The Effects of Farm Commodity and Retail Food Policies on Obesity and Economic Welfare in the United States

THE EFFECTS OF FARM COMMODITY AND RETAIL FOOD POLICIES ON OBESITY AND ECONOMIC WELFARE IN THE UNITED STATES

ABIGAIL M. OKRENT AND JULIAN M. ALSTON

Many commentators claim that farm subsidies have contributed significantly to the “obesity epidemic” by making fattening foods relatively cheap and abundant and, symmetrically, that taxing “unhealthy” commodities or subsidizing “healthy” commodities would contribute to reducing obesity rates. In this article we use an equilibrium displacement model to estimate and compare the economic welfare effects Downloaded from from a range of hypothetical farm commodity and retail food policies as alternative mechanisms for encouraging consumption of healthy food or discouraging consumption of unhealthy food, or both. We find that, compared with retail taxes on fat, sugar, or all food, or subsidies on fruits and vegetables at the farm or retail levels, a tax on calories would be the most efficient obesity policy. A tax on calories would have the lowest deadweight loss per pound of fat reduction in average adult weight, and would yield a net social gain once the impact on public health care expenditures is considered. http://ajae.oxfordjournals.org/ Key words: Fat Taxes, Food Policy, Market Model, Obesity,Welfare. JEL Codes: Q18, I18, H2.

Obesity is an escalating, worldwide problem to address childhood obesity, so children will that has received much attention recently, par- reach adulthood at a healthy weight (White ticularly in the United States. In less than HouseTaskForce on Childhood Obesity 2010).

thirty years,the prevalence of obeseAmericans Obesity has become a public health issue at University of California, Davis on May 16, 2012 has more than doubled (Flegal et al. 2002); because the consequences of obesity in terms in 1960–62, 13.4% of U.S. adults were obese, of higher risk of morbidity and mortality for an and by 2003–04, 32.2% were obese. This individual translate into increased medical care upward trend in the adult obesity rate has costs, not only for the individual but also for received a lot of press, with public health advo- society,and these costs are both large and grow- cates demanding immediate action to reduce ing. Finkelstein et al. (2009) estimated that obesity rates. Indeed, First Lady Michelle 37% of the rise in inflation-adjusted per capita Obama launched the ‘Let’s Move’ campaign health care expenditures between 1998 and 2006 was attributable to increases in the proportion of Americans who were obese. Indeed, the increased prevalence of obesity was found to be responsible for almost $40 billion of Abigail Okrent is an economist at the United States Department of Agriculture, Economic Research Service. Julian Alston is a pro- increased medical spending between 1998 and fessor in the Department of Agricultural and Resource Economics 2006. Across all insured individuals, in 2006 and Director of the Robert Mondavi Institute Center forWine Eco- per capita medical spending for the obese was nomics at the University of California, Davis, as well as a member of the Giannini Foundation of Agricultural Economics. The views $1,429 (roughly 42%) higher than for some- expressed here are those of the authors and not necessarily those one of normal weight, and more than half of of the United States Department of Agriculture. the expenditures attributable to obesity were This project was supported by the National Research Initiative of the Cooperative State Research, Education and Extension Service, financed by Medicare and Medicaid. USDA,Grant # 2006-55215-16720. We also gratefully acknowledge The recent upward trend in the adult financial and indirect support from the University of California Agricultural Issues Center and the Giannini Foundation of Agri- obesity rate is attributable to an energy cultural Economics. Joanna Parks provided substantial assistance imbalance, whereby calories consumed are with some calculations, and two anonymous reviewers and partici- greater than calories expended, given a pants at several workshops and conferences provided helpful com- ments and suggestions. We gratefully acknowledge these helpful genetic predisposition. Arguably, the genetic contributions to this work. composition of the United States has not

Amer. J. Agr. Econ. 94(3): 611–646; doi: 10.1093/ajae/aar138 Received 1 November 2011; published online February 22, 2012

Published by Oxford University Press on behalf of the Agricultural and Applied Economics Association 2012. All rights reserved. For permissions, please e-mail: [email protected] 612 April 2012 Amer. J. Agr. Econ. changed significantly in the past 20 years; thus, more abundant and therefore cheaper. How- increases in the rate of obesity imply that many ever, several economic studies have found individuals have increased their consumption these effects to be small or nonexistent (Alston, of calories or decreased their physical activ- Sumner, and Vosti 2006, Alston, Sumner, and ity, or both. Over the past two decades, median Vosti 2008, Beghin and Jensen 2008, Miller and body weight increased 10–12 lbs for adult men Coble 2007, Schmidhuber 2004, Senauer and and women. This rate of gain required a net Gemma 2006). calorie imbalance of 100 to 150 calories per day To date, most evaluations of food taxes and (Cutler, Glaeser, and Shapiro 2003). Because subsidies as obesity policies have primarily the daily energy imbalance is relatively small, focused on consumer responses, largely ignor- many economic factors such as price and ing the potential role that producers play income changes, coupled with changes in indi- in food production and consumption. In this vidual preferences, could have contributed to paper we model and quantify the potential the observed gain in body weight. impacts on food consumption, body weight, Downloaded from Policy makers have discussed a variety of and social welfare that would result from policies to address obesity in the United States. subsidies and taxes on food products, or on Regulatory and fiscal instruments have been farm commodities used to produce food. To suggested as ways to change the eating habits do so, we develop a framework that is a of individuals: for instance, taxing foods with generalization of models of commodity-retail high fat or high sugar content, or subsidizing product price transmission discussed in the http://ajae.oxfordjournals.org/ healthier foods such as fresh fruits and veg- marketing margins literature. Based on this etables. However, economists disagree about general framework, we also establish formu- the extent to which changes in food prices las for approximating policy-induced changes have contributed to the increased rate of obe- in social welfare that do not rely on a particu- sity in the United States. Some studies sug- lar choice of functional form for the consumer gest that taxation or subsidization of certain expenditure function or for the producer profit foods would be effective as a means of reduc- function. We apply these methods to simulate

ing average body weight in the United States various policies and their impacts on prices, at University of California, Davis on May 16, 2012 (O’Donoghue and Rabin 2006; Cash, Sund- consumption, and welfare. To do this, we use ing, and Zilberman 2005). A tax on foods new estimates of demand elasticities for food that are energy dense and fattening (e.g. soda and other goods,estimated specifically with this and chips) would make fattening foods more application in mind, combined with estimates expensive relative to non-fattening foods such of commodity supply elasticities from the lit- that consumers would substitute away from the erature, along with detailed data on farm-to- consumption of fattening foods and towards retail marketing costs and the nutrient content consumption of non-fattening foods. Others of different foods. argue that such pricing policies would have little effect on food consumption, and hence obesity (Schroeter, Lusk, and Tyner 2007; Kuchler, A Model of N Inter-related Food Products Tegene and Harris 2004; Chouinard et al. 2007; and L Inter-related Commodities Gelbach,Klick,and Strattman 2007) and would be regressive, falling disproportionately heav- To determine the implications of agricultural ily on the poor (e.g., Chouinard et al. 2007). policies for obesity and its economic conse- Related to the issue of whether food prices quences, we develop an equilibrium displace- have been a major contributor to obesity in ment model that can be used to examine the the United States is the question of whether transmission of policy-induced changes in com- agricultural policies make farm commodities modity prices to changes in consumption and cheaper and more abundant, especially those prices of food products. Gardner (1975) devel- that are primary ingredients in fattening foods. oped a one-output, two-input model of a com- The idea that farm subsidies have contributed petitive industry to analyze how the retail-farm significantly to the problem of obesity in the price ratio responds to shifts in the supply United States has been reported frequently in of farm commodities or marketing inputs, or the press, and has assumed the character of in the demand for retail products. Gardner a stylized fact. It is conceptually possible that derived formulas for elasticities of price trans- farm policies have contributed to lower relative mission that nest the fixed proportions model prices and increased consumption of fattening of Tomek and Robinson (2003) as a special foods by making certain farm commodities case. Wohlgenant (1989) and Wohlgenant and Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 613

Haidacher (1989) developed a different one- competitive market clearing: output, two-input model for which they did not assume constant returns to scale at the indus- (1) Qn = Qn(P, An), ∀n = 1, ..., N, try level. For each of eight food products, these (2) Cn = cn(W)Qn, ∀n = 1, ..., N, authors estimated the respective elasticities of price transmission between the retail price and n n n n n (3) X = ∂c (W)/∂Wl Q = g (W)Q , the prices of a corresponding farm commodity l l and a composite marketing input. ∀n = 1, ..., N; ∀l = 1, ..., L, The linkages between markets for farm com- (4) Xl = fl(W, Bl), ∀l = 1, ..., L. modities and retail products are generally mod- eled assuming that one farm commodity and The superscripts on variables and functions one or more marketing factors are inputs into denote food products, while the subscripts the production of a particular food at home denote farm commodities and the composite (FAH) (i.e. food purchased at a retail outlet Downloaded from marketing input. Equation (1) represents the and prepared at home). For example, the farm demand for the nth retail food product in which commodity beef is the primary ingredient for the quantity demanded, Qn, is a function of an the retail food product beef. However, food N × 1 vector of retail prices, P, and an exoge- away from home (FAFH) (e.g. food purchased nous demand shifter, An, which subsumes the at restaurants) and combination FAH prod- effects of changes in total consumer expendi- http://ajae.oxfordjournals.org/ ucts (e.g. soups, frozen dinners) incorporate tures and other exogenous shifters on retail multiple farm commodities. Under the assump- demand. In equation (2), the technology for tion of ﬁxed proportions,the price transmission the industry producing good n is expressed as a between farm commodities and both combina- total cost function in which the total cost of pro- tion FAH products and FAFH would certainly ducing the nth retail product Cn is a function of be less than the price transmission between an L × 1 vector of prices of farm commodities farm commodities and non-combination FAH and the marketing input,W,and the quantity of products, because the farm commodity cost the product, Qn. Under the assumption of con-

represents a smaller share of the retail value of at University of California, Davis on May 16, 2012 stant returns to scale at the industry level, the FAH and combination food products. FAFH average cost per unit of product,n,is equivalent and combination foods now constitute more to its marginal cost (i.e. Cn/Qn = cn(W)), and, than half of personal consumption expendi- under the further assumption of competitive tures on food–41 and 14%, respectively in 2009 market equilibrium with no price distortions, (U.S. Department of Commerce, Bureau of marginal cost and average cost are equal to the Economic Analysis 2010), and the majority of retail price, Pn: average daily calories consumed are from these two categories of food–33% and 18%, respec- n = n ∀ = tively,in 2005–06 (Centers for Disease Control (5) P c (W), n 1, ..., N. and Prevention, National Center for Health Statistics 2010). Consequently, it is important The Hicksian demand for commodity l by to include these categories of food when ana- industry n in equation (3) is derived by apply- lyzing food policies and obesity. ing Shephard’s lemma to the total cost function Here we extend a system comprising one in (2). The L × N Hicksian demand equations output product with L inputs, as presented can be reduced to L equations because total by Wohlgenant (1982),toN output products demand for commodity l, Xl, is the sum of the with L-1 farm commodities used as inputs, Hicksian demands for commodity l across all along with one composite marketing input.1 retail industries, that is, The market equilibrium for this system can N be expressed in terms of N demand equations n n (6) Xl = g (W)Q , ∀l = 1, ..., L. for food products, N total cost equations for n=1 l food product supply, L supply equations for input commodities, and L × N equations for Equation (4) is the supply function for commodity l, which is a function of all of the commodity prices and an exogenous supply shifter, Bl. Totally differentiating equations (1), (4), (5), 1 For the rest of this analysis, “commodities” will include farm and (6), and expressing these equations in rel- commodities and the composite marketing input. ative change terms (i.e. using dXi/Xi = EXi) 614 April 2012 Amer. J. Agr. Econ. yields: Several simpliﬁcations can be made to the n system. First, we know that ∂c (·)/∂Wl = N n nk k n n n (7) EQ = η EP + α , Xl /Q , so equation (8) can be rewritten as: k=1 ∀n = 1, ..., N, L (17) EPn = SRn EW , ∀n = 1, .., N, = l l L ∂cn(W) W l 1 (8) EPn = l EW , = n l l 1 ∂Wl P where the share of total cost for retail product ∀n = 1, ..., N, n attributable to commodity l (farm-product share) is: N L ∗ n n (9) EXl = SC η EWm n=1 l m=1 lm n = n n n (18) SRl Xl Wl/P Q . + EQn , ∀l = 1, ..., L,

Second, the share-weighted Hicksian elasticity Downloaded from L (10) EXl = εlj EWj + βl, of demand for commodity l with respect to the j=1 price of commodity m is: ∀ = l 1, ..., L, N ∗ (19) η∗ = SCnηn . where lm n=1 l lm http://ajae.oxfordjournals.org/ ∂ Qn(P, An) Pk Finally, equation (9) can be rewritten (11) ηnk = ∂Pk Qn using (19): = L η∗ is the Marshallian elasticity of demand for (20) EXl lm EWm retail product n with respect to retail price k, m=1 N + n n ∀ = X nW SCl EQ , l 1, ..., L. n = l l n=1 (12) SCl

XlWl at University of California, Davis on May 16, 2012 This system can be modiﬁed to accommodate is the share of the total cost of commodity l policy shocks such as the introduction of taxes across all industries used by retail product n and subsidies on food products or taxes and (farm-commodity share), subsidies on farm commodities. The subsidy and taxation policies cause wedges between n n ∗ ∂ g (W)Q ηn = l Wm consumer (or buyer) and producer (or seller) (13) lm n n ∂Wm X prices of retail products or commodities. Let t l be the tax rate on food product n, and PD,n and S,n is the Hicksian elasticity of demand for com- P be the consumer and producer prices of modity l in industry n with respect to commod- retail product n, respectively, such that: ity price m, (21) PD,n = (1 + tn)PS,n. ∂ fl(W, Bl) Wj (14) ε = n lj ∂W X The introduction of t implies that the total j l differential of (21) expressed in terms of pro- is the elasticity of supply of commodity l with portionate changes is: respect to commodity price j, (22) EPD,n = tn + EPS,n. ∂ Qn(P, An) An (15) αn = EAn ∂An Qn Substituting (22) into (7) yields:

N is the proportional shift of demand for retail (23) EQn = ηnk EPSk, product n in the quantity direction, and k=1 N ∂ f (W , B ) B + ηnktk + αn. l l l l k=1 (16) βl = EBl ∂Bl Xl Likewise, the proportionate change in the is the proportional shift of supply of seller price of commodity l,EWS,l, can be writ- commodity l in the quantity direction. ten as the sum of its subsidy rate, sl, and the Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 615 proportionate change in its buyer price: α + ηN tN × , β + εLsL

(24) EWS,l = sl + EWD,l. −1 = −ε + η∗ + ηN −1 where f ( L L SC SR) .The vectors of proportionate changes in consumer Substituting (24) into (10) yields: prices of retail products and seller prices of D commodities, EP and EWS, respectively, can L L be recovered using (22) and (24). (25) EXl = εlj EWD,l + εljsl + βl. j=1 j=1 Simplifying assumptions can be used to reduce the general model to a more manageable form, such as (a) exogenous To simplify the notation, we present equa- ε =∞ tions (17), (20), (23) and (25) in matrix nota- commodity prices ( ll ), (b) exogenous S commodity quantities (εll = 0), or (c) ﬁxed

× Downloaded from tion. Letting EQ, and EP be N 1 vectors of σ = proportionate changes in quantities and pro- input proportions ( lj 0). Under the assump- ducer prices of retail products,respectively,and tion of exogenous commodity prices, equation (25) becomes: EX, and EWD be L × 1 vectors of proportionate changes in quantities and buyer prices of − = β¯ + ∀ = commodities, respectively, the system is: (28) d ln Wl l sl, l 1, ..., L, http://ajae.oxfordjournals.org/ ¯ ⎡ ⎤ where βl is a proportionate shift in supply N N ⎡ ⎤ I −η 00 EQ of commodity l in the price direction. Under ⎢ N N − ⎥ ⎢ S ⎥ ⎢ 0 I 0 SR⎥ ⎣ EP ⎦ this assumption, the solution in (27) reduces (26) ⎣− T −η∗ ⎦ SC 0 IL L EX to the ﬁrst column in table 1. Wohlgenant T T 0 0 IL −εL EWD and Haidacher (1989) and Wohlgenant (1989) ⎡ ⎤ assumed that farm commodity supply is prede- N N α + η t termined with respect to the farm commodity ⎢ ⎥ = ⎣ 0 ⎦ price in the current period, which implies that

, at University of California, Davis on May 16, 2012 0 εlj = 0, ∀j, l = 1, ..., L, such that (25) becomes: β + εLsL (29) EXl = βl, ∀l = 1, ..., L. where IN and I are N × N and L × L L This implies that the general model reduces to identity matrices, 0N and 0 are N × N and × ηN × the second column in table 1. Lastly, under an N L matrices of all zeros, is an N N assumption of ﬁxed proportions, the Hicksian matrix of Marshallian elasticities of demand for retail products (equation(11)), η∗ is elasticity of demand between two factor L inputs l and j in output n is zero (i.e. ηn∗ = 0, an L × L matrix of Hicksian elasticities of lj demand for commodities (equation (19)), SR ∀l, j = 1, ..., L, ∀n = 1, ..., N).2 Hence, the is an N × L matrix of farm-product shares solution with ﬁxed input proportions is that (equation (18)), SC is an L × N matrix of from the general model with η∗ = 0 , or the ε L L farm-commodity shares (equation(12)), L is last column in table 1. an L × L matrix of elasticities of supply of commodities (equation(14)),and α + ηN tN and β + ε × × LsL are N 1 and L 1 vectors of exogenous Measures of Changes in Social Welfare factors affecting the demand for retail products and the supply of commodities, respectively. Using matrix block inversion, the solutions for Based on the general price transmission model, S we formulate equations for estimating the EQ, EP , EX and EWD are:

⎡ ⎤ EQ 2 To show the implications of this assumption for the gen- ⎢ S ⎥ ⎢ EP ⎥ eral model, note that the elasticity of substitution can be writ- (27) ⎣ ⎦ 2 n n n n n n EX ten as: σn = ∂ C (W,Q ) Cn(W, Qn)/ ∂C (W,Q ) ∂C (W,Q ) ij ∂Pi∂Pj ∂Pi ∂Pj EWD (Sato and Koizumi 1975). Conveniently, this deﬁnition of the elas- ⎡ − − ⎤ ticity of substitution relates directly to the Hicksian elasticity of IN − ηN SRf 1SC ηN SRf 1 ∗ demand for the inputs, ηn = σnSRn, ∀l, j = 1, ..., L, ∀n = 1, ..., N. ⎢ − −1 −1 ⎥ lj lj l = ⎢ SRf SC SRf ⎥ Substituting this into (18), the farm-product-share-weighted Hick- ⎣ − η∗ + ηN −1 η∗ + ηN −1⎦ IL ( L SC SR)f SC L SC SR f sian elasticity of demand for commodity l with respect to price of − − ∗ − 1 1 η∗ = N nσn n f SC f commodity m becomes lm n=1 SCl lm SRl . 616 April 2012 Amer. J. Agr. Econ.

Table 1. Price and Quantity Effects of Taxes and Subsidies on Retail Products and Farm Commodities for Nested Cases of the General Model Perfectly Elastic Perfectly Inelastic Fixed Factor Commodity Supply Commodity Supply Proportions εll =∞ εll = 0 σlj = 0

α N − ηN ˜−1 ˜ α N − ηN ˆ−1 ˆ α ¯ − ηN ¯ (I SRf SC)X (I SRf SC)X EQ X SRXβ ˜− ˜ ˆ− ˆ +ηN SRf 1Xβ +ηN SRf 1Xβ ˜− ˜ α ˜− ˜ ˆ− ˆ α ˆ− ˆ EPS −SRXβ SRf 1SCX + SRf 1Xβ SRf 1SCX + SRf 1Xβ

¯ α N ˆ−1 ˆ α SCX ˜ (IL − SCη SRf )SCX EX Xβ − ηN + η∗ ¯ + ηN ˆ−1 ˆ (SC SR L)Xβ SC SRf Xβ − α − − α − ¯ ˜ 1 ˜ ˜ 1 ˜ ˆ 1 ˆ ˆ 1 ˆ Downloaded from EWD −Xβ f SCX + f X f SCX + f Xβ

¯ α N N ¯ ¯ Notes: X = α + η t , Xβ = β + sL ˜ α = α + ηN N ˜ = β ˜−1 = η∗ + ηN −1 X t , Xβ , f ( L SC SR) ˆ α N N ˆ ˆ−1 N −1 X = α + η t , Xβ = β + εLsL, f = (−εL + SCη SR) change in social welfare from a subsidy or tax measure of the change in social welfare for http://ajae.oxfordjournals.org/ policy. Changes in social welfare are measured a representative consumer, retail product pro- as the sum of benefits (costs) that accrue to ducer, and commodity producer is: consumers, producers, and taxpayers from a policy shock. Measures of compensating vari- (31) SW =[π(P(1), W(1)) − π(P(0), W(0))] ation (CV) and changes in profit and taxpayer +[π (1) − π (0) ] revenue (expenditure) are used to represent (W ) (W ) these benefits (costs). This measure of social +[g(P(1), W(1)) − g(P(0), W(0))] welfare is then adjusted to account for exter- at University of California, Davis on May 16, 2012 nalities that are borne by taxpayers who bear −[e(P(1), u(0)) − e(P(0), u(0))], some of the costs for the health care services of obese individuals who use government-funded where the last term in square brackets is the insurance. amount of income that must be taken away Following Martin and Alston (1992, 1993) from consumers after prices change from P(0) and Just, Hueth and Schmitz (2004), we define to P(1) to restore the consumer’s original util- social welfare (SW) as: ity at u(0) (i.e. compensating variation, CV).4 Martin and Alston (1992) demonstrated how N L a second-order Taylor series expansion of (30) = [π n ]+ [π ] ( ) ( ) (30) SW (P , W) (Wl) around (P 0 , W 0 ), holding utility constant at n=1 l=1 u(0), can be used to approximate (31) without I specifying functional forms for the consumer expenditure and profit functions: + g(P, W) − e(P, ui), i=1 (32) SW(P, W, u(0)) where e(P, u ) is the minimum expenditure i ≈ SW(P(0), W(0), u(0)) necessary to obtain a given level of utility, ui for individual consumer i at product prices, P; + T∇ SW(P(0), W(0), u(0)) π(Pn,W) is profit for retail product producer n, where W is an L × 1 vector of commodity + 0.5T∇2 SW(P(0), W(0), u(0)), prices; π(Wl) is profit for commodity producer l;and g(P,W) is change in government revenue generated by the introduction of the policy being analyzed.3 A compensating variation be greater than one dollar, as is implied by the fact that general taxation measures involve deadweight losses (Alston and Hurd 1990). Doing so would shift the balance of the equation in favor of the tax policies. 4 Since retail producers are assumed to make zero profit (i.e. 3 This treatment assumes that one dollar of government revenue equation 2), is worth one dollar. It would be a straightforward extension to allow [π (1) (1) − π (0) (0) ]= for the marginal social opportunity cost of government revenue to (P , W ) (P , W ) 0. Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 617 where ∇ and ∇2 denote the gradient government revenue from introducing a set of and Hessian of the social welfare retail taxes, and line (e) comprises the change function, respectively, the T superscript in government revenue from introducing a set denotes the transpose of a matrix, and of commodity subsidies. T D S =[P P WD WS],isa We augment the measures of change in social 2(N + 1) vector of changes in producer and welfare to reflect changes in public health consumer prices of products and commodities, care expenditures related to changes in obe- respectively. sity status. To quantify the change in govern- Evaluating (32)at(PD(1), PS(1), W(1), W(1)) ment health care expenditures associated with D S policy-induced changes in food consumption ( (0) (0) (0)) and then subtracting SW P , W , u from and obesity status, we use a multiplier esti- both sides yields an approximation to the mated by Parks, Alston, and Okrent (2011) change in social welfare implied by a change based on evidence regarding the relationship in prices from (P(0), W(0))to(P(1), W(1))as between health expenditures and body mass Downloaded from would be implied by a policy simulation using index (BMI), and knowledge of the distri- the price transmission model: bution of the U.S. population by BMI.5 This multiplier (e) measures the change in public = (1) (1) (0) (33) SW SW(P , W , u ) health care expenditures for a one pound per (0) (0) (0) person change in average adult body weight. − SW(P , W , u ) http://ajae.oxfordjournals.org/ Thus, the total change in public health care ≈ (1)T∇SW(P(0), W(0), u(0)) expenditures (H) is given by: + (1)T ×∇2 0.5 N ¯ ¯ n ∂B n (0) (0) (0) (1) (35) H = eB = e Q EQ , SW(P , W , u ) , ∂Qn n=1 where (1)T =[PD(1) − P(0) PS(1) − P(0) W(1) D where B¯ is average adult body weight, ∂B¯ /∂Qn (0) (1) (0)

− − ] at University of California, Davis on May 16, 2012 W WS W . is the marginal change in pounds of average The approximation in (33) reduces to: body weight for a one-kilogram increase in the consumption of food n, which reﬂects both the T (0) (34) SW ≈ (EWS) DW X caloric content of food and the translation of dietary calories into weight, and EQn is the + T ε 0.5(EWS) DWX LEWS (a) proportional change in annual consumption of −[(EPD)TDPQ(0) + 0.5(EPD)T (b) good n. The full measure of the annual change in social welfare from a policy shock that × DPQ(ηN + ηN,MwT)EPD] (c) induces changes in public health care spending, N T N T is therefore: + (t ) DPQ + (t ) DPQEQ (d) ∗ T T = − ¯ (ηBQ)T − (sL) DW X − (sL) DWX EX (e) (36) SW SW eB EQ,

(see Technical Appendix). where SW is the annual change in social wel- ηBQ × In this equation the measure of social welfare defined in (34), is an N 1 vector of fare change depends on the initial prices and elasticities of weight with respect to quantities quantities of food products and of commodities consumed of different foods,and EQ is defined used as inputs to produce them, the elasticities in (27) for the general model and in table 1 for of commodity supply and product demand, the the nested cases. exogenous rates of tax and subsidy,and the proportional changes in prices of commodities and products that would result from introducing 5 BMI is defined as body weight (B) in kilograms divided by those taxes and subsidies. The approximation height (H) in meters squared. Much has been written document- of social welfare in (34) is graphically intu- ing the weaknesses of BMI as a measure of obesity. For example, itive; note that line (a) and lines (b) and (c) in Parks, Smith, and Alston (2011) reviewed the relevant literature and evaluated BMI compared with alternatives. Nevertheless,BMI equation (34) are the change in profits across is widely used as an index of obesity, and consequently informa- all commodity markets and the compensat- tion about the relationship between obesity and health outcomes ing variation across all retail product markets, is often expressed as a relationship between BMI and health outcomes, such that it is reasonable to use BMI as we do in the present respectively. Line (d) comprises the change in context. 618 April 2012 Amer. J. Agr. Econ.

Data conditions; those estimates were used to solve the price transmission model and compute the The data necessary to parameterize the model implied changes in calorie consumption and include (a) Marshallian elasticities of demand body weight, holding all other parameters con- for food products; (b) farm-retail product stant. The solutions were used to generate shares (i.e. the cost of each individual farm empirical posterior distributions for the effects commodity as a share of the value of each retail of interest, and we report the means from food product) and farm-commodity shares the posterior distributions and standard devi- (i.e. the share of each commodity used in ations around those means. Table 2b includes the production of each retail food product); the means of the elasticities from the empiri- (c) elasticities of supply of farm commodi- cal posterior distribution, which are generally ties and the composite marketing input; (d) similar to the corresponding point estimates in elasticities of substitution between farm com- table 2a, and their standard deviations. modities and the composite marketing input For the elasticities of supply of farm com- Downloaded from ε (i.e., Hicksian elasticities of demand for commodities ( L), we examine two cases. First, modities); (e) food-to-weight multipliers; and we assume that commodity prices are exoge- (f) weight-to-health-expenditure multipliers. nous. The assumption of exogenous commod- In all of the simulations, we assumed fixed ity prices is implicitly an extreme assumption about the elasticities of supply. In this case, proportions technology in the food industry, http://ajae.oxfordjournals.org/ such that all Hicksian elasticities of demand for the elasticities of supply of the commodities η∗ = are all effectively infinite, and the solutions to commodities are zero (i.e., L 0). First, to parameterize ηN we use elastici- the general model collapse to the nested solu- ties of demand based on estimates taken from tions in table 1. The assumption of exogenous Okrent and Alston (2011) for eight FAH prod- prices may be extreme, but it has been applied ucts (i.e. cereals and bakery products, red widely in models of food policy and obesity. meat, poultry and eggs, seafood and fish, dairy, As a more complicated but also more realis- fruits and vegetables, other foods, and non- tic alternative, we also analyzed a case with alcoholic beverages), a FAFH composite, and endogenous prices of food and farm commodi- at University of California, Davis on May 16, 2012 alcoholic beverages. The Marshallian elasticities. For this case we used own-price elasticities ties of demand for these products evaluated of the supply of farm commodities based on the at the sample means of the data are listed in lower- and upper-bound estimates of Chavas ε ε table 2a.6 and Cox (1995), denoted as Lower and Upper, Predicted changes in quantities and the respectively. Because the farm commodities in implied welfare measures based on the price Chavas and Cox do not exactly correspond to transmission model are largely dependent on the farm commodities being analyzed in this the estimates of elasticities of demand for food study, we assumed that each of the disaggre- products. To gauge the sensitivity of our results gated commodities has the same own-price to errors in estimation of the elasticities of elasticities as their corresponding aggregate demand for food products, we used Monte commodity group (table 3). Lastly,we assumed Carlo integration (Piggott 2003;Chalfant,Gray that the elasticity of supply of the market- and White 1991). The elasticities of demand in ing input is large and close to being perfectly table 2a are based on a vector of parameter elastic. We discuss in detail the results using estimates (γˆ) with an associated covariance the lower-bound estimates of supply elastic- ˆ ities from Chavas and Cox (1995) compared matrix (). We randomly drew parameters with the results using perfectly elastic supply. from a multivariate normal distribution with γˆ ˆ These two sets of results bracket those from mean and covariance matrix . The elas- using the upper-bound estimates of supply elasticities of demand were re-estimated for each ticities from Chavas and Cox (1995), which draw that satisfied curvature and monotonicity are reported to further illustrate the effects of the values of the supply elasticities on the simulation results. 6 Okrent and Alston (2011) estimated these elasticities specifically with the present application in mind. They estimated the We estimated the farm-retail product shares National Bureau of Research (NBR) model (Neves 1987) with (SR), farm-commodity shares (SC) and values annual Personal Consumption Expenditures and Fisher-Ideal price indexes from 1960 to 2009 (U.S. Department of Commerce, Bureau for the total output of retail products and com- PQ of Economic Analysis 2010). They evaluated these elasticities and modities (DWX and D , respectively) using preferred them compared with those from other models they esti- the Detailed Use Table (after redefinitions) mated (that were dominated statistically by the NBR model) and compared with others from the literature. from the 2002 Benchmark Input-Output (I-O) Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 619 ) ) ) 1.07 0.32 0.26 ) 0.95 ) 0.13 ) 0.36 ) 0.02 0.26 ) 0.28 ) 0.34 0.19 ) 0.64 0.86 0.84 0.79 0.97 0.27 0.50 0.28 − 0.69 With Respect to )( )( )( )( 1.25 )( 0.33 )( 0.38 )( 0.24 0.42 0.03 )( 0.38 )( 0.34 0.46 )( 0.34 − 0.69 − 0.37 − 0.19 − 0.94 − 0.50 − 0.59 − 0.16 − 0.13 )( )( Downloaded from 0.06 )( 0.13 )( 0.37 )( 0.09 )( 0.10 0.01 )( 0.13 )( 0.08 )( 0.14 0.16 )( − 0.06 0.39 − 0.20 0.22 − 0.12 − 0.02 − 0.03 − 0.50 Alcoholic )( )( )( )( )( 0.10 0.19 )( 0.54 0.20 0.14 0.01 )( 0.19 )( 0.12 0.21 )( 0.18 )( http://ajae.oxfordjournals.org/ − 0.42 − 0.08 0.18 − 0.26 0.17 − 0.55 − 0.02 − 0.22 )( )( )( )( 0.05 )( 0.07 )( 0.22 0.04 0.10 0.00 0.07 )( 0.06 )( 0.08 )( 0.05 )( − 0.09 0.23 0.20 − 0.04 − 0.77 − 0.02 − 0.01 )( )( )( )( 0.07 )( 0.10 0.32 0.05 )( 0.10 0.01 )( 0.10 0.11 )( 0.11 )( 0.08 )( 0.26 0.20 at University of California, Davis on May 16, 2012 − 0.12 − 0.54 0.27 0.25 − 0.62 0.05 0.12 0.00 − 0.15 0.11 0.20 − 0.02 )( )( )( )( 0.05 )( 0.10 0.30 0.06 )( 0.08 )( 0.00 0.14 0.07 )( 0.11 )( 0.08 )( With Respect to Price of − 0.09 − 0.47 − 0.11 − 0.58 − 0.01 − 0.02 0.00 0.10 Fruits & Other Nonalcoholic )( )( . Standard errors are in parentheses. 0.05 )( 0.09 )( 0.28 )( 0.91 0.05 )( 0.08 )( 0.00 0.09 )( 0.07 )( 0.14 0.07 )( − − 0.07 0.06 0.05 − 0.07 − 0.01 )( )( )( )( )( )( 0.02 0.03 )( 0.14 0.02 0.03 )( 0.00 0.03 )( 0.02 0.04 0.03 )( 0.03 0.21 0.13 0.08 − 0.73 0.66 − 0.04 0.15 − 0.05 − 0.02 0.10 )( )( )( Okrent and Alston (2011) 0.13 )( 0.10 0.36 )( 0.06 )( 0.12 0.01 )( 0.11 )( 0.10 0.13 )( 0.08 )( − 0.40 0.05 0.00 0.16 − 0.22 − 0.17 − 0.03 0.00 )( 0.16 0.00 0.08 0.00 0.33 0.02 0.24 1.00 ( 0.05 )( ( 0.13 )( ( 0.29 )( ( 0.06 )( ( 0.08 )( ( 0.00 ( 0.11 )( ( 0.07 )( ( 0.11 )( ( 0.09 )( − 0.93 0.04 0.02 0.14 0.13 0.45 − 0.06 − 0.15 0.13 0.01 − 0.05 0.24 Cereals & : Elasticities evaluated at means of sample data, taken from Eggs Meat Dairy Cereals & bakery Note Elasticity of Demand for Bakery Meat Eggs Dairy Vegetables Food Beverages FAFH Beverages Nonfood Total Expenditure FAFH Other food Nonalcoholic beverages Fruits & vegetables 0.14 0.32 Nonfood Table 2a. Marshallian Elasticities of Demand for FAH and FAFH Products Alcoholic beverages 620 April 2012 Amer. J. Agr. Econ. ) ) 1.06 0.31 ) 0.25 ) 0.02 0.26 ) 0.26 ) 0.93 ) 0.13 ) 0.36 ) 0.32 0.19 ) 0.75 0.72 0.35 0.90 0.89 0.92 0.49 0.21 − 0.69 With Respect to )( )( )( )( 1.25 )( 0.32 0.36 )( 0.03 )( 0.31 )( 0.37 )( 0.22 0.42 0.44 0.31 )( − 0.67 − 0.95 − 0.50 − 0.15 − 0.36 − 0.17 − 0.51 − 0.04 )( )( )( Downloaded from 0.06 )( 0.12 0.01 )( 0.08 )( 0.12 0.35 )( 0.08 )( 0.09 )( 0.13 )( 0.14 − 0.08 0.46 − 0.19 0.28 − 0.01 − 0.04 − 0.10 − 0.57 Alcoholic )( )( 0.09 )( 0.18 )( 0.01 )( 0.11 )( 0.18 )( 0.52 0.17 )( 0.13 )( 0.20 0.16 )( http://ajae.oxfordjournals.org/ − 0.36 − 0.04 0.15 − 0.02 − 0.21 0.15 − 0.64 − 0.18 )( )( )( 0.05 )( 0.06 )( 0.00 0.06 )( 0.06 )( 0.22 0.03 )( 0.10 0.07 )( 0.05 )( − 0.10 0.21 0.18 − 0.05 − 0.78 − 0.01 − 0.01 )( )( 0.06 )( 0.09 )( 0.00 0.11 )( 0.09 )( 0.31 )( 0.05 )( 0.10 0.11 )( 0.07 )( 0.24 0.19 at University of California, Davis on May 16, 2012 − 0.09 − 0.53 0.28 0.22 − 0.65 0.05 0.16 0.01 − 0.12 0.12 0.12 − 0.02 )( )( . Standard deviations are in parentheses. 0.05 )( 0.09 )( 0.00 0.07 )( 0.13 )( 0.29 )( 0.06 )( 0.08 )( 0.10 0.08 )( With Respect to Price of − 0.48 − 0.09 − 0.63 − 0.07 − 0.01 − 0.03 0.01 0.08 Fruits & Other Nonalcoholic )( 0.05 )( 0.09 )( 0.00 0.07 )( 0.09 )( 0.94 0.27 )( 0.05 )( 0.08 )( 0.13 )( 0.07 )( − 0.05 − − 0.06 0.03 0.07 − 0.01 Okrent and Alston (2011) )( )( )( )( )( )( 0.02 0.03 )( 0.00 0.02 0.03 )( 0.14 0.02 0.03 )( 0.03 )( 0.02 0.03 0.20 0.14 0.09 − 0.74 0.66 − 0.04 0.14 − 0.05 − 0.01 0.08 − 0.00 )( )( )( )( 0.10 0.09 )( 0.01 )( 0.08 )( 0.10 0.34 0.05 )( 0.12 0.11 )( 0.07 )( − 0.51 0.05 0.01 0.14 − 0.11 − 0.25 − 0.03 )( )( 0.13 0.02 0.08 0.31 0.23 0.96 0.03 ( 0.05 )( ( 0.13 )( ( 0.00 ( 0.07 )( ( 0.10 ( 0.29 )( ( 0.06 )( ( 0.08 )( ( 0.11 )( ( 0.08 )( − 0.98 0.07 0.02 0.11 0.17 0.43 − 0.06 0.23 − 0.08 − 0.13 0.12 0.01 − 0.00 Cereals & : Simulations were based on estimates of parameters and their covariances from Eggs Meat Other food Nonalcoholic beverages Dairy Cereals & bakery Note Elasticity of Demand for Bakery Meat Eggs Dairy Vegetables Food Beverages FAFH Beverages Nonfood Total Expenditure FAFH Fruits & vegetables 0.18 0.28 Nonfood Table 2b. Simulated Marshallian Elasticities of Demand that Satisfy Curvature and Monotonicity for FAH and FAFH Products Alcoholic beverages Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 621

Table 3. Own-Price Elasticities of Supply of Lastly, we quantify changes in public health U.S. Farm Commodities and a Marketing Input care expenditures associated with policy- induced changes in food consumption using ε ε Lower Upper the multiplier from Parks, Alston, and Okrent Oilseed crops 0.60 1.31 (2011), who estimated that a one-pound Sugar cane & beets 0.60 1.31 increase in average adult body weight would Other crops 0.60 1.31 increase public health expenditures by $2.66 Food grains 0.59 2.93 for a nationally representative sample. To Vegetables & melons 0.42 1.77 obtain this estimate, Parks,Alston, and Okrent Fruits & tree nuts 0.44 1.65 (2011) estimated a two-part model (Cameron Cattle 0.81 1.61 and Trivedi 2005, p. 545) of public medical Other animals 0.81 1.61 expenditures (the sum of medical payments Milk 0.81 1.61 by Medicaid, Medicare, other Federal, other Poultry 0.81 1.61 Fish 0.40 0.40 public,Veterans Affairs,TRICARE, and other Downloaded from Marketing input 1000 1000 state and local government) as a function of BMI, the square of BMI, age, the square of Notes: Based on Chavas and Cox (1995). age, race, and sex, using data from the 2008 wave of the Medical Expenditure Panel Sur- Accounts (U.S. Department of Commerce, vey (MEPS). The authors used the results from Bureau of Economic Analysis 2007). The the two-part model to calculate the uncon- http://ajae.oxfordjournals.org/ Detailed Use Table shows the use of farm ditional marginal effects of the explanatory commodities, retail products, and services by variables on public medical expenditures and different industries (intermediate input use) to predict public medical expenditures as a and ﬁnal users (personal consumption, net function of the explanatory variables for the imports, private ﬁxed investment, inventories, U.S. adult population using both (a) the actual and government). The estimated shares and NHANES 2007-2008 data on the distribution retail product and commodity values for 2002 of the population by weight and height, and are presented in tables 4, 5, and 6.

(b) a counterfactual distribution in which each at University of California, Davis on May 16, 2012 Once the proportionate changes in quan- person had gained one pound. Thus, they esti- tities of retail products have been calculated mated the change in public health care expen- for a given policy using the model as rep- ditures for a one pound per person increase resented in (27), the changes in quantities in body weight for the entire adult population consumed can be translated into measures of as being $2.66 per pound per person, which changes in calorie consumption and changes = $ ηWQ is equivalent to e 604.8 million in total per in weight ( ). First, we used one day of 24- pound per capita increase in average adult hour dietary recall data collected in the 2003-04 body weight. We use this multiplier as a mea- National Health and Nutrition Examination sure of the impact of policy-induced changes Survey (NHANES) to estimate average daily grams of the nine foods consumed, as well as the associated average daily calories,and grams aspects. Nevertheless, such treatments are common in models of of fat and added sugar for individuals 18 years obesity and policy. In the analysis presented in this paper, we are and older (table 7). Second, we converted the simulating a change in policy of the type that would typically be changes in calorie consumption resulting from implemented on an enduring basis. The resulting changes in consumption would therefore be ongoing, and the consequent annual a policy to changes in body weight for the aver- changes in bodyweight would be cumulative. We abstract from the age individual adult. One frequently used rela- detail of these difficult dynamics in our analysis, which is explic- tionship in textbooks (e.g. Whitney, Cataldo, itly comparatively static in nature. However, we deal with these dynamics effectively through our use of multiplier that is consistent and Rolfes 1994) and academic articles that with the steady-state impacts of policy changes. A small number address the potential impacts of fiscal policies of studies have estimated the change in steady-state weight for a permanent change in caloric consumption, which is a relevant on weight (e.g. Chouinard et al. 2007; Smith, concept for our context. Hall et al. (2009) developed a formula Lin and Lee 2010) is that a pound of fat tis- (equation 14, p. 5) which implies that an increase in consumption sue contains about 3,500 calories. We used this of 220 kcal per day would be consistent with an increase in body weight of 10 kg (which translates approximately to a 10 kcal per day multiplier to convert changes in annual calorie per pound increase of steady state-body weight). Hall and Jordan 7 consumption into changes in body weight. (2008) reported tables of multipliers such that, for a 115 kg man or a 90 kg woman, a permanent decrease in consumption of 100 kcal per day would result in a steady-state weight loss of 6.4 kg, which translates to 7.1 kcal per day per pound. The figure of 3,500 kcal 7 The relationship between caloric consumption and obesity is per pound is equivalent to 9.6 kcal per day per pound, which falls clearly much more complex than this use of a simple, fixed mul- between the estimates from Hall et al. (2009) and Hall and Jordan tiplier would suggest, and has significant nonlinear and dynamic (2008). See also Hall et al. (2011). 622 April 2012 Amer. J. Agr. Econ. Alcoholic Alcoholic Downloaded from http://ajae.oxfordjournals.org/ Fruits & Other Nonalcoholic Fruits & Other Nonalcoholic ). at University of California, Davis on May 16, 2012 Attributable to Retail Product Share of Total Cost for Retail Products ). U.S. Department of Commerce, Bureau of Economic Analysis 2007 0.9309 0.5806 0.3149 0.7227 0.5144 0.8264 0.96680.0781 0.9523 0.0849 0.9599 0.0015 0.0493 0.0335 0.1191 0.0430 0.5469 0.0439 Bakery Meat Eggs Dairy Vegetables Food Beverages FAFH Beverages Bakery Meat Eggs Dairy Vegetables Food Beverages FAFH Beverages Cereals & Cereals & U.S. Department of Commerce, Bureau of Economic Analysis 2007 : Based on 2002 Benchmark I-O Tables ( : Authors’ calculations based on 2002 Benchmark I-O Tables ( Oil-bearing cropsGrainsFruits & tree nutsSugar cane & beetsOther cropsCattle productionOther 0.0000 livestock productionDairy farmingPoultry & egg productionFish 0.0000 production 0.0027 0.0000 0.0000 0.0593 0.0000 0.0000 0.0063 0.0000 0.0726 0.0000 0.0009 0.0000 0.0000 0.0000 0.0000 0.1907 0.0000 0.0000 0.0923 0.0000 0.0000 0.0000 0.0000 0.0012 0.0000 0.0000 0.0000 0.6851 0.0000 0.0000 0.0000 0.0000 0.0638 0.0022 0.0619 0.2062 0.0000Oil-bearing crops 0.0000 0.0000 0.0000Grains 0.0027 0.0000 0.0000 0.2739 0.0006Fruits 0.0184 & 0.0030 0.0000 tree 0.0131 nuts 0.0000 0.0000Sugar cane & 0.0345 beetsOther crops 0.0000 0.0000Cattle 0.0039 production 0.0294 0.0210 0.0000Other 0.0000 0.0027 0.0039 0.0000 livestock productionDairy farming 0.0000Poultry 0.0009 & 0.0000 egg production 0.0000Fish 0.0000 production 0.0000 0.0003 0.0113 0.0018 0.0000 0.0038 0.0046 0.0000 0.0006 0.3812 0.0038 0.0000 0.0000 0.0000 0.0094 0.0254 0.0000 0.0051 0.7769 0.0213 0.0000 0.0000 0.0000 0.0000 0.0186 0.0010 0.0000 0.0000 0.0164 0.0000 0.0000 0.8374 0.0000 0.0000 0.0000 0.6465 0.0096 0.0000 0.0000 0.0000 0.0024 0.0000 0.0072 0.0000 0.0041 0.0000 0.0000 0.0000 0.1517 0.0000 0.0000 0.0000 0.0000 0.0000 0.6777 0.0000 0.0073 0.8525 0.6812 0.0000 0.0000 0.0000 0.0000 0.0134 0.0000 0.0000 0.7682 0.0018 0.1347 0.0313 0.0000 0.8525 0.0000 0.0000 0.3811 0.0000 0.0000 0.0270 0.0665 0.7665 0.0000 0.1475 0.0187 0.0000 0.0000 0.0054 0.0000 0.0000 0.0000 0.0027 0.0528 0.0428 0.1918 0.1475 0.1670 0.0000 0.1626 0.1403 0.0494 0.0000 0.0000 0.0000 0.1440 0.0573 0.0000 0.2264 0.0000 0.0281 0.3010 0.0000 0.0000 Vegetables & melons 0.0000 0.0000 0.0000 0.0000 0.2722 0.0167Vegetables & melons 0.0000 0.0000 0.0020 0.0000 0.0000 0.0000 0.0000 0.8337 0.1133 0.0000 0.0530 0.0000 Farm Commodity Marketing inputs Farm Commodity Marketing inputs Note Note Share of Total Cost of Table 4. Farm-Retail Product Shares Table 5. Farm-Commodity Shares Attributable to Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 623

Table 6. Total Annual Value of Food Products but none of the previous studies quantified and Farm Commodities and Marketing Inputs the impacts. The second set of policy simulations quantifies the effects of subsidizing Millions of Dollars fruit and vegetable commodities and fruit and FAH vegetable retail products; both policies have Cereals and bakery 55,069 Meat 103,490 been suggested by nutritionists (Tohill 2005; Eggs 3,921 Guthrie 2004) and mentioned in the Farm Dairy products 46,762 Bill debate (Guenther 2007; Bittman 2011)as Fruits & vegetables 48,552 ways of addressing obesity. The third and final Other foods 100,308 set of policies are taxes on the nutrient con- Nonalcoholic beverages 28,672 tent of foods—that is, taxes on food products FAFH 372,264 based on their content of calories, sugar, or Alcoholic beverages 36,025 fat. If the goal of a policy is to reduce the Farm commodities weight and hence BMI status of a popula- Downloaded from Oil-bearing crops 8,874 tion, then a calorie tax would intuitively be Grains 11,039 the most efficient tax, but proponents typically Vegetables & melons 17,740 favor taxes on particular energy-dense foods Fruits & tree nuts 16,690 (such as sodas) or sources of calories (such Sugar cane & beets 1,877 as sugar or fat). Several papers have exam- Other crops 3,321 ined the potential caloric and social welfare http://ajae.oxfordjournals.org/ Cattle production 28,246 effects of nutrient or energy taxes, or both, but Other livestock production 11,541 have all assumed perfectly elastic supply and Dairy farming 20,632 have not considered the effects of such policies Poultry & egg production 17,426 Fish production 11,361 on public health care expenditures (Chouinard Marketing inputs 646,315 et al. 2007; Miao, Beghin and Jensen 2010; Smed, Jensen and Denver 2007; Salois and Notes: Based on 2002 Benchmark I-O Tables (U.S. Department of Commerce, Tiffin 2011). Bureau of Economic Analysis 2007). at University of California, Davis on May 16, 2012 in adult body weight on public health care Removal of Farm Subsidies 8 expenditures. We computed the effects of eliminating farm Table 8 summarizes all the parameters, data subsidies using estimates of their price impacts sources, and assumptions used to simulate tax from several sources and treating commodity and subsidy policies using the model. prices as exogenous. Sumner (2005) estimated that eliminating subsidies for corn, wheat, and rice would increase the world prices of these Simulations crops by 9–10%, 6–8%, and 4–6%, respectively, based on market prices and policies We simulated the price, quantity, calorie, body in the early 21st century. Using the value of weight, and social welfare effects for various U.S. production of each crop relative to their policies that have been suggested by policy- sum as weights, we calculated the value-share- makers and others as means of reducing the weighted effect of the elimination of grain costs of obesity in the United States. The first subsidies on the composite food grain price set of policy simulations addresses the notion as being an 8.4% increase (table 9). Elimi- that subsidies to farmers are an important key nating the corn subsidy would also affect the driver of obesity patterns in the United States price of feed grains, and hence, the cost of (e.g. Pollan 2003, 2007; Tillotson 2004; Muller, production and prices of livestock commodi- Schoonover, and Wallinga 2007). Agricultural ties. The effect that removing corn subsidies economists have argued that farm subsidies would have on the price of a livestock com- have had minimal impacts on obesity (e.g. modity is computed as the percentage change Alston, Sumner, and Vosti 2006; Alston, Sum- in the world market price of corn from the ner, and Vosti 2008; Beghin and Jensen 2008), elimination of the subsidy, multiplied by the cost share of corn in the production of that commodity. 8 Parks,Alston, and Okrent (2011) also estimated a Tobit model Applying these implied price changes in the in which the corresponding multiplier was e = $655.3 million. simulation model, eliminating farm subsidies 624 April 2012 Amer. J. Agr. Econ.

Table 7. Average Daily Quantities of Food, Sugar and Fat and Energy Intake by Food Group for Individuals Aged 18 and Older, 2003–2004 and 2002 Per Capita Budget Shares Body Weight to Energy Quantity Sugar Fat Budget Share Food Multipliera kcal grams grams grams percentage pounds/kilograms Total 2,274.79 2,609.23 86.23 129.38 FAH Cereals & bakery 351.94 133.04 9.38 16.37 9.46 0.76 Meat 162.20 67.59 9.85 0.22 11.02 0.69 Eggs 34.26 20.72 2.47 0.36 0.57 0.47 Dairy 166.13 186.49 8.38 13.80 4.35 0.25 Fruits & vegetables 124.36 195.58 2.41 12.88 6.97 0.18 Other food 362.30 183.11 18.25 13.43 13.14 0.57 Nonalcoholic beverages 178.48 925.31 1.10 36.29 6.44 0.06 Downloaded from FAFH 821.38 710.94 35.19 36.31 34.48 0.33 Alcohol 122.05 272.12 0.01 1.38 13.58 0.13

Note: Calculations for the consumption of foods and associated nutrient and energy content are based on one day of dietary recall data for respondents aged 18 or older from the 2003–2004 NHANES (Centers for Disease Control and Prevention, National Center for Health Statistics 2007). The budget shares are based on 2002 personal consumption expenditures (U.S. Department of Commerce, Bureau of Economic Analysis, National Income and Product Accounts 2010). http://ajae.oxfordjournals.org/ aThe pounds of body weight to kilograms of food consumption multiplier (i.e. ∂B/∂Qn) is calculated as energy per gram of food consumed (i.e. kcal/kilogram) times 1 pound of body fat tissue per 3,500 calories (lbs/kcal); ∂B/∂Qn is used to calculate the elasticity of body weight with respect to consumption of food (i.e. ηB,Q = ∂B/∂Qn × Qn/B) and the change in pounds of body weight from a policy (i.e. dB = ∂B/∂Qn × EQn × Qn).

on grain commodities would result in a The removal of border measures would decrease in consumption of 567 calories per result in lower prices and increases in the adult per year,which corresponds to a decrease consumption of some commodities (table 10, in body weight of 0.16 kilograms per year panel a). We represented this policy in the at University of California, Davis on May 16, 2012 for an average adult in the United States model as the introduction of an equivalent set (table 10, panel a). The probability that the of subsidies in conjunction with the removal removal of farm subsidies on grain commodi- of the other farm subsidies already discussed. ties would result in a decrease in calorie con- The net effect would be to increase calorie sumption is 94% based on the empirical poste- consumption. Not surprisingly, calories from rior distribution estimated using Monte Carlo the consumption of dairy and fruit and veg- integration. Removing the U.S. grain subsidy etable food products would increase (by 1,744 would increase social welfare, but the actual kcal and 836 kcal, respectively) if subsidies magnitude of the net gain cannot be deter- were introduced that would have effects equiv- mined using the social welfare measure pre- alent to eliminating the 2006 CSEs. Compared sented in this paper because this measure does to eliminating only grain subsidies, eliminat- not reflect the government revenue effects of ing all farm subsidies would result in a larger changes in border measures or other details reduction in the consumption of calories of of the actual subsidies that are represented cereals and bakery products (−1,458 kcal ver- in our analysis as fully coupled equivalent sus −448 kcal). This result is driven by greater rates. substitution out of cereals and bakery products Some agricultural policies entail benefits or into fruits and vegetables and dairy because the costs to consumers in addition to those implied increase in the price of grain commodities is by changes in world market prices, including now accompanied by a reduction in the price trade barriers for sugar, dairy, and some fruit of milk, fruit, and vegetable commodities. and vegetable commodities. To capture the Eliminating all subsidies,including trade bar- effects of these policies on commodity prices riers, would lead to an increase in annual paid by buyers, we used the commodity- per capita consumption in the range of 165 specific consumer support estimates (CSEs) to 1,435 calories (equivalent to an increase calculated by the Organization for Economic in body weight of 0.03% to 0.23%), depend- Co-operation and Development (2010) for ing on the size of the policy-induced price three periods: 1989–2009, 2000–2009, and 2006 wedges to be removed, as represented by the (table 9). CSEs. The probability of increased calorie Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 625

Table 8. Description of Parameters and Assumptions Used in the Simulations Description Source Table Parameters for equilibrium displacement model Elasticities of ηN 9 × 9 matrix Authors’ simulated values, 2 demand for (homogeneity, based on Okrent and Alston retail products adding-up (2011). imposed) Elasticities of εL 12 × 12 diagonal Authors’ calculations based on 3 supply of farm matrix (no upper- and lower-bound commodities cross-price effects); estimates of Chavas and ∞ Cox (1995). Farm-retail SR 12 × 9 matrix Authors’ calculations based on 4 product shares 2002 Benchmark Input-Output Accounts. Downloaded from Farm-commodity SC 12 × 9 matrix Authors’ calculations based on 5 shares 2002 Benchmark Input-Output Accounts. η∗ × Hicksian L 12 12 zero matrix Fixed proportions assumption – elasticities of demand for http://ajae.oxfordjournals.org/ commodities Commodity sL 12 × 1 vector Authors’ calculations based on 8 subsidies Sumner (2005) and Rickard, Okrent and Alston (2011). Retail product tN 9 × 1 vector Authors’ calculations based on 10, A-1 taxes 2003-04 NHANES assuming $5 tax per gram of fat, or near equivalent.

Additional parameters for social welfare model at University of California, Davis on May 16, 2012 Budget shares w 9 × 1 vector Authors’ calculations based on 7 2002 Personal Consumption Expenditures in the National Income and Product Accounts Value of total DWX (DW X)12× 12 diagonal Authors’ calculations based on 6 output for retail matrix (12 × 1 2002 Benchmark products vector) Input-Output Accounts Value of total DPQ (DPQ)9× 9 diagonal matrix Authors’ calculations based on 6 output for (9 × 1 vector) 2002 Benchmark commodities Input-Output Accounts Parameters for health care expenditures related to obesity Marginal increase e scalar e = $604.8 in public health Parks, Alston and Okrent million expenditures (2011) per for increase in pound weight per adult Elasticity of body ηBQ 9 × 1 vector Authors’ calculations based on 7 weight with 2003-04 NHANES and respect to food assuming 3,500 kcal per year consumption contributes one pound of body fat

consumption is 60% or 80%, depending on fruits and vegetables. These results indicate which CSE is used. Even though individuals that U.S. farm policy, for the most part, has not would consume less calories from cereals and made food commodities signiﬁcantly cheaper bakery products and FAFH, they would con- and has not had a signiﬁcant effect on caloric sume more calories from dairy products and consumption. 626 April 2012 Amer. J. Agr. Econ.

Table 9. Commodity Policies Simulated Elimination of Elimination of Elimination of Grain Grain Grain 16.24% Subsidies and Subsidies and Subsidies and Subsidy on Elimination Trade Barriers Trade Barriers Trade Barriers Fruit & of Grain Based on CSEs Based on CSEs Based on CSEs Vegetable Subsidies in 2006 in 2000–2009 in 1989–1999 Commodities Percentage Tax Equivalents Oilseed 0.00 0.00 0.00 0.00 0.00 Food grains −8.40 −8.40 −8.40 −8.40 0.00 Vegetables & melons 0.00 4.00 4.00 4.00 16.24 Fruits & tree nuts 0.00 6.00 6.00 6.00 16.24 Sugar cane & beets 0.00 31.00 54.20 55.69 0.00 Other crops 0.00 0.00 0.00 0.00 0.00 Downloaded from Beef cattle −2.85 −2.85 −2.85 −2.85 0.00 Hogs & other meat animals −2.85 −2.85 −2.85 −2.85 0.00 Milka −2.85 9.55 24.95 31.78 0.00 Poultry & eggs −4.75 −4.75 −4.75 −4.75 0.00 Fish & aquaculture 0.00 0.00 0.00 0.00 0.00 http://ajae.oxfordjournals.org/

Note:Authors’ calculations based on Sumner (2005), and Rickard, Okrent, and Alston (2011). Entries are ad valorem tax equivalents in the context of the model. A commodity policy with sl < 0 denotes a tax on commodity l and a commodity policy with sl > 0 denotes a subsidy on commodity l. aEliminating corn subsidies would implicitly increase the price of milk by 2.85%. If grain subsidies and trade barriers as captured by the CSE for milk in 2006 were removed, then the price of milk would increase by 9.55% (=−2.85% + 12.4%).

Subsidies Applied to Fruits and Vegetables A slightly different story unfolds when we allow for an upward-sloping supply of farm We estimated the likely effects from two types commodities (table 10, panel b). Speciﬁcally, of subsidies applied to fruits and vegetables: consider the results using the lower-bound esti- at University of California, Davis on May 16, 2012 (a) subsidies applied to fruit and vegetable mates of supply elasticities. In this case the retail products at a rate of 10%, and (b) subsi- subsidy on fruit and vegetable retail prod- dies applied to fruit and vegetable farm com- ucts would increase overall calorie consump- modities at a rate of approximately 16.24 % tion but the effect is much smaller (16 kcal (table 11). The subsidy rate of 16.24% on fruit per year compared with 343 kcal per year). and vegetable commodities was chosen so that When the supply of farm commodities is less the cost of both policies would be roughly equal than perfectly elastic, the effect of the fruit to $5,846 million per year given our baseline and vegetable product subsidy on food prices, assumptions and exogenous prices. and thus on consumption, is smaller across all In the case of exogenous commodity prices,a food products, but especially smaller for food 10% subsidy on fruit and vegetable retail prod- products that have relatively large farm-retail ucts would cause the consumption of fruits and product shares. The food products with the vegetables to increase (table 10,panel a). How- biggest farm-retail product shares include eggs, ever, because fruits and vegetables are substi- dairy, and fruits and vegetables. Hence, when tutes for cereals and bakery products, meat, we allow for an upward-sloping commodity nonalcoholic beverages and FAFH, consump- supply, the effect of the subsidy policy on con- tion of these foods, and hence, calories taken sumption of these food products is dampened from them would decrease (by 2,172 kcal per to a much greater degree compared with FAFH year, 829 kcal per year, 907 kcal per year, and and cereals and bakery products, which have 913 kcal per year, respectively). The net effect relatively small farm-retail product shares. The of a policy of subsidizing fruit and vegetable result is a larger decrease in calories consumed retail products at 10% would be to increase per year for foods that are substitutes for calorie consumption by 343 calories per year fruits and vegetables, relative to the increase for an average adult in the United States. How- in calories consumed per year for fruits and ever, the total caloric effect of the policy is vegetables and its complements. Ultimately, measured somewhat imprecisely, with a fairly average body weight would increase by less large standard deviation around the posterior than 0.01 pounds per adult per year under the mean (i.e. 2,076). assumption of upward-sloping supply.It should Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 627 0 < 1.00 1.00 1.00 1.00 0.39 0.22 0.19 0.42 0.94 0.30 Probabilities that ) ) ( 1.33 ) ( 1.36 ) ( 1.17 ) ( 0.11 ) ( 0.92 ( 0.24 ( 0.47 ) ( 0.58 ) ( 0.59 ) ( 0.46 ) Pounds − 5.97 − 5.59 − 5.85 − 5.93 − 0.16 Downloaded from − 567 − 20,901 − 19,567 − 20,467 − 20,762 − 546 − 139 1,288 0.37 − 204 1,747 0.50 − 1,007 http://ajae.oxfordjournals.org/ − 913 123 343 0.10 − 571 168 795 0.23 − 8,903 − 8,742 451 − 10,688 181 − 10,505 808 − 214 282 16 − 615 493 7 210 0.06 − 907 − 527 − 2,392 − 6,927 − 1,171 1,422 − 1,765 − 1,411 1,848 at University of California, Davis on May 16, 2012 − 541 − 155 − 721 − 3,349 − 1,534 − 1,461 − 1,071 Calories − 353 − 116 − 491 2,373 − 445 Change in calorie consumption − 4,023 − 3,114 − 1,266 ) − 231 702 109 − 717 1,500 − 212 1,744 836 − 544 4,132 941 − 699 5,207 981 − 1,025 =∞ ε − 242 − 430 − 156 894 − 457 − 233 258 − 474 − 829 599 406 2,870 1,166 − 631 490 161 2,234 1,327 − 192 (189) (74) (66) (124) (73) (164) (103) (255) (55) (370) (468) (131) (141) (289) (198) (353) (205) (618) (132) (834) (868) (231) (257) (596) (325) (665) (382) (1,173) (245) (1,641) − 448 (901) (231) (279) (489) (452) (669) (376) (1,239) (256) (1,595) (1,877) (616) (631) (1,201) (678) (1,572) (995) (3,030) (507) (4,652) (1,322) (413) (410) (755) (453) (1,009) (699) (2,029) (380) (3,203) (2,019) (659) (633) (1,218) (668) (1,743) (1,360) (2,395) (482) (4,753) (1,065) (282) (315) (743) (393) (822) (470) (1,450) (301) (2,036) (1,659) (559) (541) (982) (594) (1,301) (925) (2,543) (501) (4,103) (1,177) (299) (366) (633) (589) (877) (492) (1,619) (335) (2,076) − 6,907 48 − 1,458 − 4,756 − 2,175 − 4,338 − 2,431 − 2,172 − 1,858 − 2,259 Bakery Meat Eggs Dairy F & V Food Drinks FAFH Drinks Total Body Weight Weight Cereal & Other Nonalcohol Alcohol Change in Change in Body : These estimates are based on the special case of exogenous commodity prices using the general price transmission model. The estimates are the means of the posterior distributions from the Monte Carlo simulations. The numbers in 2006 CSE 2000–2009 CSE 1989–2009 CSE Removal of all subsidies a. Assuming Commodity Prices are Exogenous ( Note parentheses represent the standard deviations ofleft the of means zero. of F&V the represents posterior fruit distribution. & The probability vegetables. that a policy will induce a negative change in body weight is the area under the posterior distribution of the change in body weight to the Removal of grain subsidies only Calorie tax Sugar tax Uniform tax F&V product subsidy F&V commodity subsidy Fat tax Table 10. Change in Annual Calorie Consumption and Body Weight per Adult 628 April 2012 Amer. J. Agr. Econ. 0 < 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.29 0.43 0.49 0.29 Probabilities that ) ) ) ( 1.07 ) ( 1.12 ( 1.18 ) ( 1.25 ) ( 1.04 ( 1.22 ( 1.28 ) ( 0.38 ) ( 0.53 ) ( 0.29 ) ( 0.41 ) ( 0.99 ) Pounds − 5.59 − 5.76 − 5.61 − 5.82 − 5.55 − 5.72 − 5.50 − 5.64 Downloaded from − 19,565 − 20,172 − 19,642 − 20,368 − 19,434 − 20,036 − 19,264 − 19,750 − 992 − 318 − 333 − 1,020 http://ajae.oxfordjournals.org/ − 730 29 16 0.00 − 906 83 261 0.07 − 410 91 513 0.15 − 552 135 720 0.21 − 9,513 − 9,708 − 8,269 407 − 8,429 403 − 10,165 − 10,310 − 10,296 116 − 10,518 125 − 589 − 773 − 284 − 424 − 1,794 − 1,746 − 1,657 − 1,601 − 6,852 − 6,814 at University of California, Davis on May 16, 2012 − 212 − 298 − 1,130 − 1,324 − 2,966 597 − 3,200 719 Calories − 214 − 400 − 139 − 302 − 111 − 227 − 276 2,131 − 448 2,186 Change in calorie consumption ∞ ) 915 1,054 < − − 3,180 − 3,546 − 1,578 − 1,789 − 2,280 − 2,617 − ε − 981 − 205 − 222 − 1,031 − 460 356 273 1,798 619 − 674 514 347 2,550 1,039 − 345 289 92 1,382 838 − 510 417 134 1,970 1,192 − 115 − 109 − 131 748 − 101 781 − 157 243 − 144 220 (713) (164) (224) (333) (258) (542) (317) (1,056) (219) (1,335) (533) (123) (167) (253) (193) (400) (237) (788) (162) (998) (789) (185) (239) (390) (368) (576) (334) (1,108) (228) (1,418) (1,041) (241) (317) (508) (484) (763) (440) (1,463) (303) (1,865) (1,512) (436) (469) (739) (370) (1,119) (842) (2,440) (480)(1,594) (476) (3,741) (500) (843) (523) (1,203) (876) (2,482) (491) (3,918) (1,676) (473) (541) (882) (422) (1,334) (884) (2,854) (475) (4,124) − 1,279 − 1,919 (1,782) (522) (583) (1,017) (592) (1,447) (934) (2,931) (489) (4,387) − 1,140 − 1,642 − 2,678 − 2,506 (1,387) (380) (410) (692) (321) (1,034) (767) (2,062) (376) (3,452) (1,464) (416) (440) (793) (451) (1,114) (796) (2,110) (385) (3,636) − 5,951 111 − 5,989 130 (1,823) (519) (541) (892) (410) (1,501) (1,280) (2,205) (448) (4,264) (1,915) (562) (577) (1,022) (578) (1,602) (1,303) (2,273) (461) (4,480) − 4,741 − 4,709 − 4,443 − 4,394 Bakery Meat Eggs Dairy F & V Food Drinks FAFH Drinks Total Body Weight Weight Cereal & Other Nonalcohol Alcohol Change in Change in Body : See Table 10a. Lower Upper F&V product subsidy F&V product subsidy b. Assuming Upward-Sloping Supply of Commodities ( Note ε F&V commodity subsidy F&V commodity subsidy Fat tax Fat tax ε Calorie tax Calorie tax Sugar tax Sugar tax Uniform tax Uniform tax Table 10. Change in Annual Calorie Consumption and Body Weight per Adult Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 629

Table 11. Food Policies Simulated: Ad Valorem Tax Equivalents 10 % Subsidy $0.005 Tax $0.000165 Tax $0.002688 Tax 5.03% Tax on Fruit and Per Gram Per Per Gram Uniform Tax on Vegetables Fat Caloriea Sugara Food Productsa percentage taxes Cereals & bakery 0.00 5.50 6.81 5.16 5.03 Meat 0.00 4.95 2.69 0.06 5.03 Eggs 0.00 24.06 11.01 1.86 5.03 Dairy 0.00 10.69 7.00 9.47 5.03 Fruits & vegetables −10.00 1.92 3.27 5.51 5.03 Other food 0.00 7.70 5.05 3.05 5.03 Nonalcoholic beverages 0.00 0.94 5.07 16.81 5.03 FAFH 0.00 5.66 4.25 3.07 5.03 Alcoholic beverages 0.00 0.0035 1.64 0.30 5.03 Downloaded from

Note: Entries are ad valorem tax equivalents in the context of the model. A retail product policy with tn > 0 denotes a tax on food product nand a retail food product policy with tn < 0 denotes a subsidy on food product n. aThese tax rates reflect the assumption of exogenous commodity prices and are constructed to achieve approximately the same calorie reduction as the $.005 tax per gram fat. The tax rates on sugar and calories for the case of endogenous commodity prices differ slightly (i.e. t = $0.002637 tax per gram sugar, t = $0.0001632 tax per calorie, and t = 4.973% uniform tax). Hence, the ad valorem taxes for each food product for the case of endogenous commodity prices are also slightly different. http://ajae.oxfordjournals.org/ be noted that under both assumptions about which is substantially less than the decrease commodity supply, the 10% subsidy on fruit in calories consumed from FAFH caused by and vegetable products has very little impact the subsidy on fruit and vegetable products on calorie consumption. (913 kcal per adult per year). The same ratio- Suppose the government were to spend the nale holds for both scenarios of upward-sloping same amount of money but chose to sub- supply of commodities. However, the mean sidize fruit and vegetable farm commodities changes in total calorie consumption from at University of California, Davis on May 16, 2012 rather than use a 10% subsidy on fruit and the fruit and vegetable commodity subsidies vegetable food products. This would translate implied by the empirical posterior distribution into a 16.24% subsidy on fruit and vegetable have large standard deviations, and the proba- commodities, depending on the assumptions bility of the mean effect being positive is only made about the supply of commodities. Subsi- 50% or 70%, depending on the assumptions dies on fruit and vegetable commodities would about the elasticity of commodity supply. cause consumption of calories to increase to If the objective is to reduce the consumption a much greater extent than subsidies on fruit of calories and body weight,these results imply and vegetable products would. The difference that a tax, not a subsidy, should be applied to arises largely because fruit and vegetable com- fruit and vegetable farm commodities. Given modities are used as inputs in the produc- that the model is approximately linear over the tion of FAFH, and consequently a subsidy on small changes being analyzed, the effects of a fruit and vegetable commodities reduces the tax can be seen by multiplying all the results for cost of FAFH production, as well as fruit and a subsidy by minus one in table 10.9 For com- vegetable retail products. Consumers would parison with other policies aiming to reduce still substitute away from FAFH and towards food consumption and obesity, in table 12 we now relatively cheaper fruits and vegetables, report the welfare impacts of taxes (rather than but this effect is dampened by the implicit sub- subsidies) on fruit and vegetable commodi- sidy to FAFH from the fruit and vegetable ties and products, along with other food tax commodity subsidies. Hence, the reduction in policies. calories consumed from FAFH is smaller under Consider a tax on fruit and vegetable retail the fruit and vegetable farm commodity sub- products. In the case of perfectly elastic sup- sidy compared with the fruit and vegetable ply, the net change in social welfare would be retail product subsidy, and the net effect is an increase in calories consumed. Assuming that the supply of commodities is perfectly elastic, calories consumed from FAFH would decrease 9 The equilibrium displacement model and measure of public by 571 kcal per adult per year in response to the health care costs associated with obesity are linear but the measure subsidy on fruit and vegetable commodities, of social welfare is nonlinear in the tax rate chosen. 630 April 2012 Amer. J. Agr. Econ. 5.54 − 0.38 − 1.23 − 1.79 − 1.67 − 1.48 Public Health Including Care Costs Changes in a Weight 8.22 2.25 1.42 0.86 0.98 1.17 Decrease in Body Public Health Excluding Care Costs Changes in Annual Cost per Pound b Downloaded from − 22 − 52 − 1,358 − 1,271 − 1,330 − 1,349 Adults per Year of Body Change in Pounds Weight for all U.S. Millions of Pounds Dollars per Pound http://ajae.oxfordjournals.org/ 0 > 0.37 0.55 0.99 1.00 1.00 1.00 Public Health Care Costs SW Including Probability that at University of California, Davis on May 16, 2012 20 1,675 2,280 2,232 2,000 (365) (278) (653) (483) (694) (600) − 122 SW Including Change in Public Health Care Costs ). ) − 59 (359) (276) (804) (554) (821) (709) − 137 − 3,612 − 3,381 − 3,537 − 3,588 =∞ Care Costs ε Public Health Annual Change in Millions of Dollars Parks, Alston, and Okrent 2011 (37) (22) (235) (109) (170) (183) − 181 − 117 − 1,937 − 1,102 − 1,305 − 1,587 Social Welfare ( SW) Excluding Changes in Public Heath-Care Costs Annual Change in : These estimates were calculated using 1,110 draws from the posterior distribution that satisfied monotonicity and curvature locally. The estimates refer to the mean of the posterior distribution for each variable, and the numbers in Evaluated at posterior means of data. The U.S. population aged 18 and older in 2008 was 227,364,210 ( a b a. Assuming Exogenous Prices of Commodities ( Note parentheses represent the standard deviation. F & V product tax F & V commodity tax Fat tax Calorie tax Sugar tax Uniform tax Table 12. Net Social Costs of Selected Policies Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 631 − 0.54 − 0.44 − 1.31 − 1.28 − 1.77 − 1.74 − 1.73 − 1.71 − 1.54 − 1.53 Public Health Including a Care Costs Changes in Weight 2.51 9.472.19 6.82 1.34 1.38 0.90 0.91 0.93 0.94 1.12 1.13 Decrease in Body Public 112.21 109.15 Health Excluding Care Costs Changes in Annual Cost per Pound b Downloaded from − 1 (92) − 17 − 47 − 33 (121) (285) (236) (291) (255) − 1,276 − 1,323 − 1,262 − 1,302 − 1,251 − 1,283 − 1,271 − 1,310 Adults per Year of Body Change in Pounds Weight for all U.S. Millions of pounds Dollars per Pound http://ajae.oxfordjournals.org/ 0 > 0.18 0.29 0.25 0.18 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Public Health Care Costs SW Including Probability that at University of California, Davis on May 16, 2012 18 21 1,677 1,694 2,228 2,277 2,169 2,203 1,959 1,995 (228) (319) (172) (244) (600) (628) (526) (547) (641) (665) (564) (583) − 109 − 116 SW Including Change in Public Health Care Costs ∞ ) − 3 < − 45 − 89 (231) (322) (172) (245) (713) (758) (596) (628) (737) (774) (646) (677) − 124 ε − 3,394 − 3,520 − 3,358 − 3,462 − 3,329 − 3,413 − 3,381 − 3,486 Care Costs Public Health Millions of dollars Annual Change in (9) (16) (31) (18) − 71 (185) (206) (112) (123) (134) (148) (147) (161) − 112 − 161 − 103 − 1,717 − 1,826 − 1,131 − 1,185 − 1,159 − 1,210 − 1,422 − 1,491 Social Welfare ( SW) Excluding Changes in Public Heath-Care Costs Annual Change in F & V product tax F & V product tax F &V commodity taxes F & V commodity taxes Fat tax Fat tax Calorie tax Calorie tax Sugar tax Sugar tax Uniform tax Uniform tax Lower Upper b. Assuming Upward-Sloping Supply of Commodities ( ε ε Table 12. Net Social Costs of Selected Policies 632 April 2012 Amer. J. Agr. Econ. a loss of $181 million per year, which is statisti- on all foods (roughly 5%) that would achieve cally significantly different from zero (table 12, approximately the same reduction in calories panel a). This measure excludes the savings per day. to the government from decreases in body weight. The decrease of 0.10 pounds in body Fat Tax. A fat tax would cause total annual weight for the average adult would reduce consumption of calories to decrease by 19,642 body weight for the entire U.S. population by kcal per adult, with an upward-sloping supply 22 million pounds and save $59 million in public of commodities and 20,901 kcal per adult with health care expenditures, reducing the dead- exogenous commodity prices. More than half weight loss to $122 million per year. The fruit of the reduction in calories consumed would and vegetable farm commodity tax would be come from decreased consumption of FAFH, less distortionary than the fruit and vegetable which is a gross substitute for meat, fruits, and product tax (i.e. $117 million net annual cost vegetables. In the simulation these foods are versus $181 million) and would have a greater taxed at lower rates than FAFH (5.66% tax Downloaded from impact on annual public health care costs (i.e. on FAFH compared to a 1.92% tax on fruits $137 million net annual cost versus $59 mil- and vegetables and a 4.95% tax on meat). In lion), sufficiently so that the farm commodity addition,FAFH is a gross complement for cere- tax would yield a net social benefit of $20 als and bakery products and dairy, two of the million per year. The results are very simi- most heavily taxed foods. Hence, consump- lar in the case of upward-sloping supply, but tion of FAFH decreases not only because of http://ajae.oxfordjournals.org/ the impacts are generally dampened (table 12, an increase in its own price, but also because panel b). of strong cross-price effects from increases in other prices. Not surprisingly, the reduction Food Taxes in calories consumed under the fat tax also reflects a decrease in calories from both dairy We derived ad valorem taxes for foods that and cereals and bakery products. would correspond to per unit taxes on their The magnitude of the deadweight loss nutrient content in fat, calories, and sugar

under the two supply scenarios is approxi- at University of California, Davis on May 16, 2012 (table 11) (see Technical Appendix for more mately equivalent: $1,937 million when com- details).We arbitrarily chose a tax of half a cent 10 modity supply is perfectly elastic and $1,717 per gram of fat (i.e. $5 per kilogram). Sub- million using the lower-bound estimates of sequently, we chose the sugar tax ($0.002637 supply elasticities. Public health care expen- per gram) and the calorie tax ($0.0001632 per ditures attributable to obesity would decline calorie) such that the resulting annual reduc- by approximately $3,612 million in the case tion in calories consumed per adult would be of exogenous commodity prices, and $3,394 approximately the same under each tax policy. million using the lower-bound estimates of sup- We also analyzed the policy of a uniform tax ply elasticities. These measures are statistically significantly different from zero, and the probability of a negative change in total welfare 10 Since the social welfare measure is nonlinear in the tax rate used, we tested the sensitivity of our results to the choice of tax (including changes in public health care costs rates by estimating the changes in social welfare with various tax associated with changes in body weight) from rates including $2.5 and $10 tax per kilogram of fat, and taxes on a fat tax under all the supply regimes is essen- sugar, calories, and all food that generated approximately the same calorie reduction as the fat tax (see appendix tables A-2a,A-2b and tially zero. The fat tax would ultimately save A-3.). At a $2.5 tax per kilogram of fat, the tax rates required to between $0.15 and $0.23 per pound of weight achieve the same reduction in calorie consumption are roughly a $1.344 tax per kilogram of sugar, a $0.0001632 tax per calorie and a lost by adult Americans. 2.5% uniform tax.At a $10 tax per kilogram of fat,the tax rates that would generate an equivalent reduction in calorie consumption are Calorie Tax. Suppose the U.S. government roughly a $5.376 tax per kilogram of sugar,a $0.00033 tax per calorie and a 10% uniform tax. Our findings are generally robust to the taxed food products at a rate of approximately choice of tax rate except for the fat tax policy in the extreme case of $0.00016 per calorie to achieve approximately doubling the tax rate, which resulted in a net social cost rather than the same reduction in calories as the fat tax a net social benefit.When the fat tax is doubled,the probability that the change in social welfare (including a provision for public health of $5 per kilogram. Again, more than half of care costs associated with obesity) is greater than zero, is between the calorie reduction would be the result of 0.3 and 0.5 depending on the slope of commodity supply. Because the deadweight loss associated with tax collection is quadratic in t a decrease in calories consumed from FAFH. and the public health care costs are linear in t, as we increase the However, unlike the fat tax, under a calorie tax tax rate the measure of deadweight loss associated with a policy about one-quarter of the total decrease in calo- will eventually become greater than the savings associated with a reduction in public health care costs. In the case of the doubling of ries consumed per adult per year would result the fat tax, this is what occurred. from reduced consumption of cereals and Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 633 bakery products. Again, changes in the con- under exogenous commodity prices,and $1,251 sumption of dairy products would contribute million under an upward-sloping commodity importantly to the reduction in consumption supply. When the reduction in public health of calories (a reduction of 1,578 kcal per year care expenditures associated with the calorie using the lower-bound estimates of supply elas- reduction is included, the change in social wel- ticities, or 1,500 kcal per year with perfectly fare becomes a net gain (between $2,169 and elastic commodity supply), although the mag- $2,232 million). Including the changes in health nitude of the change is smaller compared with care costs from the sugar policy, the benefit the fat tax. would be between $1.67 and $1.73 per adult Compared with the fat tax, the calorie tax pound lost, which is smaller than the benefit would distort relative prices and consumption from an equivalent calorie tax, but still better less, which implies a smaller deadweight loss. than the fat tax. The deadweight loss from the calorie tax ranges between $1,102 million and $1,131 million per Uniform FoodTax. The last tax policy we ana- Downloaded from year, both statistically significantly different lyze is a uniform tax on all foods at a rate of from zero. Because the tax rates under the dif- about 5%. The uniform tax rate was chosen to ferent tax policies were constructed to achieve achieve approximately the same reduction in approximately the same reduction in calorie calories as the taxes on fat, calories, or sugar consumption per adult per year, the change would, that is, around 18–19,000 kcal per adult in public health care expenditures is approx- per year. The uniform tax is more distortionary http://ajae.oxfordjournals.org/ imately the same under the calorie tax as it is than the sugar and calorie taxes are, but less so under the fat tax. The change in social wel- than the fat tax. The deadweight loss excluding fare, including changes in public health care changes in health care costs induced by the uni- expenditures, from the calorie tax is positive form tax would be between $1,422 million and (between $1,262 million and $1,271 million per $1,587 per year. Like the calorie tax and sugar year), which reflects the smaller deadweight tax, the uniform tax could potentially result in loss associated with the calorie tax compared a net gain if changes in public health care costs

with the fat tax. A calorie tax would cost are considered. The uniform tax would bene- at University of California, Davis on May 16, 2012 $0.89 per pound lost for an American adult fit the United States by $1.28 per pound lost, if we do not account for the resulting reduc- in the case of upward sloping supply, or $1.54 tion in health care expenditures associated with per pound lost in the case of perfectly elastic decreases in obesity. Including these savings supply. implies a benefit of $1.77 per pound lost under a calorie tax. Summary and Conclusion Sugar Tax. Suppose, alternatively, that the U.S. government taxed food products at a rate Previous studies of the potential impacts of of $0.0026 per gram of sugar to achieve approx- food and farm policies on obesity have imposed imately the same reduction in calories as would restrictive assumptions on their analysis. For the fat and calorie tax. Like the fat and calo- example, studies of the potential impacts of rie taxes, more than half of the reduction in food policies on obesity have all assumed that calories consumed would reflect a decrease 100% of the incidence of a tax or subsidy would in calories consumed from FAFH. However, be borne by final consumers. A related issue unlike taxes on fat or calories, a reduction in is the determination of the relevant counter- calories consumed from nonalcoholic bever- factual alternative in policy analysis. Many of ages would account for about one-quarter of these studies evaluated the effect of a tax or the total decrease in calories consumed per subsidy on one group of foods (e.g., beverages adult per year. Similar to the fat and calo- or snack foods) without considering substitu- rie taxes, changes in the consumption of dairy tion effects on the consumption of foods not products are an important source of calorie included in their analysis. reduction (reductions of 2,280 kcal per adult We set out to analyze and evaluate the effects per year using the lower-bound estimates of of food and farm policies on food consumption, supply elasticities, compared with 3,114 kcal adult body weight, and social welfare in the per adult per year under a perfectly elastic com- United States. To address this goal, we devel- modity supply). Compared with the fat and oped an equilibrium displacement model that calorie taxes, the sugar tax would be associ- allows for multiple inter-related food products ated with a deadweight loss of $1,330 million to be vertically linked to multiple inter-related 634 April 2012 Amer. J. Agr. Econ. farm commodities and marketing inputs. We should be taxed more heavily than calories established the structure of the equilibrium dis- generally). Conversely, the overall nutritional placement model to make it possible to obtain composition of an individual’s diet, and not corresponding approximations to exact money just the caloric content, may have health impli- metric measures of welfare changes associ- cations that matter (a diet of only grapefruit, ated with policy changes. Moreover,we showed which is low in calories, would be nutritionally how the solutions of the equilibrium displace- poor), but would not be addressed by a calorie ment model could be used to estimate the tax. Finally, a calorie tax would be regressive, effects of any of the policies on social welfare falling disproportionately heavily on the poor. and its distribution between consumers and Consideration of these complications need not producers. rule out a calorie tax, and it does not seem The first set of policy experiments showed likely to change the efficiency ranking of a that eliminating farm subsidies–including calorie tax relative to the other taxes and sub- direct subsidies on grains and indirect subsi- sidies considered here. However, it does imply Downloaded from dies from trade barriers on dairy, sugar, and that a calorie tax might have to be imple- fruit and vegetable commodities–would have mented as part of a package, together with very limited impact on calorie consumption, other instruments such as education programs, and hence, obesity. Second, we found that for product information, and food assistance pro- both supply scenarios, the most efficient policy grams, and possibly combined with other taxes, would be a tax on food based on its caloric subsidies, and regulations. The design of such http://ajae.oxfordjournals.org/ content. A tax of $0.0165 per 1,000 calories policies might also need to account for the would yield a net benefit to national welfare potential role of induced innovation in the food of $2,280 million, or $10 per adult, which is industry, which would make endogenous the equivalent to about $1.79 per pound of fat lost. nutrient content of particular food groups that An equivalent sugar tax would also yield a has been treated as fixed in our analysis and benefit under both supply scenarios, although is a dimension with significant potential for less than the calorie tax. A comparable fat change.

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United States Department of Commerce, rewrite the 2(N + L) × 1 gradient of the social Bureau of Economic Analysis. National welfare function as: Income and Product Accounts, Per- ⎡ ⎤ sonal Consumption Expenditures and ∇PD SW(·) ⎢ ∇ S SW(·) ⎥ Prices, Underlying Detail Tables. 2010. (1A-1) ∇SW(P, W, u) = ⎣ P ⎦ , Available at: www.bea.gov/national/ ∇W SW(·) ∇ D · nipaweb/nipa_underlying/Index.asp. WS SW( ) Accessed 10 March 2010. United States Department of Commerce, where ∇PD and ∇PS denote the vector of N × Bureau of Economic Analysis. 2007. 2002 1 ﬁrst-order partial derivatives of the social Benchmark Input-Output Detailed Use welfare function with respect to consumer ∇ ∇ Table. Available at: http://www.bea.gov/ and producer retail prices, and WD and WS × industry/io_benchmark.htm#2002data. denote the vector of L 1 ﬁrst-order partial Accessed 10 March 2010. derivatives of the social welfare function with Downloaded from White House Task Force on Childhood Obe- respect to buyer and seller commodity prices. The gradient of the social welfare function sity Report to the President. Solving the ( (0) (0)) Problem of Childhood Obesity Within a at P , W is: Generation. Washington, DC, May 2010. (1A-2) ∇SW(P(0), W(0), u(0))

Available at: http://www.letsmove.gov/ ⎡ ⎤ http://ajae.oxfordjournals.org/ ∇ (0) (0) (0) −∇ (0) (0) (0) pdf/TaskForce_on_Childhood_Obesity_ PD g(P , W , u ) PD e(P , W , u ) ⎢ ∇ (0) (0) (0) −∇ (0) (0) (0) ⎥ May2010_FullReport.pdf. Accessed 1 = ⎢ PS g(P , W , u ) PS e(P , W , u ) ⎥ ⎣∇ π (0) (0) (0) +∇ (0) (0) (0) ⎦, August 2010. WD (P , W , u ) WD g(P , W , u ) ∇ π(P(0), W(0), u(0)) +∇ g(P(0), W(0), u(0)) Whitney, E., C. Cataldo, and S. Rolfes. 1994. WS WS Understanding Normal and Clinical Nutri- tion. Minneapolis,St. Paul:West Publishing where ∇PD e(·), ∇PD g(·), ∇PS e(·), and ∇PS g(·) Company. are N × 1 gradients of the consumer expen- Wohlgenant, M. K. 1982. The Retail-Farm diture and the government revenue functions, ∇ π · ∇ · ∇ π · Price Ratio in a Competitive Food Indus- respectively,and W ( ), W g( ) W ( ) and at University of California, Davis on May 16, 2012 ∇ · × D D S try With Several Marketing Inputs. North WS g( ) are L 1 gradients of the profit and Carolina State University Department of government revenue functions with respect to Economics and Business, Working Paper consumer and product prices of commodities, 12, 1982. respectively. Wohlgenant, M. K., and R. C. Haidacher. Several substitutions can be made to sim- 1989. Retail-to-Farm Linkage for a Com- plify (1A-2). Since the producer prices of plete Demand System of Food Com- retail products have no effect on the consumer modities. Washington, DC: USDA Eco- expenditure on goods and the buyer prices nomic Research ServiceTechnicalBulletin of commodities have no effect on profits for 1775. commodity producers: Wohlgenant, M. K. 1989. Demand for Farm (0) (0) (0) Output in a Complete System of Demand (1A-3) ∇PS e(P , W , u ) = 0, Functions. American Journal of Agricul- tural Economics 71: 241–252. (1A-4) ∇ π(P(0), W(0), u(0)) = 0. ———. 2001. Marketing Margins: Empirical WD Analysis. In Handbook of Agricultural Second, Shephard’s lemma implies that the Economics, Vol. 1., ed. B. Gardner and G. derivative of the consumer expenditure func- Rausser, p. 934–970. Amsterdam: Elsevier tion with respect to price n is the Hick- Science BV. sian demand for good n. Hence, the gradient of the consumer expenditure function with respect to consumer prices of retail prod- Technical Appendix of Derivations of Social ucts is an N-vector of Hicksian demands · ∇ (0) (0) = Welfare Formula for retail products, h( ) : PD e(P , u ) h(P(0), u(0)).At(P(0), W(0)), Hicksian demands The formula for social welfare (equation (34)) for retail products are equal to their Marshal- is derived by first solving the gradient of the lian counterparts, so: social welfare function and then the Hessian (0) (0) (0) of the social welfare function in (33). We first (1A-5) ∇PD e(P , u ) = Q . 638 April 2012 Amer. J. Agr. Econ.

Third, Hotelling’s lemma implies that the Second, Hotelling’s lemma implies: partial derivative of the proﬁt function with respect to the producer price of commodity l ∇2 π (0) =∇ (0) β(0) is the supply of commodity l. Hence, stacking (1A-11) WS (W ) WS XS(W , ), the L partial derivatives into an L × 1 vector yields the gradient of the proﬁt function, (0) (0) where ∇ S X (W , β ) is an L × L matrix which is equal to an L × 1 vector of commodity W S (0) (0) of partial derivatives of commodity demands supplies, commodity demands at (P , W ): with respect to commodity prices. Substituting (1A-10) and (1A-11) into (1A-9), the Hessian ∇ π (0) = (0) (1A-6) WS (W ) X . of the social welfare function becomes:

After substituting (1A-3)–(1A-6) into (1A-12) ∇2SW(·) (1A-2), the gradient of the social welfare ⎡ ⎤

2 Downloaded from ∇ g(·) − S(·) ∇ D S g(·) 00 PD P P becomes: ⎢ 2 ⎥ ⎢ ∇ S D g(·) ∇ g(·) 00⎥ = ⎢ P P PS ⎥ T T 2 . ⎣ 0 0 ∇ g(·) ∇W W g(·) ⎦ (0) (0) (0) WD D S (1A-7) ∇SW(P , W , u ) T T 2 0 0 ∇W W g(·) ∇W X(·) +∇ g(·) ⎡ ⎤ S D S WS (0) (0) (0) (0) ∇PD g(P , W , u ) − Q ⎢ (0) (0) (0) ⎥ ∇ S g(P , W , u ) http://ajae.oxfordjournals.org/ = ⎢ P ⎥ . The change in social welfare from a policy- ⎣ ∇ g(P(0), W(0), u(0)) ⎦ WD induced price change is found by substituting X(0) +∇ g(P(0), W(0), u(0)) WS (1A-7) and (1A-12) into (1A-2) and multiplying out the block matrices: The 2(N + L) × 2(N + L) Hessian of the social welfare function is: D T (0) (1A-13) SW ≈ P ∇PD g(·) − Q (1A-8) ∇2SW(·) S T ⎡ ⎤ + P ∇PS g(·) ∇2 · ∇ · D SW( ) PDPS SW( ) 00 P at University of California, Davis on May 16, 2012 ⎢ 2 ⎥ T (0) ⎢∇ S D SW(·) ∇ SW(·) 00⎥ + +∇ · = ⎢ P P PS ⎥ (WS) X WS g( ) T T 2 , ⎣ 0 0 ∇ SW(·) ∇W W SW(·)⎦ WD D S T T 2 T 0 0 ∇W W SW(·) ∇ SW(·) + (W ) ∇ g(·) S D WS D WD D T 2 + 0.5 P ∇ D g(·) − S(·) where 0 is a N × L matrix of zeros, ∇2 , P PD ∇2 ∇ ∇ × T S PDPS and PSPD denote the N N second- S D P + P ∇ S D g(·) P order partial derivatives of the social welfare P P function with respect to consumer and pro- + D T ∇ · ∇2 ∇2 ∇ 0.5 P PDPS g( ) ducer retail prices, and W , W WDWS and ∇ D ×S WSWD denote the vector of L L second- S T 2 S + P ∇ S g(·) P order partial derivatives of the social welfare P function with respect to buyer and seller com- T + 0.5 (WS) ∇W W g(·) modity prices.The Hessian of the social welfare S D function can be rewritten as: T 2 + (WD) ∇ g(·) WD WD ∇2 · T (1A-9) SW( ) + 0.5 (WS) (∇W X(·) ⎡ ⎤ S 2 2 ∇ g(·) −∇ e(·) ∇ D S g(·) 00 PD PD P P 2 ⎢ 2 ⎥ +∇ (·)) ⎢ ∇ S D g(·) ∇ g(·) 00⎥ W g = ⎢ P P PS ⎥ S T T 2 ⎣ 0 0 ∇ g(·) ∇W W g(·) ⎦ WD D S T T T 2 2 + ∇ · 0 0 ∇ g(·) ∇ π(·) +∇ g(·) (WD) WDWS g( ) WS. WS WD WS WS

Several substitutions can be made to simplify Letting IP and IQ be N × N identity matri- (1A-9). First, the Hessian of the expenditure ces with diagonal elements Pn(0)/Pn(0), ∀n = function with respect to consumer prices is the 1, ..., N, and Qn(0)/Qn(0), ∀n = 1, ..., N, N × N Slutsky matrix, S(P(0), u(0)): respectively, and IW and IX be L × L identity matrices with diagonal ele- 2 (0) (0) (0) (0) ∇ =∇ D (0) (0) (1A-10) PD e(P , u ) P h(P , u ) ∀ = ments, Wl /Wl , l 1, ..., L and = (0) (0) (0) (0) ∀ = S(P , u ). Xl /Xl , l 1, ..., L, respectively, (1A-13) Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 639 T can be rewritten as: + 0.5 (EWS) DW ∇W W g(·) S D T 2 + (EWD) DW ∇ g(·) DW EWD (1A-14) WD D T P (0) + T ε SW ≈ P I ∇ D (·) − Q 0.5 (EWS) DWX L EWS P T + T ∇2 · + S P∇ · 0.5 (EWS) DW W g( )DW P I PS g( ) S + T ∇ · + T (0) +∇ · (EWD) DW WDWS g( )DW EWS, (WS) IW X WS g( ) + T ∇ · P Q × (WD) IW WD g( ) where D and D are N N diagonal matri- n(0) ∀ = D T P 2 Q ces where the diagonal elements are P , n + ∇ (·) − (·) n(0) 0.5 P I PD g I S 1, ..., N and Q , ∀n = 1, ..., N, respectively, × T DW and DX are L L diagonal matrices + S P∇ · P D (0) Downloaded from P I PSPD g( ) I P where the diagonal elements are W , ∀l = l 1, ..., L and X (0), l = 1, ..., L, respectively, ηN∗ + D T P∇ · l 0.5 P I PDPS g( ) is an N × N matrix of Hicksian elasticities of demand for retail products and εL is an L × L + S T P∇2 · P S P I PS g( ) I P matrix of elasticities of supply of commodities. Using the Slutsky equation, (1A-15) can http://ajae.oxfordjournals.org/ + T ∇ · be modified as: 0.5 (WS) IW WSWD g( ) T 2 (1A-16) + (WD) IW ∇ g(·) IW WD T (0) WD SW ≈ (EWS) DW X T T + ∇ · + 0.5(EWS) DWX εLEWS (a) 0.5 (WS) IW IX WS X( ) −[(EPD)TDPQ(0) + 0.5(EPD)T (b) +∇2 g(·) WS × PQ ηN + ηN,M T D] D ( w )EP (c) at University of California, Davis on May 16, 2012 + (W )T I ∇ g(·) I W . D W WDWS W S + D T P∇ · + S T (EP ) D PD g( ) (EP ) (d) P × D ∇ S g(·)(e) When the identity matrices are multiplied P + D T P∇2 · P D through (1A-14), the vectors of price dif- 0.5(EP ) D PD g( )D EP (f) ferences are transformed into proportionate S T P 2 P S D S + 0.5(EP ) D ∇ g(·)D EP (g) changes in prices, EP , EP , EWD, and EWS PS and ∇ X(·) and S(·) are transformed into D T P P S WS + 0.5(EP ) D ∇ D S g(·)D EP (h) matrices of elasticities: P P + S T P∇ · P D 0.5(EP ) D PSPD g( )D EP (i) (1A-15) + (EW )TD ∇ g(·) + (EW )T (j) S W WS D D T P (0) ≈ ∇ D (·) − × ∇ · SW EP D P g Q DW WD g( ) (k) + S T P∇ · + 0.5(EW )TD ∇2 g(·)(l) EP D PS g( ) D W WD × + T (0) +∇ · DW EWD (m) (EWS) DW X WS g( ) T 2 T + 0.5(EW ) D ∇ g(·)(n) + ∇ · S W WS (EWD) DW WD g( ) × T DW EWS (o) − 0.5 EPD DPQη∗N EPD + 0.5(EW )TD ∇ g(·)(p) D W WDWS + D T P∇2 · P × 0.5 EP D PD g( )D DW EWS (q) + T ∇ · S T P P D 0.5(EWS) DW WSWD g( )(r) + EP D ∇PSPD g(·)D EP × D EW , (s) W D D T P + 0.5 EP D ∇PDPS g(·) N T where η is an N × N matrix of Marshal- + S P∇2 (·) P S EP D PS g D EP lian elasticities of demand for retail products 640 April 2012 Amer. J. Agr. Econ. with respect to retail price, ηN,M is an N × 1 (1A-21) vector of elasticities of demand with respect to N × S T P n Sn n(0) n(0) total expenditure, and w is an N 1 vector of (EP ) D ∇PS g(·) =− δ EP P Q , consumer budget shares. n Now we must find the first- and second- order partial derivatives of the government j where δj = 1 if t >0 , ∀j = 1, ..., N. revenue function with respect to all prices. 0 otherwise The government can generate revenue by tax- The second-order partial derivatives of the ing commodities, retail products, or both. The government revenue function are: government revenue generated from taxing J (M) retail product (commodity) markets is the (1A-22) sum of the differences between the producer 2 j k Sj ∂ g(P, W) ∂Q (·) ∂Q (·) (seller) price, P (WSj), and the consumer = +

Dj Dj Dk Dk Dj Downloaded from (buyer) price, P (WDj) times the correspond- ∂P ∂P ∂P ∂P j J ing quantity sold in the taxed market, Q (Xj): ∂2Ql + (PDl − PSl) , ∂PDj∂PDk (1A-17) l=1 J ∀ = = Dj − Sj j k, j 1, ..., J, g(P, W) (P P )Q http://ajae.oxfordjournals.org/ j=1 (1A-23) ∂2 ( ) ∂ j(·) ∂ k(·) M g P, W =− Q + Q Sj Sk Sk Sj + (WDm − WSm)Xm. ∂P ∂P ∂P ∂P m=1 J ∂2Ql + (PDl − PSl) , Sj Sk For brevity, we show the calculations for the = ∂P ∂P case of a retail tax policy but the effects of a l 1 commodity tax policy on government revenue ∀k, j = 1, ..., J, at University of California, Davis on May 16, 2012 are symmetric to those of a retail tax policy. (1A-24) The first-order partial derivatives of the gov- 2 j · k · ernment revenue function with respect to all ∂ g(P, W) = ∂Q ( ) − ∂Q ( ) the prices are: ∂PDj∂PSk ∂PSk ∂PDj J ∂2Ql (1A-18) + (PDl − PSl) , Dj Sk J l ∂P ∂P ∂g(P, W) ∂Q l=1 = Qj + (PDl − PSl) , ∂PDj ∂PDj ∀ = l=1 k, j 1, ..., J, ∀j = 1, ..., J, (1A-25) ∂2g(P, W) ∂Qj(·) ∂Qk(·) (1A-19) = − Sj Dk Dk Sj J l ∂P ∂P ∂P ∂P ∂g(P, W) j Dl Sl ∂Q =−Q + (P − P ) , J 2 l Sj Sj Dl Sl ∂ Q ∂P = ∂P + (P − P ) , l 1 Sj Dk = ∂P ∂P ∀j = 1, ..., J. l 1 ∀k, j = 1, ..., J. Note that when (1A-18)–(1A-19) are evalu- ( ) ated at P 0 ,the second term on the RHS is zero Again, note that when (1A-22)–(1A-25) ∇ · ( ) in both equations. Hence, substituting PD g( ) are evaluated at P 0 , the third term on the ∇ · and PS g( ) into (1A-16) and expressing the RHS is zero in these equations. Evaluat- results in summation notation yields the fol- ing (1A-22)–(1A-25)atP(0), and substituting lowing equations for the first-order effects of a ∇2 · ∇2 · ∇ · ∇ · PD g( ), PS g( ), PDPS g( ), and PSPD g( ) into retail tax policy on government revenue: lines (f) – (i) in (1A-16) gives (1A-20) N (1A-26) D T P n Dn n(0) n(0) (EP ) D ∇ D g(·) = δ EP P Q P D T P∇2 · P D n (EP ) D PD g( )D EP Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 641 N N N N Because EQn = ηnjEPDj, EQn = = 2 δjEPDjPj(0)Qj(0)ηjnEPDn, j j εnjEPSj, and tn = EPDn − EPSn, this equation n j can be more succinctly written as: (1A-27) N S T P 2 P S ∇ · ( ) ( ) (EP ) D PS g( )D EP (1A-31) g = tnQn 0 Pn 0 (1 + EQn). N N n =−2 δjEPSjPj(0)Qj(0)εjnEPSn, n j Symmetrically, the change in government revenue from a tax or subsidy policy on com- (1A-28) modities can be expressed as: D T P P S (EP ) D ∇PDPS g(·)D EP N N (1A-32) Downloaded from j Sj j(0) j(0) jn Dn L = δ EP P Q η EP (0) (0) g =− slX W n j l l l N N L j Dn n(0) n(0) nj Sn − δ EP P Q ε EP , − (0) (0) slXl Wl EXl. n j http://ajae.oxfordjournals.org/ l (1A-29) S T P P D In matrix notation, equations (1A-31) and (EP ) D ∇PSPD g(·)D EP (1A-32) can be rewritten as: N N j Sj j(0) j(0) jn Dn =− δ EP P Q η EP (1A-33) n j N T N T g = (t ) DPQ + (t ) DPQEQ, N N j Dn n(0) n(0) nj Sn (1A-34) + δ ε at University of California, Davis on May 16, 2012 EP P Q EP . T T g =−(sL) DW X − (sL) DWX EX, n j where D X and DPQ are L × 1 and N × 1 vec- After (1A-20), (1A-21) and (1A-26)– W tors of total expenditures on commodities and (1A-29) are substituted into lines (d)–(i) in products, respectively. (1A-16), noting that equations (1A-28) and (1A-29) cancel each other out, the change in government revenue from a retail tax policy can be expressed as: Technical Appendix: Derivation of Ad Valorem Taxes on Foods (1A-30) We derived ad valorem taxes for foods that g|tN > 0 would correspond to per unit taxes on their content of fat, calories, or sugar. First, we cal- D T P S T P = (EP ) D ∇PD g(·) + (EP ) D ∇PS g(·) culated the nutrient content of a pound of each food measured as calories, fat grams or sugar + D T P∇2 · P D 0.5(EP ) D PD g( )D EP grams per pound using one day of dietary recall S T P 2 P S data from the 2003-04 National Health and + 0.5(EP ) D ∇ S g(·)D EP P Nutrition Examination Survey (column (3) in N table A-1). The per unit tax per pound of each = δnQn(0)Pn(0)(EPDn − EPSn) food category is equal to the per unit tax per n calorie,gram of fat,or gram of sugar,multiplied N N by the fat,sugar,or calorie intensity of that food + δnQn(0)Pn(0)EPDn ηnjEPDj (column (4)) (i.e. calorie intensity is calories n j per pound of food consumed, and sugar and fat intensity are grams of sugar or fat per pound N N of food consumed). The average unit value for ( ) ( ) + δnQn 0 Pn 0 EPSn εnjEPSj. each food category in 2005 is calculated as per- n j sonal consumption expenditures per adult per 642 April 2012 Amer. J. Agr. Econ. day from the National Income and Product category consumed per day per adult (column Accounts (U.S. Department of Commerce, (6)). The ad valorem tax rate is the tax rate in Bureau of EconomicAnalysis 2010) divided by dollars per pound in column (4) divided by the the average number of pounds of food in that unit values in dollars per pound in column (6). Downloaded from http://ajae.oxfordjournals.org/ at University of California, Davis on May 16, 2012 Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 643 100 × l. )/( 6 ) 1.64 3.07 3.27 9.47 2.69 1.86 0.06 5.07 3.05 6.81 0.30 6.81 5.16 5.05 5.51 4.25 11.01 16.81 ( 4 percentage percentage = 7 ) U.S. Department of Commerce, a )( a ( 5 )/( 2 $/lb $/lb 2.05 2.10 1.46 0.95 1.13 6.68 1.13 6.68 0.29 2.94 2.91 2.05 2.91 2.91 2.94 1.46 2.10 0.29 = ( 6 ) Downloaded from $ 0.000165 Tax Per Calorie $ 0.005 Tax per Gram of Fat (5) 1.22 3.11 0.63 0.05 0.99 0.39 0.05 0.99 0.58 1.18 0.85 1.22 0.85 0.85 1.18 0.63 3.11 0.58 $/day $/day = = t t http://ajae.oxfordjournals.org/ $ 0.002688 Tax per Gram of Sugar = t ( 3 ) × t $/lb $/lb 0.03 0.06 0.05 0.12 0.09 0.02 0.18 0.00 0.01 0.09 0.20 0.01 0.20 0.15 0.15 0.08 0.09 0.05 = ) 4 at University of California, Davis on May 16, 2012 )( 7.84 1.47 2.31 ( 1 )/( 2 24.00 33.63 87.68 33.31 55.94 29.94 17.83 203.87 289.01 753.98 899.04 540.91 = kcal/lb 1090.80 1202.45 1202.45 grams/lb ( 3 ) $ 0.0001632 tax per calorie). Hence, the ad valorem taxes for each food product for the case of endogenous commodity prices are slightly different as wel = t (2) 0.60 1.48 0.43 0.05 0.41 0.05 0.15 0.15 2.04 0.40 0.29 0.60 0.29 0.29 0.40 0.43 1.48 2.04 lbs/day 0.36 0.22 1.38 (1) 35.55 34.24 13.80 13.43 16.37 12.88 36.29 122.05 124.36 162.20 178.48 351.94 351.94 362.33 801.13 kcal/day $ 0.002637 tax per gram sugar and grams/day lbs/day grams/lb $/lb $/day $/lb percentage grams/day lbs/day = Sugar/Calories Foods Intensity of Food Pound of Food Food (2002$) Value of Food Tax Sources of Fat/ Weight of Fat/Sugar/Calorie Per Unit Tax Per Expenditure on Average Unit Ad Valorem t ). : Based on one-day dietary recall data from the 2003-04 NHANES (Centers for Disease Control and Prevention, National Center for Health Statistics 2007) and 2002 Personal Consumption Expenditures ( These tax rates reflect the assumption of exogenous commodity prices and are constructed to achieve approximately the same caloric reduction as the $0.005 tax per gram fat. The tax rates on sugar and calories for the case of endogenous Cereals & bakeryMeatEggsDairyFruits & vegetablesOther foodNonalcoholic drinks 9.38FAFH 18.25 35.18 9.85 0.29 2.47 2.41 1.10 0.40 1.48 0.01 0.15 0.05 32.05 0.43 2.04 45.28 0.60 23.75 66.22 54.33 0.16 5.61 0.54 0.23 0.01 0.12 0.33 0.27 0.03 0.85 0.00 1.18 0.00 3.11 0.99 0.05 2.91 0.63 0.58 2.94 1.22 2.10 6.68 1.13 5.50 1.46 0.29 7.70 2.05 5.66 4.95 24.04 1.92 0.94 0.0035 Bureau of Economic Analysis 2010 Nonalcoholic drinks FAFH FAFH Other food Fruits & vegetables Nonalcoholic drinks Other food Fruits & vegetables Dairy Eggs Dairy Eggs Cereals & bakery Meat Cereals & bakery Meat commodity prices differ slightly (i.e. Note a Table A-1. Derivations of Ad Valorem Taxes on Food Based on a Per Unit Tax Per Gram of Fat, Per Gram of Sugar, and Per Calorie Alcohol drinks 9.38 0.29 32.05 0.16 0.85 2.91 5.50 Alcohol drinks Alcohol drinks 644 April 2012 Amer. J. Agr. Econ.

Table A-2a. Sensitivity of Net Social Cost to Doubling of Tax Rates Annual Change in SW Probability Social Welfare Annual Including that SW (SW) Excluding Change in Change in Including Changes in Public Public Health Public Health Public Health Heath-Care Costs Care Costs Care Costs Care Costs > 0 Millions of dollars εLower Fat tax (t = 0.10 per gram −6,872 −6,790 −83 0.45 of fat) (741) (1,426) (1,059) Calorie tax (t = 0.000326 −4,623 −6,791 2,167 0.99 per calorie) (457) (1,206) (950)

Sugar tax (t = 0.005274 −4,813 −6,784 1,971 0.96 Downloaded from per gram of sugar) (559) (1,502) (1,141) Uniform food tax −5,817 −6,839 1,022 0.83 (t = 9.946 percent) (600) (1,308) (1,034)

εUpper

Fat tax (t = 0.10 per gram −7,308 −7,040 −267 0.40 http://ajae.oxfordjournals.org/ of fat) (823) (1,517) (1,094) Calorie tax (t = 0.000326 −4,846 −7,001 2,156 0.99 per calorie) (504) (1,271) (975) Sugar tax (t = 0.005274 −5,021 −6,955 1,934 0.96 per gram of sugar) (615) (1,578) (1,164) Uniform food tax −6,101 −7,051 950 0.81 (t = 9.946 percent) (657) (1,370) (1,056) ε =∞ at University of California, Davis on May 16, 2012 Fat tax (t = 0.10 per gram −7,751 −7,224 −527 0.32 of fat) (940) (1,608) (1,125) Calorie tax (t = 0.00033 −5,039 −7,132 2,093 0.99 per calorie) (561) (1,324) (989) Sugar tax (t = 0.005376 −5,221 −7,076 1,856 0.95 per gram of sugar) (679) (1,643) (1,177) Uniform food tax −6,349 −7,175 827 0.78 (t = 10.06 percent) (731) (1,418) (1,068)

Note: Authors’ calculations based on doubling the tax rates in Table A-1. See Table 12a and 12b for more details. Okrent and Alston The Effects of Farm Commodity and Retail Food Policies 645

Table A-2b. Sensitivity of Net Social Cost to Halving of Tax Rates Annual Change in SW Probability Social Welfare Annual Including that SW (SW) Excluding Change in Change in Including Changes in Public Public Health Public Health Public Health Health Care Costs Care Costs Care Costs Care Costs > 0 Millions of dollars εLower Fat tax (t = 0.025 per gram −430 −1,697 1,268 1.00 of fat) (46) (357) (326) Calorie tax (t = 0.0000816 −289 −1,698 1,409 1.00 per calorie) (29) (302) (283)

Sugar tax (t = 0.0013185 per −301 −1,696 1,395 1.00 Downloaded from gram of sugar) (35) (375) (350) Uniform food tax −365 −1,713 1,348 1.00 (t = 2.4865 percent) (38) (328) (305)

εUpper

Fat tax (t = 0.025 per gram −457 −1,760 1,303 1.00 http://ajae.oxfordjournals.org/ of fat) (51) (379) (344) Calorie tax (t = 0.0000816 −303 −1,750 1,447 1.00 per calorie) (32) (318) (296) Sugar tax (t = 0.0013185 per −314 −1,739 1,425 1.00 gram of sugar) (38) (394) (365) Uniform food tax −383 −1,766 1,383 1.00 (t = 2.4865 percent) (41) (343) (317) ε =∞ at University of California, Davis on May 16, 2012 Fat tax (t = 0.025 per gram −485 −1,806 1,321 1.00 of fat) (59) (402) (361) Calorie tax (t = 0.0000825 −315 −1,783 1,468 1.00 per calorie) (35) (331) (306) Sugar tax (t = 0.001344 per −327 −1,770 1,443 1.00 gram of sugar) (42) (411) (378) Uniform food tax (t = 2.515 −398 −1,797 1,399 1.00 percent) (46) (355) (326)

Note: Authors’ calculations based on halving the tax rates in table A-1. See table 12a and 12b for more details. 646 April 2012 Amer. J. Agr. Econ.

Table A-3. Annual Cost per Pound Change in Body Weight for Various Tax Rates Excluding Changes in Public Health Including Changes in Public Health Care Costs Care Costs t∗ = 1/2 × tt t∗ = 2 × tt∗ = 1/2 × tt t∗ = 2 × t Dollars per pound εLower Calorie tax 0.45 0.90 1.81 −2.21 −1.77 −0.85 Sugar tax 0.47 0.93 1.89 −2.19 −1.73 −0.77 Uniform tax 0.57 1.12 2.26 −2.09 −1.54 −0.40 Fat tax 0.67 1.34 2.69 −1.99 −1.31 0.03 εUpper Calorie tax 0.46 0.91 1.84 −2.20 −1.74 −0.82

Sugar tax 0.48 0.94 1.92 −2.18 −1.71 −0.74 Downloaded from Uniform tax 0.58 1.13 2.30 −2.08 −1.53 −0.36 Fat tax 0.69 1.38 2.76 −1.97 −1.28 0.10 ε =∞ Calorie tax 0.47 0.86 1.88 −2.19 −1.79 −0.78 Sugar tax 0.49 0.98 1.96 −2.17 −1.37 −0.70

Uniform tax 0.59 1.17 2.35 −2.07 −1.28 −0.31 http://ajae.oxfordjournals.org/ Fat tax 0.72 1.42 2.85 −1.95 −1.23 0.19

Note: Authors’ calculations based on doubling and halving the tax rates in table A-1. Estimates evaluated at the posterior means of data. at University of California, Davis on May 16, 2012