled full-fat and semi-skimmed dessert yogurts. Identification of the variance The variance of the distribution of the labelling coefficient is identified by the degree to which consumers of labelled products are willing to switch to unlabelled products following a utility change for labelled products. For example, if consumers of labelled products tend to switch to other labelled products when prices increase, this will imply that some consumers have a strong taste for labelling. On the contrary, if consumers substitute away from a labelled product to both labelled and unlabelled products in proportion to market shares, this will imply little heterogeneity in the taste for labelling. Table A.2 reports the probability transitions between different categories of products from one period to the next. For instance, 13.30% of consumers of a semi-skimmed unlabelled dessert yogurt at time t choose a semi-skimmed fromage blanc with a label at time t + 1. Although there is some inertia in choices, there are also transitions between dessert yogurts and fromages blancs and between

O. Allais et al. / Journal of Health Economics 43 (2015) 27–44


Table A.2 Probability transitions between different categories of products from one period to the next. Outside

Outside option Skimmed fromages blancs Semi-skimmed fromages blancs Full-fat fromages blancs Semi-skimmed dessert yogurts with no label Semi-skimmed dessert yogurts with label Full-fat dessert yogurts

21.67 4.64 5.32 4.25 5.91 4.56 2.40

Fromages blancs

Dessert yogurts




Semi-skimmed with no label

Semi-skimmed with label


17.23 71.07 5.60 6.25 4.93 4.56 3.64

36.81 12.79 74.86 14.06 13.30 11.58 11.67

10.70 5.75 6.68 62.59 5.42 7.02 9.85

4.70 0.94 0.72 1.04 54.68 2.11 1.16

2.09 1.20 1.22 1.91 2.96 58.25 2.48

6.79 3.61 5.60 9.90 12.81 11.93 68.79

Notes: Period t is shown in row and period t+1 in column; so, for instance, 13.30% of the consumers of semi-skimmed unlabelled dessert yogurts at time t choose semi-skimmed fromages blancs with a label at time t+1.

labelled and unlabelled products. In addition, about 12% of transitions from labelled products are toward unlabelled products while 36% of transitions from unlabelled products are toward labelled products. These transitions do not occur in proportion of market shares (20% for the unlabelled products and 75% for the labelled products). Hence, consumers have important idiosyncrasies in their taste for labelling. This explains why the estimated variance is high (about 3.7). A.3. Choice probabilities and estimation procedure Define yijt as an indicator variable which equals 1 if household i purchases good j in period t, and 0 otherwise. Each household is supposed to choose the utility-maximizing option, and assuming that ties occur with probability zero, the choice criterion is yijt = 1 if uijt > uikt = 0 otherwise.

∀j = / k,

εijt , i.e. the utility function only through the additive error term  si = i = 0, the model reduces to the standard Multinomial Logit model (MNL).29 p In the hypothetical situation where  εijt ,  εlijt and i are observed and are different from zero, the above model corresponds to a MNL formulation where the observed product characteristics and household attributes are interacted, with choice probabilities given by30


exp(vijt (i ) + ϕ(ijt ))

k∈Jit ,k = / 0

exp(vikt (i ) + ϕ(ikt ))

, (A.1)

p {ijt , lijt },  is the full parameter set, P(yijt

= 1 | ijt , i ; ) where ijt = is the probability that alternative j is purchased by household i at time t conditional on ijt and i , and the utility derived from the consumption of the outside alternative is normalized to zero. The probability of observing the sequence of choices made by household i in periods t = 1, . . ., T, denoted wi =

P(wi | ijt , i ; ) =


P(wi | ) =

P(wi | ijt , i ; )g(ijt )f (i )di dijt ,


where f(i ) is the joint density function of i and g(ijt ) = p (ijt )(lijt ), with (•) being the standard normal density function. Given that each component of ijt and i adds a dimension to the integral, it is not possible to solve (A.2) analytically by integrating out over ijt and i . The most common solution is to replace the choice probability by the following unbiased, smooth and tractable simulator 1  P (wi | ) = P(wi | ijtd , id ; ), D




Under the additional assumptions that there is no error compop εijt =  εlijt = 0, and that household heterogeneity enters nent, i.e. 

P(yijt = 1 | ijt , i ; ) =

However, since ijt and i are not actually observed, the relevant probability has to be unconditional, as follows


yijt = 1


, is then

yijt P(yijt = 1 | ijt , i ; ).

t=1 j∈Jit

29 Although very attractive because of its extreme tractability, the MNL model unreasonably restricts substitution patterns (see, for example, Berry, 1994). 30 In order to make the presentation simpler here, all of the other conditioning arguments (product and consumer attributes, reduced form residuals) are omitted.

where ijtd and id denote the dth draw from the distributions of ijt and i , and D is the number of draws. The simulated log-likelihood function can then be written as

L() =


ln  P (wi | ).



The estimation procedure consists of two steps. First, the residp uals  ˆ ijt and  ˆ lj are predicted by regressing the price and label variables on the instruments, all product characteristics, including their interactions with household attributes, as listed in Table 3, and the distribution channel and brand fixed effects. Note that the two identifying Instrumental Variables (IVs) are separately and jointly significant with large F-statistics in both price and label equations (see Table A.3). But with only two IVs for two endogenous variables, we cannot test the validity of the exclusion restrictions. The residuals are then used as control functions in the above likelihood function. The variance-covariance matrix is corrected to account for the additional variance introduced by the first-stage estimation.31 Finally,  note that market share j can be calculated as sj (p ; ) = i,t P(yijt = 1 | ), where

P(yijt = 1 | ) =

P(yijt = 1 | ijt , i ; )g(ijt )f (i )di dijt ,


which can be approximated by simulation, with P(yijt = 1 | ijt , i ; ) given by (A1). One difficulty with MMNL models is that the simulated log-likelihood functions are not as well-behaved as standard loglikelihood functions. In particular, using too few draws in the simulator (A3) may mask identification issues (see Chiou and

31 The estimations are performed using an augmented version of the mixlogit Stata command (see Hole, 2007).


O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

Table A.3 First-stage OLS estimates.

Semi-skimmed Full-fat Fromage blanc Low-quality Medium-quality Below 200g Organic/bifidus Smooth Constant IV for the price F-test P-value IV for the label F-test P-value IVs joint F-test P-value R2

price of good j produced and sold by firm m must satisfy the following first-order conditions Price


0.050*** (0.005) 0.453*** (0.005) −0.247*** (0.006) −1.186*** (0.015) −0.783*** (0.013) 0.742*** (0.003) −0.186*** (0.005) −0.742*** (0.004) 4.463*** (0.030)

−0.002** (0.001) −0.002*** (0.001) 1.019*** (0.001) 0.018*** (0.002) −0.030*** (0.002) −0.006*** (0.000) 0.045*** (0.001) 0.005*** (0.001) −0.275*** (0.005)

−0.214*** 517.21 (0.000) 0.121*** 345.93 (0.000) 437.7 (0.000) 0.585

0.012*** 216.37 (0.000) 0.709*** 5.1.105 (0.000) 2.6.105 (0.000) 0.894

Notes: Standard errors are in parentheses; * the IV for the price of product j in period t for household i is the average price of all products (excluding j) available in period t in the distribution channels visited by i; the IV for the label is the interaction between the dessert yogurt and full-fat dummy variables; the other control variables are the interaction terms considered in Table 4, fixed effects for the 14 distribution channels and the 15 firms or groups of firms (results available from the authors upon request). *** Significance at the 1% level. ** Significance at the 5% level. * Significance at the 10% level.

sj (p; ) +

(p − ck ) k


∂sk (p; ) (1 + ) = 0, ∂pj

. Solving (A6) for all j ∈ Gm and m = 1, . . ., M, and where pj = (1 + )p j provides the price-cost margins for each product, as a function of the estimated demand parameters. Given the observed consumer average price pj and estimate (sj (p ; ), (∂sk (p ; )/∂pj )) for all j ∈Gm and m = 1, . . ., M, the marginal costs are identified. The mandatory labelling policy This policy implies the replacement of the label variable by a vector of ones, l* .32 The algorithm used to obtain the new set of equilibrium prices, given the marginal costs of each product for each firm, and the estimate of the full set of parameters , is as follows: 1 Calculate, for each firm m and each item in Gm , the new market shares implied by the mandatory labelling policy, sj (˜p; ), and the derivatives, ∂sk (˜p; )/∂p˜ j , where vijt and ϕijt are now as follows

vijt = vij = −˛pi p˜ j + ˛li lj∗ + ˇi xj and p

where p˜ denotes the new consumer price vector raw jth element p , ˆ ijt and  ˆ lijt are the residuals of p˜ j is given by p˜ j = (1 + )˜p j,iter−1 p

the first-stage regressions (4), and ijt and lijt are simulated i.i.d. standard normal noises. , using the first-order 2 Find the new producer price vector, p˜ iter conditions

(˜p − ck ) k,iter


A.4. Simulation algorithm In this appendix, we explain how marginal costs are recovered and we describe the simulation algorithm used to find a new set of equilibrium prices implied by the implementation of a mandatory labelling and a fat tax policies. We first describe the algorithm for the mandatory labelling policy, and then show how it applies for the fat tax policy. Marginal costs There are M firms operating in the market. Each firm m produces a subset Gm of the set of all available alternatives G, and makes a profit m that can be written as m =

(p − cj )sj (p; ), j


where p is the producer price chosen by the firm for item j, j

and sj (p ; ) the predicted market share of product j for all j ∈ G, depending on the consumer prices of all products, p, and demand parameters . Market share j is given by (A5) in Appendix A.3. Assuming a pure-strategy Nash equilibrium in producer prices, the


ˆ ijt + l  ˆ lijt +  p ijt +  l lijt , ϕijt = p 

sj (˜p; ) + Walker, 2007). These can be revealed by the instability of parameter and standard error estimates as the number of draws increases. We estimated the model for D = 100, 200, 300, 500 and 1000 draws, and obtained stable estimates from D = 300 onwards. These results are available upon request from the authors. All of the estimations presented in the text are obtained using 500 Halton draws.


∂sk (˜p; ) (1 + ) = 0, ∂p˜ j

− p˜ | < 10−5 , then the equilibrium prices are If maxj |˜p j,iter j,iter−1 unchanged. Otherwise, go back to step 1 using the new producer prices p˜ . j,iter The algorithm is initialized using the average, over periods and distribution channels, of the mean unit prices computed in Section 2.3, i.e. p˜ j = pj . The fat tax policy We assume that the fat tax is ad valorem, proportional to the fat content, such that the new consumer price for product j is , p˜ j = (1 + + cat,j )˜p j where cat,j is the variation in the tax rate assigned to product j in the fat-content category cat. Below, cat,j is set equal to −0.5%, +4.5% or +14.5% when j is a skimmed, semi-skimmed or full-fat product, respectively. In the same way as for the algorithm described for the mandatory labelling policy, but with the existing label variable l, we iterate over steps 1 and 2 to get a new vector of producer prices until − p˜ | < 10−5 . The only difference is that now, we maxj |˜p j,iter+1 j,iter

32 We assume that the labelling cost is zero or negligible for two reasons: first, as the fat content is listed in the nutrient facts displayed on the packaging of all products, its determination for dessert yogurts is costless; second, as mandatory labelling simply consists in sticking a fat-content label on the front of the packaging, the associated costs are small relative to the total unit cost of the product.

O. Allais et al. / Journal of Health Economics 43 (2015) 27–44

obtain the new vector of producer prices, p˜ , at the iter + 1th j,iter+1 iteration, solving sj (˜p; ) +

(˜p − ck ) j,iter+1


∂sk (˜p; ) (1 + + cat,j ) = 0, ∂p˜ j

for all j ∈ Gm and m = 1, . . ., M, where p˜ stands for the new consumer price vector whose jth element p˜ j is given by p˜ j = (1 + + . We start the step 1 of the algorithm with the following cat,j )˜p j,iter consumer price p˜ j = (1 + cat,j /(1 + ))pj , ∀j.

A.5. Distribution of household WTP conditional on observed choices The estimates resulting from the maximisation of (A4), can be used to determine the distribution of tastes over the sampled households, {˛i , ˇi }, as well as functions of these, conditional on the household observed choices, product characteristics and the distributions of unobserved preferences (Revelt and Train, 2000). Formally, if h(˛i ) is such a function, its conditional expectation is given by E(h(˛i ) | wi ; )


E(h(˛i ) | wi , ijt , i ; )g(ijt | wi )f (i | wi )di dijt ,

where g(ijt | wi ) and f (i | wi ) are the densities of ijt and i conditional on the household observed choice sequence. From Bayes’ rule, we have E(h(˛i ) | wi ; )


E(h(˛i ) | wi , ijt , i ; )P(wi | ijt , i ; )g(ijt )f (i )di dijt P(wi | )


Similarly to (A.2), and still denoting by ijtd and id the dth draws from the distribution of ijt and i , this expectation can be approximated through simulation by

D E(h(˛i ) | wi ; ) =


E(h(˛i ) | wi , ijtd , id , ; )P(wi | ijtd , id ; )

 P (wi | )



where  P (wi | ) is given by (A3). With h(˛i ) = ˛li , (A.7) shows the p

household expected taste for fat-content labels; if h(˛i ) = ˛li /˛i , then it describes the household expected willingness-to-pay for labels. A.6. Household consumer surplus

The consumer surplus CSi (pt , lt ) for household i in period t is calculated using the log-sum formula proposed by Small and Rosen (1981)

⎡ ⎤ Jit  (maxj uijt (pt , lt )) 1


= p ln ⎣ exp(uijt (pt , lt ))⎦ ,



 CS i (pt , lt ) =





where ˛i is the estimated marginal disutility of price for

consumer i. Consumer surplus is calculated given the householdspecific taste parameters, using the formula in equation (A.7). The change in surplus from mandatory fat-content labels, implying new equilibrium prices p* and label variable l* , is given by CS i (p∗t , lt∗ ) − CS i (pt , lt ). With a fat tax, only the equilibrium prices vary, and lt is unchanged. Note that the consumer surplus depends on the utility obtained from all alternatives, including the outside option. It therefore varies across households not only through the


price sensitivity of observed choices, but also through the variations in the utility of each alternative. This allows us to take into account the changes in household utility produced by substitutions between the alternatives.

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