Three essays on consumer choices on food

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1 Graduate Theses and Dissertations Graduate College 2014 Three essays on onsumer hoies on ood Miyoung Oh Iowa State University Follow this and additional works at: Part o the Eonomis Commons Reommended Citation Oh, Miyoung, "Three essays on onsumer hoies on ood" (2014). Graduate Theses and Dissertations This Dissertation is brought to you or ree and open aess by the Graduate College at Iowa State University Digital Repository. It has been aepted or inlusion in Graduate Theses and Dissertations by an authorized administrator o Iowa State University Digital Repository. For more inormation, please ontat digirep@iastate.edu.

2 Three essays on onsumer hoies on ood by Miyoung Oh A dissertation submitted to the graduate aulty in partial ulillment o the requirements or the degree o DOCTOR OF PHILOSOPHY Major: Eonomis Program o Study Committee: Helen H. Jensen, Major Proessor David A. Hennessy Aliia L. Carriquiry John C. Beghin Brent Kreider Iowa State University Ames, Iowa 2014 Copyright Miyoung Oh, All rights reserved.

3 ii TABLES OF CONTENTS LIST OF TABLES... LIST OF FIGURES... GENERAL ABSTRACT.... iv vi vii CHAPTER 1. GENERAL INTRODUCTION Introdution Organization o the Dissertation... 6 CHAPTER 2. DYNAMIC FOOD DEMAND AND HABIT FORMING BEHAVIORS: BAYESIAN APPROACH TO A DYNAMIC TOBIT PANEL DATA MODEL WITH UNOBSERVED HETEROGENEITY Introdution... 8 Habit Formation... 8 Empirial hallenge: Censoring Empirial Model Estimation Sampling Density and Priors Gibbs Sampling rom the Posterior Data Results Conlusions REFERENCES CHAPTER 3. IMPACT OF WIC PROGRAM PARTICIPATION ON FOOD EXPENDITURES Introdution Bakground Empirial Methodology Treatment Eet... 42

4 iii Propensity Sore: Program partiipation model Mathing Proedure Data Identiiation o WIC Partiipation Identiiation o WIC Related Food Expenditures Results Conlusion REFERENCES APPENDIX A. ADDITIONAL MATERIAL FOR CHAPTER CHAPTER 4. UPSTREAM AND DOWNSTREAM STRATEGIC FOOD SAFETY INTERACTIONS Introdution Model setup First best outomes Weakest Link Best Shot Bakward Indution Stage II: when irm moves irst Stage I Simultaneous Moves Disussion REFERENCES APPENDIX B. ADDITIONAL MATERIAL FOR CHAPTER CHAPTER 5. GENERAL CONCLUSIONS ACKNOWLEDGEMENTS

5 iv LIST OF TABLES Table 2.1 Dairy Produt Categories and Distribution Table 2.2 Distributions o Monthly Average Quantities and Pries Table 2.3 Deinitions and Statistis on the Variables Table 2.4 Bayesian Dynami Tobit Estimation or eah Dairy Group s Demand Table 2.5 Bayesian Dynami Tobit Estimation or Milk Demand by Dierent Inome Group Table 2.6 Elastiities o Dairy Produt Demands Table 2.7 Elastiities o Milk Demand by Dierent Inome Group Table 3.1 Distributions o WIC reporting Households in Homesan Data Table 3.2 WIC Eligible and Non-eligible Households in WIC Households Table 3.3 WIC Reporting Households in Eligible Households Table 3.4 WIC Reporting Households in Eligible Households with Grain Purhases in Three Conseutive Years Table 3.5 Deinitions and Statistis on the Variables Table 3.6 Summary Statistis on Monthly Average Grain Expenditures Table 3.7 Program Partiipation Model Table 3.8 Balaning Test Table 3.9 Treatment Eets o WIC Partiipation on Whole Grain Expenditures Table 3.10 WIC reporting HHs in eligible HHs with Subsample Table 3.11 WIC Reporting Households in Eligible Households with Grain Purhases in Three Conseutive Years with Subsample... 74

6 v Table 3.12 Treatment Eets o WIC Partiipation on Whole Grain Expenditures with Subsample Appendix 3.1 Distribution o WIC Households with Any Food Purhases in Three years Appendix 3.2 Distribution o WIC Households with Three-year Grain Purhases Appendix 3.3 Poliy implementation dates... 79

7 vi LIST OF FIGURES Figure 3.1 Distribution o the Estimated Propensity Sores Figure 4.2 Firm s eort under weakest link tehnology and strit liability, as inentives Change Figure 4.3 Consumer s private optimality ondition as irm eort hanges

8 vii GENERAL ABSTRACT The dissertation investigates how onsumer hoies on ood are aeted by habit orming behaviors o onsumers, publi poliy and the unertainty o the risk rom ood saety hazards and strategi interation with ood proessors. Three stand-alone analyses on onsumer hoie onsist o empirial rameworks to estimate parameters o dynami demand, the treatment eets on program partiipation, and an analytial approah to modeling downstream onsumer s and upstream irm s handling o ood saety risk. The irst analysis ouses on dynamis in household demand. Inorporating dynamis suh as habit ormation in analysis o ood demand an make estimation more reliable and help to explain the stikiness in onsumer demand behavior. Capturing this response is important or evaluating onsumers response to new inormation about produts whether nutrition, ood saety or other event. Sanner data allow many repeated observations o the same household so are ideal or analyzing the impat o habit on ood demand. In addition to that, sanner data allow us to easily observe the presene o zero purhases. The presene o zero purhases is an important eonometri issue in empirial modeling on ood demand in the sense that ignoring the ensoring issue an lead to biased estimation results. The irst study investigates the impat o state dependene on dairy ood demand using 2009 and 2010 Nielsen HomeSan data. In this analysis, we take into aount the ensored nature o ood expenditure data and employ a Bayesian proedure to estimate the dynami demand models on dairy produts. By ontrolling the individual heterogeneity in the model the soure o endogeneity or the lagged dependent variable is removed. The empirial evidene o habitual behaviors partiularly in milk demand provides support or onsidering a model with dynamis in a study o ood demand.

9 viii The seond analysis examines the relationship between The Speial Supplemental Nutrition Program or Women, Inants, and Children (WIC) partiipation and purhases o WIC related oods during the period shortly ater introdution o hanges in the WIC pakage. We use Nielsen Homesan data 2008 to 2010to assess how partiipation in the WIC program relates to ood expenditures by WIC eligible households. The researh inludes analysis o selet ood purhases by WIC eligible households both o those reporting partiipation in the WIC program and those not partiipating in the program. In our analysis, we onentrate our attention on seleted whole grain oods in the WIC ood pakage as these oods are prominent in the revised WIC ood pakage and grain produts are purhased by most households. A propensity sore mathing estimator was used or estimating treatment eets and dierene-in-dierene method was onduted to ontrol the poliy hange in the 2009 WIC pakage revision. The study ontributes to urrent literature on WIC to onirm that the WIC pakage hange in 2009 had a signiiant inluene on WIC partiipating households to enourage greater whole grain expenditures relative to non-partiipating households. The third analysis onerns the unertainty o the risk rom ood saety hazards and strategi interation with ood proessors. Domesti water onsumers in many developing ountries that boil water beore use are presumably onerned about quality ontrol on the part o upstream water authorities. In this third analysis, we investigate strategi inentives or ood saety eorts by upstream ood proessors and downstream onsumers. The strategi setting is where ood proessors move irst and onsumers reat to pereptions about proessor behavior. We onsider two tehnologial environments in whih ood saety is assured: i) weakest-link where both proessor and onsumer behavior must sueed; ii)

10 ix best-shot where it suies or eorts by either party to sueed. We study privately optimal behavior under negligene and strit liability rules, and also investigate the role o onsumer risk aversion.

11 1 CHAPTER 1. GENERAL INTRODUCTION 1. Introdution Both publi health workers as well as poliymakers are onerned about the prevalene o obesity and other health problems assoiated with unhealthy dietary behaviors o onsumers as well as the potential risk o ood related illnesses. These health issues are substantially related to onsumers hoies about ood -- rom the deision making o onsumers over ood purhases to ood handling praties. The hoies and poliies related to the onsumer hoies have beome a onern or all: government, agriultural industries and onsumers. Thus, taking a loser look in the onsumer s ood related hoies may be the starting point to approah these publi health issues. The main objetive o this dissertation is to explore the various ators that an inluene onsumer s deision-making related to ood, to examine the eonomi impats o those ators on onsumers ood purhases and ood praties and ind the poliy impliations assoiated eah analysis. Eating patterns and hoies are important in prevention o health problems and improving health status. Many o the hoies an be explained by investigating market demand or ood. Analysis o demand is o onsiderable interest not only or understanding onsumer s ood hoies but also or inorming publi poliies under onsideration. The irst topi o this dissertation, presented in Chapter 2, explores how habitual behaviors related to ood purhases ontribute to the onsumer s responses to the ood pries in ood demand. We onsider a demand model with dynamis to examine the assoiation between past and urrent purhases o ood as it is supported rom the empirial evidene o habitual behaviors in

12 2 demand. Nielsen 2009 and 2010 HomeSan data are used in the estimation proess o the dynami ood demand and seleted ood groups are dairy produts. In analysis o household level data, one o the main empirial hallenges is the presene o zero purhases. Generally, households do not purhase or onsume all goods available in the market in the time period observed, and this is oten true or ood produts. Ignoring the ensoring issue on ood onsumption data an lead to biased estimation results. Also aounting or dynami aspets that arise rom habit ormation among other reasons an also make the demand analysis more reliable. In this hapter, we take into aount the ensored nature o ood expenditure data. The ensoring arises when households do not purhase or onsume all goods available in the market in the time period observed. This leads to ensoring o the dependent variable in the estimation o demand or onsumption equations. We also ontrol or unobserved household heterogeneity to estimate dynami demand or dairy produts. Unobserved individual heterogeneity arises when estimating the eet o habit. By aounting or unobserved heterogeneity in miro data, we an avoid overestimation o the underlying habit ormation. For estimating dynami ood demand, the hapter uses the dynami Tobit panel model with unobserved household heterogeneity. The estimation results show that habit-orming eets on dairy demands exist onditional on unobserved household heterogeneity. In partiular, the empirial evidene on milk expenditure shows the largest habit orming eet in milk demand. Consumer hoies on ood purhases are inluened by also publi poliies through partiipation in ood assistane programs. The Speial Supplemental Nutrition Program or Women, Inants, and Children (WIC) is one o the largest ood assistant programs in the

13 3 United States and is designed to enhane the oods eaten by target, at risk women, inants and young hildren. The program provides healthy ood (WIC pakage ood), nutrition ounseling, and aess to health servies or low-inome inants, hildren up to age ive, and pregnant, breasteeding, and postpartum women or improving health o people at nutritional risk. The seond topi o this dissertation, presented in Chapter 3, addresses how partiipating in the WIC program aets household ood purhases. We use sanner data in the analysis. Investigating the eet o partiipating in the WIC program on ood hoies is an important aspet to understanding the role o the WIC in assuring improved long run health outomes among program partiipants. As the WIC program aims to improve healthy eating behaviors o target people, the analysis o onsumption patterns o WIC partiipants allows us to see whether the program leads to improved healthy ood purhases. And this would be one way to measure the eetiveness o the program. There are relatively ew reent studies about WIC eets on ood onsumption. Other studies have examined the impats o WIC on health status and dietary onditions o the target population. Existing literature on the WIC program inds that household deisions are important in evaluating the use o WIC provided oods, and suggests that there is a need or inormation about overall WIC household hoies, expenditures and behaviors. In this sense, this paper ontributes by providing an analysis o the impat o the WIC program on household ood expenditures. The hapter inludes: (1) analysis o the reliability o the WIC partiipation variable; (2) identiiation o subgroups o survey households by WIC inome eligibility riteria and type o WIC individuals in the household; and (3) a omparison o selet ood purhases between eligible WIC reporting and eligible WIC not-reporting

14 4 households. The empirial analysis o ood expenditures or WIC partiipating households is onduted by omparing the WIC partiipating households to eligible, non-partiipating households. We use a propensity sore mathing estimator to estimate the treatment eets on whole grain expenditures and the dierene-in-dierene method to ontrol the poliy hange in the 2009 WIC pakage revision. The 2009 hange in WIC pakage made a number o hanges to the paking and inluded whole grain produts. The results show that there was a signiiant impat o WIC partiipation on whole grain expenditure over three onseutive years and the WIC pakage hange implemented in Otober 2009 was positively assoiated with this treatment eets in the year ollowing its implementation. Addressing the problem o the existene o ood related risk presents another important ator that inluenes on onsumers deision making related to ood. The risk o oodborne illnesses an be redued by onsumers pratie toward ood saety based upon how the onsumers pereive the risk. The deision on ood saety eorts an be made together with ood hoies beore onsumers purhase ood or onsidered as a separate deision ater ood hoies had been made. In either way, onsumers protetion inentives are heavily related to the ood saety eorts by upstream ood proessors. Modeling the deision-making proess o onsumers on ood saety has not reeived muh attention in the literature. The objetive o the third topi o this dissertation, Chapter 4, is to examine how the interation between downstream onsumers and upstream irms inluenes the onsumer s inentives to exert eort to redue ood saety risk, and to identiy how poliy rules may aet the interation. Eonomi analysis through modeling o the onsumers protetion

15 5 inentives on the risk o ood-borne illnesses addresses an important option or ood saety ontrol and an provide a rigorous theoretial oundation or poliy impliations. In Chapter 4, we onstrut a Stakelberg model with asymmetri timing in moves, allowing the upstream agents to move irst and onsumers make deisions later as seondmovers. Our analysis is distint rom earlier work by allowing sel-protetive inentive to redue the probability o a loss as we diretly apply risk aversion on the onsumer s part. The unertainty that is an essential eature o ood saety events has impliations or onsumer behavior. Finally the timing and risk aversion dimensions in our model give us the opportunity or poliy analyses not available in earlier works. In our analysis, we ontrast ood saety inentives and outomes aross two dimensions, tehnology and liability assignment. Food saety eort by eah party an be either a suess or a ailure based on the assumption o statistial independene between the suess probabilities. Two very dierent tehnologies between eort outomes and ood saety outomes are onsidered: weakest link and best shot. In the weakest link, i one or both o two ations ails then the outome is a ailure, i.e., a ood saety event ours. In best shot i either or both o the ations is a suess then the ood is sae. We examine how the sort o tehnial interation between upstream and downstream eorts aets the behavior strategies in response to ood saety risk. In the seond ontrast set orth under dierent liability rules, two liability rules are onsidered: strit liability and negligene in a bilateral aident setting. Thus, the inentives under our settings (weakest link, best shot) (strit liability, negligene) are developed. By bakward indution, we solve the expeted utility maximization problem or a downstream onsumer in Stage II and or the upstream proessor s Stage I ost minimization

16 6 problem to obtain the optimal levels o preventative eort. Ater solving or the Stakelberg equilibrium in eah ase, we provide omparative statis to asertain strategi interations between both eorts as well as how onsumer risk aversion aets eah eort type. The indings show that the strategi interations under dierent tehnologies, the onsumer reats dierently to an inrease in proessor ood saety eort. Several o our indings might be viewed as ounterintuitive and these stem partly rom the sel-protetive nature o ood saety eorts. 2. Organization o the dissertation This dissertation provides the eonomi analysis on onsumers deision making over ood purhases and praties when they ae internal and external ators that aet their hoies. While eah o these hapters an be a stand-alone study, they are all dediated to an investigation o onsumer hoie on ood. A brie overview o the remainder o this dissertation is outlined as ollows: Chapter 2 examines the eets o habit-orming behaviors on demand or dairy produts by inorporating dynami aspets in the demand equations. Chapter 3 onduts the estimation or the treatment eet o the WIC program to investigate the relationship between WIC program partiipation and purhases o WIC related oods. The period investigated inludes the period shortly ater introdution o hanges in the WIC pakage. Chapter 4 develops a Stakelberg model with sel-protetion motives to examine the interation among downstream onsumers and upstream irms in the presene o unertainty o ood saety risk, and explores how the ood saety inentives and outomes aross

17 7 dierent dimensions o tehnology and liability rules are determined in a strategi model setting. Chapter 5 highlights the indings and impliations o the three investigations addressed in this dissertation and outlines uture diretions.

18 8 CHAPTER 2. DYNAMIC FOOD DEMAND AND HABIT FORMAING BEHAVIORS: BAYESIAN APPROACH TO A DYNAMIC TOBIT PANEL DATA MODEL WITH UNOBSERVED HETEROGENEITY 1 1. Introdution Habit ormation Eating behaviors and habits ontribute to health outomes and thus understanding ators assoiated with eating hoies is important to eorts to protet and improve health status. Food habits are also important in explaining observed stikiness in ood demand when onsumers reeive new inormation about ood saety and risk. Food hoies an be explained, in large part, by investigating market demand or ood. The empirial evidene o habitual behaviors in demand provides support or onsidering a model with dynamis in a study o the ood demand. Following Pollak (1970), habit orming goods are deined as goods assoiated with preerenes or whih urrent onsumption behavior relies on the past onsumption experiene. Thereore, lagged dependent variables are used to show how habit ormation inluenes the demand. A number o empirial studies in ood demand have analyzed habit ormation using maro and miro level panel data. Habit orming behaviors are ound in various ategories o ood produts inluding produts suh as beverages, meats, ereal, heese, kethup and snaks, as well as ood at home, ood away rom home and aggregate ood (Zhen et al, 2010; Wohlgenant and Zhen, 2006; Thunström, 2009; Arnade et al., 2008; Seetharaman, 2004; Rihards et al., 2007; Heien and Durham, 1991; Naik and Moore, 1996). Although ood 1 An earlier version was prepared and presented as a Seleted Paper at the Agriultural & Applied Eonomis Assoiation s 2013 AAEA & CAES Joint Annual Meeting, Washington, DC, August 4-6, 2013.

19 9 demand models generally exhibit habit ormation, the evidene o habit ormation varies over empirial methods used (Dauneldt et al., 2011). For example, Naik and Moore (1996) use a single demand untions model and show habit ormation in individual ood onsumption using aggregated ood onsumption o household panel data. In ontrast, Dynan (2000) uses a lie-yle onsumption model and inds no evidene o habit ormation using the same data set. And, Browning and Collado (2007) ind habit ormation or onsumption o ood outside the home while there is no state dependene or ood at home. Other important example is ound in studies o non-aloholi beverages. Zhen et al. (2011) examine state dependene over beverage demand and ind strong evidene or habit ormation. As an alternative to the traditional state dependene approah, reent work o Adamowiz and Swait (2012) evaluates a oneptual ramework o deision strategy whih would minimize ognitive eort using panel data. They ind signiiant evidene o a habitual deision strategy partiularly in the ase o atsup whih has a relatively longer inter-purhase period while they ind evidene o variety-seeking preerene in the ase o yogurt. Controlling or the unobserved individual heterogeneity is one distint issue that arises when estimating the eet o habit. Oten, the literature on habit ormation is onerned with possible soures o persistene in onsumer s behavior and addresses whether the assoiation between urrent and past onsumption relets state dependene or individual heterogeneity (Naik and Moore, 1996; Carraso et al., 2005: Browning and Collado, 2007). Failure to ontrol or unobserved heterogeneity in miro data may lead to overestimation o the underlying habit ormation. In order to distinguish between heterogeneity among individuals and the eet o habit, researhers have estimated models

20 10 that inlude ixed eets to explain the time invariant unobserved heterogeneity aross households and provide a strong tool or testing the habit ormation hypothesis. Naik and Moore (1996) onlude that ontrolling or heterogeneity redues estimated habit eets; the importane o aounting or time invariant unobserved individual eets has been shown in Carraso et al. (2005). Most o the literature reerened above on habit ormation employs dynami linear panel data models to estimate dynami demand. In the linear models with unobserved individual eets, the unobserved eets an be eliminated by using an appropriate transormation suh as dierening; instrumental variables (IV) an be implemented to estimate the transormed model in a generalized method o moments (GMM) ramework. To date, signiiant progress has been ahieved in estimating unbiased and onsistent estimators and improving the eiieny o the estimators (Anderson and Hsiao, 1982; Arellano and Bond, 1991; Arellano and Bover, 1995; Baltagi, 1995; Bond and Hahn, 1999; Arellano and Honore, 2001; Hsiao, 2003). Empirial hallenges: Censoring Generally, households do not purhase or onsume all goods available in the market in the time period observed. It is a well-known eonometri issue in mirodata based on surveys o household expenditures that households do not purhase all goods available but only some o them in the observed time period. This leads to ensoring o the dependent variable in the estimation o demand or onsumption equations. While this zero onsumption issue an be represented as a orner solution in utility maximization (Perali and Chavas, 2000), we an also ind various reasons or a household to make a deision to purhase none o the good (zero purhases). For example, people may simply avoid ertain produts or, i

21 11 they do make purhases, do so inrequently aording to their liestyles. Alternatively, the deision related to inrequent purhases whih are observed as zero purhases in a given period o time, may be related to the apaity o storing produts and use o inventories. Other non-purhase deisions may be assoiated with ators related to inormation about the saety o produts or the dietary environment. This type o response would our as a hange in behavior rom the previous responses. With any possible reason, i there is a signiiant ration o the zero observations in the dependent variable, analysis that uses a onventional regression approah may lead to inappropriate biased and inonsistent estimators. In order to deal with ensored data, several approahes to demand systems have been taken in the eonometri literature and inlude the Kuhn-Tuker model, Amemiya-Tobin model, Hekman s two-step method and a Bayesian approah (Wales and Woodland, 1983; Lee and Pitt, 1986; Tobin, 1958; Amemiya, 1974; Heien and Wessells, 1990; Shonkwiler and Yen, 1999; Tiin and Arnoult, 2010; Ishdorj and Jensen, 2010; Kasteridis et al., 2011). For estimating dynami ood demand, this paper uses the dynami Tobit panel model with unobserved individual heterogeneity. The non-linear nature o treating ensored panel data makes the estimation even more diiult along with some omplexity that arises rom the two main eatures o the dynami panel data model: the individual speii eets and lagged dependent variables. The literature on nonlinear panel models, partiularly in the ase o ensored regression, has been developed to overome the diiulties o dierening away the unobserved eets and dealing with initial onditions (Honore, 1993; Hu, 2002, Hsiao, 2003; Honore and Hu, 2004; Wooldridge, 2005; Li and Zheng, 2008). In this paper, we apply the Bayesian approah to estimate a dynami ensored dairy ood demand. We seleted the dairy and eggs ood group beause most households purhase

22 12 some o these produts and it is a setor o interest in ood and health programs. In miro panel data, the pairs o observations orresponding to a given individual are likely to be orrelated and individual speii eet are introdued in the models to aount or this at. The orm o the orretly speiied likelihood untion might be omplex and this leads to omputational diiulties. The Bayesian approah inerene rom the parameters posterior distribution onditioned on the observations -- is our alternative to maximum likelihood estimation as it oers omputational onveniene through the simulation methods. One o the standard Markov Chain Monte Carlo (MCMC) algorithms that an be easily applied to high dimensional problems is the Gibbs sampler. This method is used in the iteration proedure or sampling the parameters rom the onditional posterior distributions. The main ontribution o this paper is to estimate a dynami demand model by using a Bayesian approah, aounting or ensored data. We apply the estimation proedures to the dairy group, a group that has relatively well deined produts. Gibbs sampling is onduted to deal with the ensored data. 2. Empirial Model The dynami single demand equations are estimated as a dynami Tobit panel data model. Following methods used in related studies, we onsider a dynami unobserved eets Tobit model in the orm y iht max[ 0, ziht g( yih t1) u ], i 1,..., n, h 1,..., H,, ih iht t 1,..., T (1) u y y z iid 2 iht ih, t 1,..., ih,0, ih, ih ~ Normal(0, iu ) where yiht is the ensored response variable o interest on the i th good by the th h household in time period t whih depends on the explanatory variables z iht, the lags o the dependent

23 13 variable y iht1 and the unobserved individual heterogeneity ih (Hu, 2002; Wooldridge, 2005; Li and Zheng, 2008). As Hekman (1981) notes, in order to interpret observed persistene in onsumption as the habit eet orresponding to the ase o true state dependene, we allow the interept in equation (1) to vary aross households to ontrol or omitted ators. ( * y, ih0 We assume that the error terms, u iht, are i.i.d. normally distributed onditional on T { iht} t 1 z, ih ) and not serially orrelated in the model. By aounting or the unobserved individual eets and the assumptions on error terms, the model exhibits strit exogeneity on z iht. In other words, the possible dynami eedbak rom realizations zih on past and uture time periods to the urrent realizations o the dependent variables is removed in the model so that the dynami nature o the model is only rom the presene o the lagged dependent variables (Hu, 2002). The model in equation (1) is well suited to orner solution appliations, however the model with lagged ensored dependent variable is not appliable or data ensoring appliations (Wooldridge, 2002; 2005). As we are to aount or a data ensoring ase, the lagged latent dependent variable will be plaed in the untion g () as was done in Hu (2002) and we speiy the model in the urrent paper as ollows: y * iht z * iht y ih u ih, iht (2) t1 where y * iht represents the latent quantities o produt i purhased by household h in t th month, * y ih, t is the lagged latent quantities o produt i purhased by household h in ( t 1) th 1 month and ziht represents the vetor o ovariates o interest: a set o own and ross pries, set o demographi variables along with total expenditures over all ood ategories(ood at home) and seasonal eets.

24 14 As the unobserved individual heterogeneity ih is a nuisane parameter, speiying the distribution o ih and its relationship with ziht is needed to omplete the model setup. We ollow the speiiation o the relationship between the individual eets and the initial onditions in Li and Zheng (2008). Li and Zheng make an assumption o the ollowing onditional mean dependene o the ih on the initial onditions and observed stritly exogenous variables E[ ih yih 0, zih ] a h( yih, 0, z ) (3), ih where a is a onstant, h() is a untion o the vetor o initial values o the dependent variable y ih0 and a matrix o time-invariant ovariates z ih whih only vary over dierent households and is a vetor o orresponding parameters. 2 An independent relationship between yih, 0 and zih is assumed. We set zih zih where ih z is the average o ziht over the entire time path as in Chib and Jeliazkov(2006). 3 Following the speiiation o h( y, z ) y z in Li and Zheng (2008), we rewrite (3) as ih0 ih ih0 1 ih 2 ih yih, 01 zih 2 ih, y (4) iid 2 ih ih0, zih ~ Normal (0, i ) where ih is an error term in the auxiliary equation. 4 This speiiation o the unobserved individual heterogeneity allows its linear orrelation with the initial observations o the dependent variable and the set o exogenous explanatory variables. 2 Alternatively, zih an be the set o all explanatory variables in all time periods, z = z,..., z ) ih ( ih1 iht multidimensional zih as in Wooldridge (2005). 3 Time-invariant variables suh as rae or ethniity annot be in both ziht and z ih or identiiation purposes (Li and Zheng; 2008). 4 * For the estimation o the model, we assume that y y, initial values o dependent variable to be unensored ollowing Hu (2002). ih0 ih0 with

25 15 3. Estimation heterogeneity We it the ollowing dynami Tobit model with the unobserved individual * y iht x iht ih u iht (or Y * X C e u ) * where x ( z, y ), iht iht ih, t1 ' ' ' (, ) and u y y z iid 2 iht ih, t 1,..., ih,0, ih, ih ~ Normal(0, iu ) (or C R ) ih r ih ih ' ' ' 1 2 ) where rih ( yih0, zih,1), (, iid 2 and y, z ~ Normal (0, ) ih ih0 ih i using a Bayesian approah by drawing samples rom the posterior distribution o the parameters in the model. 5 One thing we are onerned about is that our latent variables T { y * ih} and t 1 ih are not ompletely observable. So, we need to employ data augmentation suggested by Albert and Chib (1993) to replae the zero observations with itted values or latent dependent variables and update nuisane parameters ih through Bayesian Markov Chain Monte Carlo algorithm (MCMC) iterations. We will disuss the data augmentation in the Gibbs sampling algorithm. Sampling density and priors Reall that the distribution o uiht and equation (2) give us the sampling density o the dependent variables onditioned on the latent variables. In addition to other variables, we write the model as ollows: 5 e ( t1) ( tt ) ( t1) ( tt ) C (,...,,...,,..., )' i1 i1 ih ih

26 16 ( y ih1, y ih2,..., y iht y * ih1, y * ih2,..., y * iht, y t 1 T ih,0, z {1( y 1 * 2 ih, iht ui ih,, ) 0)1( y iht y * iht 1 exp ( y 2 2 ui ) 1( y * iht z iht iht 0)1( y y * ih, t 1 * iht 0} ih 2 ) (5) Beore we disuss how the model an be it using the MCMC, we introdue the speiiations on priors ollowing Li and Zheng (2008): ' ' ' 6 (, ) ~ improper lat prior N R ~ gamma(, ) iu 2 2 or 2 iu N R iu 2 e iu (6) Gibbs sampling rom the posterior Combining the model given in (2) and the prior inormation in (6), we an determine what the posterior onditional distributions o the parameters look like. We use the Gibbs sampler - one simple and eetive sampler in the MCMC algorithms - to generate samples 2 rom the posterior. We set initial values or, and iu, and the Gibbs iteration algorithm proeeds in the ollowing steps: Step1: For eah h 1,..., H and t 1,..., T suh that y iht 0, generate y * iht rom the trunated normal distribution on the interval [-, 0] with mean xiht r and variane ih onditional on 2 2 iu i y, x, r,,, and 2 iht iht ih i 2 iu. 6 For example, a uniorm prior distribution on the real line,, or, is an improper prior. Improper priors are oten used in Bayesian inerene sine they usually yield noninormative priors and proper posterior distributions. (SAS/STAT(R) 9.2 User's Guide, Seond edition). Aessed at 4.htm

27 Step2: Update iu and by drawing rom the joint posterior distribution o 2 iu and onditional on data and other parameters and marginalized over eah other. 1 2 iu ~ N1 nt R gamma, 2 1 ( Y * ˆ e X C )'( Y 2 * X ˆ C e ) 1 X ' X ~ Normal ˆ, 2 where ˆ 1 ' ( '( * e X X X Y C )) iu Step3: For eah h 1,..., H, update ih rom the normal distribution with mean 1 T * T 1 1 * rih ih ( ) iht iht 2 iu i iu t1 i T y x and variane 2 iu i. 2 Step4: Update by drawing rom the posterior distribution onditional on r, and i. ih ih 1 R' R ~ Normal ˆ, 2 where i 1 ˆ R ' R R ' C 2 2. i i 4. Data The dynami ood demand model is estimated by using the Nielsen HomeSan data or the period 2009 and The data are based on a representative sample o U.S. households that report on all ood purhase or eah shopping trip. The ood items are reorded by the unique Uniorm Produt Code (UPC) using a sanning devie and the inormation is olleted on weekly basis. The initial dataset onsists o dry groery purhases, dairy produts purhases, UPC-produe, meat and rozen produts purhases, and random weight purhase data. Household expenditures on ood at home are generated by using the aggregated expenditures on dairy, dry groery, rozen and random weight produts

28 18 purhase data. The data iles also ontain inormation on household soio-eonomi and demographi harateristis and purhase inormation by purhase date, produt module, UPC number, size, quantity, multipak, use o oupon and prie paid. The demographi harateristis mathed with the household purhases data inlude household inome, age, eduation and employment o household head, rae and ethniity, marital status, and presene o hildren. The total number o households reporting any ood purhase in the 2009 and 2010 sanner data is over 60,000 households. O those, more than 59,000 households report some ood purhases at least 10 months o a year. Among those households, 36,256 households report dairy produts both in 2009 and This was our sample o interest. The dairy ile inludes both dairy produts and shell eggs. We reer to this as the dairy produts group. In order to have a sample size that would simpliy the estimation proess we took a random sample o 3,626 households or our analyti sample, whih is approximately 10% o 36,256 households. In Table 2.1, the dairy produts are ategorized into our groups o produts milk, heese, egg and other dairy produts. Table 2.1 provides the number o households who purhase eah group o produts and the perentages o zero purhases o eah group. The majority o the households who reported any groery purhase inormation or at least 10 months have purhased eah group o produts at least one in 2009 and As we onsider a month as a time unit out o 24 months time period based on the expeted average shel lie o dairy produts; the number o observations is the number o households times O our inal sample, 40 perent o observations on egg purhases and 29 perent o 7 Note that the shel lie o heese might last longer than any other dairy produts in the reezer. This may inluene the results o estimation on heese demand.

29 19 observations on heese purhases had no expenditures on the respetive produts while 17 perent o observations o milk data were zero purhases. As we see some households that have zero purhase or eah ategory o produts, aounting or ensoring in the estimation is a reasonable onern. Table 2.2 provides inormation on the distribution o average quantities and imputed pries (unit values) or the our produt groups. We alulated regional pries as the regions households pries ater we aounted or the reported produt units: ounes, luid ounes and ount measures. The prie o eah group o produts or eah region is imputed as the unit value deined as the sum o households expenditure ($) in eah region or the group o produts divided by quantity purhased in ounes. In Table 2.2, monthly average quantities purhased o eah ategory and pries (unit values) are reported. As shown in the table, heese and other dairy produts are more expensive than milk and eggs on a per oune basis. Table 2.3 presents the desriptions o variables and provides the alulated means and standard deviations o the inal sample. Demographi variables inlude the household s inome, total ood (at home) expenditures, household s age, presene o hildren (kids), employment status o emale household head and rae and ethniity. The rae and ethniity are olleted rom the sample person, and may not relet the rae and ethniity o all members o the household when rae and ethniity are mixed. The household s inome is reorded as a ategorial variable. In our estimation we use the household s monthly expenditure alulated over all ood groeries as an explanatory variable, instead o reported inome (Benson et al., 2002). In doing this, similar to Benson et al. (2002), the estimation results o the demand equations solve the seond stage o a two-stage budgeting problem based upon weak separability over households preerenes. Households alloate the total

30 20 ood expenditures monthly among purhases o dairy produts and non-dairy ood produts ater the irst alloation o inome among purhases o ood at home and other goods or servies. Using total ood expenditure also redues possible endogeneity posed rom use o the dairy group expenditure as a measure o total expenditures or inome. We use the inormation o household s inome to ompare the demand o low inome households to the demand o high inome households. The presene o hildren, rae and ethniity, and the employment status o emale household head were onsidered as binary variables. The estimation proeeded as ollows: the numbers o observations or eah data ile were iterated 10,000 times; the irst 5,000 iterations were set to be burn-in periods. 5. Results Table 2.4 presents the results rom the estimation o the dynami Tobit model with individual heterogeneity on purhases o dairy produts reporting the posterior means and standard deviations o parameters or the pries and demographi variables. The probabilities o being positive that is loosely omparable to the notion o signiiane are also reported or eah set o parameters estimated or the demand model. The parameter estimates rom the main equation and auxiliary equation are shown in Table2.4. The eet o habit persistene is seen in the parameter value o Y t-1. We ind strong evidenes that past purhases o eah dairy ategory play an important role in urrent purhases o eah group o produts, as the estimates o all our demand equations present similar positive eets or the lagged dependent variable with probability o being positive 1.0. Even though we ontrolled or the eet o unobserved heterogeneity, we observe the presene o habit ormation in the

31 21 purhases o dairy produts. In partiular, milk demand exhibits the strongest habit orming behavior; we ind less eet rom the lagged dependent variable on heese demand. 8 As shown in Table2.4, the estimates o the own prie responses or all dairy demands are negative signed; most o the own prie response have probability o being positive near 0 exept or eggs. The estimated response to total ood expenditures is positive or all produts as we expeted, and with probability o being positive 1.0. The presene o hildren in all age ranges and total ood expenditures have substantial positive impats on milk demand. The eet o having kids on milk onsumption is partiularly large in the households that have hildren under 5 years o age. Some interesting result rom the estimates or the auxiliary equation is that there is a positive orrelation between the unobserved heterogeneity and Hispani ethniity in all dairy demands. In order to avoid possible orrelation expeted between total expenditure and inome, we onduted an additional analysis by separating the sample into two inome groups o households and ran the same estimation proess on milk produts only. We onverted midpoints o ategorial inome ranges into estimated inome and omputed poverty-inome ratios. Low inome household is deined i having inome less than 200% o the poverty inome level and high inome household has inome more than the ut-o level. 9 The results in Table 2.5 show that the prie and total ood expenditure responses o low inome 8 When it omes to estimating habit eets o ood demand, perishability and storage motives together with the length o lags may also matter to state dependene. As the length o lags was to be set to be onsistent with the length o shel lie or dairy produts exept or heese produts, we are not overly onerned about ontrolling storage behaviors rom state dependene. The weakest impat o the lagged variable is or heese demand among dairy demands and this result may relate to the produt s longer length o sel lie. That is, there may be possible storage behaviors in heese purhases with the result that the habit ormation ator may possibly be underestimated. 9 The oiial ut-o applied in some nutrition programs (e.g., WIC) is 185%, although higher inome households may qualiy on the basis o Mediaid or other soial assistane programs. We use 200% to inlude potentially eligible households.

32 22 households are more responsive than those o high inome households. Also, the eet o the presene o hildren is larger among the low inome households. Unompensated prie and total ood expenditure elastiities were alulated rom the posterior parameters on pries and ood expenditures and are provided in Table 2.6. Point estimates provided in eah ell are the means o the Gibbs samples and the 95% redible intervals are given in parentheses. Corresponding to the probabilities o being positive in Table 2.4, most o the own-prie elastiities and all the ood expenditure elastiities are onsidered to be signiiant as 95% redible sets exlude zero. The own-prie elastiities o eah group are negative and inelasti whih means that dairy produts are neessary goods, as we expet. Demand or heese is relatively more prie responsive than the other produts. In the ase o egg demand, there is little evidene that most o the prie elastiities are signiiant as the 95% redible sets inlude zero. Complementarity was ound among the dairy produts. 10 In addition, the ood expenditure elastiity estimates or eah group are positive. We ind some evidene o larger ood expenditure elastiities or heese and other dairy produts than or milk and eggs. Both the higher and lower inome households have similar inelasti milk demand patterns (see Table 2.7). Low inome households exhibit more elasti prie and expenditure responses or milk demand ompared to the responses o the higher inome households. 6. Conlusions This paper investigates the impat o state dependene on dairy demand using Nielsen 2009 and 2010 HomeSan data. The results o the estimation show that habit orming 10 Note that as we estimate single demand equations, no restritions suh adding-up, symmetry and homogeneity were imposed.

33 23 behaviors exist or these produts and are onditional on unobserved individual heterogeneity. As expeted in estimating demand or partiular produt ategories, problems o ensoring appear in the miro-data. In this paper, we take into aount the ensored nature o ood expenditure data and employ a Bayesian proedure to estimate the dynami demand models on dairy produts. By ontrolling the individual heterogeneity in the model, the soure o endogeneity or the lagged dependent variable has been removed. The Bayesian estimation approah used redues the burdens o having ompliated omputations through simulation methods. This researh provides a unique ontribution to a dynami ensored demand or ood by applying Bayesian method to estimate habit eets using relatively reent household panel data. We examined the dairy oods group and ind that most o the dairy produts exhibit habit ormation. These indings suggest that onsumers o these produts will be slower to adjust their purhase behavior. Subsequent analysis will expand the time period overed and examine responses to speii ood saety realls and produt inormation. Additional produt groups will be onsidered as well, inluding meats. Another area or extension o this work is to aount or some orrelation among the single equations by estimating demand as a demand system.

34 24 REFERENCES Adamowiz, W.L. and J.D.Swait Are Food Choies Really Habitual? Integrating Habits, Variety-seeking and Compensatory Choie in a Utility-maximizing Framework. Amerian Journal o Agriultural Eonomis 95(1): Albert, J. and S. Chib Bayesian Analysis o Binary and Polyhotomous Response Data. Journal o the Amerian Statistial Assoiation 88: Amemiya, T Multivariate regression and simultaneous equation models when the dependent variables are trunated normal. Eonometria 42: Arnade, C., M. Gopinath and D.Pik Brand inertia in U.S. household heese onsumption. Amerian Journal o Agriultural Eonomis 90: Benson, J.T., Breidt, F.J. and Shroeter, J.R Television Advertising and Bee Demand: Bayesian Inerene in a Random Eets Tobit Model. Canadian Journal o Agriultural Eonomis 50: Browning, Martin and M. D. Collado Habits and heterogeneity in demands: a panel data analysis. Journal o Applied Eonometris 22: Blaniorti and Green An Almost Ideal Demand System Inorporating Habits: An Analysis o Expenditures on Food and Aggregate Community Groups. Review o Eonomis and Statistis 65: Carraso, R., Labeaga, J. M. and Lopez-Salido, J. D, Consumption and habits: evidene rom panel data. The eonomi Journal 115: Chib, S. and I. Jeliazkov Inerene in semiparametri dynami models or binary longitudinal data. Journal o the Amerian Statistial Assoiation 101:

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38 28 Zhen, C., M.K. Wohlgenant, S. Karns and P. Kauman Habit ormation and demand or sugar-sweetened beverages. Amerian Journal o Agriultural Eonomis 93:

39 29 Table 2.1 The Dairy Produt Categories and Distribution or Sampled Households a % o Zero Produt Category/Produt Group Desription # o HHs Purhases* MILK % CHEESE % EGGS % OTHER BUTTER AND MARGARINE COT CHEESE, SOUR CREAM, TOPPINGS DOUGH PRODUCTS % PUDDING, DESSERTS-DAIRY SNACKS, SPREADS, DIPS-DAIRY YEAST YOGURT Total Dairy 3626 a Note: Perentage o observed month with zero purhases over all households purhasing eah ategory o produt. Data are reported on the 10% randomly drawn sample o reporting households rom Nielsen HomeSan household data Table 2.2 Distributions o Monthly Average Quantities and Pries or Sampled Households a Variable Unit Mean Std. Min. Max. Milk Oune Cheese Oune Egg Oune Other dairy Oune P_milk $/oz P_heese $/oz P_egg $/oz P_other $/oz a Note: Data are reported on the 10% randomly drawn sample o reporting households rom Nielsen HomeSan household data

40 30 Table 2.3 Deinitions and Statistis on the Variables or Sampled Households a Variable Mean Std.Dev Minimum Maximum Household inome Sum_expd Monthly total ood expenditure Household age Maximum age o the two household's heads Binary Variables (equal 1 i ollowing onditions met, and 0 otherwise) Kids Household has a kid under 5 year olds Skids Household has a kid between 5 and 11 year olds Bkids Household has a kid between13 and 17 year olds Empl Female household head is employed Blak Household s sampled person s rae is blak White Household s sampled person s rae is white Hispani Household's sampled person s ethniity is Hispani 0 1 Summer Purhasing month is in June to August Winter Purhasing month is in November to January a Note: Data are reported on the 10% randomly drawn sample o reporting households rom Nielsen HomeSan household data

41 31 Table 2.4 Bayesian Dynami Tobit Estimation Results or eah Dairy Group s Demand Milk Cheese Other Dairy Eggs Main Equation Mean Std Prob>0 Mean Std Prob>0 Mean Std Prob>0 Mean Std Prob>0 Yt log(p_milk) log(p_other) log(p_heese) log(p_egg) log(sum_expd) Kids Skids Bkids Hhage Empl Summer Winter Auxiliary Equation Mean Std Prob>0 Mean Std Prob>0 Mean Std Prob>0 Mean Std Prob>0 Yo mean o log(p_milk) mean o log(p_other) mean o log(p_heese) mean o log(p_egg) mean o log(sum_expd)

42 mean o kids mean o skids mean o bkids mean o hhage mean o empl Blak White Hispani Constant

43 33 Table 2.5 Bayesian Dynami Tobit Estimation or Milk Demand by Dierent Inome Groups Low inome High inome Main Equation Mean Std Prob>0 Mean Std Prob>0 Yt log(p_milk) log(p_other) log(p_heese) log(p_egg) log(sum_expd) Kids Skids Bkids Hhage Empl Summer Winter Auxiliary Equation Mean Std Prob>0 Mean Std Prob>0 Yo mean o log(p_milk) mean o log(p_other) mean o log(p_heese) mean o log(p_egg) mean o log(sum_expd) mean o kids mean o skids mean o bkids mean o hhage mean o empl Blak White Hispani Constant

44 34 Table 2.6 Elastiities o Dairy Produt Demand Milk Cheese Other Dairy Eggs P_milk (-0.169, ) (-0.148, ) (-0.179, ) (-0.070, 0.041) P_heese (0.000, 0.094) (-0.393, ) (0.173, 0.345) (-0183, -0.07) P_other (-0.003, 0.081) (-0.136, ) (-0.206, ) (-0.071, 0.096) P_egg (0.009, 0.079) (0.037, 0.202) (-0.017, 0.115) (-0.070, 0.069) Sum_expd (0.065, 0.067) (0.115, 0.125) (0.101, 0.107) (0.096, 0.102) Table 2.7 Elastiities o Milk Demand by Dierent Inome Groups Low inome High inome P_milk (-0.242, ) (-0.168, ) P_heese (-0.012, 0.231) (-0.005, 0.095) P_other (0.012, 0.222) (-0.024, 0.067) P_egg (-0.095, 0.008) (0.014, 0.09) Sum_expd (0.068, 0.074) (0.063, 0.066)

45 35 CHAPTER 3. IMPACT OF WIC PROGRAM PARTICIPATION ON FOOD EXPENDITURES Introdution The Speial Supplemental Nutrition Program or Women, Inants, and Children (WIC) is one o the largest ood assistane programs in the United States. WIC is a ederally sponsored program administered by the Food and Nutrition Servie (FNS) o United States Department o Agriulture (USDA) and implemented by 90 WIC State Agenies and 34 Indian Tribal Organizations (USDA, 2012). The program provides beneits in the orm o healthy oods (WIC pakage ood), nutrition ounseling, and aess to health servies to qualiying low-inome inants, hildren up to age ive, pregnant, breasteeding, and postpartum women in order to improve the health o those at nutritional risk. The program aims to serve the targeted individuals (women, inants and young hildren) by providing supplemental oods and additional nutrition eduation. To partiipate in the program, appliants need to meet the eligibility riteria o having low inome, being in an at-risk subgroup (suh as pregnant, postpartum, breasteeding women, inants and hildren up to age ive) and being at nutritional risk. The ood pakage beneits are presribed based on the age and status o the qualiying individual. The beneits inlude oods suh as inant ormula, inant ereal, juie, iron-ortiied ereal, milk, eggs, and heese with the speii ood pakage assigned by eah loal ageny to be onsistent with ederal requirements and onsistent with the eligibility o WIC partiipant. In Otober 2009, the U.S. Department o Agriulture revised the WIC ood pakage. The revised pakage inluded the introdution o 11 An earlier version was prepared and presented as a Seleted Poster at the Agriultural & Applied Eonomis Assoiation s 2014 AAEA Annual Meeting, Minneapolis, MN, July 27-29, 2014.

46 36 new whole-grain produts, lower at ontent o dairy oods, and redued juie quantities, and provision o ash-value vouhers or ruits and vegetables among other hanges (Federal Register, 2014). In this paper, we seek to identiy households partiipating in the WIC program and WIC-eligible households in order to evaluate the eet o WIC on the partiipating households. In the proess o identiying partiipating and eligible households, we ollow the work o Bitler, Currie and Sholz (2003) who analyze WIC eligibility and partiipation using dierent soures o inormation. Their paper mathes the Current Population Survey (CPS) and the Survey o Inome and Program Partiipation (SIPP) to an administrative data and ompares WIC reporting patterns among respondents. Their omparisons show that WIC partiipation is signiiantly under-reported in both the CPS and SIPP, and more so than other antipoverty programs. We estimate the assoiation between WIC program partiipation and ood expenditures using the Nielsen Homesan data national level household ood purhase data. WIC program provides partiipating household with ree ood produts that may augment or substitute or oods that might be aquired without the program beneits. Although beneits are presribed at the individual level, household level data on ood expenditure an provide useul inormation or evaluating the eets o WIC program partiipation. Household-level sanner data provide detailed inormation on eah shopping trip made over the span o several years. This level o detail allows a more preise measurement o WIC impat on ood onsumption ompared to other survey data, suh as the CPS or SIPP that provide more oarse inormation on ood purhases. The Homesan data provides

47 37 detailed inormation on ood pries, expenditures, demographis and inormation on WIC program partiipation starting rom 1999 allowing traking households aross a period that inludes the hange in program regulations. Detailed demographi inormation allows us to identiy households that are eligible but not partiipating the WIC program. Although WIC program partiipation is sel-reported in the HomeSan data and subjet to reporting errors, we address this problem by areully developing a lassiiation o WIC eligible. A ormal aount or the possibility o mislassiiation error on partiipation status is outside the sope o this researh. Sel-seletion an be a problem in estimating the treatment eet in the programs without random assignment. A sel-seletion problem arises i program partiipants systematially dier rom non-partiipants or reasons other than program partiipating status per se. For example, eligible households that preer healthier oods may be more interested in partiipating in the WIC program in order to obtain the oods they like or ree. Thus, unobserved ators suh as attitudes towards health and ood and expeted uture ood seurity may aet the deision o partiipation in the WIC program and ood onsumption. In this study, we assume that the sel-seletion is determined by observable ovariate variables. This an thus be done by imposing an ignorability ondition. Our main objetive is to examine how partiipating in the WIC program inluenes purhase patterns o households relative to non-partiipating but eligible households. 12 We assume that the WIC partiipants and their hildren are the primary beneiiaries o the WIC program and the hange in the availability o oods in the household rom WIC partiipation is a reasonable proxy or a hange in the onsumption o WIC partiipants. Ater deteting 12 As observed purhases, the eet ould be through vouhers and also nutrition eduation. We do not aount or the nutrition eduation eet.

48 38 and removing the overreporting o WIC partiipation, we estimate how partiipating in the WIC program aets ood expenditures and the purhases o grain ood produts among WIC partiipants and WIC eligible non-partiipants using data rom the Nielsen HomeSan. In addition, we aount or WIC ood pakage hange implemented in the middle o the period. Although WIC state agenies were required to implement new program rules by Otober 2009, some states implemented the revised pakages earlier (see listing in Appendix 3.1). We estimate WIC impats beore/ater the WIC pakage hanges and ontrol potential impat o the poliy hange based on the implementation dates or eah state. In our analysis, we ous on the purhases o grain produts whole grain. Whole grain produts were inluded in the 2009 WIC pakage revision beause whole grain produts are underonsumed in the target population relative to the Dietary Guidelines or Amerians (DGAs). We seleted whole grain oods in the WIC ood pakage as these oods are prominent in the WIC ood pakage and grain produts are purhased by most households. Under the new program rules, whole grain produts were added to the ood pakages or women and the young hildren. At least hal o the total number o breakast ereals state ageny ood list must be whole grain. Whole-grain bread also added to the new ood pakages, with substitutions o other whole grain produts allowed. 13 We ategorize the whole grain produts into our groups o produts breads, tortillas, ready-to-eat ereals, and brown rie. Beause the WIC program aims to enourage healthy eating among program partiipants, analysis o onsumption patterns o WIC partiipating households relative to similar non-partiipants allows us to see whether partiipation in the program is assoiated with healthy ood purhases. In partiular, this study provides a unique ontribution to 13 Possible options allowed as substitutes or whole-wheat bread are whole-grain bread, brown rie, bulgur, oatmeal, sot orn, barley, sot orn or whole-wheat tortillas.

49 39 literature on the WIC program by investigating the whole grain onsumption o WIC partiipants both beore and ater the hange o the WIC ood pakage. Whole grain produts had not been identiied expliitly in the WIC pakage prior to the 2009 pakage revisions. To date, there has been relatively little researh on the eet o the WIC program on whole grain onsumption o program partiipants. As this study deals with evaluation o the WIC program in terms o purhases on WIC-approved pakaged oods, it is an important omponent o program evaluation researh and has impliations or publi health poliy. This study provides a model or analysis o the ood omponent hanges introdued in In addition to that, as ar as the authors are aware, this paper is the irst study using national level sanner data to see WIC program eets on ood expenditures. We take advantage o using sanner data whih enables us to aess detailed inormation on the ood expenditure o households o both WIC partiipating and non-wic but eligible households. Other soures o data oten lak inormation on WIC status or o onsistent expenditures on ood. The researh also ontributes to better understanding o the potential use o sanner data or examining the reliability o reported WIC partiipation on ood demand. 2. Bakground Existing literature on the WIC program inds that partiipation in WIC has a signiiant positive impat on the health status o the target population and a signiiant ontribution to reduing ood inseurity (Edmunds et al., 2014; Colman et al., 2012; Metallinos-Katsaras et al., 2010; Lee at al., 2006; Meyers et al., 2004; Herman et al., 2004; Carlson and Senauer, 2003). Researh also supports positive assoiation between WIC partiipation and inants growth and health (Edmunds et al., 2014; Meyers et al., 2004).

50 40 Other studies show WIC partiipation o hildren to have a signiiant positive impat on the overall health o hildren and redue the risk o several nutrition-related health problems, suh as anemia and nutritional deiieny (Carlson and Senauer, 2003; Lee at al., 2006). The literature examining WIC partiipation s assoiation with ood seurity also inds a beneiial impat o WIC partiipation on household ood seurity status among irst-time program and (Metallinos-Katsaras et al., 2010; Herman et al., 2004) The main mehanism or improving health outomes or WIC program partiipants is through the ree provision o healthul oods and thereore investigating the eet o WIC program partiipation on seletion o speii oods is an important program outome o interest. As the WIC program aims to improve healthy eating behaviors o target people, the analysis o onsumption patterns o WIC partiipants allows us to see whether the program is assoiated with healthier ood purhases. This is one way to measure the eetiveness o the program. There are relatively ew studies about the eet o WIC on ood onsumption; most studies have onsidered the impats o WIC on health status and dietary onditions o the target population. These studies have ound evidene o a positive assoiation between WIC partiipation and onsumption or some WIC pakage oods and other related oods (Deming et al., 2014; Watowiz and Taylor, 2014; Oliveira and Chandran, 2005; Ponza, et al., 2004). Ponza et al.(2004) examine the nutrient intakes and eeding patterns o partiipating inants and toddlers and onlude that WIC partiipants under 24 month old were more likely than nonpartiipants to onsume many o the oods that are provided in the WIC ood pakage suh as ow s milk, 100% juie and peanut butter. The onsumption patterns o WIC ood pakages or partiipating hildren under 5 year old ompared with nonpartiipants have been investigated and similar positive results

51 41 are observed prior to the pakage hange in 2009 (Deming et al., 2014; Watowiz and Taylor, 2014; Oliveira and Chandran, 2005). Most o the studies onentrated on the question whether WIC partiipation is assoiated with the development o more healthul eating patterns, in partiular, inreased ruits and vegetables onsumption and limiting intake o sugar-sweetened beverages (Deming et al., 2014; Watowiz and Taylor, 2014; Ponza et al., 2004). Findings rom Watowiz and Taylor (2014) are based on data rom the National Health and Nutrition Examination Survey (NHANES) Two studies support the results rom the previous study o Ponza et al.,(2004) in whih WIC partiipation was assoiated with higher intakes o sugar-sweetened beverages or hildren partiipating in WIC (Deming et al., 2014; Watowiz and Taylor, 2014). Deming et al. (2014), in their study o young hildren rom the 2008 Feeding Inants and Toddlers Study (FITS) also ind that ewer WIC toddlers and preshoolers onsumed any ruit ompared to nonpartiipants and ewer inants o age 6 month-12 months old onsumed any vegetables ompared to nonpartiipants. In order to address the shortalls in intake and to improve overall onsumption o oods reommended by urrent Dietary Guidelines, USDA introdued the revision o WIC ood pakages with new ood ategories, revised maximum purhase quantities and new ood substitution poliy options or state agenies. The revisions were approved and implemented by most o states in Otober 2009 (Institute o Mediine, 2005; Andreyeva et al., 2011). Major hanges inluded in the pakage revision were plaing limitations on the amounts o alori sweeteners allowed, reduing saturated at, holesterol and total at, promoting the 14 NHANES data has only two day dietary reall to measure the ood onsumption, whih an be very noisy, whereas in Homesan data we observe the ood purhased or eah shopping trip over the years.

52 42 onsumption o ruits and vegetables through ash-value vouhers and introduing whole grain produts in the breads and ereal ood group.. There are many on-going studies o the WIC pakage revisions and assessing the potential eets o the new WIC pakage revisions on ood seletion is the main ous o this paper (See, or example, Hillier et al., 2012; Andreyeva and Luedike, 2014; Bertmann et al., 2014; Thornton et al., 2014; Rithie et al., 2014). Along with the primary intent o improving the nutrition o targeted individuals, WIC partiipation may also aet the ood onsumption patterns o unintended individuals within the WIC household (Ishdorj, Jensen and Tobias, 2008; Aria, Crouh and Kulka, 1990). The program ood pakages are presribed to qualiying individual women, inants and young hildren. Sine the beneits o WIC partiipation are aimed at speii groups o women and hildren, not a household, leakage o program beneits would our i beneits go instead to others in the household and redued or the intended individual. Related literature has ound little evidene o possible spillover beneits on the household members who are not WIC partiipants (Ishdorj, Jensen and Tobias, 2008; Aria, Crouh and Rihard, 1990). 3. Empirial methodology Deining problem: treatment eet Our approah to WIC program evaluation adopts the ounteratual (or potential outomes) ramework by Rubin (Rubin, 1974) to measure the eet o the treatment. The treatment variable, reers to whether household partiipates in the WIC program or not. Let and be the outomes with treatment and without treatment, i.e., ood expenditures o WIC partiipating and non-partiipating households. The observed outome

53 43 or household is given by. The impat o a treatment or a household treatment, is deined as the dierene between the potential outome with and without, that is, the dierene between an observed outome and a ounteratual whih we do not observe. The main measure o interest or the treatment eet suggested in Rosenbaum and Rubin (1983) is known as Average Treatment Eet (ATE): ATE E[ y y ], 1i 0i whih measures the mean dierene aross all the households inluding both treatment and ontrol group. The average treatment eet on the treated (ATET) is another measure o interest: ATET E[ y y w 1] E[ y w 1] E[ y w 1] 1i 0i i 1i i 0i i whih is obtained by averaging the impat o the treatment on those program partiipating households. Our objetive is to identiy the average treatment eet on the treated (ATET). Instead o requiring that all ontrol units have a positive probability o treatment, we only need to keep propensity sores o the treated units to be less than 1 and to have at least some ontrol units with positive propensity sores. We estimate ATET under relatively weaker onditions than the average treatment eet. Propensity sore: program partiipation model The undamental problem o estimating ausal eet is that it is impossible to observe the ounteratual when partiipants have not partiipated. Estimating the valid ounteratual outome in a relevant omparison group might be one possible way to solve the problem. To this end, we need to make sure that the omparison group has statistially idential harateristis to the treatment group in order to be the ounteratual o the

54 44 treatment group. This proess is reerred to as mathing. In a general, non-experimental setting, treatment without being randomized might result in sel-seletion bias. The basi idea o mathing is to redue the possible soures o sel-seletion bias by ontrolling or the set o observed ovariates in order to have a group that is omparable to the treated group. In other words, the irumstanes where the mathing is most likely to work are restrited in seletion on observables into the program. Propensity sore mathing imputes ounteratual outomes or program partiipants using the non-treated group with similar propensity sores. The propensity sore (Rosenbaum and Rubin, 1983) is deined as the onditional probability o reeiving the treatment. In order to implement the mathing estimator, Rosenbaum and Rubin (1983) proposed two assumptions that underlie propensity sore mathing. 15 First, the potential outomes are statistially idential ater ontrolling a set o observable ovariates. This assumption is known as onditional independene or unonoundedness or the ignorability assumption. This assumption essentially restates the main requirement o seletion on observables addressed above: Y Y 1, 0 W X. Seond, there is a positive probability o both being partiipants and not being partiipants or eah value o X. That is, there is a ommon support to ensure a similar hane o being treated or proper mathes with a suiient overlap in the harateristis: 0 Pr(W 1 X ) Rosenbaum and Rubin (1983) note that the assignment o treatment is said to be strongly ignorable i there are two onditions satisied.

55 45 The assumption o ommon support is testable by heking the distribution o estimated propensity sores or both the treatment group and the omparison group. Based on the two main assumptions or adequate mathing, we irst ondut an estimation o the program partiipation model to haraterize the propensity sore using a Logit hoie model (Rosenbaum and Rubin, 1983). The propensity sore o program partiipation is estimated using various household harateristis suh as household inome, size, age, the presene o kids under 5, ethniity and regional inormation and indiators o employment and the eduation level o household heads. Mathing proedure Ater we haraterize the expeted probability o program partiipation, the propensity sore, the next step is to determine the mathing estimator whih will ombine a treated group with a non-treated group with equal propensity sore to estimate the ounteratual outome. Note that the sample ATET we aim to estimate is given by: ATET psm N 1 N [ w ˆ i p(x i)] yi, ˆ [1 pˆ (x )] i1 i where ˆ N1 / N denotes the ration o treated units in the sample and pˆ(x ) denotes the estimated probabilities o treatment. There are several approahes to ind good mathes. The hoie o the mathing proedure is important in terms o the size o samples (Hekman, et al., 1997). In this paper, we employ three dierent mathing algorithms to our analysis based on the estimated propensity sores: nearest neighbor mathing (NNM), kernel mathing and Radius mathing. NNM is one o the most straightorward mathing estimators. It is onduted by simply omparing every treatment unit with one or more units o the non-treated group in terms o the losest propensity sore. By imposing a tolerane level on the maximum propensity sore i

56 46 dierene or aliper an analyst an improve NNM to have better mathes. Radius mathing is a variation o aliper mathing, whih speiies a aliper and hooses not only the nearest neighbor but all units whose dierenes lie within the aliper s radius. While NNM uses only a ew units rom the non-partiipation group, the Kernel mathing estimator uses weighted averages o all units in the non-treated group to onstrut the ounteratual outome o the treatment group in a non-parametri way. One might see a trade-o going on between two dierent mathing algorithms in the sense that KM ahieves more eiieny having the lower variane with more inormation but it also is at risk o possible poor mathing or some units. In ontrast, while NNM redues bias by seleting only the nearest neighbors whih harateristis are very similar, in general, to the treated it has higher variane with less inormation ignoring many untreated units or the estimation. We also perormed the inverse-probability weighted regression adjustment(ipwra) or our analyti dataset as an alternative to propensity mathing estimators as the sample size or WIC partiipating households are relatively small or obtaining reliable oeiients. We use the inverse o the predited probabilities obtained rom the propensity sore regression as weights and run regressions on the outome variable -the ood expenditures or eah group o the treated and the ontrol (Hirano and Imbens, 2001). IPWRA is onsidered to be a robust estimator as it allows or potential misspeiiations in the propensity model and it still provides a onsistent estimate o the treatment eet even under misspeiiations. 4. Data The treatment eet o WIC program partiipation is estimated by using the Nielsen HomeSan data or the period 2008 to The Homesan data are originally olleted

57 47 rom a nationally representative sample o households. Identiying WIC partiipation was based on the sel-reported WIC partiipation variable. The Homesan data report on expenditures on ood items purhased or eah shopping trip during the reporting period. The household reords all ood items by the unique Uniorm Produt Code (UPC) using a sanning devie. Inormation is olleted by Nielsen on weekly basis. Only dollar expenditures or aggregated ategories o random weight items are reported. 16 For these random-weight ategories, there is no inormation on pries and quantities. Despite the lak o detail or these items, beause the total expenditure on is reported the deiieny does not aet the report on all ood purhases or eah shopping trip. In this paper, we aggregate ood expenditure by month in order to limit the number o zeros. The Homesan dataset onsist o three UPC-oded modules: dry groery purhases, dairy produts purhases, meat and rozen produts, and a non-upc random weight module. For , almost all whole grain items reported by the households have a UPC ode. The data also ontain inormation on purhase date, produt ategory, UPC, size, quantity, multipak, use o oupon and the prie paid. Soio-eonomi and demographi harateristis inlude WIC program partiipation status, household inome, age, eduation and employment o household head, rae and ethniity, marital status, and presene o hildren. Ater narrowing down our analyti sample to WIC eligible households, we math the demographi inormation inluding WIC program partiipation with the ood expenditure data to obtain the sample or analysis. 16 Random weight items are the items whih do not have a UPC odes, they may be sold by weight or by quantity. Most o the resh ruit and vegetables are sold this way. Some breads baked in the supermarkets are sold as random weight, but they are relatively unommon.

58 48 i. Identiiation o WIC partiipation households The Homesan data were initially sreened to lassiy households as WIC-eligible and ineligible households on the basis o inome and demographis. We ound a number o possible misreporting errors on urrent WIC status (e.g., a household reporting WIC partiipation with no women and no hildren present). Initial analysis o the data suggested that 3%~21% o households reporting on WIC status may have been in error (either underreporting or over-reporting o WIC partiipation). From reported demographi harateristis and reported inome (200% o poverty or below), we worked to distinguish eligible and ineligible households or as over-reporting. We eliminated potential overreporting errors (observed as WIC reporting by ineligible households). The underreporting issue is more diiult to deal with. We identiied WIC reporting households or eah year (2008, 2009 and 2010) based on the variable: Currently enrolled in WIC. Although the total number o households in eah year is a bit dierent rom eah other, the patterns that emerge in the datasets are similar. Table 3.1 shows unweighted and weighted distributions o households reporting that they are urrently enrolled in WIC in eah year. 17 In unweighted distribution, there were 674 households in 2008, 372 households in 2009 and 439 households in 2010 that reported urrent WIC enrollment. We observe that the perentage o the WIC reporting households in eah year o the Homesan data was a bit under 2% o the total number o households based 17 Household universe weights are available at the ounty level or all demographi targets. These numbers are kept updated at the beginning o eah year and population growth is oreasted eah month to allow or population growth. Projetion ators or the data are basially omputed using these numbers. The projetion ators relet the sample design and eah ator relets the representation o eah household in the U.S. population, Projetion ator = universe o households / sample households. The projetion ator produes demographi weighting as well as household population projetion. The projetion system also takes into aount the orrelation between household demographis and item purhases. Additional weighting is also inluded in the ase o lower inome households beause o slight under-sampling due to the diiulty o reruiting households in this group. The values o the weights range rom small to large and relet the dierential probabilities o household seletion. (Harris, 2005)

59 49 on weighted distributions o households. 18 Connor et al. (2011) report that in April 2010, 10,021,136 women, inants, and hildren were enrolled in the WIC program and this number represents an inrease o 5 perent over WIC enrollment reported in As the supplemental data set by state agenies in Connor et al. (2011) inludes the number o household members reeiving WIC beneits by eah state, the weighted average number o people in the partiipant s household was alulated as 2.35 based on the projetion weights in 2010 Homesan data. By using this average number o household s members we an onvert the number o WIC households in Table 3.1 to the number o total WIC partiipants, 1.9 million to 4.6 million. This estimate whih is still less than the hal o the total WIC reporting individuals in Connor et al.(2011), and the results rom the data analysis in Table 3.1 indiate that the households report o WIC partiipation is likely to be under-reported (Bitler, Currie and Sholz: 2003). Under-reporting in WIC an be partially explained by the inding in Bitler, Currie and Sholz (2003) that male respondents are less likely to report WIC partiipation in the household than emale respondents other things being equal. The general WIC eligibility riteria inlude inome, ategorial and nutrition risk requirements. Individuals in households with inome 185% o poverty inome meet the inome requirements. Inants, hildren up to age ive, pregnant, breasteeding, and postpartum women are ategorially eligible or WIC and they should be onsidered to be in low inome households and at nutritional risk. In the data we annot observe pregnany, latation, and nutritional risk status. Individuals may be automatially eligible i they are 18 In separate analysis we ind that nearly 10% o all households in the NHANES data report reeiving WIC beneits in the last 12 months (9.06% in and based on weighted data rom the NHANES) and while 2.8% ~ 3.2% o all individuals inluding hildren and women report urrently reeiving beneits in the WIC program. Based on the NHANES weights, 3.2% o urrent WIC partiipants in NHANES data relet nearly 9.6 million number o people whih is lose to 10,021,136, the number o WIC partiipants in 2010 (Connor et al., 2011).

60 50 eligible to reeive SNAP beneits, Mediaid, or beneits rom the Temporary Assistane or Needy Families (TANF, ormerly known as AFDC, Aid to Families with Dependent Children) program. Beause eligibility or these programs is oten higher than 185% poverty inome, individual may qualiy or WIC even though their inome is above the 185% level. Thereore, we identiy households that are potentially eligible or WIC by inluding households that have members in a WIC qualiying age group, and have inome less than and equal to 200% poverty inome ratio. To this end, we examined whether those households reporting WIC do, in at, meet the eligibility requirements o WIC based on having an eligible household member and having low inome level (200% poverty inome). We establish three measurements to use in identiying WIC eligible households: (a) low inome level, (b) hildren under 5 years-old, and () having a woman o hildbearing age. We estimate poverty inome (PIR) as a ratio o the inome reeived (using the mid-point o the inome ategory) to the poverty inome level or that size household, multiplied by 100. Low inome households are deined as having inome less than 200% o the poverty level. All individuals in the household are reported by age, inluding hildren. In order to identiy the WIC reporting households that inlude pregnant, breasteeding or postpartum women, we sreen or households that report any emale age years old (the age range used in the IOM WIC report). Based on the three measurements desribed above, the sreening or WIC eligible households was applied to those low inome households with hildren under 5 years-old and those low inome households with a woman o hild bearing age. Thus, all eligible households need to be poor and have either hildren under 5 yearsold or woman o hild bearing age.

61 51 In Table 3.2, we hek the number o households that are determined to be eligible against those reporting WIC enrollment during eah year. We would expet the number to be the same as the total WIC reporting households i all eligible households also reported partiipation. However, as we see in the unweighted distribution o the reported data, in 2008 only 398 o the 654 total households reporting WIC enrollment (61% o the WIC households), satisy the loosened eligibility riteria and 57% - a slightly smaller perentage o the households in 2009 were determined WIC eligible. In 2010, there are 287 households identiied as eligible, or 65% o the WIC partiipating households. Table 3.2 also shows more detail on the households that reported WIC but are likely ineligible. We observe 35% - 43% o WIC reporting households do not satisy the eligibility requirements (based on inome and demographis) or eah year. Most households that we onsider erroneously reported WIC status were disqualiied on the basis o high inome levels. It is possible that some o these households will not qualiy during the next program reertiiation, or may in at qualiy based on partiipation in another program (e.g., Mediaid). Ater removing the 35-43% o WIC-partiipating but not eligible households, we use the remaining households that satisy WIC eligibility riteria in the subsequent analysis. Table3.3 represents the distribution o WIC partiipation among eligible households in eah year. For panel analysis, we are interested in looking at the households that are in three onseutive years. O all the households that remained in the sample during the three years (39,834), almost hal o the total sample o eligible households in eah year, stayed in the data system. The seond part o Table 3.3 shows the distribution o WIC reporting and eligible households among households with any purhases over three years. One we apply the additional ilter o reporting three onseutive years o WIC partiipation, the number o

62 52 WIC reporting and eligible households in eah year gets smaller. For example, only 223 households o 398 households that reported on WIC partiipation and were eligible in 2008 also were in the data system during the three years. Some o these 223 households partiipated in WIC in 2009 or in 2010 while some portion would have dropped out o the program during the next two years. Likewise, eligibility status may also vary over the three years. Appendix 3.2 shows a more detailed distribution o WIC status and eligibility status in 2008, 2009 and As shown in Appendix 3.2, we are able to hek how many households hanged their WIC partiipation status and eligibility status during the years. For example, 119 households o the 223 WIC reporting households in 2008 were not on WIC or the next two years and 31 households returned to the program in 2010 while 73 households ontinued on the program in 2009; 38 households o those 73 households retained WIC status in For the analysis, we deine treatment in the model to be partiipation in the WIC program at least one during three onseutive years or simpliity; the ontrol is deined as households that were never on WIC but eligible at least one year during the 3 years. ii. Identiiation o WIC related ood expenditures Our tentative target ood o interest is grain oods, a group o oods that are widely presribed in the WIC oods pakage. There are our ategories o grain produts in the WIC pakages: bread, ready-to-eat ereal, rie and tortillas. The Final Rule deines whole grain produts as: whole grain or whole wheat bread must onorm to FDA standard o identity (21 CFR ), must be the primary ingredient by weight in all whole grain bread produts and must meet FDA labeling requirements or making a health laim as a whole grain ood with moderate at ontent. Among the new WIC pakage requirements were to require that

63 53 at least one hal o breakast ereals be identiied as whole grain and that whole-grain bread was introdued with allowable substitutions o other whole grains (rie, tortillas) allowed. In this paper, we onstruted a dataset o grain produts that onsist o our ategories as in the WIC pakages: bread, read-to-eat ereal, rie and tortillas. We do not onsider buns, rolls, bagels, or muins as bread but only take bakery bread type; rie inludes pakaged and bulk, anned, mixes and instant orms. In order to ous on the expenditures o grain produts allowed in WIC pakages, we exlude any other grain produts that are not relevant to the WIC program, suh as snak, bread mixes, anned bread, granola or hot ereals et. For the treatment eet analysis, we identiy whole grain produts by separating grain produts into two parts, reined grain produts and whole grain produts based on UPC desription, grain type and produt ategory (produt module) variables in the sanner data. For our analysis o data rom 2008 to 2010, we restrited our inal analyti sample to 3,198 WIC eligible households that reported grain expenditures in all three years as shown in Table 3.4. There are 3,198 households with grain expenditure in three onseutive years that are eligible some time during the years and 312 households report WIC at least one during three years. Similar to previous analysis in Appendix 3.1, we an indiate WIC identiiation and eligibility status or those with three years o grain purhases in Appendix 3.3. By omparing Appendix 3.3 with the previous table o distributions (Appendix 3.2), we note that all o households who were on the WIC program at least a year over the three year period purhased some grain produts during the time period while very ew o households never on the WIC program did not purhase grain produt.

64 54 5. Results Based on our analyti dataset rom the previous setion, we estimate the treatment eet o the WIC program on grain produt expenditure through the propensity sore mathing proedure. Note that as our treatment group is eligible WIC partiipating households, the omparison group is restrited to eligible households not partiipating in WIC. To lariy the terms we use rom now on in the estimation, eligible means eligible at least a year during three onseutive years and partiipating reers to partiipating in the program at least a year during the time period. In the estimation o the propensity sore, the set o ovariates inludes household inome, size, maximum age o the household's heads, the presene o kids under 5, and indiators o employment and eduation level o household heads, rae/ethniity, and regional loation. The desription o variables and summary statistis are shown in Table Several WIC partiipation indiators inluding WIC partiipation at least one during three years and partiipation in eah year are also given. We would expet that household inome and the presene o kids under 5 might be orrelated with partiipation in the WIC program and ood expenditure as those variables are not peretly ontrolled rom the analyti steps or our inal sample. We would expet that the household size and the employment status o either household head (male, emale) might aet the deision to partiipate in the program. Note that it is still possible to have an inome higher than the maximum inome or eligibility in one o the years and still be in the inal sample. For example, a household might have been eligible in the irst two years (2008, 2009) and not be eligible in 2010 beause o earning high inome in We inlude this 19 We alulated summary statistis with the weighted distributions o households in the sanner data.

65 55 household in our analyti sample aording to our deinition o eligibility in the estimation beause the household was eligible at least one year during the three years. Summary statistis or purhases on grain produts are reported in Table 3.6. We alulate monthly average o whole and reined grain expenditures and weights over the 3 years o pooled data, beore and ater the implementation o the WIC pakage hange. Although Otober 2009 was the date approved or implementing the pakage hanges, some states implemented the new rules earlier (see Appendix 3.1). We mathed the inormation on implementation dates to eah household s loation to alulate monthly average expenditures and weights beore and ater the hange in poliy. Table 3.6 shows that both whole grain and reined grain expenditures and weights o WIC partiipating households are greater than those o non-wic households aross the 3 years, beore the hange and ater the hange. In addition, whole grain expenditures and weights o WIC households inreased ater the pakage hange and this at suggests that there may be a potential impat o the WIC hange in boosting expenditures and weights by WIC partiipating households relative to non-partiipating households. In order to have better understanding o the hanges, we ondut a dierene-in-dierene analysis to estimate the WIC impat exluding the possible inluene o the poliy hange in the estimation. The propensity sore is estimated through a logit partiipation model. We are interested in the deision to partiipate in WIC or at least one year during the three years. Table 3.7 presents the results o the estimation o the probability o the household s partiipation in the WIC program at least one in the 3 years. The results with signiiant levels show that household size and the presene o kids under 5 are highly orrelated with WIC partiipation in the model and that the employment o a household s emale head is

66 56 negatively orrelated with WIC program partiipation. The households with relatively older male or emale head are less likely to partiipate in the program. We also observe some loational eets on the partiipation: households in west or south in the United States are less likely to join the program. In order to have a relevant estimator or program evaluation, one might be interested in testing i there is a proper imposition o the ommon support ondition in the estimation o propensity sores through the distribution o propensity sores or eah group. For the assumption to hold true there must be an overlap o the propensity sores o the treatment group and ontrol group. In Figure 1, as an example we report the distribution o predited propensity sores o both treatment and omparison groups in our main model evaluated under the ase o at least one-year partiipation. Most o propensity sores in both treatment and omparison groups all into the range o [0, 0.79]. Thus, it is not unreasonable to impose an assumption o ommon support to ensure that there are suiient overlaps o the probability o the program partiipation in the harateristis. It satisies the irst requirement o using mathing or estimating the treatment eet o WIC program partiipation. We mathed WIC treated and untreated observations based on the estimated propensity sore. In order to hek i the mathing improved the balane o the ovariates among two groups, we ondut balaning tests omparing the mean o eah ovariate beore (unmathed) and ater mathing (mathed) and report the results o the main model in Table 3.8. The average values o eah ovariate, the perentage dierene in means (perentage bias) and p-values or t-statistis o the mean dierenes are reported. Table 3.8 shows that most o variables have more balaned values ater the mathing as the perentage bias o

67 57 eah ovariate were redued exept or ew variables suh as male and emale eduation. 20 The redution o overall bias through the mathing an be seen rom the dierene in mean bias between two samples in unmathed and mathed. With two dierent tests above, we an onlude the propensity sore mathing proess is relevant and suessul or our study on WIC partiipation. Table 3.9 represents the mathing results o average treatment eet on treated (ATET) using estimated propensity sores or the WIC partiipation indiator. We also report the results o inverse-probability weighted regression adjustment (IPWRA) as an alternative to propensity mathing estimators. We estimate at least one year o WIC partiipation on whole grain produt purhases. We are interested in looking at how the experiene o WIC partiipation during the three onseutive years aeted whole grain onsumption over the three years. As the new WIC pakage was implemented during 2009, one might also be interested in seeing the treatment eets beore and ater the introdution o the pakage hange. 21 In addition to that, merely examining treatment eets without the impat o WIC pakage hanges as a positive demand shok is useul. Thereore, we have our outome measures in the analysis between the treatment (WIC program partiipation) and ontrol: (1) the dierene in monthly average expenditure o whole grain produts in , (2) the dierene in average whole grain expenditure beore pakage hange, (3) the dierene in average whole grain expenditure ater pakage hange and (4) the dierene in dierene in 20 Table 3.8 and Figure 3.1 are based on the estimation o NNM(n=10) as the method gives us smaller bias and no o support observation. 21 We reated a variable that indiates whether eah transation o purhasing grain produts ourred beore or ater the partiular date o the poliy implementation. All WIC agenies should have hanged the pakage by Otober In appendix 3, there is inormation o implementation dates or WIC ood pakages by state agenies.

68 58 average whole grain expenditure over WIC pakage hanges. We ompare the results o dierent mathing methods suh as Nearest neighbor mathing, Kernel mathing and Radius mathing to hek the robustness o the estimation results o average treatment eets. We use 10 neighbors in the non-partiipating households to math eah partiipating households omparing with one-to-one mathing. We use 0.06 bandwidth or Kernel estimator and 0.05 radius or Radius estimator whih it well with the data. In Table 3.9, the signiiant dierenes o monthly average whole grain expenditures during three years between treatment and ontrol group are shown over all our mathing mehanisms. Results on households with at least one-year WIC partiipation (Outome A) indiate that WIC partiipating households purhased more whole grain produts over the three years, on average. One interesting observation is that the dierenes o expenditures made ater the WIC pakage hanges are generally higher than the dierenes over the periods that inlude times beore the hanges (Outomes C and B). The treatment eet o WIC partiipation on whole grain expenditures ater the poliy hange seems to be stronger than the eets over all three years. However, there should be positive impat o WIC pakage hanges promoting whole grain onsumption so we need to ontrol the impat o the hange on whole grain expenditures. For the last outome measure (Outome D), we irst took dierenes between average expenditures beore and ater the poliy hanges or eah group and ompared these dierenes by dierent groups. Applying dierene-in-dierene to propensity sore mathing estimation redues the treatment eet by dereasing the size o estimates rom the irst outome to the ourth outome. From this observation, it might be possible to show indiretly the potential impat o the implementation o the WIC pakage hange as being

69 59 positive shok or whole grain purhases. Most o mathing proedures exept one-to-one NNM give us the onsistent result that there is no signiiant treatment eet o WIC partiipation on whole grain expenditures ater we ontrol or the positive eet o the poliy hange on demand. We an interpret the results presented here as showing a signiiant and positive eet o the WIC pakage revision on inreasing whole grain expenditures. The estimation results under our main speiiation are based on the loosened eligibility riteria inluding all potentially eligible households that have either hildren under 5 years-old or woman o hild bearing age. However, there are many women in the age range years old who do not have hildren under 5 or are not pregnant. In order to hek the robustness o our main indings, we disard the observations or households with women o hild bearing age and no hildren under 5. By limiting to households with hildren under 5, we are likely to only miss pregnant women without other hildren at home. We expet this number to be small. We an ontrol or pregnany by looking at whih households added inants in the next year s survey; there were no additional inants reported over in the data. Table 3.10 and 3.11 show that dropping households with no hildren redued the number o total eligible households or eah year and the number o observations ultimately delined to 448 rom The estimation results with the new subsample are shown in the Table By omparing the results in Table 3.9, we observe a similar order o magnitude in the estimates with less statistial signiiane over most o the methods due to a deline o statistial signiiane with the smaller sample size. There are no substantial, signiiant dierenes in 22 This sample has almost 40% o eligible women on WIC, whih is a better math to the national statistis. 23 Table 3.10, Table 3.11 and Table 3.12 with the new subsample are omparable to Table 3.3, Table 3.4, and Table 3.9 with the main speiiation.

70 60 the monthly average whole grain expenditures during the three years (outome A). The period beore the pakage hange (outome B) between treatment and ontrol group are shown over all mehanisms. Most o mathing proedures exept NNM provide some signiiant eet assoiated with WIC partiipation on whole grain expenditures ater the pakage hange outome C - while there is no signiiant treatment eet or outome D on the dierene in dierene estimation. Thus, we onlude that the signiiant eets on outome C were more likely attributed to the poliy hange and not rom the WIC partiipation itsel. Estimating with two dierent samples allows us to show that the results in this paper are onsistent and robust. 6. Conlusion This paper investigates the impat o partiipating in the WIC program on ood purhasing patterns o households. Using Nielsen HomeSan data or , we ompare expenditures on whole grain produts o WIC partiipating households to those o non-partiipating but eligible households using propensity sore mathing methods. The results o the average treatment eet estimation show that the monthly average whole grain expenditures o households with at least one-year WIC partiipation are signiiantly higher than the ontrol (eligible but not partiipating in WIC). The inding that WIC partiipating households purhase more whole grain produts than non- partiipating eligible households is useul or evaluating the eetiveness o WIC program partiipation. A major objetive o the WIC program is to inrease onsumption o healthy oods. Furthermore, in terms o whole grain expenditures, this study may address the issue o reent poliy hange to the WIC ood pakage whih inluded the introdution o whole grain produts to the WIC

71 61 pakages. In order to see the WIC partiipation eet over the pakage hanges, we use dierene-in-dierene propensity mathing estimator and this provides us the result o the potential impat o the ood pakage hanges, implemented as a positive poliy shok. In all three mathing methods, we observed onsistently that it was the poliy shok that played an important role relative to purhasing whole grains rather than the treatment eet o WIC partiipation itsel. A possible extension o the work is to examine the inluene o the WIC pakage hanges on the expenditure o the other relevant ood groups suh as ruit and vegetable might in the similar analysis.

72 62 REFERENCES Andreyeva, T., J. Luedike, A. E. Middleton, M. W. Long and M. B. Shwartz Changes in Aess to Healthy Foods ater Implementation o the WIC Food Pakage Revisions. ERS Report No. 66. Andreyeva, T. and J. Luedike Inentivizing ruit and vegetable purhases among partiipants in the Speial Supplemental Nutrition Program or Women, Inants, and Children. Publi Health Nutrition May(9): 1-9 Aria, G. J., L. A. Crouh and R. A. Kulka Impat o the WIC Program on Food Expenditures. Amerian Journal o Agriultural Eonomis 72(1): Bertmann F. M. W, C. Barroso, P. Ohri-Vahaspati, J. S. Hampl, K. Sell and C. M. Wharton Women, Inants, and Children ash value vouher (CVV) use in Arizona: A qualitative exploration o barriers and strategies related to ruit and vegetable purhases. Journal o Nutrition Eduation and Behavior 46(S1):S53-S58. Bitler, M., J. Currie and J. Sholz WIC Eligibility and Partiipation. Journal o Human Resoures38: Carlson, A and B.Senauer The impat o the speial supplemental nutrition program or Women, Inants, and Children on hild health. Amerian Journal o Agriultural Eonomis 85(2): Colman, S., I. P. Nihols-Barrer, J. E. Redline, B. L. Devaney, S. V. Ansell and Joye, T Eets o the Speial Supplemental Nutrition Program or Women, Inants, and Children (WIC): A Review o Reent Researh. Speial Nutrition Assistane Programs Report No. 7368, Eonomi Researh Servie, U.S. Department o Agriulture.

73 63 Connor, P., S. Bartlett, M. Mendelson, K. Lawrene, K. Wen, et al WIC Partiipant and Program Charateristis Speial Nutrition Programs Report No. WIC-10- PC, Food and Nutrition Servie, U.S. Department o Agriulture. Dehejia, R. H. and S. Wahba Causal Eets in Non-Experimental Studies: Reevaluating the Evaluation o Training Programs. Journal o the Amerian Statistial Assoiation 94(448): Deming D.M., R. R. Brieel and K. C. Reidy Inant eeding praties and ood onsumption patterns o hildren partiipating in WIC. Journal o Nutrition Eduation and Behavior, 46(S3):S29-S37. Edmunds, L. S., J. P. Sekhobo, B. A. Dennison, M. A. Chiasson, H. H. Stratton and K. K. Davison Assoiation o Prenatal Partiipation in a Publi Health Nutrition Program with Healthy Inant Weight Gain. Amerian Journal o Publi Health 104(S1) Herman, D. R., G. G. Harrison, A.A. Aii and E. Jenks The Eet o the WIC Program on Food Seurity Status o Pregnant, First-Time Partiipants. Family Eonomis and Nutrition Review 16(1) Harris, J. M Using Nielsen Homesan Data and Complex Survey Design Tehniques To Analyze Conveniene Food Expenditures. Seleted Paper prepared or presentation at the Amerian Agriultural Eonomis assoiation Annual Meeting, Providene, Rhode Island, July 24-27, Hillier, A., J. MLaughlin, C.C. Cannusio, M. Chilton, S. Krasny and A. Karpyn The Impat o WIC Food Pakage Changes on Aess to Healthul Food in 2 Low-

74 64 Inome Urban Neighborhoods. Journal o Nutrition Eduation and Behavior 44(3): Hirano, K and Imbens, G W Estimation o Causal Eets Using Propensity Sore Weighting: An Appliation to Data on Right Heart Catheterization. Health Servies and Outomes Researh Methodology 2(3-4): Institute O Mediine WIC ood pakages: Time or a hange. The national aademies press. Ishdorj, A., H. H. Jensen, and J. Tobias Intra-household Alloation and Consumption o WIC Approved Foods: A Bayesian Approah. Advanes in Eonometris, 23: Lee, B., L. Makey-Bilaver, and M. Chin Eets o WIC and Food Stamp Program Partiipation on Child Outomes. Contrator and Cooperator Report No. 27, Eonomi Researh Servie, U.S. Department o Agriulture. Metallinos-Katsaras, E., K. S. Gorman, P. Wilde and J. Kallio A Longitudinal Study o WIC Partiipation on Household Food Inseurity. Maternal and Child Health Journal 15(5): Meyers, A. F., T. Herren, S. Levenson, P. H. Casey, C. Berkowitz, N. Zaldivar, J. T. Cook, M. M. Blak, D. B. Cutts, D. A. Frank, J. Geppert and A. Skaliky Partiipation and Inants' Growth and Health: A Multisite Surveillane Study. Pediatris 114(1). Oliveira, V. and R. Chandran Children s Consumption o WIC-Approved Foods. Food Assistane and Nutrition Researh Report No. 44, Eonomi Researh Servie, U.S. Department o Agriulture.

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76 66 Table 3.1 The number o WC reporting households (HHs) in Homesan data WIC-urrently reporting Sanner 2008 Sanner 2009 Sanner 2010 Unweighted WIC reporting HHs 654(1.06%) 372(0.61%) 439(0.72%) Blank (Missing) 60786(98.94%) (99.39%) (99.28%) Total 61440(100%) 60506(100%) (100%) Weighted WIC reporting HHs 2,322,106(1.97%) 1,476,452(1.25%) 1,901,481(1.60%) Blank (Missing) 115,380,000(98.03%) 117,020,000(98.75%) 116,920,000(98.40%) Total 117,702, ,496, ,821,481 Soure: Nielsen Homesan

77 67 Table 3.2 WIC eligible and non-eligible HHs in reporting HHs Sanner 2008 Sanner 2009 Sanner 2010 WIC reporting HHs 654(100%) 372(100%) 439(100%) WIC eligible 398(60.86%) 212(56.99%) 287(65.38%) kids and no hbr women 19(2.91%) 9(2.42%) 8(1.82%) no kids and hbr women 85(13.00%) 52(13.98%) 71(16.17%) kids and hbr women 294(44.95%) 151(40.59%) 208(47.38%) WIC non-eligible 256(39.14%) 160(43.01%) 152(34.62%) high inome 230(35.17%) 141(37.90%) 138(31.33%) no kids and no hbr women 26(3.98%) 19(5.11%) 14(3.19%) Soure: Nielsen Homesan

78 68 Table 3.3 WIC reporting HHs in eligible HHs (pir <=200 and hildren or hbr women) Sanner 2008 Sanner 2009 Sanner 2010 WIC reporting and eligible HHs in eah year WIC reporting HHs 398(8.50%) 212 (4.75%) 287 (6.49%) Blank (Missing) 4286(91.50%) 4377 (95.25%) 4137 (93.51%) Total WIC eligible HHs 4694(100%) 4459 (100%) 4424 (100%) WIC reporting and eligible HHs among HHs with any purhases o three onseutive years WIC reporting HHs 223(9.84%) 128 (5.79%) 123 (5.62%) Blank (Missing) 2039(90.16%) 2081(94.21%) 2067(94.38%) Total WIC eligible HHs 2266(100%) 2209(100%) 2190 (100%) Soure: Nielsen Homesan Table 3.4 WIC reporting HHs in eligible HHs with grain purhases in three onseutive years Sanner WIC reporting and eligible HHs* 312 Non-WIC but eligible HHs 2886 Total eligible HHs with any grain purhases 3198 Total HHs with any grain purhases in three years HHs with any grain purhases in eah year in in In Soure: Nielsen Homesan * At least one year o WIC reporting with at least one year o WIC eligible.

79 69 Table 3.5 Deinitions and Statistis on the Variables or Sampled Households Variable Mean Std.Dev Minimum Maximum N Number o inal analyti sample HHin Household inome ($) HHage Maximum age o the two household's heads Fhage Age o the household s emale head HHsize Household size Binary Variables (equal 1 i ollowing onditions met, and 0 otherwise) WIC_id Household reports WIC partiipation at least one during WIC08 Household reports WIC partiipation in WIC09 Household reports WIC partiipation in WIC10 Household reports WIC partiipation in Kids Household has a kid under 5 year olds Edmsol Male household head s eduation is ollage level Edsol Female household head s eduation is ollage level Empl Female household head is employed Emplm Male household head is employed Blak Household's sampled person s rae is Blak Hispani Household's sampled person s ethniity is Hispani West Region is west South Region is south Central Region is entral Soure: Nielsen Homesan The number relets the total number o eligible households with any grain purhases in three onseutive years households do not have inormation o emale head age.

80 70 Table 3.6 Summary Statistis on Monthly Average Grain Expenditures ($) and Weights (OZ) Ater 3 year pooled data Beore pakage hange pakage hange WIC Whole Grain Exp.(N=309) (N=312) Reined Grain Exp.(N=312) Total Grain Exp Non WIC Whole Grain Exp.(N=2853) (N=2886) Reined Grain Exp.(N=2885) Total Grain Exp Di. in Whole Grain Exp. Between WIC and Non-WIC HHs WIC (N=312) Whole Grain Weight(OZ) (N=309) Reined Grain Weight(OZ) (N=312) Total Grain Weight(OZ) Non WIC Whole Grain Weight(OZ) (N=2853) (N=2886) Reined Grain Weight(OZ) (N=2885) Total Grain Weight(OZ) Di. in Whole Grain Weight(OZ) Between WIC and Non-WIC HHs Soure: Nielsen Homesan

81 71 Table 3.7 Partiipation model WIC partiipation at least one over three years Coe. Std. Err. In=hhin/ hhsize 0.375*** hhsize*in kids 3.554*** in*kids hsize*kids hhage ** hhage edmsol empl ** edsol emplm blak hispani west ** south ** entral _ons Number o obs Log likelihood LR hi2(17) Pseudo R Soure: Nielsen Homesan

82 72 Table 3.8 Balaning test Unmathed Mean %redut t-test Variable Mathed Treated Control %bias bias t p>t in Unmathed Mathed hhsize Unmathed Mathed kids Unmathed Mathed hhage Unmathed Mathed edmsol Unmathed Mathed empl Unmathed Mathed edsol Unmathed Mathed emplm Unmathed Mathed blak Unmathed Mathed hispani Unmathed Mathed west Unmathed Mathed south Unmathed Mathed entral Unmathed Mathed Sample p>hi2 MeanBias MedBias Raw Mathed Soure: Nielsen Homesan

83 73 Table 3.9 Treatment eets o WIC partiipation on whole grain expenditures ($) Treatment: Partiipation during three onseutive years Nearest Nearest Kernel Radius IPWRA Unmathed Neighbor Neighbor Mathing (N=1) (N=10) (BW=0.06) (r=0.05) Outome A =Di in Average Expenditure o Whole Grain in (Monthly ) 1.135** 1.100*** 1.092*** 1.066*** 0.968*** 1.333*** (0.3610) (0.3431) (0.3130) (0.3021) (0.2951) (0.2202) Outome B = Di in Average Whole Grain Expenditure beore pakage hange *** *** (0.3580) (0.3457) (0.3230) (0.2753) (0.2947) (0.2331) Outome C = Di in Average Whole Grain Expenditure ater pakage hange 1.578*** 1.442*** 1.450*** 1.660*** 1.268*** 1.738*** (0.3705) (0.3776) (0.3406) (0.2979) (0.3251) (0.2483) Outome D = Di in Di in Average Whole Grain Expenditure over WIC pakage hanges 0.862** *** (0.3055) (0.2840) (0.2843) (0.2973) (0.2712) (0.197) Number o observations Number o treated(wic ever) used Number o untreated(never WIC) used Soure: Nielsen Homesan The standard errors in parenthesis are alulated rom bootstrapping with 500 repetitions. *** signiiant at the 1 perent level, ** signiiant at the 5 perent level, * signiiant at the 10 perent level.

84 74 Table 3.10 WIC reporting HHs in eligible HHs with Subsample (or Robustness hek) Sanner 2008 Sanner 2009 Sanner 2010 WIC reporting and eligible HHs in eah year WIC reporting HHs 313(27.38%) 160 (15.72%) 216 (22.27%) Blank (Missing) 830(72.62%) 858 (84.28%) 754 (77.73%) Total WIC eligible HHs 1143(100%) 1018(100%) 970(100%) WIC reporting and eligible HHs among HHs with any purhases o three onseutive years WIC reporting HHs 141(29.38%) 74(16.41%) 85(20.38%) Blank (Missing) 339(70.63%) 388(83.59%) 332(79.62%) Total WIC eligible HHs 480(100%) 451(100%) 417(100%) Soure: Nielsen Homesan Table 3.11 WIC reporting HHs in eligible HHs with grain purhases in three onseutive years with Subsample (or Robustness hek) Sanner WIC reporting and eligible HHs* 177 Non-WIC but eligible HHs 271 Total eligible HHs with any grain purhases 448 Total HHs with any grain purhases in three years HHs with any grain purhases in eah year in in In Soure: Nielsen Homesan

85 75 Table 3.12 Treatment eets o WIC partiipation on whole grain expenditures ($) in Subsample (or Robustness hek) Treatment: Partiipation during three onseutive years Nearest Nearest Kernel Radius IPWRA Unmathed Neighbor Neighbor Mathing (N=1) (N=10) (BW=0.06) (r=0.05) Outome A =Di in Average Expenditure o Whole Grain in (Monthly) * 1.118* 1.313*** Outome B = Di in Average Whole Grain Expenditure beore pakage hange Outome C = Di in Average Whole Grain Expenditure ater pakage hange * 1.486** 1.493** 1.543*** 1.695*** Outome D = Di in Di in Average Whole Grain Expenditure over WIC pakage hanges Number o observations Number o treated(wic ever) mathed Number o untreated(never WIC) mathed Soure: Nielsen Homesan

86 Propensity Sore never on WIC WIC more than one Figure 1 The distribution o the estimated propensity sores Soure: Nielsen Homesan

87 77 APPENDIX A. ADDITIONAL MATERIAL FOR CHAPTER 3 Appendix 3.1 Poliy Implementation Dates: Month in 2009 when State WIC Agenies implemented the ood pakage revisions State Month in 2009 Delaware, New York January Kentuky, South Carolina May Colorado June Utah July Illinois, Kansas, Mihigan, Oklahoma, Oregon, August Wisonsin Minnesota, South Dakota Alabama, Alaska, Arizona, Arkansas, Caliornia, Connetiut, Florida, Georgia, Hawaii, Idaho, Indiana, Iowa, Louisiana, Maine, Maryland, Massahusetts, Mississippi, Missouri, Nebraska, Nevada, New Hampshire, New Jersey, New Mexio, North Carolina, North Dakota, Ohio, Pennsylvania, Rhode Island, Tennessee, Texas, Vermont, Virginia, Washington, West Virginia, Wyoming, Distrit o Columbia September Otober Montana November Note: List does not inlude Indian Tribal Organizations (ITO).

88 78 Appendix 3.2 The distribution o WIC reporting and eligible HHs with three-year reporting Table o Elig status by WIC status Frequeny Elig status WIC status Perent never 08only 09only 10only 08 & & & 10 08,09 & 10 Total 08only only only & & & ,09 & Total Soure: Nielsen Homesan

89 79 Appendix 3.3 The distribution o WIC reporting and eligible HHs with three-year grain purhases Table o Elig status by WIC status Frequeny Elig status WIC status Perent never 08only 09only 10only 08 & & & 10 08,09 & 10 Total 08only only only & & & ,09 & Total Soure: Nielsen Homesan

90 80 CHAPTER 4. UPSTREAM AND DOWNSTREAM STRATEGIC FOOD SAFETY INTERACTIONS Introdution When making inal preparations or home meals, the preparers views on ingredient wholesomeness matter. These views determine eort at the last deense or preventing oodborne illnesses. For example, the risk o ross-ontamination an be redued by washing hands and utting boards in meal preparation, and by keeping ood at the right temperature. Thoroughly ooking meats and raw eggs might be one good way to redue the risk o inetion by pathogens suh as E. oli O157:H7. That onsumer s pratie toward ood saety plays an important role in reduing ood-related risk has been irmly established aross a wide variety o praties. The sope o analyses on onsumer ood handling is varied. Literature speii to ood saety behaviors onsiders praties suh as leaning the kithen area, transporting and storing o seleted oods, keeping ood temperatures, and ooking hamburgers (Fein et al., 2011; Mattik et al., 2003; Godwin and Coppings, 2005; Hudson and Walley, 2009; Ralston et al., 2001). Meanwhile, muh o the eonomis literature on ood saety presumes that the household, and speiially the main meal preparer, praties sae ood handling and studies onentrate more on ontrols at the ood produer setors. In the literature related to onsumer responses to ood saety signals, studies mainly ous on the eets o inormation and quality o ood, ood saety risk, the eets o ood saety inidents and shoks, and the value that onsumers plae on ood saety (Piggott et al., 2007; Jensen and Choi, 1991; 26 An earlier version was prepared and presented as a Seleted Paper at the Agriultural & Applied Eonomis Assoiation s 2014 AAEA Annual Meeting, Minneapolis, MN, July 27-29, 2014.

91 81 Grunert, 2005; Arnade et al., 2008; Kivi and Shogren, 2010). A gap exists in the literature in regard to eonomi analyses o how the onsumer s protetion inentives aet the risk o ood-borne illnesses. Little is known about modeling the onsumer s deision-making proess in regard to own ood saety eorts. The oversight is important beause the beneit to be derived rom poliies that seek to inluene on-arm and proessor ood saety eorts will depend upon how onsumer eorts adjust to these poliies. In this study, we investigate strategi interations among ood saety eorts by upstream ood proessors and downstream onsumers in the presene o unertainty. One o the ew studies to examine suh interations is Elbasha and Riggs (2003). They investigate a simultaneous-move game solving Nash equilibrium or ood saety eorts when losses are inident on both parties. While their model presumes simultaneous moves, in reality onsumers make deisions later and have reason to take produer ations as given so that a natural alternative is to posit an upstream irm as irst mover and onsumers as seondmovers. Our Stakelberg model setting is more similar to Roe (2004). Roe (2004) ompares liability assignment rules or a onsumer and produer, both risk neutral, in a two-stage deision setting and provides an in-depth investigation o damage untion non-onvexities. He ontrasts the impats o strit liability with negligene liability rules. We will also make this omparison. Our analysis is distint in several ways. The model onsiders asymmetri timing in moves, thus allowing the upstream agent to move irst. By ontrast with earlier work we allow or risk aversion on the onsumer s part so that the unertainty that is an essential eature o ood saety events has impliations or onsumer behavior. Finally the timing and

92 82 risk aversion dimensions in our model allow or poliy analyses not available in earlier works, and we ollow through on these opportunities. Our analysis ontrasts ood saety inentives and outomes aross two dimensions, tehnology and liability assignment. In the tehnology ontrast, ood saety eort by eah party an be either a suess or a ailure and we assume statistial independene between the suess probabilities. Given this, however, two very dierent maps between eort outomes and ood saety outomes are onsidered: weakest link and best shot (Hirshleier, 1983). In weakest link i one or both o two ations ails then the outome is a ailure, i.e., a ood saety event ours. This relationship is an instane o omplementary interations between eorts beause the marginal value o one entity s eort inreases with the other entity s eort level. In best shot i either or both o the ations is a suess then the ood is sae. In this ase eorts are substitutes in that one party s eort has less impat at the margin when the other party inreases eort. We examine how the sort o tehnial interation between upstream and downstream eorts aets behavior strategies when responded to ood saety risk. The seond ontrast is between inentives under dierent liability rules. Aommodating the liability rules or ood saety has reeived attention in the ood saety literature (Rouvière and Caswell, 2012; Pouliot and Sumner, 2008; Buzby and Frenzen, 1999; Roe, 2004). Roe (2004) is the losest in spirit to our work in that it also onsiders two liability rules- strit liability and negligene in a bilateral aident setting. However, the urrent study diers in having a riher tehnologial struture, inluding risk aversion and allowing or onjetures other than nash. The analysis in this paper is ounded on the ramework o sel-protetion and sel-

93 83 insurane aing ood saety risk. As probability and severity are the two elements that deine risk, dereasing either element, privately or olletively, an redue risk (Shogren, 1990; Ehrlih and Beker, 1972). Ehrlih and Beker (1972) deined and systematially illustrated sel-protetion, a redution in loss probability, and sel-insurane, a redution in loss size. We expliitly examine the sel-protetion inentives o both onsumer and produer to derease the probability o ood saety risk with the ixed severity o a loss under the assumption that there is no sel-insurane motive to derease the size o loss. The relevant example o an undesirable environmental externality in the sel-seletion literature is investigated in Shogren and Croker (1991). Shogren and Croker (1991) analyze selprotetion investments by ooperative and nonooperative agents or transerable externality and extend the model to a Stakelberg two-stage game to examine the eets o strategi ommitment upon sel-protetion. However, the assoiation between sel-protetion and risk aversion is absent in their study. The relationship between sel-protetion inentive and risk aversion is an intriguing issue (Lee, 2012; Briys and Shlesinger, 1990; Dionne and Eekhoudt, 1985). For example, Dionne and Eekhoudt (1985) and Briys and Shlesinger (1990) demonstrate that selinsurane eorts inreases as risk aversion inreases, but this is not neessarily true or selprotetion eorts (Jullien et al., 1999). In this paper, we explore how risk aversion aets onsumer and upstream behavior, where it is known that more risk-averse agents may possibly protet less. As ar as we know, none o the extant literature on sel-protetion inentives onsiders strategi issues. The paper is organized as ollows. We irst explain our general two-stage model setup, whih allows or dierent tehnologies as well as or dierent liability rules. The irst-

94 84 best hoies are identiied. Turning to strategi settings, we develop inentives under our settings (weakest link, best shot) (strit liability, negligene). We use bakward indution to solve the expeted utility maximization problem or a downstream onsumer in Stage II. Then we solve or the upstream proessor s Stage I ost minimization problem to obtain the optimal levels o preventative eort. Ater solving or the Stakelberg equilibrium in eah ase, omparative statis are provided to asertain strategi interations between both eorts as well as how onsumer risk aversion aets eah eort type. We lose with a summary and disussions o poliy impliations. 2. Model Set-up We model a single upstream ood proessor and a representative downstream ood user. The user ould be a restaurant or an at-home onsumer. Ations are taken at two time points, or stages. At Stage I the upstream irm takes ation at ost x. At later Stage II the onsumer takes ation osting x. The onsumer moves in ull knowledge o the irm s earlier ation. Food prie is ixed throughout the analysis and will be ignored. Two liability rules are onsidered, strit liability and negligene. One intent in this inquiry is to relate these rules to tehnial settings. Under strit liability, whih we label as SL, the upstream irm is liable whenever a ood inident ours. Under negligene, labeled as N, the irm is liable whenever the irm is negligent even i the onsumer s ation does not sueed. Let Gx ( ) and H( x ) be the respetive probabilities that the onsumer and irm sueed in their part when seuring sae ood. Respetive irst derivatives are given by gx ( ) and hx ( ). Probabilities o ailure in either task are written with a bar on top, i.e., Gx ( ) and H( x ).

95 85 We assume that these events are independent, but how suess in these ativities maps into sae ood is another matter. In the manner o a opula (Sklar, 1959), these suess probabilities ombine to orm the umulative probability o having sae ood to eat as J[ G( x ), H( x )]. Where onvenient, to simpliy notation we will write J ( x, x ) or short. Eah ation has positive but delining marginal impat on this outome, i.e., J ( ) 0, J ( ) 0, J ( ) 0 and J ( ) 0. Ations involve sel-protetion in the sense o Ehrlih and Beker (1972), i.e., they aet state probabilities and not state outomes. It remains to state and then motivate the struture o J (, ). Weakest Link Assumption The weakest link, or WL, tehnology setting is when J( x, x ) G( x ) H( x ), i.e., both irm and onsumer must sueed i the ood is to be sae. Notie that J ( ) 0, i.e., eorts are tehnial omplements in the most diret sense. As the weakest link terminology suggests, eorts are likely to omplement when the intent o both is to keep a pathogen out. An instane is washing ativities, whih ours on paking lines and in kithens. A ontamination event will our i either a proessor or at home user allows produe to be ontaminated. In this ase, Pr(se: ) 1 and Pr(se: s) Gx ( ) where we use se or ood saety event, or irm ails, and s or irm sueeds. Thus, Pr(se) J ( x, x ) 1 G( x ) H( x ) in the ase o weakest link. Best Shot Assumption The best shot, or BS, tehnology setting is when J( x, x ) 1 G( x ) H( x ), i.e., it is only neessary that one or other party sueeds or the ood to be sae. Here, J ( ) 0 so

96 86 that eorts are tehnial substitutes in this very diret sense. Eorts are likely to substitute when the intent o both is to kill a pathogen that is already in, so that ooking and irradiation (mirowave) are examples. I either eort sueeds then the problem has been addressed. In this ase, Pr(se: ) Gx ( ) and Pr(se: s) 0. We model the impat o damage through saling ator D e on onsumer utility. Quantity L is the monetary liability aed by the upstream irm, while [0,1] indiates extent o traeability/transpareny whih we take to be the ration o liability that is olleted. Damage and traeability parameters allow us to onsider poliy interventions through government penalties, ourt imposed ines and publi investments in traing tehnologies. The model an be adapted to aommodate alternative orms o poliy intervention. Roe (2004) and Pouliot and Sumner (2008) study related, but distint problems, absent risk aversion and strategi dimensions. Elbasha and Riggs (2003) do onsider the strategi dimensions but absent risk aversion and presuming simultaneous moves. The onsumer is held to have initial wealth w, CARA risk preerenes risk aversion parameter 0, so that utility in the healthy state is e (wealth) and ( w x ) e and utility in the unhealthy state is D ( w x L) D ( w x L) e e e. Note here that damage and inome onsiderations enter the utility untion in distint ways, where inome/wealth eets are mediated by the degree o risk aversion but damage is not. In this way we separate monetary risk preerenes rom preerenes over adverse health events. We assume that D L so that ompensation does not exeed damage. As liability and the traeability/transpareny index enter in a multipliative manner throughout, or the sake o simpliity we will write P L rom this junture on. We intend or P to be interpreted broadly, to inlude marketplae penalty or damage to reputation as well as any diret regulatory penalty. Also, due to the CARA utility struture, wealth w may be ignored and we will do so rom this

97 87 point on. The upstream irm is risk-neutral and seeks to minimize the expeted sum o preventive and liability osts while reognizing the onsumer s reation. The our (WL, BS) (SL, N) settings lead to the ollowing our objetive untions or the irm s Stage I problem; (1) *, WL min x C( x, ( )) x x *, BS min x C( x, ( )) x x N : min x x ( ), H x P *,WL,SL SL: min x x [1 ( ( )) ( )], G x x H x P *,BS SL: min x x ( ( )) ( ), G x x H x P *,BS N : min x x ( ( )) ( ). G x x H x P with generi solution *, x. The determination o x *,WL,SL ( x ) and x *,BS ( x ) will be explained shortly. Several omments are in order onerning (1) above. One is that under BS the Stage I inentive strutures are the same or the irm regardless o liability rule. Were the irm to sueed in its task then the liability rule does not matter. Were the irm to ail then the events o strit liability and negligene are synonymous. The seond is that or either rule expeted osts are weakly larger under WL than under BS as there are more ways to ail under WL. Under WL too, expeted osts are larger when the strit liability rule applies than when the negligene rule applies as the irm s probability o inurring a ine is larger when subjet to the strit liability rule. In addition, or WL the expeted ost redues to the same expression under either rule when G x *, ( ( x )) 1. I the onsumer always sueeds then the distintion between liability rules is moot regardless o tehnology orm. Finally, the negligene rule possesses an interesting strategi onsequene when the tehnology is WL. Then the irm is always ound to be negligent when it ails beause suess in its task is essential. This essentiality separates the irm s hoie rom the onsumer s hoie and the irm has no

98 88 strategi motive to at, where by strategi motive we mean an intent to inluene hoie x. By ontrast, when the tehnology is BS then the irm may seek to underinvest in eort and ore the onsumer to inur the ood saety ost. Corresponding to (1), there are three Stage II onsumer problems. For WL and SL the onsumer s problem is to (2) WL,SL D( xp) x max x U ( x, ) max [1 ( ) ( )] ( ) ( ), x x G x H x e G x H x e with generi solution x *,WL,SL ( x ). Here there are two possible outomes; i) where there is not a se (ourring with probability G( x ) H( x ) ), and ii) where there is a se so that the irm pays P (ourring with probability 1 G( x ) H( x )). For WL and N the problem is (3) WL,N D x D ( x P) x max x U ( x, ) max ( ) ( ) ( ) ( ) ( ), x x G x H x e H x e G x H x e with generi solution x *,WL,N ( x ). Here there are three possible outomes; i) as above, where there is not a se (ourring with probability G( x ) H( x ) ), ii) where there is a se, the irm ailed and pays P (ourring with probability G( x ) H( x ) G( x ) H( x ) H( x ) where the irst let-hand term represents ailure by the irm only and the seond let-hand term represents ailure by both irm and onsumer), and iii) where there is a se, the irm did not ail and P is not paid (ourring with probability G( x ) H( x ) ). For BS and either liability rule the problem is (4) BS D( xp) x max x U ( x, ) max ( ) ( ) [1 ( ) ( )]. x x G x H x e G x H x e

99 89 with generi solution x *,BS ( x ). Here there are two possible outomes; i) where there is not a se (ourring with probability 1 G( x ) H( x ) ), and ii) where there is a se so that the irm must have ailed and onsequently the irm pays P. We seek to understand the nature o the dierent reation untion x *, ( x ) that arise in the onsumer problem, inluding onditions under whih x *, ( x ) is monotone. This will allow us to understand the nature o inentives aing the upstream irm. Were x *, ( x ) inreasing then the upstream irm will be inentivized to enourage onsumer protetion by applying high eort itsel. Were the untion dereasing then the upstream irm will have inentives to ree-ride, plaing the burden on the onsumer. We also seek to understand how *, x is aeted by poliy and related parameters. Finally, we seek to understand how risk aversion parameter aets onsumer and upstream behavior, where it is known that more risk averse agents may be inentivized to protet less, see, e.g., Jullien et al. (1999). Given the problem s temporal struture the approah taken is, o ourse, to irst solve Stage II and then allow the irm to use imputed reation untions when ating in Stage I. 3. First-Best Outomes Weakest Link Assumption Under the weakest-link tehnology, the onsumer s expeted utility may be written as (5) (, ) ˆ [1 ( ) ( )] ( ) ( ), WL,SL r( x, x ) Dx x U x x u e G x H x e G x H x e so that ertainty equivalent is (6) 1 r( x, x ) ln (1 p) e pe Dx x ln [1 ( ) ( )] ( ) ( ). 1 D G x H x e G x H x x

100 90 Thereore we may write aggregate ertainty equivalent return as the dierene between onsumer ertainty equivalent and irm eort; 27 1 D (7) r( x, x ) x ln [1 G( x ) H( x )] e G( x ) H( x ) x x. This reveals that the welare maximization problem may be posed as (8) D( x x ) ( x x ) x, x G x H x e G x H x e max [1 ( ) ( )] ( ) ( ), and optimality onditions are (9) D e G( x ) H ( x ) g( x ) H ( x ) ; ; D e 1 G( x ) H ( x ) G( x ) h( x ). Some manipulation then delivers (10) gx ( ) hx ( ) ; G( x ) H ( x ) G( x ) H ( x ) g( x ) H( x ). The irst o these two optimality onditions shows that, whenever G() and H() are both logonave (Bagnoli and Bergstrom, 2005), higher irst-best values o x and x will rise or all together. Consequently it is readily apparent that an inrease in risk aversion parameter will lead to an inrease in irst-best levels o both eort hoies. Best Shot Assumption Under the best-shot tehnology, the onsumer s expeted utility is given as (11) (, ) ˆ (1 ) ; 1 ( ) ( ), BS,SL r( x, x ) Dx x U x x u e p e pe p G x H x so that aggregate ertainty equivalent return an be written as 1 D (12) r( x, x ) x ln G( x ) H( x ) e 1 G( x ) H( x ) x x. The welare maximization problem may be posed as 27 Notie that penalty is a transer and so would not enter the alulation.

101 91 (13) D( x x ) ( x x ) x, x G x H x e G x H x e max ( ) ( ) 1 ( ) ( ). First-order onditions are (14) G( x ) H ( x ) g( x ) H ( x ) ; D D ( e 1) e G( x ) H ( x ) G( x ) h( x ). D D ( e 1) e x I we set G( x ) 1 e and H( x ) 1 then the optimality onditions beome and irst-order onditions are x e (15) xx ( ) e ; D e 1 xx ( ) e. D e 1 The onditions reveal that, with the given tehnologies the eorts are peret substitutes up to a produtivity saling ator, the soially optimal solution is to use only the more ost eetive eort. Use only onsumer eort whenever, only upstream eort whenever, and be indierent whenever they are equally produtive. When then the soially optimal eort levels are x D ln[ / ( )] ln[1/ ( e 1)] and so 1 1 x 0. so When then the soially optimal eort levels are x 0 and so x D ln[ / ( )] ln[1/ ( e 1)]. Notie that in either ase irst-best eort so 1 1 delines with an inrease in risk aversion. The reason or this peuliarity is the input s selprotetive nature. 4. Bakward Indution Stage II, when Firm Moves First In this setion we seek to understand the onsumer s optimal hoie in light o the

102 92 irm s deision so as to understand onsumer reations that the irm ating at Stage I an seek to manipulate. We assume that the ost untion is onvex, but will return to the issue when x onsidering speii examples. Throughout we set G( x ) 1 and H( x ) 1 e x e. It is assumed throughout that, i.e., that the eort sensitive o onsumer s probability o task ailure d ln[ G( x )]/ dx is large when ompared with degree o risk aversion. Why this assumption is needed is explained in the appendix, where Stakelberg seond-order onditions are established. Were risk aversion the larger o the two then orner solutions would be supported in that onsumers would have unlimited inentive to protet and so redue risk exposure. Weakest Link and Strit Liability In the ase o objetive untion (2), the irst-order optimality ondition resolves to x M DP (16) ( ) e ; ; M e 1. x 1 e M 1 where we write the solution as x *,WL,SL ( x ). Letting / ( ), some algebra establishes (17) *,WL,SL 1 DP 1 x 1 1 DP x x x ( x ) ln( e 1) ln(1 e ) ln( ) ln(1 e e ). Notie here that the term 1 ln( ) is dereasing in so that the value o x *,WL,SL ( x ) may well derease in the degree o risk aversion even absent any onsideration on how irm eort is impated by risk aversion. As to why this is possibility arises, bear in mind that x is a sel-protetion input impating probability o loss and not state-onditioned extent o loss, see eqn. (2).

103 93 Weakest Link and Negligene In the ase o objetive untion (3) the optimality ondition resolves to (18) D x x ( )( e 1)(1 e ) e DP x x ( e e 1). Consequently, (19) *,WL,N 1 x DP x x D x ( x ) ln(1 e ) ln( e e 1) ln( ) ln( e 1) D *,WL,SL 1 e 1 x ( x) ln. DP e 1 and (20) *,WL,N *,WL,SL DP x dx ( x ) dx ( x ) e e 0. DP x x x dx dx ( e e 1)(1 e ) So under the weakest-link tehnology and either, ations are omplementary in the sense o tehnologial inputs. Remark 1: Under the weakest-link tehnology and either liability struture, the onsumer s reation to an inrease in proessor ood saety eort is to also inrease eort. It ollows that any poliy intervention intent on inreasing irm eort should have a positive strategi impat on onsumer eort. Best Shot In the ase o BS, the irst-order ondition arising rom (4) resolves to (21) e * x e e DP x ; 1 with solution x *,BS ( x ). Solving expliitly, we have (22) *,BS 1 DP 1 x ( x ) ln( e 1) ln( ) x,

104 94 revealing that eorts are peret substitutes. The onsumer s reation untion is haraterized by derivative dx *,BS ( x ) / dx / 0 so that we may assert; Remark 2: Under the best-shot tehnology and either liability struture, the onsumer s reation is to derease eort (and in linear manner) in response to an inrease in proessor ood saety. A omparison o remarks 1 and 2 shows that the qualitative nature o onsumer reations to irm hoies will depend upon the tehnology setting, where our view is that both weakest link and best shot tehnologies are plausible approximations to reality. Stage I We turn now to irm hoie. In addition to managing diret eets o eort on eort osts and any liabilities, the irm an take advantage o strategi opportunities to guide the onsumer s behavior. (Fudenberg and Tirole, 1984). These strategi opportunities are the matter o this setion. Weakest-Link and Strit Liability Insert expression (17) or *,WL,SL x x ( x ) into G( x ) 1 e to obtain (23) e DP ( *,WL,SL ( x )) 1 DP x. G x ( e 1)(1 e ) so that the appropriate objetive untion is (24) e P 1 DP *,WL,SL x min x C( x, ( )) min (1 ). x x x x P e P e DP Thus, the optimality ondition is *,WL,SL (1 ) P e x with expliit solution *,WL,SL x 1 ln[(1 ) P]. The expression is independent o D but not o. Figure 4.1

105 95 depits how *,WL,SL x is determined. As x 0 i and only i *,WL,SL e *,WL,SL x 1, it ollows that, or weakest-link and strit liability, x 0 i and only i (1 ) P 1. This observation will prove to be useul when interpreting expressions to ollow. Dierentiate the optimality ondition to obtain (25) *,WL,SL *,WL,SL dx 1 dx 1 0; 0; dp P d ( ) omparative statis that are readily diserned rom Figure 4.1. Remark 3: Under the weakest-link tehnology and strit liability struture, the irm inreases eort as the penalty inreases and also as the onsumer s level o risk aversion inreases. The origin o the response to a penalty is lear, that o the response to risk aversion less so. As already noted, the onsumer s response to risk aversion is ompromised due to the sel-protetive nature o eort. Given the omplementarity embedded in the weakest-link tehnology (see Remark 1) and strit liability, and to the extent that onsumer response to risk aversion is muted, the irm has a strong sel interest in stepping up its protetive eort to limit probability o liability. Perhaps ounterintuitively, the irm s ation may oneivably be more sensitive to onsumer risk aversion than the onsumer s own eort. For interior solutions, *,WL,SL * x ( ) 1 ( ) / ( ) H x e P P. From (17) then we have (26) DP *,WL,SL 1 DP 1 ( ) e P 1 x ln( e 1) ln ln( ). P Next, rom (26), (27) *,WL,SL DP 2 2 DP dx ( e 1) P e 1 P. DP DP d [( )( e 1) P]( e 1) ( P ) ( )

106 96 To asertain that this response an be negative, let P D/ so that dx *,WL,SL / d. On the other hand, when P ( ) / ( ) then the irst right hand term is inite but the 1 seond right hand term onverges on value lim 1/. As the penalty aing the irm grows the onsumer sees the probability and ost o loss derease and so risk aversion eases to be a motivation or eort. 0 Now dierentiate with respet to the penalty: (28) *,WL,SL DP DP dx ( )( e 1) P( P ) e DP DP dp ( e 1)( P ) ( )( e 1) P DP e 1 P( P ). sign The sign is undetermined without urther assumptions. Two ores are at play. Complementarity suggests that an inrease in penalty that eliits more proessor eort should also eliit more onsumer eort. On the other hand, strit liability reates a orm o moral hazard suh that the onsumer may seek to lean on irm eorts. It is lear rom (28) that i both the penalty and the oeiient o risk aversion are low then onsumer eort will respond positively to a penalty. We saw above that when the penalty is low then onsumer eort inreases strongly to an inrease in degree o risk aversion, beause level o eort is very low. However, as the oeiient o risk aversion inreases then onsumer eort beomes less responsive to the penalty. When risk aversion is strong then the onsumer is likely already applying muh eort. Given strit liability, when the penalty inreases then the onsumer sees advantage in handing over ood saety responsibilities to the irm and utting eort osts. WL and Negligene

107 97 From (1), the goal is to min x x x x e P, so the irst-order ondition is 1 e P and the optimal solution is *,WL,N x 1 ln( P) where P 1 is required to ensure an interior solution, i.e., i P 1 then x 0 so that the irm aepts penalty P with *,WL,N ertainty. Three ontrasts are apparent with *,WL,SL x as arrived at rom (24). One is that, as the objetive untion makes transparent, the irm s optimal hoie under the negligene rule is independent o D and. Firm inentives are not oupled with onsumer inentives. Another is that strit liability provides stronger inentives to the irm, i.e., *,WL,SL *,WL,N 1 (29) x x ln( ) 0. The third is that this dierene is independent o the penalty s magnitude, P, whih, as in (19) or onsumer eorts, has a ommon eet on eah eort level and nets out. Remark 4: Under the weakest-link tehnology, optimal irm eort when subjet to strit liability exeeds optimal eort when subjet to the negligene rule and the dierene is inreasing in the onsumer s level o risk aversion. Risk aversion matters only under strit liability beause then the irm an be liable when ailure ours on the onsumer side. As a onsequene, and in light o the tehnial omplementarity pointed out in Remark 1, the irm possesses a strategi motive that does not exist under the negligene legal rule. Insert *,WL,N x 1 ln( P) into the Stage II optimality ondition or WL and N, or (19), to obtain *,WL,N 1 1 DP 1 D 1 (30) x ln( P 1) ln( e P 1) ln( e 1) ln( ).

108 98 It ollows that (31) *,WL,N DP 2 dx e ( P P ) ( P 1), DP d ( e P 1)( ) and (32) *,WL,N DP dx [ ( P1)] e 0, DP dp ( P 1)( e P 1) given the assumption that P 1. Regarding (31), the denominator is ertainly positive. I P 2 P 0 then the numerator is negative and dx *,WL,N / d 0. The quadrati s maximum value is when /2 so that it suies to know whether P 4. Thus in the negligene setting, dx *,WL,N / d 0 whenever 4 / P 1/. So, assuming that penalty P is low and irm eort is interior, the omparatively more risk averse onsumer takes less eort. Again, the eort s sel-protetive nature is maniest. Remark 5: Under the weakest-link tehnology, the negligene liability rule, and interior irm eort, the privately optimal level o onsumer eort is i) inreasing in the level o penalty, and ii) dereasing in the level o risk aversion whenever 4 / P 1/. We turn now to a diret omparison o onsumer eort aross liability rules. From dierening (26) and (30) we have (33) x ( e 1)( P ) 1 e P 1 ln ln. ( e 1)[( ) e P ] P 1 DP DP *,WL,SL *,WL,N x D DP Without urther inormation we annot establish whether the onsumer aing the weakest link tehnology when under the strit liability rule takes more eort than when under the negligene rule. We know rom Remark 4 that the irm takes more eort when under the strit liability rule. Given omplementarity, this should promote omparatively more onsumer eort under the strit liability rule. On the other hand, the user s loss under strit

109 99 liability are omparatively lower and so moral hazard eets will be omparatively stronger under the strit liability rule. To probe the matter urther, suppose that the penalty is as large as we will allow it to be, speiially when P D/. Then (34) x D ln 0. ( e 1) ( D) 2 *,WL,SL *,WL,N 1 (1 1)( ) x D Alternatively, suppose that the penalty is low, suh that P 1. Then (35) x negative and inite D/ D / *,WL,SL *,WL,N 1 ( e 1) 1 e x ln ln. D D / ( e 1)[( ) e ] P 1 Remark 6: In weakest link, when the penalty is suiiently i) low then onsumer eort under strit liability exeeds that under negligene; ii) high then onsumer eort under strit liability is lower than under negligene. As to why these outomes arise, when the penalty is high and the rule is strit liability then the onsumer is better able to ree-ride o the irm. When the penalty is low then the irm takes little eort and is likely to be deemed negligent. There is little inentive to reeride o irm eort but the strategi motive to respond positively to any irm eort remains. Best Shot From (1), the goal is to x G x x H x P. From (21), we have * min x ( ( )) ( ) (36) *,BS x *,BS e ( ( x )). DP G x e 1 Thereore, G x x H x e and the goal beomes *,BS D ( ( )) ( ) 1/ ( P 1) P (37) min x x, D P e 1

110 100 with solution x 0. The irm, having the irst-move, exploits the opportunity to impose *,BS the ost o ood saety eort on the onsumer. From (22) then we have (38) *,BS 1 D P 1 x ln( e 1) ln( ), so that (39) *,BS DP dx Pe 1 0; DP d ( e 1) ( ) dx dp *,BS DP e 0. DP ( e 1) Remark 7: Under best-shot, the onsumer s eort delines as the onsumer s level o risk aversion inreases and also as the penalty inreases. As under weakest-link, the response to degree o risk aversion arises rom the input s sel-protetive nature. Turning to the adverse penalty response, this is most disturbing rom the poliy viewpoint. Due to moral hazard eets, under either liability rule an inrease in penalty redues onsumer inentive to are while the irm s onern about the penalty is dominated by its desire to oist aretaking responsibility on the onsumer. The penalty does not enourage the irm to take eort, but the prospet o ompensation disourages the onsumer rom taking eort. The poliy intervention is ineetive. Remark 8: Under best-shot and either liability rule, the probability o a ood saety event inreases as the penalty imposed or a ailure inreases. We turn now to a omparison with outomes under simultaneous moves. 5. Simultaneous Moves In this setion we modiy irm and onsumer objetive untions to the simultaneous

111 101 moves ontext. Notie rom (1) that the (40) 2 d C x (, x ) dx dx 0 or WL and SL, 0 or N, 0 or BS. Thus, the irm aing a weakest-link tehnology and strit liability has marginal ost that is dereasing in onsumer eort while the irm aing a best-shot tehnology has a marginal ost that is inreasing in onsumer eort. From (1), it is also noteworthy that (41) 0 or WL and SL, (, x) 0 or N, dx dp 0 or BS; 0 or WL and SL, (, x) 0 or N, dxdp 0 or BS. 2 d C x 2 d C x So, regardless o ontext, the marginal ost o irm eort dereases as the penalty inreases and the same is weakly true or the ross impat o penalty and onsumer eort on marginal ost. We turn now to onsumer inentives in nash equilibrium. As in (2), or WL and SL the onsumer s problem is to (42) WL,SL D( xp) x max x U ( x, ) max [1 ( ) ( )] ( ) ( ), x x G x H x e G x H x e with ross-derivative (43) 2 d U WL,SL ( x, x ) DP x h( x )[ ( ) ( )]( 1) g x G x e e. dx dx x Now with G( x ) 1 e and, the latter inequality to ensure problem onvexity, then

112 102 (44) 2 d U WL,SL ( x, x ) ( )[( ) x D P h x ]( 1) x e e e 0. dx dx The inputs omplement so that any exogenous inrease in irm eort reinores onsumer inentives. For WL and N the onsumer s problem is to (45) WL,N D x D ( x P) x max x U ( x, ) max ( ) ( ) ( ) ( ) ( ), x x G x H x e H x e G x H x e and the own-eort derivative is (46) so that du dx WL,N 0 () e G x e G x g x e e H x e du dx dx 2 WL,N D P D D x D ( x P) ( ) ( ) ( )( 1) ( ) 0, 0 () x e G( x ) e G( x ) g( x )( e 1) e h( x ) 0. D P D D (47) For BS the onsumer s problem is to (48) BS D( xp) x max x U ( x, ) max ( ) ( ) [1 ( ) ( )]. x x G x H x e G x H x e The irst-order ondition an be written as 0 BS du () x e [ g( x ) G( x )]( e 1) e H( x ) 0, dx x DP (49) so that 0 2 BS du () x [ g( x ) ( )]( 1) G x e e h( x ) 0. dx dx DP (50) Figure 4.2 depits how the onsumer s optimality ondition hanges in response to an inrease in irm eort under weakest-link and either liability rule.

113 103 Remark 9: Under i) weakest-link and either strit liability or negligene rule, nash equilibrium irm and onsumer hoies will be lower than under stakelberg; ii) best-shot and either rule, we annot ompare without urther inormation. The reasoning or i) is that in stakelberg the irm has the opportunity to oster oordination through irst movement. 28 All are better o as in neither ase are inentives suiient to support irst-best. This point has been made beore by Hennessy, Roosen and Miranowski (2001) but in a ooperative game where surplus is shared via the Shapley value. The poliy impliations o i) are several, where three are provided below. Communiation between the irm and the onsumer is a orm o irst movement where Ellingsen and Östling (2010) have shown that ommuniation ailitates oordination given positive spillover payos similar to those in our model. Examples o suh behavior are not hard to ind. As with other ommodity organizations, the National Turkey Federation o the United States seeks to link with onsumers through reipe books, at home ood saety reommendations and evidene o its members ommitment to ood saety, see, e.g., To be eetive, ommuniation must reah reeptive ears. Inormation is more likely to have the intended eet when the message is learly interpreted. Eduation matters, as in a basi understanding o mirobiology and the hemistry o ooking among the general population. Also, in reality pre-onsumer prodution and proessing typially involve many agents. Conerns about suboptimal eort are likely to grow in systems that involve many autonomous agents proessing and then trading on, see, e.g., Collins (1993). Vertial integration an signal to the onsumer that beggar thy neighbor ood saety interations in the 28 A proo an be established by arguments analogous to the proo o Proposition 1 in Hennessy, Roosen and Miranowski (2001).

114 104 marketing hannel are being addressed. Chinese government onerns about loss o onsumer onidene in its domesti prodution is a ase in point. Commening a deade or more ago, its government has sought to oster oordination through promotion o larger, more integrated proessing irms (Gale and Hu, 2012). Enored minimum proessing standards are also a means o imposing irst-mover status on the proessor, though these standards will only matter i binding. The impliations o minimum standards are most interesting or the best shot tehnology, bringing us to part ii) and more generally to poliy when eorts substitute. Minimum standards will ore the proessor not to ree-ride but will allow the onsumer to do so. Whether the resulting equilibrium is soially preerred is unlear. By ontrast, the ase or minimum standards under weakest link tehnologies is learer. Although proessors will be better motivated in stakelberg than in nash, they are unlikely to apply suiient eort. As a result, onsumers are also unlikely to apply suiient eort. A standard above the stakelberg level or proessor eort is likely to improve soial welare. 6. Disussion Food saety deisions are not made in isolation and ood systems are linked in omplex ways. The growth o downstream value added and inreased speialization in the ood hain has led to an inrease in the number o hain partiipants. A seminal insight rom Coase (1937) is that the boundaries o the irm matter, in part beause o tradeos between ageny and tehnial osts. These ageny osts an arise rom private inentives that are poorly aligned with soial welare and oordination ailures even when inentive alignment is good. This paper has onsidered a very simple problem o strategi interation between a single upstream ood proessor and a representative ood onsumer. We show how the ood saety prodution tehnology an matter, paying partiular attention to penalties and extent o

115 105 onsumer risk aversion in determining equilibrium outomes. We also ompare with irstbest and nash equilibrium to demonstrate that a role exists or leadership in poliy interventions. Several o our indings might be viewed as ounterintuitive and these stem partly rom the sel-protetive nature o ood saety eorts. Examples are where a penalty and a minimum eort standard may do more harm than good while onsumers may take less eort when they are more risk averse. The extent to whih these possible outomes arise depend on several ators. One is the atual tehnology, as in whether weakest-link and keep ood saety problems out nature or best-shot and get rid o existing ood saety problems best depits the situation. Another is whether proessors and onsumers understand the tehnology that they are dealing with. These are matters or urther investigation.

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120 110 Figure 4.1 Firm s eort under weakest link tehnology and strit liability, as inentives hange. Figure 4.2 Consumer s private optimality ondition, as irm eort hanges.