TY - JOUR
AU - Villas-Boas, Sofia, B
AB - Abstract We review the current literature on applied policy analysis and empirical structural food industrial organisation research. Within that context, we provide an overview on the state of research and summarise the core problems researchers face when estimating the demand and structural supply models implemented in applied research to date. We focus on important themes, such as providing a better understanding of vertical relationships in food markets, price formation, competition issues, environmental and nutritional policies. 1. Introduction The analysis of food markets is of utmost importance, as food expenditures represent 13 per cent of the total budget of households in the European Union (EU) in 2014, according to the Statistical Office of the EU. Moreover, this is the largest manufacturing sector in the EU, as the food and drink industry reached a turnover of 3.9 trillion Euros in 2014 and represents 10 per cent of all EU employment. In addition, food markets are critical to competition policy analysis. Concentration in the food processing industry and retail sectors is much higher than in the agricultural market. Whereas the C5 concentration ratio in agriculture in 2010 accounted for 0.19 per cent, the market share of the top five firms in the EU food industry was at an average of 56 per cent in 2012 in 14 of the EU’s member states and the share of the top five retailers exceeded 60 per cent in 13 member states at the same time. Concentration helps to achieve economies of scale but also endows higher bargaining power that could lead to unfair practices. The emergence of store brands gives rise to a series of issues such as innovation incentives, consumer choices and price levels. The regulatory environment, such as product market regulation, administrative regulation, domestic economic regulation and public health policies largely varies across countries and also affects firms’ behaviour. As an example, recently in France and Belgium, several alliances of supermarket chains were inspected by the EU competition authorities. The EU commission was investigating many cases of potential dominant market positions, such as the case of the world’s biggest beer brewer AB in Ber, for its anticompetitive behaviour in The Netherlands and France. Moreover, food prices increased significantly after the 2007 financial crisis and commodity prices have shown increased volatility since then. Better understanding of price formation and transmission has become a crucial issue. The acts of producing and consuming food can come with externalities to health and the environment. In the health policy realm, for example, governments throughout the EU have contemplated taxes on ‘sin goods’ like sugar and fat, with Ireland and UK most recently gaining approval from the EU to levy a tax on sugary drinks. In environmental policy, pressing concerns about damage from global warming, which are exacerbated by the production of food products with CO2 intensive production processes like beef, raise concerns of whether taxing such goods might help the environment without greatly reducing human welfare. All of this is to say that having a good understanding of food markets and their workings is of critical importance. Yet food markets can also be complex, with many stakeholders, intermediate inputs and other moving parts. Hence, exploring the economic underpinnings of these food markets using structural models can often be a useful exercise. The objective of this paper is to review structural empirical methods that allow tackling relevant policy questions for food markets such as price formation, competition issues or public policies such as nutritional, environmental or regulatory policies that could affect food markets. The first key issue of those analyses is the understanding of consumer behaviour for food products. How do consumers value food products and their characteristics? What drives the consumer substitution patterns? The second key issue is to determine firms’ behaviour in food and drink markets along the supply distribution chain. Two empirical approaches exist: the reduced-form approach and the structural approach resulting from the New Empirical Industrial Organization (NEIO) literature. This second approach solves the problem of reduced-form models that do not explain the link between economic policy decisions and agents’ expectations. Indeed, these models estimate the impact of economic policy measures ‘all things being equal’; in particular, leaving unchanged the expectations of agents. Structural econometrics can therefore take into account its strategic expectations. It is based, on the one hand, on the economic modelling of the agents to describe the behaviour of the actors of the agri-food chain and, on the other hand, on statistical hypotheses to infer what one does not observe. The data available on the market do not directly describe consumer substitution patterns or levels of competition upstream or downstream of a value chain. There is also no public data on contracts between the actors or on their margins. Modelling and inference make it possible to overcome this lack of observations. This survey will focus on a two-step approach.1 The basic idea of two-stage structural modelling can be described following the insight given by Rosse (1970) in the case of the analysis of the market power of a monopoly. Typically, the researcher only has demand data such as prices, quantities and values of observable product characteristics. A demand model can then be specified, and parameters estimated. On the other hand, the researcher has little information on the production costs of the products and is therefore not able to calculate price–cost margins within a sector. To circumvent this problem, Rosse shows that the marginal cost can be deduced from the first-order condition of the problem of profit maximisation of the firm and depends only on the data of prices, quantities and observable variables, as well as the estimates of the demand. This intuition can be transposed to the case of agri-food chains composed mainly of oligopolies. The specification of the demand function as well as the assumptions made on the strategic relationships between the different actors in agri-food chains then determine the flexibility of the structural model. As in food markets the products are differentiated and preferences of consumers are heterogeneous, modelling of purchasing behavior is complex and the assumptions affect price elasticities of demand, that is the percentage change in demand when the price of a products varies and, therefore the estimation of the degree of competition within the industry. To study consumer behaviour, different approaches are used in the literature: classical demand system models as AIDS, Multilevel Demand System or EASI models, and random utility approaches as Logit, nested Logit, random coefficient Logit and random coefficient nested Logit models. We will present advantages and drawbacks of those demand models. Regarding the modelling of competitive behaviour of the different actors of the food chain, we need to consider vertical relationships between manufacturers and retailers as the latter are powerful intermediaries that cannot be neglected. We will present two different approaches to model vertical interactions: take-it or leave-it offers with linear and non-linear contracts and bargaining game models. The paper is organised as follows. In Section 2, we review different ways empirical researchers have approached the issue of demand estimation in the applied contexts that we typically confront as economists doing applied policy analysis and empirical structural food industrial organisation research. Within that context, we provide an overview of the state of research and summarise the core problems researchers face when estimating demand. Section 3 turns to the structural supply models implemented in applied research to date and Section 4 reviews the main topics in policy analysis using the demand and supply models. Finally, Section 5 discusses implications of the main literature findings and contains closing suggestions for future research. 2. Structural demand models Many questions in applied policy analysis require an understanding of how consumers choose among various goods and services as a function of market and individual characteristics. First, properly estimating a demand system in its own right is an objective of interest. Second, demand systems (and their underlying parameters) are often used as providing the ‘ingredients’ to compute consumer welfare from a policy change in a partial equilibrium setting. The empirical setting of a multiple goods demand specification is a simultaneous equation demand system given by log(qj)=αpj+βpk+γxj+εj. (1) Contained in the unobservable (εj) are demand shifters that are not in the set of regressors. Prices are endogenous and this, at the very least, calls for a very demanding instrumental variable strategy, which we will turn to in future sections. Also, as the number of products increases, the number of parameters to be estimated will get very large. We address ways to deal with the dimensionality problem next. The way to reduce the dimensionality of the estimation problem is to put more structure on the choice problem being faced by consumers. In the literature, there are two main approaches to tackling such a problem. The first is to model consumers’ choices in the actual product space as classical demand systems, as well as using specific forms of the underlying utility functions that generate empirically convenient properties, such as the Exact Affine Stone Index (EASI) Marshallian Demand System (Lewbel and Pendakur, 2009); the Almost Ideal Demand System (Deaton and Muellbauer, 1980a) or, in short, AIDS, which is EASI’s most used special case; the Multilevel demand system (Hausman, 1997) and the Quadratic AIDS model (Banks, Blundell and Lewbel, 1997) or, for short, Q-AIDS, which is more general than AIDS as it allows for quadratic income effects. The second approach is to project products into a smaller dimensional characteristics space and estimate demand that results from a random utility model foundation (McFadden, 1974). We will start with product space approaches and then turn to the attribute space approaches to modelling demand in food markets. 2.1. Classical demand systems 2.1.1. AIDS and multilevel demand system The AIDS of Deaton and Muellbauer (1980a) is the state of the art for product space approaches. AIDS models were the dominant choice for applied work. In particular, the AIDS model can fit the data much better than more structural models in some applications and show you just how far you can get with a more ‘reduced-form’ model. These are also used in settings when researchers need to have a more complicated supply side, like, for example, in a dynamic entry game to ease computational burdens and capture some of the reality of the data generating process. The main disadvantage with AIDS approaches is that when anything changes in the model (more consumers, adding new products, imperfect availability in some markets), it is difficult to modify the AIDS approach to account for this type of problem. The usual empirical approach is to use a model of multilevel budgeting. The idea is to impose something akin to a ‘utility tree’ (Hausman, 1997) where consumers first choose to allocate expenditures to an upper level product grouping. Within each product grouping, consumers allocate expenditures among the products therein. When allocating expenditures within a group, it is assumed that the division of expenditure within one group is independent of that within any other group. That is, the effect of a price change for a good in another group is only felt via the change in expenditures at the group level. If the expenditure on a group does not change (even if the division of expenditures within it does) then there will be no effect on goods outside that group. To be able to allocate expenditures across groups, you have to be able to come up with a price index that can be calculated without knowing what is chosen within the group. These two requirements lead to restrictive utility specifications, the most commonly used being the AIDS of Deaton and Muellbauer (1980a).2 Starting at the within-group level, assume the expenditure functions for utility u and price vector p look like: log(e(u,p) = (1−u)log(a(p))+ulog(b(p)) (2) where it is assumed that log(a(p))=α0+∑kαklog(pk)+12∑k∑jγkj⁎log(pk)log(pj) and that log(b(p))=log(a(p))+β0∏kpkβk ⁠. Using Shephard’s Lemma, we get shares of expenditure within groups denoted as wgi and defined as wgi=∂log(e(u,p))∂logpi=αi+∑jγijlog(pj)+βilog(xP) (3) where x is total expenditure on the group, γij=12(γij⁎+γji⁎) ⁠, and P is a price index for the group. The price index that ‘deflates’ income is specified as a linear approximation (as in Stone, 1954) used by most of the empirical literature, given by log(P)=∑kwklog(pk) ⁠. For the allocation of expenditures across groups, we treat the groups as individual goods, with prices being the price indexes for each group. Once again, this depends on the initial choice of groupings. The next step is to calculate expenditure share wi of each good i using prices pi ⁠, quantities qi and total expenditure x=∑kpkqk ⁠. Then, we compute the Stone price index: logP=∑kwklog(pk) and use IV to estimate the equation: wi=αi+∑kγiklog(pk)+βilog(xP)+ξi (4) where ξi is the error term. Ultimately we recover J+2 parameters (⁠ αi,γi1, ...γiJ,βi) ⁠, where economic theory imposes that the parameters satisfy several restrictions, namely: homogeneity, symmetry and adding up.3 2.1.2. EASI Marshallian demand Like the AIDS, the EASI demand system features budget shares that are linear in parameters given real expenditures. However, unlike the AIDS, EASI demands’ Engel curves can have any shape over real expenditures, and below we will use a fifth-order polynomial, unlike the AIDS, which are linear in income (Lewbel and Pendakur, 2009). It can be thus said that AIDS is a special case of EASI. The EASI demand system has the following equation for the budget share wj of each good j ⁠: wj=∑r=05brjyr+∑d=1Z(Cdjzd+Ddjzdy)+∑d=1Z∑k=1JAdkjzdpk+∑k=1JBkjpky+εj, (5) where y is a measure of total expenditures entering as a fifth-order polynomial. The y is either approximated by the Stone index deflated log nominal expenditure x ⁠, namely y=x−∑j=1Jpjwj or given by y=(D,p,x,z)=x−∑j=1Jpjwj+∑d=1Zzdp′Adp/21−p′Bp/2 ⁠. Here, pk and the log of prices of each good k ⁠, the Z demographic characteristics zd ⁠, the interaction terms of the forms pky ⁠, zdy and zdpk ⁠, and (A,B,C,D) are the parameters to be estimated, subject to homogeneity, symmetry and adding-up demand theory restrictions on the parameters. 2.1.3. Estimation methods In the literature, there is a broad discussion of whether the demand restrictions imposed of homogeneity, symmetry and adding up hold when estimating models using aggregate choices, namely aggregate expenditures, rather than individual level expenditures (see, e.g. Deaton and Muellbauer, 1980b; Christensen, Jorgenson and Lau, 1975, that rejected symmetry and homogeneity in aggregated datasets). Hence, in practice, empirical research has used data on prices, quantities and expenditure, imposing only the adding-up condition. In addition, to estimate the several classical demand systems described here, we must deal with the dimensionality and price endogeneity issues. To reduce the dimensionality issues, demand theory restrictions are imposed on the demand parameters to be estimated. As a consequence, substitution patterns are driven by functional forms. For instance, if we were to look at substitution across segments, the AIDS model restricts substitution patterns to be the same between any two products in different segments. This is not a general assumption and is a restriction that can affect research, if, for policy analysis, we need demand that relies on having estimated elasticity patterns as revealed by consumer purchases and not as dictated by functional forms of the demand model. In addition, the major issue for the AIDS model is the high dimensionality of parameters to be estimated. Researchers then need to do some serious aggregating of products to get rid of this problem. Aggregation into higher-level product groupings is therefore a solution followed by most of the literature. Finally recall that, as usual, price is likely to be correlated with the unobservable. Given panel data on prices, quantities and incomes (expenditures) by brands over time in several markets, Hausman, Leonard and Zona (1994) propose using the prices in one market to instrument for prices in another market. This works under the assumption that the pricing rule looks like log(pjnt)=δjlog(cjt)+αjn+ωjnt where pjnt is the price of good j in market n at time t ⁠, cjt represents nation-wide product costs at time t ⁠, αjn are market specific shifters, which reflect transportation costs or local wage differentials, and ωjnt is a mean zero stochastic disturbance (e.g. local sales promotions). Here, they are claiming that market demand shocks ωjnt are uncorrelated across markets. This allows the use of prices in other markets for the same product in the same time period as instruments (if you have a market fixed effect). Often these are referred to as Hausman instruments. This strategy has been criticised for ignoring the phenomena of nation-wide advertising campaigns, suggesting that market demand shocks may be correlated under global markets. Therefore, the validity of ‘Hausman instruments’ is now often questioned and researchers use cost side data on cjt as shifters to instrument for price instead of making assumptions on ωjnt across markets. Still, Hausman instruments have been used in different ways in several different studies. Often people use factor price instruments, such as wages or the price of raw inputs, as variables that shift marginal costs (and hence prices) but do not affect the demand unobservables (⁠ ε ⁠). Instruments can also be used if there is a large price change in one period for some external reason (like a strategic shift in all the companies’ pricing decisions). Then the instrument is just an indicator for the pricing shift having occurred or not. 2.2. Random utility models To model consumer preferences, we can also consider the characteristic space approach. The random utility model considers products as bundles of characteristics and defines consumer preferences over characteristics, letting each consumer choose a bundle that maximises their utility. The random utility model restricts the consumer to choosing only one bundle. Multiple purchases are easy to incorporate conceptually but incur a big computational cost and require more detailed data than is usually available.4 These models use either consumer level data over markets, or aggregate sales data of choices of products over markets. Let the utility for good j ⁠, where j= 0,1,2...J ⁠, of the individual i be given by: Uij=U(xj,pj,vi,θ). (6) Good 0 is generally referred to as the outside option or outside good. It represents the option chosen when none of the observed goods are chosen. A maintained assumption is that the pricing of the outside good is set exogenously. J is the number of goods in the industry at hand. xj are non-price characteristics of good j ⁠, pj is the price, vi are characteristics of the consumer i and θ are the parameters of the model.5 Consumer i chooses good j when Uij>Uik,∀k≠j ⁠. This means that the set of consumers that choose good j is given by: Aj(θ)=[v|Uij>Uik,∀k] (7) Given a distribution over the v’s, f(v) ⁠, we can recover the share of good j as: sj(x,p|θ)=∫v∈Aj(θ)f(dv) (8) If we let the market size be M ⁠, then the total demand is qj(x,p|θ)=Msj(x,p|θ) ⁠. Recall that ordinal rankings of choices are invariant to affine transformations of the underlying utility function. More specifically, choices are invariant to multiplication of U by a positive number and the addition of any constant. This also implies that in modelling utility we need to make some normalisations by bolting down a basis to measure things against and allowing us the ability to interpret our coefficients and do estimation. Traditionally, we normalise the mean utility of the outside good to zero. Random utility models allow researchers to address horizontal and vertical product differentiation. Horizontally differentiated means that, setting aside price, people disagree over which product is best. In the characteristics space setting this means that, with horizontal differentiation, people do not all agree that more of an attribute is better. Vertically differentiated means that, price aside, everyone agrees on which good is best, they just differ in how much they value additional quality. In the following subsections, we will describe three types of random utility models that make slightly different assumptions about the consumers’ utility functions. First, we discuss the Logit model of McFadden (1974), where we assume that consumers’ preferences for a product are uncorrelated across all products. Next, we discuss the nested Logit model, which relaxes these strong preference assumptions and instead allows consumers to have correlated preferences over products in the same subgroup (essentially allowing products in a subgroup to be substitutes). Finally, we discuss the random coefficients Logit model, which allows consumers to have idiosyncratic preferences over product attributes that, unlike the previous two models, are not solely based on observable characteristics. 2.2.1. Logit The Logit model6 assumes that everyone has the same taste for quality but have different idiosyncratic tastes for the product. Utility is given by: Uij=δj+εij, (9) where εij is distributed iid extreme value type I, with F(ε)=e−e−ε ⁠. The probability that good j is chosen by consumer i is given by: Pri(Choicej)=Pr(Uji>Uhi)=Pr(δj+εji>δh+εhi),∀h≠j,∀i. (10) This allows for the aggregate shares, or the probability that good j is chosen across all consumers, to have an analytical form, obtained as: Pr(Choicej)=exp(δj)∑n=0Jexp(δn)=exp(δj)1+∑n=1Jexp(δn), (11) where the last simplification in equation (11) results from the fact that δ0=0 ⁠. That is, the normalised mean utility for the outside option is zero. This ease in aggregation comes at a cost. The embedded assumption on the distribution on tastes creates more structure than we would like on the aggregate substitution matrix, as well as independence of irrelevant alternatives (IIA). The problem is that the ratio of choice probabilities of consumer i between two options j and k does not depend on the characteristics and or utilities of any other product, i.e. SijSik=exp(δij)exp(δik) and cross-price elasticities are restricted to satisfy ∂sj∂pk=∂sl∂pk ∀ l≠j ⁠. If we have data with choices of individuals i ⁠, and with respondent-specific choice information and respondents’ demographics, these data enable us to consider and estimate a specification of heterogeneous preferences. The mean utility δij is specified as: δij=β0xj+β1Dixj, (12) where xj are attributes of product j ⁠, β0 is the mean taste for attributes and β1 is the specific taste according to the respondent’s observed demographics Di ⁠. This structure allows for the fact that different decision makers may have different preferences. 2.2.2. Nested Logit The nested Logit model relaxes the IIA property of the simple Logit model and allows consumers to have correlated preferences for products that belong to the same subgroup or group in a nest. As in the AIDS Model, we need to make some ‘ex-ante’ classification of goods into different segments, so each good j∈S(j) ⁠. The goods are divided into nests and we allow for a degree of independence in unobserved components within each nest. For different goods in different nests, the relative choice probabilities are now dependent on attributes of other alternatives in the two nests (McFadden, 1978; Train, 2003). Let the set of products be partitioned into K non-overlapping nests denoted as N1,N2, ...,NK ⁠. The utility that person i obtains from alternative j in nest Nk is denoted, as usual, as Uij=Vij+εij ⁠, where Vij is observed by the researcher and εij is a random variable where the vector εi=(εi1, ...,εiJ) has a generalised extreme value distribution, which is a generalisation of the distribution that gives rise to the Logit, allowing for the ε’s to be correlated within a nest. We define a parameter λk ⁠, which measures the degree of independence in unobserved utility among the alternatives in nest k where, if λk=1 for all nests k ⁠, we obtain the Logit model. Given that consumers choose the product that maximises random utility, the choice probabilities for each product j in nest Nk are given by Prij=exp(Vij/λk)(∑j∈Nkexp(δij/λk))λk−1∑l=1K(∑m∈Nlexp(δim/λl))λl). (13) We can get a simpler expression for the probability if we rewrite Vij=Wik+Yij for a good in nest Nk ⁠, where Wik depends only on variables that describe nest k that differ over nests but not over alternatives within each nest. In addition, in Yij we have variables that describe alternative j and vary over alternatives within nest k. With this decomposition of utility, the nested Logit probability can be written as the product of two standard Logit probabilities. Let the probability of choosing alternative j∈Nk be expressed as the product of a conditional probability and a marginal probability, namely Prij=Prij|NkPriNk ⁠, where PriNk is the probability that an alternative within nest Nk is chosen and Prij|Nk is the probability that the alternative j is chosen given that an alternative in Nk is chosen. For the nested Logit we get: PriNk=exp(Wik+λkIik)∑l=1Kexp(Wil+λlIil), (14) Prij|Nk=exp(Yij/λk)∑m∈Nkexp(Yim/λk) (15) where the so-called inclusive value Iik is defined as: Iik=log∑j∈Nkexp(Yij/λk) (16) This means that the nested Logit probabilities are ultimately given by: Prij=exp(Wik+λkIik)∑l=1Kexp(Wil+λlIil)exp(Yij/λk)∑m∈Nkexp(Yim/λk). (17) 2.2.3. Random coefficient Logit models Even if nested Logit model relaxes the IIA assumption of the Logit model, this model is not totally flexible as the IIA assumption holds for two alternatives within the same group. Another stream of papers estimates flexible specifications of discrete choice structural revealed preference models of consumer demand (McFadden, 1974; McFadden and Train, 2000; Train, 2003) via a random coefficient. Here we allow individual decision makers to have different preferences not just due to observable demographics Di ⁠, which sometimes may not capture all the heterogeneity, but rather allow a more general unobserved heterogeneity structure. Then we define the coefficients βi to vary according to βi=β0+σβviβ ⁠, where vi follows a parametric distribution7 capturing any heterogeneity and the price parameter is similarly defined as αi=α0+σαviα ⁠. If there is no heterogeneity in individual preferences relative to the average, then both σα and σβ will be zero and the model will correspond to a Logit model. If, however, there is heterogeneity in preferences relative to the average, then σα and σβ are different from zero. The utility is defined as: Uij=Xjβi+αiPricej+ξj+εij. (18) If εji are assumed to be independently, identically extreme value distributed (type I extreme value distribution) and consumers choose one unit of product j among all the possible products available at a certain time that maximises their indirect utility, the following closed form solution can be derived for the probability that the consumer i chooses the product j conditional that vi=(viβ,viα) is Prji=exp(Xjβi+αiPricej)∑k=0Jexp(Xkβi+αiPricek). (19) This offers flexibility in incorporating consumer heterogeneity with regard to product attributes X ⁠. To recover how Di affects the departure from mean valuations, we then project estimated βi on observed demographics Di in a second step, as described below. In a third heterogeneity specification, we define the coefficients αi and βi to be combination of the two previous heterogeneity specifications, as αi=α0+α1Di+σαviα and βi=β0+β1Di+σβviβ ⁠, where viβ and viα are normal random variables capturing any random heterogeneity and Di are observed consumer characteristics affecting heterogeneity. If, however, there is heterogeneity in preferences due to demographics relative to the average, then α1 and β1 are different from zero, and if there is additional random heterogeneity, then σα and σβ are different from zero as well. 2.2.4. Estimation methods 2.2.4.1. Micro data If we have micro-level data, we see each consumer making decisions for T different choice occasions. By defining the distribution of the θ=(α,β) parameters in general form as f(θ|α0,α1,α2,β0,β1,β2) then the probability of individual i making a sequence of choices among the N alternatives (⁠ j=0,..N ⁠) is given as: Si=∫∏t=1T∏j=0J[exp(Xijtβi+αiPricejt)1+∑k=1Jexp(Xiktβi+αiPricekt)]Yijtf(θ|α0,α1,σα,β0,β1,σβ)dθ, (20) where Yijt= 1 if the respondent i chooses alternative j for situation t and 0 otherwise. Given a total of I respondents, the parameters (α0,α1,σα,β0,β1,σβ) are estimated by maximising the simulated log-likelihood function: SLL=∑i=1Ilog(1R∑r=1R∏t=1T∏j=0J[exp(Xijtβi[r]+αi[r]Pricejt)1+∑k=1Jexp(Xiktβi[r]+αi[r]Pricekt)]Yijt), (21) where αi[r],βi[r] are the rth draw for respondent i from the distribution of α,β ⁠. 8 Let θ=(α,β) ⁠. To estimate θi we proceed as follows. The expected value of θ ⁠, conditional on a given response Yi of individual i and a set of alternatives characterised by Xi for product t ⁠, is given by E[θ|Yi,Xi]=∫θ∏t=1T∏j=0J[exp(Xijtβi+αiPricejt)1+∑k=1Jexp(Xiktβi+αiPricekt)]Yijtf(θ|α0,α1,σα,β0,β1,σβ)dθ∫∏t=1T∏j=0J[exp(Xijtβi+αiPricejt)1+∑k=1Jexp(Xiktβi+αiPricekt)]Yijtf(θ|α0,α1,σα,β0,β1,σβ)dθ, (22) Equation (21) can be thought as the conditional average of the coefficient for the subgroup of individuals who face the same alternatives and make the same choices. For each individual i we estimate a certain attribute marginal utility θi ⁠, following Revelt and Train (2000), by simulation according to the following: θˆi=1R∑r=1Rβi[r]∏t=1T∏j=0J[exp(Xijtβi[r]+αi[r]Pricejt)1+∑k=1Jexp(Xiktβi[r]+αi[r]Pricekt)]Yijt1R∑r=1R∏t=1T∏j=0J[exp(Xijtβi[r]+αi[r]Pricejt)1+∑k=1Jexp(Xiktβi[r]+αi[r]Pricekt)]Yijt, (23) where θ[r] is the rth draw for individual i from the estimated i’s distribution of θ ⁠. If prices are exogenous, the demand parameters are estimated by simulated Maximum Likelihood function defined in equation (21). However, the price exogeneity assumption cannot be hold when omitted product characteristics affect both demand and prices. Omitted characteristics could be unobserved product attributes of goods or unobserved marketing efforts as advertising, sales promotions, shelves position. Then, the method used follows simulated likelihood function control approaches as in Kuksov and Villas-Boas (2008) and Petrin and Train (2010). This method consists in regressing prices on the exogenous demand variables and instrumental variables, and capturing, through the error term of the price equation, all unobserved product characteristics that affect prices. This error term is then included in the deterministic part of the utility to avoid any correlation between prices and the remaining part of the demand error term. The choice of instrumental variables is crucial. They should be price shifters uncorrelated with demand. The ideal instrumental variables should capture the cost of producing and distributing the goods and inputs costs are good candidates, as are attributes of other products (as in Berry, Levinsohn and Pakes, 1995) or Hausman style instruments, such as average prices in other markets, assuming no national common demand unobservables. 2.2.4.2. Aggregate sales data The random coefficient Logit model using aggregate data, as in Berry, Levinsohn and Pakes, (1995) and Nevo (2000a), is probably the most commonly used demand model in the empirical food industry literature. This model includes differentiated goods, and the data are typically shares, prices and characteristics in different markets. All the standard problems, such as being endogenous and wider issues of identification, will continue to be a problem here. Estimation of this model uses variation in prices due to exogenous factors to identify demand. As in Nevo (2000a), we rewrite the utility of consumer i for product j as: Uijt=δjt(pjt,Xjt,ξjt;α0,β0)+μijt(pjt,vi;σβi,σαi), (24) where δjt=α0pjt+β0Xjt+ξjt is the mean utility, while μijt=α1pjtDi+σαpjtμiα+β1XjtDi+σβXjtμiβ+ɛijt is the deviation from the mean utility that allows for consumer heterogeneity in price response. Let the distribution of μijt across consumers be denoted as F(μ) ⁠. The aggregate share Sjt of product j in market t across all consumers is obtained by integrating the consumer level probabilities: Sjt=∫exp(δjt+μijt)1+∑n=1Jexp(δnt+μint)dF(μ). (25) This aggregate demand system not only accounts for consumer heterogeneity but also provides more flexible aggregate substitution patterns than the homogeneous Logit model. If price is correlated with demand unobservables ξ then the coefficients are not consistently estimated by OLS. Using aggregate data on market shares by product over markets, to estimate the random parameters Logit demand model the literature uses the GMM-estimator proposed by Berry, Levinsohn and Pakes (1995) and Nevo (2000a). When estimating demand, the goal is to derive parameter estimates that produce product market shares close to the observed shares. As shown, this procedure is non-linear in the demand parameters to be estimated. Berry (1994) constructs a demand-side equation that is linear in the parameters to be estimated. This follows from equating the estimated product market shares.9 Once this inversion has been made, given starting values of the random coefficients α1 ⁠, β1 ⁠, σα and σβ ⁠, one obtains equation (26), which is linear in the linear parameters, and then instrumental variable methods can be applied directly. δjt(α1,β1,σα,σβ)=αpjt+Xjtβ+ξjt. (26) Finally, the random coefficient parameters α1 ⁠, β1 ⁠, σα and σβ are obtained by feasible simulated method of moments following Nevo’s (2000a) estimation algorithm using equation (26). 3. Structural supply models of food markets Empirical work in food supply chains either assumes manufacturers sell directly to consumers, or that the intermediate distributor or retailer remains passive (as in Baker and Bresnahan, 1985; Berry and Pakes, 1993; Werden and Froeb, 1994; Nevo, 2000a), or models the supply chain strategic pricing formally. In these models, manufacturing decide in a take it or leave it setting the wholesale prices (Villas-Boas and Zhao, 2005; Villas-Boas, 2007a) or non-linear contracts (Bonnet and Dubois, 2010) when contracting or instead via bargaining with retailers (Misra and Mohanty, 2006; Draganska, Klapper and Villas-Boas, 2010; Bonnet, Bouamra-Mechemache and Richards, 2018), who in turn decide the retail prices that consumers have to pay. Consider a set of J products sold by R retailers and M manufacturers. Each retailer r sells a subset Sr of products and each manufacturer m sells to retailers a subset Gm of products, such that J=∑r=1RSr=∑m=1MGm ⁠. 3.1. Take-it or leave-it offers 3.1.1. Linear contracts We assume a manufacturer Stackelberg model in which M manufacturers set wholesale prices pw first, in a Nash–Bertrand manufacturer-level game, and then R retailers (chains) follow, setting retail prices p in a Nash–Bertrand fashion. Let each retailer’s r marginal costs for product j be given by cjr ⁠, and let manufacturers’ marginal costs be given by cjw ⁠.10 Solving by backwards induction, we assume that each retail chain r maximises profit function defined by: πr=∑jεSrM[pj−pjw−cjr]sj(p)forr= 1, ...R, (27) where M is the size of the market, and sj is defined, given a potential market, as the market share of product j ⁠. The first-order conditions, assuming a pure-strategy Nash equilibrium in retail prices, are: sj+∑mεSr[pm−pmw−cmr]∂sm∂pj= 0forj∈Sr (28) Switching to matrix notation, let Δr be a matrix with general element Δr(i,j)=∂sj∂pi ⁠, containing consumer demand substitution patterns with respect to changes in the retail prices of all products and Ir the diagonal ownership matrix of retailer r where element (j,j) takes 1 if j is sold by the retailer r and 0 otherwise. Solving equation (28) for the price–cost margins for all products in vector notation gives the price–cost margins γ for all the products in the retail chains under Nash–Bertrand pricing: γ=p−pw−cr=−∑r=1R[IrΔrIr]−1Irs(p), (29) which is a system of J implicit functions that expresses the J retail prices as functions of the wholesale prices. Manufacturers choose wholesale prices pw to maximise their profits given by: πm=∑jεGm[pjw−cjw]sj(p(pw)), (30) knowing that retail chains behave according to equation (29).11 Solving for the first-order conditions from the manufacturers’ profit maximisation problem, assuming again a pure-strategy Nash equilibrium in wholesale prices and using matrix notation, yields: Γ=(pw−cw)=−∑f=1M[IfΔwIf]−1Ifs(p), (31) where If is a diagonal ownership matrix of manufacturer f with element (i,j)=1 ⁠, if the manufacturer sells product j ⁠, and equal to zero otherwise; Δw is a matrix with general element Δw(i,j)=∂sj∂piw containing changes in demand for all products when wholesale prices change. Given retail markup pricing behaviour assumed in equation (29), Δw can be decomposed as the impact of retail prices on demand and the impact of wholesale prices on retail prices, to obtain Δw(i,j)=∑l=1J∂sj∂pl∂pl∂piw ⁠. In matrix notation, we get Δw=PwΔr where Pw is the matrix of the derivatives of retail prices with respect to wholesale prices, and can be deduced from the total differentiation of the retailer’s first-order conditions equation (28) with respect to wholesale price. Defining Sppj the (J×J) matrix of the second derivatives of the market shares with respect to retail prices whose element (l,k) is ∂2sk∂pj∂pl ⁠, we obtain Pw as12: Pw=IrΔr′Ir[ΔrIr+IrΔr′Ir+(Spp1Irγ|...|SppJIrγ)Ir]−1. (32) Under the above model, given the demand parameters θ ⁠, the implied price–cost margins for all J products can be calculated as mr(θ) for the retailers and mw(θ) for the manufacturers.13 3.1.2. Non-linear contracts Bonnet and Dubois (2010) consider that manufacturers have all market power and simultaneously propose take-it or leave-it offers of two-part tariff contracts to each retailer. These contracts are public information and involve specifying franchise fees and wholesale prices. In the case of these two-part tariff contracts, the profit function of retailer r is: Πr=∑j∈Sr[M(pj−pjw−cjr)sj(p)−Fj] (33) where Fj is the franchise fee paid by the retailer for selling product j ⁠. Manufacturers set their wholesale prices pkw and the franchise fees Fk in order to maximise profits equal to: Πm=∑k∈Gm[M(pkw−ckw)sk(p)+Fk] (34) for firm m ⁠, subject to retailers’ participation constraints Πr≥Π¯r ⁠, for all r= 1,…,R ⁠, where ∏¯r is an exogenous outside option of retailer r. The expressions for the franchise fee Fk of the binding participation constraint can be substituted into the manufacturer’s profit equation (34) to obtain the following profit for firm m: Πm=∑k∈Gm(pk−ckw−ck)sk(p)+∑k∉Gm(pk−pkw−ck)sk(p)−∑j∉GmFj (35) This shows that each manufacturer fully internalises the entire margins on his products but internalises only the retail margins on rivals’ products. Note that the additional term ∑j∉GmFj is constant for the manufacturer m and thus maximising the profits of m is equivalent to maximising the sum equation (35) without this term. They then set wholesale prices in the following maximisation programme: max{wk}∈Gm∑k∈Gm(pk−μk−ck)sk(p)+∑k∉Gm(pk−wk−ck)sk(p). Then, the first-order conditions are, for all i∈Gm ⁠: ∑k∂pk∂wisk(p)+∑k∈Gm[(pk−μk−ck)∑j∂sk∂pj∂pj∂wi]+∑k∉Gm[(pk−wk−ck)∑j∂sk∂pj∂pj∂wi]= 0. These conditions allow us to estimate the price–cost margins, given demand parameters. Then the first-order conditions become (in matrix notation), for all i∈Gf: IfPws(p)+IfPwΔrIfΓ+IfPwΔrγ= 0. This implies that the manufacturer price–cost margin is: Γ=∑f=1M(IfPwΔrIf)−1[−IfPws(p)−IfPwΔrγ] (36) which allows for an estimate of the price–cost margins with demand parameters, using equation (29) to replace γ and equation (32) for Pw ⁠. Note that different vertical restraints can be used with two-part tariff contracts. Indeed, manufacturers can also choose retail prices in the case where manufacturers use resale price maintenance (RPM) as in Bonnet and Dubois (2010) or uniform pricing (Bonnet et al., 2013). 3.2. Bargaining models Among the most recent approaches to modelling vertical food supply chains, Draganska, Klapper and Villas-Boas (2010) and Bonnet and Bouamra-Mechemache (2016) allow for non-unilateral bargaining power and model the price negotiation between retailers and manufacturers using bargaining in the German coffee market and in the French fluid milk market, respectively. This methodology enables researchers to estimate the bargaining power for each pair of manufacturers and retailers and infer the resulting profit sharing between them, contrary to take-it or leave-it offers that consider that all market power is in the retailers’ or manufacturers’ hands. These models specify the vertical channel as a two-tier industry consisting of M upstream firms and R downstream retailers. Retailers’ profit functions are given by equation (27). Retail margins result from the retailers’ choice of final prices and the maximisation of the retail profit. Retailers are assumed to compete with each other in Bertrand–Nash fashion in the goods market and set prices for each product as in equation (29). Then, wholesale price equilibrium results from the negotiation between firms and retailers and negotiation on wholesale prices is modelled as a Nash bargaining game. Each pair of firms and retailers are assumed to secretly and simultaneously contract over the wholesale price of the product j ⁠. Moreover, firms and retailers have rational expectations, such that the ultimate equilibrium outcome is anticipated by both parties.14 The main difficulty comes from the linkage across negotiations, which raises arduous questions: a key difficulty is identifying what each manufacturer knows about its rivals’ contract terms. Indeed, when negotiating, each manufacturer must conjecture the set of terms its rivals have or have not been offered. In equilibrium, this conjecture must be correct but out-of-equilibrium beliefs may be important in determining the bargaining outcome. In the cooperative bargaining approach, this problem is solved by assuming that any bargaining outcome must be bilaterally renegotiation-proof, i.e. no manufacturer–retailer pair can deviate from the bargaining outcome in a way that increases their joint profit, taking as given all other contracts. Bargaining between each retailer–manufacturer pair is assumed to maximise the two players’ joint profit, taking as given all other negotiated contracts and that each player earns its disagreement payoff (i.e. what it would earn from the sales of its other products if no agreement on this product is reached) plus a share [λj∈0,1] (respectively, 1−λj ⁠) of the incremental gain from trade going to the retailer (respectively to the manufacturer). A manufacturer negotiates with a given retailer for each of its products, that each product is negotiated separately with the manufacturer, and that retail prices are not observable when bargaining over the wholesale prices. Then, retail prices are considered as fixed when solving for the bargaining solution. The equilibrium wholesale price for product j is derived from the bilateral bargaining problem between a firm and a retailer such that each firm and retailer pair maximises the Nash product [πjr(pjw)−djr]λj[πjm(pjw)−djm](1−λj) where πjm(pjw) and πjr(pjw) are, respectively, the profits of the firm and the retailer for product j. They are given by: πjm(pjw)=(pj−pjw−cjr)Msj(p)=γjMsj(p)πjr(pjw)=(pjw−cjw)Msj(p)=ΓjMsj(p). (37) The payoffs the manufacturer and the retailer can realise outside of their negotiations are denoted, respectively, djm and djr ⁠. The retailer could gain djr if it removes the supplier’s product j from its stores but contracts with other suppliers. Similarly, the firm could get profits djm from the sales of its other products as well as from the sales of products to other retailers if the negotiation fails. If the retail prices are fixed during the negotiation process, the disagreement payoffs djm and djr are given by: djr=∑k∈Rr−{j}γkMΔsk−j(p)djm=∑k∈Gm−{j}ΓkMΔsk−j(p) (38) where the term MΔsk−j(p) is the change in market shares of product k that occurs when the product j is no longer sold on the market. Those quantities can be derived through the substitution patterns estimated in a random coefficient Logit demand model as follows: Δsk−j(p)=∫exp(δk+μik)1+∑l=1/{j}Jexp(δl+μil)−exp(δkt+μik)1+∑l=1Jexp(δl+μil)dPν(ν). (39) Solving the bargaining problem in equation (??) leads to the following first-order condition: λj(πjm−djm)∂πjr(pjw)∂pjw+(1−λj)(πjr−djr)∂πjm(pwj)∂wj= 0. (40) Under the assumption that the matrix of prices for final commodities is treated as fixed when the wholesale prices are decided during the bargaining process, we have ∂πjr(wj)∂wj=−Msj(p) and ∂πjm(wj)∂wj=Msj(p) from equation (37). Equation (40) can thus be written as πjm−djm=1−λjλj(πjr−djr) ⁠. Using equations (37) and (38), the following expression can be derived for the bargaining solution: ΓjMsj(p)−∑k∈Sr−{j}ΓkMΔsk−j(p)=1−λjλj[γjMsj(p)−∑k∈Gf−{j}γkMΔsk−j(p)]. (41) Using equation (41) for all products j ⁠, we obtain the matrix of firms’ margins:15 Γ=∑f=1M∑r=1R[(IfSIf)−1(1−λλ∗(IrSIr)γ)]. (42) where S is the (J×J) matrix with market shares as diagonal elements and changes in market shares otherwise: S=[s1−Δs2−1⋯−ΔsJ−1−Δs1−2s2⋯−ΔsJ−2⋮⋮⋱⋮−Δs1−J−Δs2−J⋯sJ] (43) Equation (42) shows the relationship between the wholesale margin on the one hand and the retail margin on the other hand. This relationship first depends on the disagreement payoffs and thus on the market share changes that are determined by the substitution patterns estimated in the demand model. It also depends on the exogenous parameter λj ⁠, the relative power of the retailer relative to the firm when bargaining over the wholesale price. The higher λj ⁠, the lower the share of the joint profit the firm will get from the bargaining. Adding equations (42) and (29) yields the total margin of the firm/retailer pair over product j ⁠: γ+Γ=[∑f=1M∑r=1R(IfSIf)−1(1−λλ∗(IrSIr))+I](IrSpIr)−1Irs(p) (44) where I is the (J×J) identity matrix. Because we do not directly observe firms’ marginal production costs as well as retailers’ marginal distribution costs, we are not able to determine analytically the bargaining power parameter λj. We rather conduct an estimation specifying the overall channel marginal cost Cjt for each product j ⁠. We follow the following specification for the total marginal cost Cj=θωj+ηj where ω is a vector of cost shifters and η is a vector of error terms that account for unobserved shocks to marginal cost. The final equation to be estimated is thus given by: p=θω+[∑f=1M∑r=1R(IfSIf)−1(1−λλ∗(IrSIr))+I](IrSpIr)−1Irs(p)+η. (45) We are then able to get an estimate of λ for each product. Hence, we can deduce manufacturers’ margins from equation (42). Moreover, from the estimates of the cost shifters and the error term of equation (45), we get the estimated total marginal cost, which is the sum of the marginal cost of production and the marginal cost of distribution for each product j ⁠. 4. Topics in policy analysis In this section, we will consider how the models presented in the previous sections can be useful for policy analysis in food markets. Hence we briefly review papers that utilise structural demand and/or supply models in order to better understand food policy issues. This review is not necessarily meant to be comprehensive, but rather to brush on important themes in the literature, including vertical relationships in food markets, price formation, competition issues, environmental and nutritional policies. Counterfactual food policy analysis through simulations is used to recover variation in prices, consumption, consumer welfare and profit of policy scenario. 4.1. Vertical relationships Data on contracts and relationships between manufacturers and retailers in food markets are generally not publicly available. Structural empirical models allow palliating this lack of information making some assumptions about the nature of competition and vertical contracts. Vuong (1989), Smith (1992) and Rivers and Vuong (2002) propose and refine likelihood ratio, Cox-type and encompassing tests for a variety of nested and non-nested supply models, providing a foundation for testing different structural models. Bonnet and Dubois (2010) find empirical support in the French bottled water market for non-linear pricing and RPM practices using a random coefficient Logit demand and testing linear and non-linear pricing contracts. This result is corroborated by Bonnet and Réquillart (2013a) in the French soft drink market, Bonnet et al. (2013) in the German coffee market, Villas-Boas (2007a) in the US yogurt market, and Bonnet and Réquillart (2015) in the fluid milk and dairy dessert sectors in France. Structural models can also be designed to determine bargaining power using the methods presented in Section 3.2. Draganska, Klapper and Villas-Boas (2010) evaluate how bargaining power is split throughout the distribution channel in the German coffee market, finding that bargaining power is not an inherent characteristic of a firm but instead depends on the negotiation partner. Additionally, applications with structural models show that product differentiation like organic labelling (Richards, Acharya and Molina, 2011; Bonnet and Bouamra-Mechemache, 2016), product complementarity (Bonnet et al., 2018) and introduction of private labels (Meza and Sudhir, 2010) are all important determinants of bargaining power along the distribution channel. The nature of the shock could also affect the pass-through rates. For example, Bonnet and Villas-Boas (2016), allowing for demand asymmetry responses for consumers in a random coefficient Logit approach, show that cost pass-through is higher from a positive cost shock than a negative one. Another example shows that the design of the regulatory tools as taxation policies could affect the transmission of the tax. Bonnet and Réquillart (2013b) and Griffith, Nesheim and O’Connell (2018) show that an excise tax will be overtransmitted to consumer while ad-valorem tax leads to a lower consumer incidence on the French soft drink market and the UK butter and margarine market, respectively. 4.2. Competition issues Structural approaches are particularly popular for merger and collusive behaviour analysis. Slade (2004), for instance, uses a structural approach to look for evidence of collusive behaviour in the UK brewing market and finds no evidence of any sort of coordinated behaviour. Merger simulations, a prominent application of the tools discussed above, consist in assuming that both firms form a new entity and recovering new price equilibrium given this new structure. Nevo (2000b) is the classical paper on merger analysis in food markets using random coefficient Logit models while Hausman, Leonard and Zona (1994) is the primary reference for merger analysis in food markets using AIDS. Both papers estimate a demand system and resulting firm profit margins given pre-merger pricing behaviour. Extending previous merger approaches, Villas-Boas (2007b) finds empirical evidence that authorities should consider incorporating the role of retailers in upstream merger analysis, especially in the presence of an increasingly consolidated retail food industry. Bonnet and Dubois (2010) also extend merger analysis to cases of use of non-linear contracts by manufacturers and retailers. 4.3. Price formation The price formation literature seeks to understand how input price changes throughout the supply chain are passed through into intermediate and final prices for food items, and specifically explain situations where this pass-through is imperfect, considering explanations such as price rigidities, local non-traded costs or markup adjustment of manufacturers and retailers due to consumer substitution patterns, market structure and market power in industries. Goldberg and Hellerstein (2008) develop a structural approach that can be used to identify the determinants of incomplete exchange-rate pass-through (one prominent example of incomplete pass-through), exploring markup, marginal cost and nominal-rigidity channels. Goldberg and Hellerstein (2013) build on this approach, using a random coefficient model of demand to explore incomplete pass through in the beer market, and highlight the role of local non-traded costs. This result is corroborated in the coffee market by Nakamura and Zerom (2010) in the USA and by Bettendorf and Verboven (2000) in the Netherlands. Considering other types of pass-though, Nakamura (2008) finds that price variation observed over time seems to arise from retail-level rather than manufacturer-level demand and supply shocks, when looking at US grocery purchases. Markup adjustment could be due to the degree of competition. Indeed, Kim and Cotterill (2008) look at cost pass through of changes in inputs for US processed cheese using a mixed Logit framework under different regimes, and find that under collusion, the pass-through rates for all brands are much lower than under Nash–Bertrand competition. Nakamura and Zerom (2010) also show that the elasticity patterns of demand affect the markup adjustment in the imperfect pass-through. Vertical integration structures determine pass-through as well; Hellerstein and Villas-Boas (2010) show that pass-through is positively related to firms’ degree of vertical integration across industries. Bonnet et al. (2013) find that retailers are limited in their ability to make markup adjustments when faced with RPM restrictions in a context of non-linear pricing contracts, leading to higher pass-through rates. Heterogeneity in firms, including differences in market size or structure also determine pass-through. Atkeson and Burstein (2008), for instance, consider a model of Cournot competition in which firms do not fully pass through changes in their marginal costs to prices because their optimal markup depends on market share. Auer and Schoenle (2016) show that the firms that react the most to changes in their own costs also react the least to changing prices of competing importers. Firm size can also matter; Berman, Martin and Mayer (2011) find that higher performance French exporter firms react to a currency depreciation by increasing their markup significantly more and by increasing their export volume less than other firms. 4.4. Food policy To fight against unhealthy food consumption or the carbon foot print of the food consumption, public authorities need to think about effective policy tools to change food consumption. Structural approaches provide a suitable ex-ante analysis method to anticipate consumers’ and firms’ reaction to food policy. 4.4.1. Nutritional labelling Structural demand models are used in the literature to understand nutritional label preferences and measure their effect on consumption.16 In the milk industry, Dhar and Foltz (2005) use data from US cities and Q-AIDS method to estimate the value of organic and rBST-free labels on milk, and find consumer benefits from organic milk and to a lesser extent from rBST-free milk, suggesting value from the corresponding characteristics labels. Kiesel and Villas-Boas (2007) also look at the premium consumers place on a USDA organic label using a random coefficient Logit framework, and find that the USDA organic seal increases the probability of purchasing organic milk. Brooks and Lusk (2010) similarly find that consumers are willing to pay large premiums to avoid milk from cloned cows. Allais, Etilé and Lecocq (2015) evaluate front-of-pack nutrition labels and nutrition taxes in the dessert yogurt and fromage blanc markets. Using a supply model of oligopolistic price competition, they find that both taxes and food labels are effective in reducing the purchase of fatty foods. 4.4.2. Fiscal policies An alternate method to nudge consumers to make healthier nutritional choices is to tax ‘sin goods’, such as sugar and fat. Allais, Bertail and Nichèle (2010) look at the effects of a ‘fat tax’ (a special tax on food items high in calories, fat or sugar) on the nutrients purchased by French households across different income groups estimating a complete AIDS. They find that taxing cheese, butter, cream and sugar-fat products reduces total calories purchased, particularly with respect to saturated fat (but also reduced overall food purchases). Bonnet and Réquillart (2011) show with a random coefficient Logit model that some European CAP reforms could damage the nutritional objectives of public authorities, and specifically that the reduction of the price of raw sugar by 36 per cent would increase the consumption of sugar-sweetened drinks in France. Given the environmental impact of food consumption, several structural analyses address the issue of environmental taxes on food products. For example, Bonnet et al. (2018) implement a random coefficient Logit model to look at how food consumption behaviour could change under environmental taxes on all animal products. They find that high taxes 200 per ton of CO2 would only lead to a 6 per cent reduction in GHG emissions. Caillavet, Fadhuile and Nichèle (2016) and Edjabou and Smed (2013), using an AIDS demand model, also show that the potential for emission reduction is low in France and Denmark, respectively. 5. Conclusion This review presented structural demand and supply models useful for food policy analysis. Improvements in methodology have paid particular attention to model consumers’ and firms’ behaviour in food markets, and structural approaches are increasingly used as computational power and the availability of data steadily rise. Structural models become especially powerful as more accurate measurements on cost, contractual terms and profit shares become available, as these data are helpful in dealing with various identification issues posed above. Restrictive assumptions remain in the methodologies described and further improvements are required to understand complex behaviours of firms and consumers. Firms’ strategic behaviour should be analysed while accounting for the complexity of their multiple decisions (e.g. price, quantity sold, quality and variety), suggesting that structural approaches should be improved in the context of vertical relationships. Given the high concentration of unfair practices in the food market, competition authorities will need more and more precise studies of these practices, such as: as tying contracts, cartels and exclusive dealings, as well as their implications on food supply and profit sharing. As issues of the revenue of upstream actors (producers or producers’ organisations) in the agri-food chain are currently being debated in Europe, policy analyses are required to deal with a three-level interactions between producers, manufacturers and retailers. One of the next challenges of structural approaches is to develop vertical interaction models including the upstream sector. This would allow understanding the implications of Common Agricultural Policy reforms on producers, concentration moves at the manufacturer or retail levels, or environmental and health public policies. There are also methodological avenues of future research given that the majority of the work in agri-food organisation has focused on a single product type and is static in its core approach. A first step would be to extend consumer choices allowing for multiple good choices in the context of multi-category approaches, as well as incorporating firm level, multi-product, strategic behaviour. Allowing for dynamics in demand as well as on the supply side is also another avenue to extend the state of the art in agri-food applied work. In so doing, topics that are inherently dynamic in nature could be addressed by empirical work pertaining to innovation, storage, new product introductions and predatory pricing and other dynamic anticompetitive strategies. Finally, integrating recent work in the field of behavioural economics, which suggests consumers often do not make ‘rational’ choices in the lens of the standard neoclassical framework, into structural models is a promising area for future research as well. Acknowledgements We thank the editor Salvatore Di Falco and an anonymous reviewer for their invaluable suggestions as well as Peter Berck for helpful comments. Footnotes 1 Another approach exists where supply and demand are modelled simultaneously. These simultaneous approaches require restrictive statistical assumptions about the relationships between the error terms of the non-necessary supply and demand equations in the two-step approach we present here. 2 See Deaton and Muellbauer (1980a), which goes through all the micro-foundations. 3 Note that the Q-AIDS model (see Banks, Blundell and Lewbel, 1997 for the details) is more general, as it allows for quadratic income effects. 4 Working on elegant ways around this problem is an open area for research. One approach, presented in Dubé (2004), is multiple-discrete choice, where, recognising that the time of purchase of a good is often not the actual time of consumption, consumers are modelled as purchasing bundles of goods in anticipation of a stream of distinct consumption occasions before their next trip to the supermarket. Another potential approach to deal with multiple purchases is with multiple-discrete continuous choice models, which allows consumers to choose continuous quantities of multiple goods. Kim, Allenby and Rossi (2002) and Richards, Gómez and Pofahl (2012) both do this using the multiple-discrete continuous extreme value model of Bhat (2005), while Song and Chintagunta (2006) apply a ‘shopping basket’ model where consumers choose a utility-maximising bundle of goods. 5 In these assumptions, we are implicitly supposing that the characteristics of given products are fixed and do not vary over different consumers. This seems sensible, but could actually be an issue if, for example, choice sets of consumers are different (due, for instance, to differences in transportation means that would determine the set of stores they could visit) in ways the researcher cannot observe. 6 See McFadden (1974) for details on the construction. 7 Train (2016) develops a semi-parametric form of the distribution of preferences. 8 Normal distribution is common assumption. Log-normal distribution can be used to impose positivity of parameters. 9 The product market share is approximated by the Logit smoothed accept-reject simulator. Solving for the mean utility (as in Berry, 1994) has to be done numerically (see Berry, Levinsohn and Pakes, 1995; Nevo, 2000a). 10 One can also assume that the manufacturers depart from Bertrand–Nash; namely, that they maximise joint profits over the set of products they all produce (Villas-Boas, 2007a). 11 Note that in this market manufacturers may, if they choose to, set different wholesale prices for the same brand sold to different retailers. In another study, Villas-Boas (2007b) considers the welfare effects from imposing uniform wholesale pricing restrictions in the coffee market. 12 We use the notation (a|b) for horizontal concatenation of a and b ⁠. 13 If the profit maximising retail markup, γ(θ) is non-varying with quantity, then the linear pricing model is indistinguishable from a model where retailers charge a constant retail markup γconstant ⁠, if γconstant=γ(θ) ⁠. For special cases of demand models, where ∂γ(θ)∂q=0 this may be true. For general demand models, this is not the case. 14 In this case, the wholesale prices are determined independently of possible changes to retail prices. For a discussion on the wholesale price negotiation and retailer competition games and the justification of the related assumptions, see Draganska, Klapper and Villas-Boas (2010) and the literature mentioned therein. Bonnet, Bouamra-Mechemache and Richards (2018) relax this assumption. 15 The * means an element by element multiplication between the vectors 1−λλ and [(IfSIf)−11−λλ(IrSIr)γ] ⁠. 16 See Kiesel et al. (2011) for a review of various demand approaches to estimating demand in the presence of nutritional labels. References Allais , O. , Bertail , P. and Nichèle , V. ( 2010 ). The effects of a fat tax on French households’ purchases: a nutritional approach . American Journal of Agricultural Economics 92 ( 1 ): 228 – 245 . Google Scholar Crossref Search ADS Allais , O. , Etilé , F. and Lecocq , S. ( 2015 ). Mandatory labels, taxes and market forces: an empirical evaluation of fat policies . Journal of Health Economics 43 : 27 – 44 . Google Scholar Crossref Search ADS PubMed Atkeson , A. and Burstein , A. ( 2008 ). Pricing-to-market, trade costs, and international relative prices . American Economic Review 98 ( 5 ): 1998 – 2031 . Google Scholar Crossref Search ADS Auer , R. A. and Schoenle , R. S. ( 2016 ). Market structure and exchange rate pass-through . Journal of International Economics 98 : 60 – 77 . Google Scholar Crossref Search ADS Baker , J. B. and Bresnahan , T. F. ( 1985 ). The gains from merger or collusion in product-differentiated industries . The Journal of Industrial Economics 1985 : 427 – 444 . Google Scholar Crossref Search ADS Banks , J. , Blundell , R. and Lewbel , A. ( 1997 ). Quadratic Engel curves and consumer demand . The Review of Economics and Statistics 79 ( 4 ): 527 – 539 . Google Scholar Crossref Search ADS Berman , N. , Martin , P. and Mayer , T. ( 2011 ). How do different exporters react to exchange rate changes? Theory and empirics . Quarterly Journal of Economics 127 ( 1 ): 4437 – 4493 . Berry , S. ( 1994 ). Estimating discrete-choice models of product differentiation . RAND Journal of Economics 25 ( 2 ): 242 – 262 . Google Scholar Crossref Search ADS Berry , S. , Levinsohn , J. and Pakes , A. ( 1995 ). Automobile prices in market equilibrium . Econometrica: Journal of the Econometric Society 63 : 841 – 890 . Google Scholar Crossref Search ADS Berry , S. and Pakes , A. ( 1993 ). Some applications and limitations of recent advances in empirical industrial organization: Merger analysis . The American Economic Review 83 ( 2 ): 247 – 252 . Bettendorf , L. and Verboven , F. ( 2000 ). Incomplete transmission of coffee bean prices: evidence from the Netherlands . European Review of Agricultural Economics 27 ( 1 ): 1 – 16 . Google Scholar Crossref Search ADS Bhat , C. R. ( 2005 ). A multiple discrete-continuous extreme value model: formulation and application to discretionary time-use decisions . Transportation Research Part B: Methodological 39 ( 8 ): 679 – 707 . Google Scholar Crossref Search ADS Bonnet , C. and Bouamra-Mechemache , Z. ( 2016 ). Organic label, bargaining power, and profit sharing in the French fluid milk market . American Journal of Agricultural Economics 98 ( 1 ): 113 – 133 . Google Scholar Crossref Search ADS Bonnet , C. , Bouamra-Mechemache , Z. and Corre , T. ( 2018 a). An environmental tax towards more sustainable food: empirical evidence of the consumption of animal products in France . Ecological Economics 147 : 48 – 61 . Google Scholar Crossref Search ADS Bonnet , C. , Bouamra-Mechemache , Z. and Richards , T. J. ( 2018 b). Complementarity and bargaining power . European Review of Agricultural Economics 45 ( 3 ): 297 – 331 . Google Scholar Crossref Search ADS Bonnet , C. and Dubois , P. ( 2010 ). Inference on vertical contracts between manufacturers and retailers allowing for non linear pricing and resale price maintenance . Rand Journal of Economics 41 ( 1 ): 139 – 164 . Google Scholar Crossref Search ADS Bonnet , C. , Dubois , P. , Villas-Boas , S. B. and Klapper , D. ( 2013 ). Empirical evidence on the role of non linear wholesale pricing and vertical restraints on cost pass-through . Review of Economics and Statistics 95 ( 2 ): 500 – 515 . Google Scholar Crossref Search ADS Bonnet , C. and Réquillart , V. ( 2011 ). Does the EU sugar policy reform increase added sugar consumption? An empirical evidence on the soft drink market . Health Economics 20 ( 9 ): 1012 – 1024 . Google Scholar Crossref Search ADS PubMed Bonnet , C. and Réquillart , V. ( 2013 a). Impact of cost shocks on consumer prices in vertically related markets: the case of the French soft drink market . American Journal of Agricultural Economics 95 : 1088 – 1108 . Google Scholar Crossref Search ADS Bonnet , C. and Réquillart , V. ( 2013 b). Tax incidence with strategic firms on the soft drink market . Journal of Public Economics 106 : 77 – 88 . Google Scholar Crossref Search ADS Bonnet , C. and Réquillart , V. ( 2015 ). Price transmission in food chains: the case of the dairy industry. In: S. McCorriston (ed.) , Food Price Dynamics and Price Adjustment in the EU . Oxford University Press , 65 – 101 . Bonnet , C. and Villas-Boas , S. B. ( 2016 ). An analysis of asymmetric consumer price responses and asymmetric cost pass-through in the French coffee market . European Review of Agricultural Economics 43 ( 5 ): 781 – 804 . Google Scholar Crossref Search ADS Brooks , K. and Lusk , J. L. ( 2010 ). Stated and revealed preferences for organic and cloned milk: combining choice experiment and scanner data . American Journal of Agricultural Economics 92 ( 4 ): 1229 – 1241 . Google Scholar Crossref Search ADS Caillavet , F. , Fadhuile , A. and Nichèle , V. ( 2016 ). Taxing animal-based foods for sustainability: environmental, nutritional and social perspectives in France . European Review of Agricultural Economics 43 ( 4 ): 537 – 560 . Google Scholar Crossref Search ADS Christensen , L. R. , Jorgenson , D. W. and Lau , L. J. ( 1975 ). Transcendental logarithmic utility functions . The American Economic Review 65 ( 3 ): 367 – 383 . Deaton , A. and Muellbauer , J. ( 1980 a). An almost ideal demand system . The American Economic Review 70 ( 3 ): 312 – 326 . Deaton , A. and Muellbauer , J. ( 1980 b). Economics and Consumer Behavior . Cambridge University Press . Dhar , T. and Foltz , J. D. ( 2005 ). Milk by any other name consumer benefits from labeled milk . American Journal of Agricultural Economics 87 ( 1 ): 214 – 228 . Google Scholar Crossref Search ADS Draganska , M. , Klapper , D. and Villas-Boas , S. B. ( 2010 ). A larger slice or a larger pie? An empirical investigation of bargaining power in the distribution channel . Marketing Science 29 ( 1 ): 57 – 74 . Google Scholar Crossref Search ADS Dubé , J. P. ( 2004 ). Multiple discreteness and product differentiation: demand for carbonated soft drinks . Marketing Science 23 ( 1 ): 66 – 81 . Google Scholar Crossref Search ADS Edjabou , L. D. and Smed , S. ( 2013 ). The effect of using consumption taxes on foods to promote climate friendly diets – the case of Denmark . Food Policy 39 : 84 – 96 . Google Scholar Crossref Search ADS Goldberg , P. K. and Hellerstein , R. ( 2008 ). A structural approach to explaining incomplete exchange-rate pass-through and pricing-to-market . American Economic Review 98 ( 2 ): 423 – 429 . Google Scholar Crossref Search ADS Goldberg , P. and Hellerstein , R. ( 2013 ). A structural approach to identifying the sources of local currency price stability . Review of Economic Studies 80 ( 1 ): 175 – 210 . Google Scholar Crossref Search ADS Griffith , R. , Nesheim , L. and O’Connell , M. ( 2018 ). Income effects and the welfare consequences of tax in differentiated product oligopoly . Quantitative Economics 9 : 305 – 341 . Google Scholar Crossref Search ADS Hausman , J. A. ( 1997 ). Valuation of new goods under perfect and imperfect competition. In: T. F. Bresnahan and R. J. Gordon (eds) , The Economics of New Goods . Chicago/London : The University of Chicago Press . Hausman , J. , Leonard , G. and Zona , J. D. ( 1994 ). Competitive analysis with differentiated products . Annales d’Economie et de Statistique 1994 : 159 – 180 . Google Scholar Crossref Search ADS Hellerstein , R. and Villas-Boas , S. B. ( 2010 ). Outsourcing and pass-through . Journal of International Economics 81 : 170 – 183 . Google Scholar Crossref Search ADS Kiesel , K. , McCluskey , J. and Villas-Boas , S. B . ( 2011 ). “Nutritional Labeling and Consumer Choices: A Review” . Annual Review of Resource Economics , Vol.3. Kiesel , K. and Villas-Boas , S. B. ( 2007 ). Got organic milk? Consumer valuations of milk labels after the implementation of the USDA organic seal . Journal of Agricultural and Food Industrial Organization 5 ( 1 ): 4 , Article. Google Scholar Crossref Search ADS Kim , J. , Allenby , G. M. and Rossi , P. E. ( 2002 ). Modeling consumer demand for variety . Marketing Science 21 ( 3 ): 229 – 250 . Google Scholar Crossref Search ADS Kim , D. and Cotterill , R. W. ( 2008 ). Cost pass-through in differentiated product markets: the case of US processed cheese . The Journal of Industrial Economics 56 ( 1 ): 32 – 48 . Google Scholar Crossref Search ADS Kuksov , D. and Villas-Boas , J. M. ( 2008 ). Endogeneity and individual consumer choice . Journal of Marketing Research 45 ( 6 ): 702 – 714 . Google Scholar Crossref Search ADS Lewbel , A. and Pendakur , K. ( 2009 ). Tricks with hicks: the EASI demand system . American Economic Review 99 ( 3 ): 827 – 863 . Google Scholar Crossref Search ADS McFadden , D. ( 1974 ). Conditional Logit analysis of qualitative choice behavior. In: P. Zarembka (ed.) , Frontiers in Econometrics , 105 , New York : Academic Press , 105 – 142 . McFadden , D. ( 1978 ). Modeling the choice of residential location . Transportation Research Record 673 : 72 – 77 . McFadden , D. and Train , K. E. ( 2000 ). Mixed MNL models for discrete response . Journal of Applied Econometrics 15 : 447 – 470 . Google Scholar Crossref Search ADS Meza , S. and Sudhir , K. ( 2010 ). Do private labels increase retailer bargaining power? Quantitative Marketing and Economics 8 ( 3 ): 333 – 363 . Google Scholar Crossref Search ADS Misra , S. and Mohanty , S. ( 2006 ). Estimating bargaining games in distribution channels. Working Paper. University of Rochester. Nakamura , E. ( 2008 ). Pass- through in retail and wholesale. American Economic Review 98 : 430 – 437 . Google Scholar Crossref Search ADS Nakamura , E. and Zerom , D. ( 2010 ). Accounting for incomplete pass-through . Review of Economic Studies 77 ( 3 ): 1192 – 1230 . Google Scholar Crossref Search ADS Nevo , A. ( 2000 a). A practitioner’s guide to estimation of random-coefficients Logit models of demand . Journal of Economics & Management Strategy 9 ( 2000 ): 513 – 548 . Google Scholar Crossref Search ADS Nevo , A. ( 2000 b). Mergers with differentiated products: the case of the ready-to-eat cereal industry . RAND Journal of Economics 31 ( 1 ): 395 – 421 . Google Scholar Crossref Search ADS Petrin , A. and Train , K. ( 2010 ). A control function approach to endogeneity in consumer choice models . Journal of Marketing Research 47 ( 1 ): 3 – 13 . Google Scholar Crossref Search ADS Revelt , D. and Train , K. ( 2000 ). Customer-specific taste parameters and mixed Logit: households’ choice of electricity supplier. Working Paper No. E00-274, Department of Economics . Berkeley : University of California . Richards , T. J. , Acharya , R. N. and Molina , I. ( 2011 ). Retail and wholesale market power in organic apples . Agribusiness 27 ( 1 ): 62 – 81 . Google Scholar Crossref Search ADS Richards , T. J. , Gómez , M. I. and Pofahl , G. ( 2012 ). A multiple-discrete/continuous model of price promotion . Journal of Retailing 88 ( 2 ): 206 – 225 . Google Scholar Crossref Search ADS Rivers , D. and Vuong , Q. ( 2002 ). Model selection tests for nonlinear dynamic models . The Econometrics Journal 5 ( 1 ): 1 – 39 . Google Scholar Crossref Search ADS Rosse , J. N. ( 1970 ). Estimating cost function parameters without using cost data: illustrated methodology . Econometrica: Journal of the Econometric Society 1970 : 256 – 275 . Google Scholar Crossref Search ADS Slade , M. E. ( 2004 ). Market power and joint dominance in UK brewing . The Journal of Industrial Economics 52 ( 1 ): 133 – 163 . Google Scholar Crossref Search ADS Smith , R. J. ( 1992 ). Non-nested tests for competing models estimated by generalized method of moments . Econometrica: Journal of the Econometric Society 1992 : 973 – 980 . Google Scholar Crossref Search ADS Song , I. and Chintagunta , P. K. ( 2006 ). Measuring cross-category price effects with aggregate store data . Management Science 52 ( 10 ): 1594 – 1609 . Google Scholar Crossref Search ADS Stone , R. ( 1954 ). Linear expenditure systems and demand analysis: an application to the pattern of British demand . The Economic Journal 64 ( 255 ): 511 – 527 . Google Scholar Crossref Search ADS Train K. ( 2016 ), Mixed logit with a flexible mixing distribution , Journal of Choice Modelling , 40 – 53 . Train , K. E. ( 2003 ). Discrete Choice Methods with Simulation . Cambridge University Press . Villas-Boas , S. B. ( 2007 a). Vertical relationships between manufacturers and retailers: inference with limited data . The Review of Economic Studies 74 ( 2 ): 625 – 652 . Google Scholar Crossref Search ADS Villas-Boas , S. B. ( 2007 b). Using retail scanner data for upstream merger analysis . Journal of Competition Law and Economics 3 ( 4 ): 689 – 715 . Google Scholar Crossref Search ADS Villas-Boas , J. M. and Zhao , Y. ( 2005 ). Retailer, manufacturers, and individual consumers: modeling the supply side in the ketchup marketplace . Journal of Marketing Research 42 : 83 – 95 . Google Scholar Crossref Search ADS Vuong , Q. H. ( 1989 ). Likelihood ratio tests for model selection and non-nested hypotheses . Econometrica: Journal of the Econometric Society 1989 : 307 – 333 . Google Scholar Crossref Search ADS Werden , G. J. and Froeb , L. M. ( 1994 ). The effects of mergers in differentiated products industries: Logit demand and merger policy . The Journal of Law, Economics, & Organization 10 ( 2 ): 407 – 426 . Author notes Review coordinated by Salvatore Di Falco © Oxford University Press and Foundation for the European Review of Agricultural Economics 2018; all rights reserved. For permissions, please e-mail: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - Food markets’ structural empirical analysis: a review of methods and topics
JO - European Review of Agricultural Economics
DO - 10.1093/erae/jby045
DA - 2018-12-21
UR - https://www.deepdyve.com/lp/oxford-university-press/food-markets-structural-empirical-analysis-a-review-of-methods-and-vtsRtDenOj
SP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -