## Consumer Demand for Me at Cuts and Seafood 1 Christopher Davis, 2 Steven Yen, and 3 Biing-Hwan Lin



# Selected Paper

American Agricultural Economics Association 2007 Annual Meeting, July 29- August 1, Portland, Oregon

1 Economist with the Markets an d Trade Economics Division, Economic Research Service, U.S. Department of Agriculture. 1800 M street, NW, Washington D.C. 20036. Phone: (202) 694-5167. Email Address: chrisdavis@ers.usda.gov 2 Associate Professor in the Department of Agricultural Economics the University of Tennessee, Knoxville, Tennessee. Phone: (865) 974-7474. Email address: syen@utk.edu

3 Senior Economist with the Food Economic Division, Economic Research Service, U.S. Department of Agriculture. 1800 M Street, NW, Washington D.C. 20036. Phone: (202) 694-5458. Email Address: blin@ers.usda.gov1

Abstract Household at-home consumption of different ty pes and cuts of meat and fish products is investigated by estimating a large censored dema nd system with a two-step procedure using

ACNielsen’s Homescan data. We find different price and expenditure elasticities between lowincome and high-income households. High inco me households are less responsive to price changes, and the substitution patterns also diffe r between the low- and high-income households. Whereas the uncompensated elasti cities suggest a mixture of gr oss substitutes and complements among the products for both low- and high-inco me households, the compensated elasticities suggest net substitution is the obvious pattern for the low-income households 1

.

Key words : censored dependent variables; sa mple selection model; meat; fish

JEL Classification: D12; C34

1 Disclaimer : The opinions and analysis presented represent the authors’ idea and do not necessarily reflect Economic Research Servi ce or the U.S. Department of Agriculture position.2

Meat is the number one source of protein for most Americans in th eir daily diets and is the maincourse of each meal they consume. Americans’ per-capita meat consumption is one of the topthree highest in the world. Consumption of beef, pork, and fish over the past decade has declined or increased only marginally compared to the re latively rapid increase for poultry, resulting in a growing per-capita consumption of total meat and fish. In 2004, each American consumed 201 pounds, on a boneless “carcass” weight, of beef, pork, poultry and fish (USDA-ERS). Identifying the factors that underlie the grow ing meat consumption will allow examination of the effects of policy and market shocks on and prediction of futu re meat demand. U.S. me at industries can also make use of such information to design effective meat marketing strategies. Coinciding with the growth in meat consum ption have been challenges both consumers

and meat industries have had to consider. There ha ve been a number of di sease outbreaks in the beef cattle and poultry industries around the world that have fueled a growing interest in determining what effects these types of incident s have had or might have on the consumption of meat products. Essential pieces of information fo r understanding consumers’ responses to meet supply shocks are the demand elas ticities for the meat products. The overall objective of this analysis is to investigate the pr ice and non-price factors affecting the demand for specific cuts of meat, such as steaks, ground beef, pork ham, por k chops, processed pork, chicken/turkey breasts and wings, leg-quarters, ot her meat cuts, as well as types of fish. There is a large body of empirical literature on demand for meat products in the U.S., but less has been done to examine such demand by cuts. Aggregated meat models have been estimated extensively and re ported throughout the literature (Eales and Unnevehr 1993; Kinnucan et al. 1997; Moschini and Meilke 1989; Purcell and Raunikar 1971; Thompson 2004). Results from the aggregate meat models, spec ifically the price and the income/expenditure3

relationships and statistical significance, are im portant information and pr ovide insights to the validity and to some degree, the accuracy of our research findings. Using a dynamic framework based on in the A lmost Ideal Demand System for beef, pork and chicken, Kesavan et al. ( 1993) found demands for beef and pork are not as price responsive as chicken, results that are in contrast with the Moschini and Meilk e (1989) findings that demands for beef and pork are much more own-pr ice and expenditure elastic than chicken or fish. Kesavan et al. (1993) also reported th at beef, pork, and chicken are substitutes among themselves rather than complements as found by Moschini and Meilke (1989) except for beef and pork which are found to be substitutes. To tal expenditure elasticiti es for beef, pork, and

chicken are all inelastic and are so demands for the products not very responsive to changes in disposable income according to Kesavan et al. (1993). Eales and Unnevehr (1988) conducted one of the few studies that examine disaggregate meat products, particularly whole birds, parts and processed chicken, hamburgers, beef table cuts, pork, and non-meat foods also using a dyna mic Almost Ideal Demand System approach. Their results indicated that significant and fairly large cross-price substitution effects existed between two chicken products and between two beef products, as well as among chicken parts, processed chicken and pork. The empirical results suggest that whole birds and hamburgers are inferior goods, while chicken parts/proce ssed and beef table cu ts are normal goods. Cheng and Capps (1988) investigated th e demand for finfish (cod, flounder/sole, haddock, perch and snapper) and sh ellfish (crabs, oysters and shrimp). Each expenditure equation was estimated separately, using the tw o-step procedure for Heckman’s (1979) sample selection model. Explanatory variables incl uded regional, urbanization and demographic variables as well as prices of poultry (whole chicken), red m eat (sirloin steak, round steak,4

ground beef, and loin chops) and fish. All own-pr ice elasticities for fr esh and frozen seafood products were negative, statisti cally significant, and inelastic except for oysters (which was elastic). Poultry is a gross complement for snappe r, and red meat is a gross substitute for both cod and snapper. Income elasticities for crabs, oysters, and total finfish are positive and statistically significant, implyi ng that these goods are normal goods. Capps and Lambregts (1991) disaggregated finfish (including cat fish, oreodory, tuna, pollock, perch, scrod, salmon, flounder, trout, white fish, halibut, swordfish, rockfish and shark) and shellfish (such as shrimp, crab, lobster, oysters, and scallops) products obtained from scanner data and estimated their relationships to the demand for beef, pork and poultry using a seemingly unrelated regression approach. Their findi ngs indicated that all own-price elasticities are negative, elastic (with the exception of oysters), and statis tically significant. Cross-price elasticities signify that poultry and beef are co mplements for shrimp and lobster; pork is a substitute (complement) for rockfish (tuna); poultry is a substitute (complement) for tuna (trout); and beef is a substitute for pollock, swordfish, a nd rockfish. They also found other finfish to be substitutes for catfish, whitefish, halibut, swordfish, and rockfish. In this study we disaggregated beef, pork, and poultry into mo re cuts than in previous studies, and unlike the single-equation approach as used in Cheng and Capps (1988), we investigate the demand for these meat products al ong with different types of fish by estimating a theoretically plausible system of demand functions (henceforth, demand system). We separate fish into finfish and shellfish as in Cheng and Capps (1988) and Capps and Lambregts (1991),

but divide finfish into saltwater and freshwater fish, along with three of the more popular fish products consumed: shrimp, tuna and salmon. This study also includes non-price variables such as socio-demographic characteristics. AC Nielsen’s 2004 Homescan data are used. The5

Homescan data include weekly household food pur chases (expenditures a nd quantities) for home consumption, product attributes, and promotion information (sales and use of coupons). The sample data contains zero observations in the expenditure levels of most products that are accommodated with a multivariate sample selection model (Yen and Lin 2006), estimated with a two-step procedure initiate d by Shonkwiler and Yen (1999).

Demand Specification and Econometric Procedure Our empirical analysis is based on the assumption that meat and fish are separable from all other consumer goods. We use a demand system derive d from the Translog indirect utility function (Christensen, Jorgenson, and Lau 1975) for n goods:

(1) 1 0 1 11 1 log ( ,..., , ) log( / ) log( / )log( / ), 2 n nn n i i ij i j i ij Vp p m p m p m p m

= == =α − α − β ∑ ∑∑

where p 1 ,..., p n are prices and m is total meat and fish expenditu re (henceforth, to tal expenditure). Applying Roy’s identity to Equatio n (1) yields the deterministic equations for expenditure-share ( s i )

(2) 1

1 11 log( / ) , 1,..., . log( / ) n j i ij j i n nn j kj j kj j p m s in p m =

= ==

α+ β ∑

= = α+ β ∑ ∑∑ Homogeneity is implicit in Equations (1) and (2) by the use of normalized prices ( p i / m ), and the symmetry restrictions (3) , ij ji i j β =β ∀

are imposed. Demographic variables h l are incorporated in the demand system (2) by6

parameterizing α i such that 2

(4) 0 1 , 1,..., 1. L ii i hi n

= α =α + α = − ∑ l l l Such demographic specifications for the n –1 equations (only) are explained below.

To accommodate zero observations in th e expenditure shares, we use a two-step estimation procedure suggested by Shonkwiler a nd Yen (1999), formally motivated by the multivariate sample selection model of Yen (2005) and Yen and Lin (2005). Let

1 1 [log / ,...,log / , ,..., ] n L p m p mh h ¢ = x be a vector of explan atory variables and let θ be a vector containing all parameters ( α ’s and β ’s), and consider an n -equation system in which each expenditure share w i is generated by a deterministic function f i ( x ; θ ) which constitutes the RHS of the share equations (2), a nd an unobservable error term i v . The first k equations are subject to the sample selection rule

(5) [ ( ; ) ], 1,..., ( ; ) , 1,... i ii i

i i w df v i k f v ik n = +=

= + =+ x

x θ θ

such that each indicator variable d i is modeled with a binary probit (6) 1( 0), 1,..., i ii d u ik ′ = +> = z γ where 1(

⋅ ) is a binary indicator function, z is a vector of explanatory variables, i γ is a vector of parameters, and u i is a random error.

2 It can be verified that along with the specifi c form of the indirect utility function (1) this linear demographic specification implies the effect of demographic variable h l on expenditure for good i is directly related to the corresponding parameter i α l . The Translog indirect utility function is often written with opposite signs fo r the coefficients of the linear terms log( p i / m ) to those in Equation (1), in which case the effect of h l on expenditure of good i are indirectly related to i α l .7

The expenditure shares in Equati on (5) do not add up to unity unless 1 ... 1, k d d = = = that is, when none of the dependent variables are subj ect to sample selection. We follow the simple approach suggested in Yen and Lin (2006), by estimating the first n

− 1 equations with the n th good treated as a residual category (cf. Pudney 19 89). The resulting estimates are not invariant with respect to the equation excluded. Yen and Lin (2006) however demonstrated in an application to food consumption in China that excluding alternative equations from the system

did not cause discernable differences in the elasticity estimates. Assuming the concatenated error vector 1 1 11 [ ,..., , ,..., , ,..., ] k kk n u uv vv v + - ¢ is distributed as ( k + n –1)-variate normal distribution with zero means a nd a finite covariance matrix with elements ( , 1,..., 1) ij ij k n σ = + - , the sample selection model can be estimated with the ML procedure

(Yen and Lin 2006). However, for a large syst em (14 equations), the ML procedure would require estimation of a much larger number of parameters than the two-step procedure and, worse of all, evaluations of k -level integration (where k is the number of products containing zero expenditures) for all sample observations wh ich, along with the large sample size for the current application, is not feasible. 3 A practical alternative is to estimate the system with a twostep procedure. The two-step procedure is motivated by the unconditional mean of the expenditure shares (7)

, ( ) ( ) ( ; ) ( ), 1,..., i i i i k ii i i Ew f i k + ′ ′ =Φ +σ φ = zx z

γθ γ

where φ (

⋅ ) and Φ (

⋅ ) are univariate standard normal pr obability density and cumulative

distribution functions , respectively, and

, k ii + σ is the covariance between the error terms of the i th

3 In the current application we estimate n – 1 = 13 equations with k = 12 equations subject to sample selection, which requires estimation of a 25 × 25 covariance matrix with 325 elements.8

selection ( u i ) and the i th level equation ( v i ). The unconditional means (7) follow from the bivariate normality of error terms [ , ] i i u v ¢ for i = 1,..., k , and suggest a two-step estimation procedure which, as initially suggested in Shonkwiler and Yen (1999) for a linear system, consists of two steps: (i) a probit es timation based on a binary outcome for d i = 1( w i > 0) to

obtain ML estimates ˆ i γ for each of i = 1,..., k ; (ii) estimate the partially augmented nonlinear

system

(8) ˆ ˆˆ ( ) ( ; ) ( ) , 1,..., ( ; ) , 1,..., 1 i ii i i i

i i w f ik f v ik n ′ ′ =Φ +ηφ +ξ =

= + =+ − zx z

x γθ γ θ with ML or other procedures, such as an iterated seemingly unrelated regression procedure (where i ξ is a composite and heteroscedastic error term). The partially augmented second-step system (8) relates to the partially selected syst em in Equation (5) and (6) (also see Yen and Lin (2006)) and is a slight modification of the procedure in Shonkwiler and Yen (1999) where sample selectivity is corrected for every equation in the system. This slight modification is needed in modeling systems with mixed censo red-noncensored goods as the first-step probit

cannot be estimated for commodities with no or few zero observations. The two-step estimates are less efficient than the ML procedure in Yen and Lin (2006) but are st atistically consistent. Demand elasticities can be derived by differentiating the unconditional mean (7) for censored goods and by differentiating the share equations for other goods by conventional means.

Data Data for the different cuts of meat and type s of fish are compiled from ACNielsen’s 2004

Homescan data. The data come from a nationa lly representative pa nel of U.S. household consumers, who recorded food items purchased for at-home consumption. At home panel9

householders scanned in either the Uniform Pr oduct Code (UPC) or a designated code (for random weight food items) for all food items purchas ed at all retail outlet s. The data include product characteristics, quantity and expenditure for each food item purchased by the household, as well as detailed household demographics. Th e Homescan data are well suited for estimating household food demands for home consumption. The complete Homescan panel consists of more than 50,000 households, but only 12,000 households reported purchases of both random-w eight and UPC-coded food items in 2004. We use data from 8,229 of these households that repo rted purchases for at least 10 months in 2004.

Household income and household size are used to express income as a percent of the Federal poverty level, defined as the poverty-income ratio (PIR). At a cutoff PIR of 350 percent, the sample is stratified into low- and high-income groups. Numerous types of meat and fi sh products were recorded in the Homescan data, which is especially true for UPC-coded foods. There is a detailed description of each UPC-coded food item. As the first step, we specified about 100 si milar types of meat and fish products. Then we calculated their shares of the total spending on meat and fish and then combined them into 46 groups. For example, there are 7 different cuts of beef, ground beef, steak, roast, stew, ribs, beef bacon, and other beef. It is not feasible to es timate a demand system for 46 food categories. In this study, we put more emphasis on fish products than has previously been done, focusing on 14 meat and fish groups: ground beef, beef steaks, other beef, pork, boneless poultry (chicken and turkey), other poultry, other meat, shrimp, other sh ellfish, freshwater fish (mainly catfish, trout, and tilapia), salmon, other saltwater finish, canne d tuna, and other canned fish. All expenditures are aggregated to an annual level. Descriptive statistics for these product groups are provided in

table 1.10

The price for each product group is derived as the unit value—defined as the expenditure divided by the corresponding quantity. One methodol ogical issue relates to unobserved prices, or unit values, for products not purchased by the hou seholds. Empirical analysts have struggled with only limited success in addressing the missing-price issues, drawing on the missing wage literature in labor supply es timation (e.g., Wales and Woodla nd 1980). Apart from a lack of instruments to predict prices paid by consumers with differe nt characteristics, the common practice of attributing price differentials solely to quality differences (thus mixing the missingand endogenous-price issues ) is also questionable. 4 We follow a simple procedure of filling the missing prices with regional averages for co rresponding market areas where the households reside. The Homescan data provide two types of location data—four Census regions and 52

scantrack markets for all urban areas. In this stud y, we derived average prices for each of the 14 meat and fish groups by the 52 scantrack markets plus all rural areas as a whole to proxy the prices faced by non-consuming households. 5 This “zero-order imputation” is both simple and straightforward, although more complicated appr oaches to such missing- price issues might be considered in future analyses. Table 1 presents the sample statistics. Ot her meat is a broad category consisting of sausage, hot dogs, various lunch meats, and cann ed meats. It was consumed by 98.2% of the low-income households and 97.6% of the high- income households; it also has the highest average expenditure (over $100 per year) and ex penditure share (approximately 30%) among all products considered, for both the low-income a nd high-income households. Other poultry is the

4 Whereas demographic variables such as gende r and education can be good predictors of wage rates according to human-cap ital theory, using these variables to predict prices paid for food items is less convincing.

5 Alternative proxies for missing prices might include average prices by Census regions.11

next popular item for both low- and high-income households, with over 80% of the households consuming and nearly $50 per year in average spending. This is followed by ground beef, with over 80% of the households consuming and for which low-income households spend considerably more (an average of $56.4 per year among the c onsuming households) than highincome households ($49.8 per year). Pork was consumed by about 79.6% of the households and averaged over $60 per years in spending by both the low-income and high-income households. It is also worth noting that steaks were consumed by a larger propor tion of households in the highincome sample than that of the low-income sa mple; the average spending is also much higher among the high-income households ($73.9 per year among the consuming) than the low-income households ($54.3 per year among the consuming). These different consumption patterns, such as the larger average expend iture of ground beef by low-income households, steaks by highincome households, and larger proportion of st eak-consuming households in the high-income sample, are likely to be disguised by the use of pooled sample and highlight the importance of segmenting the households by income level. Among the fish products, canned tuna was consumed by over 70% of the low-income households with an average spending of $13. 1 per year, and by 69.4% of the high-income households with an average spending of $15.5 pe r year among the consum ing. Other canned fish includes all canned fish except ca nned tuna (the bigge st canned fish item), which was consumed by slightly over 80% of both low-income and hi gh-income households, with a mean spending of over $16 per year. The proportion of consuming households are considerably lower among both low-income and high-income households for othe r fish products, most of which have a mean expenditure share of under 7% ev en among the consuming households . In general, higher prices for fish were paid than for meat products. For in stance, the average price of shrimp paid by the12

low-income households is as high as $6.41 per lb., followed by $4.88 for other shellfish, $4.88 for freshwater finfish, and $4.73 for salmon. The prices of meat products are considerably lower except steaks, which is $4.25 per lb. paid by the low-income households. High-income households in general paid a slightly higher price for each corresponding product than did lowincome households. The lowest prices paid are se en in other poultry and other canned fish, at $1.34 and $1.26 per lb. respectively, for the low-income households. Also presented in table 1 are sample stat istics for demographic variables. Average household size is 2.54 for the low-income sample and 2.24 for the high-income sample. Both samples are dominated by households headed by individuals between 40 and 60 years of age,

with 56% of the low-income households in th at category and an even higher proportion (67%) for the high-income sample. The racial and ethnic ity distribution of Homescan panelists is 75% Whites, 14% Blacks, 9% Hispanics, 2% Asians and 2% other races for the low-income sample. The high-income sample features a slightly higher propor tion of Asians (4%). It is important to note that this is household distribution not popula tion distribution. Hispanic households tend to be larger in size than other households, so the Hi spanic share of U.S. households is smaller than the share of U.S. population.

Estimation Results An empirical issue in the two-step estimation is selection of explanatory variables for the first and second steps. Due to the nonl inear functional forms in the selectivity te rms and expenditure share equations the model is fully identified even without exclusion restri ctions. Our empirical strategy is to economize on the demographic variable s in the second-step due to the large size of13

the demand system. 6 Variables used in both steps are household size, and dummy variables indicating age of the household head (< 40 and 40–60), races (White, Black, Hispanic and Asian), regions (East, Central and South) and pres ence of children. As the first-step requires only univariate probit estimation, additional variable s are included in the selection equation. These variables are PIR and dummy vari ables indicating marital status of household head (married, widowed and divorced), education (high school, some college, and college and above), and employment status of household heads. Our jus tification for excluding these variables from the second step is that the relevant income variable in a demand syst em is total expenditure (and not income) and these education and employment variab les are directly related to household income.

While the marital status variables are not direct ly related to income, they are excluded mainly because of the problems encountered during nonlinear estimation. The large proportions of households consumi ng other meat (98.2% for the low-income sample and 97.6% for the high-income sample) prevented reliable estimation of the selection equation and therefore, following the partially augmented second-st ep system in equation (8), this product category was not co rrected for sample selectivity. ML estimates of the selection equations are not presented due to space consideration, but

we summarize the results here. 7 First, inclusion of all variables is justified by statistical significance. For instance, for th e low-income sample, household si ze is significant in all but four (pork, freshwater finfish, salmon and othe r saltwater finfish) of the thirteen equations estimated, and PIR is significant in all but three equations (g round beef, other shellfish and canned tuna), while presence of children is si gnificant in only three equations (ground beef,

6 Nonlinear functional form can fa il to generate sufficient variat ion to identify the parameters in some applications.

7 First-step results are available upon request.14

boneless chicken and other saltwater finfish). All multiple-category dummy variables (age, races, regions, marital statuses, and educa tion) are also justified by statis tically significant. Second, as to goodness of fit, McFadden’s R 2 values are mostly below the 5% statistical significance level, despite the large sample size, which is not unusual for cross-sectional data. However, for correction of sample selectivity, predictive power of the selection equations weighs more heavily than goodness of fit. The percenta ge of correct predictions, at a probability cut-off of 0.5 (Wooldridge 2002, p. 465), are all greater than 60 %, ranging from 64.2% for shrimp to 81.6% for ground beef and other poultry for the low-in come sample. The predictive powers of the selection equations are comparab le for the high-income sample. The second-step estimates for the Translog de mand system are presented in table 2 for the low-income sample. Among the demographic va riables, household size has negative effects on the consumption of pork, freshwater finfish, salmon and other saltwater finfish. Relative to their older counterparts, house holds headed by younger individua ls (age < 40, 40–60) spend less (i.e., a smaller proportion of tota l expenditure) on other beef, por k, other poultry, but more on ground beef and salmon. Racial differences are notable, with White households spending more on ground beef and steaks but less on freshwat er finfish; Black house holds spending more on pork and other poultry but less on other meat a nd canned tuna; Hispanic households spending more on steaks, other beef, other poultry but le ss on freshwater finfis h and other saltwater finfish; and Asian households spending more on steaks and pork but less on other saltwater

finfish and canned tuna. That As ian households spend less on finf ish is somewhat of a puzzle, given the important role of fish in Asian’s diet (Bean 2003). As in the probit analysis, regional differences are also obvious. Specifi cally, relative to those in th e West, households in the East spend more on pork, shrimp and canned tuna but less on ground beef, steak s, other beef, other15

meat and other saltwater finfish; households in the Central region spe nd more on pork and other meat but less on steaks, other beef, boneless pou ltry, other poultry and canned tuna; whereas households in the South spend more on pork but less on boneless poultry and other poultry. Presence of children increases consumption of ground beef, boneless poultry and freshwater finfish but decreases consumption of other meat. Among the 105 coefficients for the quadratic price terms ( β ij ), slightly under one-half (or 47) are statistically significant at the 10% level of significance or higher. As to the selectivity terms, the covariance estimates for all the meat products and tw o of the fish products (shrimp and canned tuna) are significant at the 10% leve l or higher. The significance of the covariance estimates (and selectivity variables) highlight s the importance of accommodating the zeros in expenditure shares. Turning to the second-step estimates for th e high-income households, presented in table 3, the effects of age are sim ilar to those for the low-inco me sample. Specifically, younger households spend less on other beef, pork, and other poultry than older households, whereas spending on other shellfish is also lower by households in the 40–60 age category. Whites spend more on boneless poultry and other meat but less on other poultry, fr eshwater finfish, salmon and other saltwater finfish; Blacks spend more on other poultry but less on ground beef, steaks, other beef, salmon and other saltwater finfish; Hi spanics spend more on steaks and boneless poultry

but less on other saltwater finfish. The Asia n households spend more on shrimp, less on ground beef and, similar to findings for the low-in come sample, less on ground beef, other saltwater finfish and canned tuna. As in the low-income samp le, regional differences are also notable. As for coefficients for the quadratic price terms, over one half (or 56%) of the coefficients are statistically significant at the 10% level of significance or higher. In addition, the selectivity16

terms are significant in all but one equation (other saltwater finfish) at the 10% level or higher.

Demand Elasticities

Low-Income Households Table 4 presents the uncompensat ed price and expenditure elas ticities for the low-income sample. All own-price elasticities are statistically signi ficant, are slightly greater than (though not statistically different from) unity (in absolute values) for ground beef, other poultry, shrimp and other shellfish, and statistically greater than unity for pork, bone less poultry, freshwater finfish, salmon, and other saltwater finfish. Demands for freshwater finfish and salmon are notably elastic, having own-price elasticities of –1.89 and –1.72, resp ectively. About one third of the uncompensated cross-price el asticities are significant, s uggesting a mixture of gross complements and substitutes among the products. Both substitutability and complementarity exist among the meat products. For instance, grou nd beef is a gross complement for steaks but gross substitutes to boneless poul try, other poultry and freshwater finfish. Pork is a gross substitute to boneless poultry and th ree of the fish products (other saltwater finfish, canned tuna and other canned fish), and bonele ss poultry is a gross substitute to the other meat products such as ground beef, other beef, pork and other poultry. Gross substitutability is the more obvious pattern among the fish products. The total expenditu re elasticities vary widely, ranging from 0.21

for canned tuna and 0.38 for other canned fish to 1.18 for other beef and other saltwater finfish. Although the expenditure elasticit ies for ground beef, steaks, other beef, pork, boneless poultry, other poultry, shrimp, other shellfish, freshwat er finfish and other sa ltwater finfish are only slightly above unity, they are all estimated with relative high precision, re latively to the crossprice elasticities, and are si gnificantly greater than unity.17

Table 5 presents the compensated price el asticities for the low-income households. The compensated own-price elasticities are significantly greater th an unity for boneless poultry (– 1.28), freshwater finfish (–1.78) and salmon (–1.62) and are no diffe rent (statistically) from unity for ground beef (–0.94), pork (–0.95), other poultry (–1.01), shrimp (–1.08), other shellfish (– 1.07) and other saltwater finfish (–1.24). The remaining products have compensated own-price elasticities under unity, ranging from –0.59 for other meat to –0.81 for other beef. Unlike the uncompensated elasticities which suggest a mixt ure of gross substitutes and complements among the meat and fish products, the compensated cros s-price elasticities suggest a pattern of net substitutions. For no obvious reason, steaks are ne t complements for ground beef, other beef and salmon, as are ground beef and other beef for steaks, boneless poultry for canned tuna, and other canned fish for ground beef and boneless poultry. Ground beef, pork and other meats are net substitutes to most other products according to the cross-price elastic ities. The compensated cross-price elasticities exhibit le ss of a pattern for freshwater fi nfish, salmon and other saltwater finfish, with about one half of the cross-price elasticities being positive.

High-Income Households The uncompensated price and total expenditure elasticities for high-income households are presented in table 6. All own-pri ce elasticities are significant a nd negative but, in contrast to

elasticities for the low-income households, these elasticities are all significantly less than unity, ranging from a low –0.26 for shrimp, to –0.34 for ca nned tuna, to as high as –0.91 for pork and – 0.94 for other poultry. Among the significant cross- price elasticities, 54 are negative and 38 are positive. Unlike the low-income households for whic h steaks are not responsive (significantly) to most other prices, the cross-price elasticities su ggest steaks are a gross complement for all other18

meat products except pork and for three of the fish products (salmon, other saltwater finfish and canned tuna). Pork, other beef, other poultry and other meat are gross complements for most of the other meat products. Other more obvious patte rns include the cross- price elasticities of salmon and other canned fish and, perhaps less o bviously, other saltwater finfish, which suggest gross substitution among many of the other fish products. The total expenditure elasticities are also ve ry precisely estimated as in the low-income sample. The expenditure el asticities are only slightly (but significantly) above unity for most products, within a narrow range of 1.03 for shrimp to 1.17 for pork and other shellfish. As in the low-income sample, the expenditure elasticities are also very low for canned tuna (0.54) and other canned fish (0.15). Table 7 presents the compensated price el asticities for high-inco me households. Unlike results for the low-income sample which suggest net substitution among mo st products, 29 of the compensated cross-price elasticities are signific ant and negative while 67 are positive. Steaks, shrimp and other shellfish are obviously net comp lements for many other meat and fish products, whereas ground beef, pork, other poultry, other m eat, other saltwater finfish and, most obviously other canned fish, are net subst itutes for many products. All comp ensated own-price elasticities are significant, negative and less than unity, ranging from –0.28 for steaks to –0.86 for other poultry.

Concluding Remarks We investigate at home consumption by households of different types and cuts of meats and fish products by estimating parameters of an unusua lly large demand system. The Homescan data offer a unique opportunity for such an investigation. As in other micro survey data, our data19

features zero purchases of ma ny products even though the data were aggregated to the annual level, mainly due to the disaggregate levels of the products considered. Although many statistical estimators exist for censored systems, the large number of products considered in this study prevents the use of ML estimator s such as the system Tobit es timator (Yen, Lin, and Smallwood 2003), the multivariate sample selection esti mator (Yen and Lin 2006), the Kuhn-Tucker approach (Wales and Woodland 1983), and the virtual-price appr oach (Lee and Pitt 1986). The two-step procedure used in the cu rrent study is the result of prac tical considerations associated with having to estimate a large demand system. Although the two-step estim ator is less efficient than the ML estimator of Yen and Lin (2006) wh ich motivates the two-step procedure, it is statistically consistent. We investigate the demand for meat and fish products separately for low-income and high-income samples. We find not able differences in the elasti city estimates between the two groups of households. In general, higher-income households are less responsive to price changes, and the substitution patterns also differ between the low- and high-income households. Whereas the uncompensated elasticities suggest a mixt ure of gross substitutes and complements among the products for both low- and high-income house holds, the compensated el asticities suggest net substitution is the obvious patt ern among low-income households.20

Reference

ACNielsen. 2004. “Consumer Pa nel.” Online. Available at http://www.acnielsen.com/ services/consumer/ (Accessed 28 October 2006.) Bean, R. 2003. “In China, Fish Means Prosperity.” AgExporter 14(1):17

− 19. Capps, O. Jr., and J.A. Lambregts. 1991. “Asse ssing Effects of Pri ces and Advertising on

Purchases of Finfish and Shellfis h in a Local Market in Texas.” Southern Journal of Agricultural Economics 23(1):181–94. Cheng, H., and O. Capps, Jr. 1988. “Demand Analys is of Fresh and Frozen Finfish and Shellfish

in the United States.” American Journal of Agricultural Economics 70(3):533–42. Christensen, L.R., D.W. Jorgenson, and L.J. Lau. 1975. “Transcendental Logarithmic Utility

Functions.” American Economic Review 65(3):367

− 83. Eales, J.S., and L.J. Unnevehr. 1988. “Demand fo r Beef and Chicken Products: Separability and Structural Change.” American Journal of Agricultural Economics 70(3):521–32. Eales, J.S., and L.J. Unnevehr. 1993. “Simulta neity and Structural Change in U.S. Meat

Demand.” American Journal of Agricultural Economics 75(2):259–68. Heckman, J.J. 1979. “Sample Selecti on Bias as a Specification Error.” Econometrica 47(1):153

− 61. Kesavan, T., Z. A. Hassan, H. H. Jensen and S.R. Johnson. 1993. “Dynamics and Long-run

Structure in U.S. Meat Demand.” Canadian Journal of Agricultural Economics 41:139–

53. Kinnucan, H.W., H. Xiao, C. Hsia, and J.D. Jack son. 1997. “Effects of Health Information and Generic Advertising on U.S. Meat Demand.” American Journal of Agricultural

Economics 79(1):13–23.21

Lee, L-F., and M.M. Pitt. 1986. “Micro econometric Demand Systems with Binding Nonnegativity Constraints: The Dual Approach.” Econometrica 54(5):1237

− 42. Moschini, G., and K. D. Meilke. 1989. “Modeling th e Pattern of Structural Change in U.S. Meat

Demand.” American Journal of Agricultural Economics 71(2):253–61. Pudney, S.E. 1989. Modelling Individual Choice: The Ec onometrics of Corners, Kinks, and

Holes . Cambridge, UK: Blackwell Publishers. Purcell, C.P., and R. Raunikar. 1971. “Price Elas ticities from Panel Data: Meat, Poultry, and

Fish.” American Journal of Agricultural Economics 53(2):216–21. Shonkwiler, J.S., and S.T. Yen. 1999. “Two-Step Estimation of A Censored System of Equations.” American Journal of Agricultural Economics 81(4):972

− 82. Thompson, W. 2004. “Using Elasticities From An Almost Ideal Demand System? Watch Out For Group Expenditure.” American Journal of Agricultural Economics 86(4):1108–16. U.S. Department of Agriculture, Economic Research Service (USDA-ERS). No date. Data: Food consumption (per capita) Data System . Available at: http://www.ers.usda.gov/Data/FoodC onsumption. Accessed 28 October 2006. Wales, T.J., and A.D. Woodland. 1980. “Sample Selectivity and the Estimation of Labor Supply

Functions.” International Economic Review 21(2):437

− 68. Wales, T.J., and A.D. Woodland. 1983. “Estima tion of Consumer Demand Systems with Binding Non-negativity Constraints.” Journal of Econometrics 21(3):263

− 85. Wooldridge, J.M. 2002. Econometric Analysis of Cr oss Section and Panel Data . Cambridge,

MA: MIT Press. Yen, S.T. 2005. “A Multivariate Sample-Sel ection Model: Estimating Cigarette and Alcohol

Demands with Zero Observations.” American Journal of Agricultural Economics22

87(2):453

− 66. Yen, S.T., and B. Lin. 2006. “A Sample Sel ection Approach to Censored Demand Systems.” American Journal of Agricultural Economics 88(3):742–49. Yen, S.T., B. Lin, and D.M. Smallwood. 2003. “Quasi and Simulated Likelihood Approaches to Censored Demand Systems: Food Consumption by Food Stamp Recipients in the United

States.” American Journal of Agricultural Economics 85(2):458

− 78.23

Table 1. Sample Statistics Low-Income Sample High-Income Sample

Variable % consuming Mean S.D. % consuming Mean S.D. Expenditures ($ / year) Ground beef 46.09 59.78 40.17 47.42 Consuming households 81.77 56.36 61.58 80.61 49.84 48.04 Steaks 37.44 63.88 54.13 87.50 Consuming households 68.96 54.29 70.73 73.25 73.89 94.83 Other beef 31.01 46.80 34.85 51.54 Consuming households 72.21 42.95 50.21 71.60 48.68 55.11 Pork 51.27 64.39 52.73 61.08 Consuming households 79.58 64.43 66.04 79.60 66.25 61.58 Boneless poultry 24.26 40.24 30.19 45.96 Consuming households 65.14 37.24 44.75 71.69 42.12 49.44 Other poultry 39.85 53.79 37.74 48.49 Consuming households 81.62 48.82 55.74 80.93 46.63 49.91 Other meat 101.12 103.56 108.69 107.62 Consuming households 98.15 103.02 103.59 97.56 111.40 107.56 Shrimp 9.73 24.88 14.95 32.16 Consuming households 35.88 27.13 35.40 45.89 32.59 40.99 Other shellfish 6.52 18.13 10.37 27.75 Consuming households 31.46 20.74 27.40 36.83 28.15 39.89 Freshwater finfish 5.18 21.25 9.06 27.54 Consuming households 24.57 21.08 38.78 32.87 27.57 42.41 Salmon 4.91 16.41 9.83 25.87 Consuming households 22.62 21.71 28.73 33.94 28.97 37.65 Other saltwater finfish 2.79 11.58 3.00 11.92 Consuming households 16.38 17.05 24.00 17.33 17.33 23.91 Canned tuna 9.64 18.32 10.73 18.74 Consuming households 73.33 13.14 20.29 69.41 15.46 20.81 Other canned fish 13.20 18.61 13.56 17.50 Consuming households 80.32 16.43 19.44 80.41 16.86 18.03 Quantities (lb. / year) Ground beef 22.77 30.10 17.49 21.15 Consuming households 27.85 31.09 21.69 21.53 Steaks 9.60 15.57 10.91 16.33 Consuming households 13.91 17.07 14.89 17.4624

Other beef 12.40 19.22 11.87 17.63 Consuming households 17.17 20.73 16.57 18.87 Pork 26.36 37.43 23.01 30.18 Consuming households 33.12 39.19 28.90 31.22 Boneless poultry 10.34 17.69 11.71 18.28 Consuming households 15.86 19.81 16.34 19.76 Other poultry 36.72 50.49 31.65 43.30 Consuming households 44.98 52.47 39.08 45.01 Other meat 31.38 29.77 28.63 26.81 Consuming households 31.97 29.74 29.34 26.76 Shrimp 1.62 3.96 2.21 4.68 Consuming households 4.52 5.53 4.80 5.95 Other shellfish 1.63 4.50 2.14 11.53 Consuming households 5.17 6.79 5.81 18.43 Freshwater finfish 1.32 5.56 1.79 5.28 Consuming households 5.38 10.19 5.46 8.05 Salmon 1.16 3.77 2.03 5.09 Consuming households 5.14 6.52 5.97 7.26 Other saltwater finfish 0.89 3.80 0.93 4.69 Consuming households 5.45 7.96 5.35 10.17 Canned tuna 4.87 9.19 4.56 7.34 Consuming households 6.64 10.17 6.57 8.03 Other canned fish 14.01 17.93 11.83 14.36 Consuming households 17.20 18.51 14.58 14.70 Expenditure shares Ground beef 0.11 0.11 0.09 0.09 Consuming households 0.14 0.11 0.11 0.09 Steaks 0.08 0.10 0.10 0.11 Consuming households 0.11 0.10 0.14 0.11 Other beef 0.07 0.08 0.07 0.08 Consuming households 0.10 0.08 0.10 0.08 Pork 0.12 0.11 0.11 0.10 Consuming households 0.15 0.10 0.14 0.09 Boneless poultry 0.06 0.09 0.07 0.09 Consuming households 0.09 0.09 0.10 0.10 Other poultry 0.10 0.10 0.09 0.09 Consuming households 0.12 0.10 0.11 0.09 Other meat 0.30 0.20 0.29 0.20 Consuming households 0.31 0.20 0.29 0.2025

Shrimp 0.02 0.05 0.03 0.07 Consuming households 0.07 0.07 0.07 0.09 Other shellfish 0.02 0.04 0.02 0.05 Consuming households 0.05 0.06 0.06 0.07 Freshwater finfish 0.01 0.04 0.02 0.05 Consuming households 0.05 0.07 0.06 0.07 Salmon 0.01 0.05 0.02 0.06 Consuming households 0.06 0.09 0.07 0.08 Other saltwater finfish 0.01 0.03 0.01 0.03 Consuming households 0.04 0.05 0.04 0.05 Canned tuna 0.04 0.08 0.03 0.07 Consuming households 0.05 0.09 0.05 0.08 Other canned fish 0.05 0.09 0.04 0.08 Consuming households 0.06 0.09 0.06 0.09 Prices ($ / lb.) Ground beef 2.22 0.61 2.47 0.68 Steaks 4.25 1.61 5.02 2.07 Other beef 2.76 0.92 3.14 1.13 Pork 2.36 0.92 2.67 1.00 Boneless poultry 2.56 0.76 2.73 0.85 Other poultry 1.34 0.72 1.50 0.83 Other meat 3.43 1.31 4.05 1.51 Shrimp 6.41 1.39 6.81 1.75 Other shellfish 4.88 1.92 5.33 2.22 Freshwater finfish 4.83 1.22 5.24 1.60 Salmon 4.73 1.12 4.97 1.48 Other saltwater finfish 3.70 0.72 3.85 0.79 Canned tuna 2.18 1.00 2.50 1.15 Other canned fish 1.26 1.10 1.54 1.54 Demographic variables Used in 1st and 2nd steps : Household size 2.54 1.57 2.24 1.08 Age < 40 (household head) 0.14 0.13 Age 40–60 0.56 0.67 Age > 60 (ref.) 0.30 0.20 White 0.73 0.74 Black 0.14 0.1326

Hispanic 0.09 0.08 Asian 0.02 0.04 Other race (ref.) 0.02 0.02 East 0.22 0.22 Central 0.18 0.16 South 0.41 0.37 West (ref.) 0.19 0.25 Children (present) 0.31 0.19 Used in 1st step only : Married 0.50 0.62 Widowed 0.13 0.05 Divorced 0.19 0.13 Single (ref.) 0.18 0.19 PIR (poverty income ratio) 2.18 0.82 5.72 1.71 < High school 0.03 0.01 High school 0.27 0.09 Some college 0.37 0.25 College (and above) 0.33 0.65 Female head employed 0.44 0.62 Male head employed 0.39 0.60 Sample size 4005 4224 Source: ACNielsen’s Homescan panel, 2004.27Table 2. Second-Step Estimates of Translog Demand System: Low-Income HouseholdsVariableGroundBeef SteaksOtherBeef PorkBonelessPoultryOtherPoultryOtherMeatDemographic variables (αij)Constant –0.014 –0.232*** –0.036 –0.081*** –0.044 –0.034 0.538***(0.038) (0.039) (0.030) (0.030) (0.036) (0.029) (0.037)Household size 0.003 –0.003 0.000 –0.009*** 0.000 0.004 0.005(0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.004)Age < 40 0.035*** 0.009 –0.069*** –0.066*** 0.057*** –0.053*** 0.052***(0.011) (0.012) (0.012) (0.013) (0.011) (0.012) (0.015)Age 40–60 0.025*** 0.008 –0.037*** –0.032*** 0.024*** –0.018*** 0.024**(0.007) (0.007) (0.007) (0.008) (0.007) (0.007) (0.010)White 0.052* 0.052** –0.004 0.036 0.020 –0.030 –0.013(0.028) (0.026) (0.022) (0.023) (0.024) (0.021) (0.030)Black –0.022 –0.017 –0.027 0.065*** –0.002 0.146*** –0.055*(0.028) (0.027) (0.022) (0.024) (0.024) (0.024) (0.032)Hispanic 0.015 0.067** 0.042* 0.019 –0.003 0.043* –0.028(0.029) (0.028) (0.023) (0.025) (0.025) (0.023) (0.033)Asian –0.019 0.057* 0.039 0.070** –0.031 0.012 –0.112***(0.036) (0.035) (0.028) (0.031) (0.033) (0.029) (0.042)East –0.022** –0.023** –0.034*** 0.020** –0.008 0.004 –0.036***(0.010) (0.010) (0.008) (0.009) (0.009) (0.009) (0.014)Central 0.011 –0.027*** –0.017** 0.042*** –0.022** –0.034*** 0.041***(0.010) (0.011) (0.008) (0.010) (0.010) (0.009) (0.014)28South 0.001 –0.004 –0.001 0.019** –0.017** –0.017** 0.007(0.009) (0.008) (0.007) (0.009) (0.008) (0.008) (0.012)Children 0.017* –0.008 –0.007 –0.009 0.030*** 0.009 –0.031**(0.010) (0.010) (0.008) (0.010) (0.010) (0.009) (0.015)Quadratic price coefficients (βij)Ground beef –0.017(0.012)Steaks –0.050*** 0.061***(0.007) (0.009)Other beef 0.002 –0.031*** 0.019**(0.007) (0.006) (0.008)Pork –0.001 0.002 –0.010* –0.029***(0.007) (0.006) (0.006) (0.009)Boneless poultry 0.026*** –0.004 0.016*** 0.031*** –0.047***(0.008) (0.007) (0.006) (0.007) (0.010)Other poultry 0.016*** 0.000 –0.017*** –0.014*** 0.011** –0.013**(0.006) (0.005) (0.005) (0.005) (0.006) (0.007)Other meat –0.019** –0.015** –0.015** –0.040*** 0.000 –0.005 0.077***(0.009) (0.008) (0.007) (0.008) (0.008) (0.007) (0.013)Shrimp 0.003 0.001 0.000 –0.003 –0.011 –0.004 0.008(0.009) (0.007) (0.007) (0.008) (0.008) (0.006) (0.009)Other shellfish 0.008 0.016*** 0.007 –0.007 –0.006 –0.012** –0.007(0.006) (0.006) (0.005) (0.006) (0.006) (0.005) (0.007)Freshwater 0.013 –0.010 0.001 –0.015** 0.007 –0.012** 0.013*finfish (0.008) (0.007) (0.007) (0.007) (0.007) (0.006) (0.008)29Salmon 0.005 –0.029*** –0.011 0.010 –0.008 0.011 0.006(0.010) (0.009) (0.008) (0.009) (0.009) (0.007) (0.010)Other saltwater 0.007 –0.012* 0.000 0.008 –0.012 0.002 –0.017**finfish (0.009) (0.007) (0.007) (0.008) (0.008) (0.006) (0.008)Canned tuna 0.000 0.004 –0.003 0.012** –0.013** 0.003 0.009(0.006) (0.005) (0.005) (0.005) (0.006) (0.005) (0.006)Other canned –0.021*** 0.013** 0.009** 0.000 –0.008 0.006 0.028***fish (0.005) (0.005) (0.004) (0.005) (0.005) (0.005) (0.007)Selectivity term: 0.042** 0.166*** 0.120*** 0.086*** 0.095*** 0.232***Covariance (0.022) (0.025) (0.020) (0.019) (0.021) (0.026)30Table 2 continuedVariableShrimpOtherShellfishFreshwaterFinfish SalmonOther Saltwater FinfishCannedTunaOtherCanned FishDemographic variables (αij)Constant 0.021 0.003 0.178*** 0.152*** 0.111* 0.243***(0.034) (0.039) (0.040) (0.050) (0.063) (0.036)Household size –0.004 –0.002 –0.013*** –0.016*** –0.012*** 0.003(0.003) (0.003) (0.003) (0.004) (0.003) (0.003)Age < 40 –0.006 0.005 0.011 0.066*** 0.023 –0.009(0.014) (0.013) (0.014) (0.023) (0.024) (0.009)Age 40–60 –0.006 –0.008 0.006 0.022* 0.008 0.003(0.008) (0.008) (0.009) (0.013) (0.011) (0.006)White –0.016 –0.003 –0.043** 0.030 –0.022 –0.017(0.021) (0.018) (0.022) (0.037) (0.026) (0.021)Black 0.011 0.023 –0.049 0.020 –0.034 –0.038*(0.021) (0.018) (0.023) (0.039) (0.030) (0.021)Hispanic –0.024 –0.024 –0.045* 0.042 –0.045* –0.007(0.023) (0.024) (0.024) (0.040) (0.025) (0.023)Asian 0.002 0.010 –0.029 0.014 –0.068** –0.093***(0.026) (0.024) (0.028) (0.045) (0.031) (0.030)East 0.031*** 0.006 –0.001 –0.003 –0.024* 0.016**(0.010) (0.013) (0.013) (0.013) (0.013) (0.009)Central 0.000 –0.017 –0.005 0.008 –0.005 –0.014*(0.012) (0.011) (0.012) (0.021) (0.012) (0.008)31South 0.006 –0.007 0.004 0.014 –0.018 0.000(0.009) (0.009) (0.011) (0.015) (0.012) (0.007)Children –0.004 –0.008 0.022** 0.001 0.013 0.008(0.010) (0.009) (0.011) (0.015) (0.011) (0.008)Quadratic price coefficients (βij)Shrimp –0.012(0.013)Other shellfish –0.012** –0.008(0.007) (0.007)Freshwater –0.009 0.004 –0.073***finfish (0.008) (0.006) (0.010)Salmon 0.010 –0.007 0.016* –0.070***(0.010) (0.008) (0.009) (0.016)Other saltwater –0.006 0.008 –0.011 0.019* –0.026**finfish (0.009) (0.006) (0.008) (0.010) (0.012)Canned tuna –0.004 –0.004 0.013** 0.004 –0.003 0.021***(0.006) (0.005) (0.006) (0.007) (0.006) (0.006)Other canned 0.027*** 0.009 0.043*** 0.035*** 0.018** 0.002 –0.058***fish (0.006) (0.006) (0.006) (0.008) (0.007) (0.004) (0.013)Selectivity term: 0.051** 0.026 –0.036 –0.029 –0.031 0.057*Covariance (0.022) (0.026) (0.024) (0.027) (0.038) (0.030)Log likelihood 68774.698Note: Asymptotic standard errors in parentheses. Levels of statistical significance: *** = 1%, ** = 5%, * = 10%.32Table 3. Second-Step Estimates of Translog Demand System: High-Income HouseholdsVariableGroundBeef SteaksOtherBeef PorkBonelessPoultryOtherPoultryOtherMeatDemographic variables (αij)Constant 0.061*** –0.288*** 0.005 –0.005 –0.030 0.091*** 0.460***(0.024) (0.035) (0.022) (0.024) (0.030) (0.020) (0.029)Household size 0.002 0.011*** 0.005* –0.003 0.006* –0.004 0.001(0.003) (0.004) (0.003) (0.003) (0.003) (0.003) (0.004)Age < 40 0.029*** –0.012 –0.056*** –0.038*** 0.082*** –0.023*** 0.015(0.008) (0.010) (0.010) (0.009) (0.010) (0.008) (0.011)Age 40–60 0.015*** 0.013** –0.026*** –0.015*** 0.034*** –0.010** 0.001(0.005) (0.006) (0.005) (0.005) (0.007) (0.005) (0.008)White 0.004 0.022 –0.013 0.000 0.048*** –0.035*** 0.038*(0.016) (0.019) (0.014) (0.017) (0.017) (0.014) (0.022)Black –0.048*** –0.067*** –0.028* 0.022 0.019 0.058*** 0.026(0.017) (0.021) (0.015) (0.017) (0.018) (0.015) (0.023)Hispanic –0.003 0.037* –0.002 –0.016 0.033* –0.011 0.012(0.017) (0.021) (0.016) (0.018) (0.018) (0.015) (0.024)Asian –0.047*** 0.006 0.008 0.022 –0.002 0.009 –0.031(0.019) (0.022) (0.017) (0.019) (0.021) (0.017) (0.027)East 0.009 0.003 –0.035*** –0.006 –0.003 0.008 –0.019**(0.006) (0.007) (0.006) (0.006) (0.007) (0.006) (0.009)Central 0.020*** –0.006 –0.023*** 0.021*** –0.013* –0.020*** 0.031***(0.007) (0.008) (0.006) (0.007) (0.007) (0.006) (0.010)33South 0.018*** –0.001 –0.023*** 0.007 –0.002 –0.007 0.008(0.006) (0.007) (0.005) (0.006) (0.006) (0.005) (0.008)Children –0.004 –0.026*** –0.017*** –0.012* 0.003 0.002 0.017(0.007) (0.009) (0.007) (0.007) (0.007) (0.006) (0.011)Quadratic price coefficients (βij)Ground beef 0.028***(0.008)Steaks –0.024*** 0.113***(0.005) (0.010)Other beef –0.014*** –0.025*** 0.065***(0.005) (0.005) (0.007)Pork 0.015*** –0.011** –0.019*** 0.010(0.005) (0.005) (0.005) (0.007)Boneless poultry 0.012** –0.026*** –0.002 0.011** 0.024***(0.006) (0.005) (0.005) (0.005) (0.008)Other poultry –0.001 –0.012*** –0.009** –0.016*** 0.009** 0.007(0.004) (0.004) (0.004) (0.004) (0.004) (0.004)Other meat –0.019*** –0.026*** –0.016*** –0.025*** 0.005 0.009* 0.079***(0.006) (0.006) (0.005) (0.006) (0.006) (0.005) (0.010)Shrimp –0.002 0.009 –0.009* 0.003 –0.018*** –0.004 0.010(0.006) (0.006) (0.005) (0.005) (0.006) (0.004) (0.006)Other shellfish –0.001 0.013*** 0.005 –0.006 –0.004 –0.008** –0.015***(0.004) (0.005) (0.004) (0.004) (0.005) (0.004) (0.005)Freshwater 0.005 –0.002 –0.004 –0.008 –0.006 –0.007* 0.012**finfish (0.005) (0.005) (0.005) (0.005) (0.005) (0.004) (0.005)34Salmon 0.001 –0.018*** 0.005 0.005 –0.019*** 0.008* 0.013*(0.006) (0.006) (0.005) (0.006) (0.006) (0.005) (0.007)Other saltwater 0.002 –0.024*** –0.003 0.008 0.010* –0.003 –0.003finfish (0.006) (0.005) (0.005) (0.005) (0.006) (0.004) (0.006)Canned tuna –0.004 –0.009*** 0.000 0.001 0.001 0.001 0.001(0.004) (0.004) (0.003) (0.004) (0.004) (0.003) (0.004)Other canned –0.009*** –0.003 0.002 –0.002 –0.004 0.014*** 0.016***fish (0.003) (0.004) (0.003) (0.003) (0.004) (0.003) (0.005)Selectivity term: 0.031* 0.256*** 0.096*** 0.071*** 0.125*** 0.105***Covariance 0.017 0.024 0.015 0.015 0.020 0.01935Table 3 continuedVariableShrimpOtherShellfishFreshwaterFinfish SalmonOther Saltwater FinfishCannedTunaOtherCanned FishDemographic variables (αij)Constant–0.055 –0.082*** 0.031 0.098*** 0.195*** 0.100***(0.036) (0.034) (0.030) (0.034) (0.054) (0.023)Household size–0.009*** –0.007** –0.007** –0.016*** –0.009*** 0.003(0.004) (0.003) (0.003) (0.004) (0.004) (0.003)Age < 400.004 0.003 –0.003 0.007 0.004 –0.012(0.011) (0.010) (0.011) (0.011) (0.014) (0.008)Age 40–600.007 –0.010* –0.006 –0.001 0.002 0.002(0.007) (0.006) (0.006) (0.007) (0.008) (0.004)White–0.011 –0.023 –0.044** –0.052** –0.064*** 0.007(0.019) (0.018) (0.019) (0.022) (0.018) (0.013)Black0.004 0.014 –0.027 –0.041* –0.059*** –0.004(0.020) (0.019) (0.019) (0.023) (0.021) (0.013)Hispanic0.005 –0.020 –0.032 –0.047 –0.058*** 0.017(0.021) (0.020) (0.020) (0.024) (0.019) (0.014)Asian0.053** 0.019 0.014 –0.022 –0.066*** –0.051***(0.022) (0.020) (0.021) (0.025) (0.021) (0.018)East0.023*** 0.017** 0.022*** –0.011 –0.035*** 0.015***(0.008) (0.008) (0.007) (0.008) (0.009) (0.006)Central–0.018* –0.027*** –0.011 –0.023** –0.002 –0.002(0.010) (0.009) (0.010) (0.012) (0.010) (0.005)South0.004 –0.002 0.003 –0.013* –0.031*** 0.004(0.007) (0.007) (0.007) (0.007) (0.011) (0.005)36Children0.019** –0.001 0.001 0.015 0.011 –0.003(0.009) (0.008) (0.009)(0.010) (0.009) (0.006)Quadratic price coefficients (βij)Shrimp 0.064***(0.010)Other shellfish 0.005 0.030***(0.005) (0.006)Freshwater –0.026*** –0.003 0.032***finfish (0.006) (0.004) (0.007)Salmon –0.030*** –0.026*** 0.010* 0.023**(0.007) (0.005) (0.006) (0.009)Other saltwater –0.004 –0.001 –0.037*** 0.015** 0.011finfish (0.006) (0.004) (0.006) (0.007)(0.008)Canned tuna –0.003 –0.005 0.005 –0.002 0.010*** 0.032***(0.004) (0.003) (0.004) (0.004) (0.004) (0.004)Other canned 0.006 0.006 0.019*** 0.010** 0.008* –0.004 0.011fish (0.004) (0.004) (0.004) (0.005) (0.005) (0.003) (0.007)Selectivity term: 0.116*** 0.111*** 0.037** 0.066*** –0.041 0.094***Covariance (0.026) (0.020) (0.017) (0.019) (0.031) (0.020)Log likelihood 74020.665Note: Asymptotic standard errors in parentheses. Levels of statistical significance: *** = 1%, ** = 5%, * = 10%.37Table 4. Uncompensated Price and Total Meat Expenditure Elasticities: Low-Income HouseholdsVariableGroundBeef SteaksOtherBeef PorkBonelessPoultryOtherPoultryOtherMeatGround beef–1.07*** –0.22*** 0.03 0.03 0.14*** 0.10*** –0.11***(0.06) (0.04) (0.03) (0.04) (0.04) (0.03) (0.04)Steaks –0.25***–0.67*** –0.15*** 0.03 –0.02 0.01 –0.08*(0.04)(0.05) (0.03) (0.03) (0.03) (0.03) (0.04)Other beef 0.02 –0.19***–0.86*** –0.05 0.11*** –0.10*** –0.11*(0.05) (0.04)(0.05) (0.04) (0.04) (0.03) (0.05)Pork 0.01 0.04 –0.02–1.09*** 0.14*** –0.04* –0.19***(0.03) (0.03) (0.03)(0.04) (0.03) (0.02) (0.03)Boneless poultry 0.19*** –0.01 0.12*** 0.23***–1.33*** 0.08* –0.01(0.05) (0.05) (0.04) (0.05)(0.07) (0.04) (0.06)Other poultry 0.10*** 0.02 –0.09*** –0.06* 0.07*–1.06*** –0.04(0.03) (0.03) (0.03) (0.03) (0.03)(0.04) (0.04)Other meat –0.03 0.00 –0.01 –0.06*** 0.01 0.01–0.84***(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)(0.03)Shrimp 0.03 0.02 0.01 –0.01 –0.10 –0.03 0.07(0.08) (0.07) (0.07) (0.07) (0.07) (0.06) (0.08)Other shellfish 0.11 0.22*** 0.10 –0.08 –0.07 –0.14* –0.09(0.08) (0.07) (0.07) (0.07) (0.07) (0.06) (0.09)Freshwater0.19* –0.06 0.06 –0.12 0.11 –0.12* 0.14finfish(0.10) (0.09) (0.08) (0.09) (0.09) (0.07) (0.10)Salmon0.08 –0.24*** –0.08 0.16 –0.07 0.14* 0.04(0.11) (0.09) (0.09) (0.09) (0.10) (0.08) (0.11)Other saltwater0.15 –0.11 0.05 0.19* –0.15 0.07 –0.28*finfish(0.13) (0.11) (0.11) (0.11) (0.11) (0.09) (0.13)Canned tuna0.01 0.09 –0.04 0.23* –0.23* 0.06 0.16(0.11) (0.09) (0.09) (0.10) (0.10) (0.08) (0.11)Other canned0.12 0.02 0.18* 0.25*** –0.47*** 0.04 0.09fish(0.09) (0.07) (0.08) (0.08) (0.08) (0.06) (0.09)38Table 4 continued.VariableShrimpOtherShellfishFresh-waterFinfish SalmonOther Saltwater FinfishCannedTunaOtherCanned FishTotal MeatExpenditureGround beef 0.02 0.05 0.08* 0.03 0.05 –0.03 –0.17***1.06***(0.04) (0.03) (0.04) (0.05) (0.04) (0.03) (0.03)(0.01)Steaks 0.01 0.09*** –0.05 –0.15*** –0.06 0.01 0.04*1.25***(0.04) (0.03) (0.04) (0.05) (0.04) (0.03) (0.03)(0.01)Other beef 0.00 0.05 0.01 –0.07 0.01 –0.03 0.031.18***(0.05) (0.03) (0.04) (0.05) (0.05) (0.03) (0.03)(0.01)Pork 0.00 –0.02 –0.05* 0.05 0.05 0.03 –0.06***1.17***(0.03) (0.02) (0.03) (0.04) (0.03) (0.02) (0.02)(0.01)Boneless poultry –0.08 –0.04 0.05 –0.06 –0.08 –0.11*** –0.09***1.10***(0.06) (0.04) (0.05) (0.06) (0.05) (0.04) (0.04)(0.02)Other poultry –0.02 –0.06* –0.06* 0.06 0.02 0.00 0.011.12***(0.03) (0.03) (0.03) (0.04) (0.03) (0.03) (0.02)(0.01)Other meat 0.03 –0.01 0.05*** 0.02 –0.02 –0.01 0.000.86***(0.02) (0.02) (0.02) (0.02) (0.02) (0.01) (0.02)(0.01)Shrimp–1.10*** –0.11* –0.08 0.09 –0.05 –0.04 0.23***1.09***(0.12) (0.06) (0.07) (0.10) (0.08) (0.06) (0.05)(0.03)Other shellfish –0.15*–1.09*** 0.06 –0.08 0.11 –0.06 0.081.10***(0.08)(0.09) (0.07) (0.10) (0.08) (0.06) (0.06)(0.03)Freshwater–0.10 0.07–1.89*** 0.21* –0.11 0.11 0.41***1.12***finfish(0.10) (0.07)(0.13) (0.11) (0.10) (0.07) (0.06)(0.03)Salmon0.11 –0.06 0.19*–1.72*** 0.23* 0.00 0.25***0.98***(0.11) (0.08) (0.09)(0.17) (0.11) (0.08) (0.07)(0.04)Other saltwater–0.08 0.13 –0.14 0.30*–1.35*** –0.10 0.13*1.18***finfish(0.14) (0.09) (0.11) (0.15)(0.17) (0.10) (0.07)(0.04)Canned tuna–0.06 –0.07 0.23* 0.07 –0.04–0.64*** 0.020.21***(0.11) (0.09) (0.11) (0.13) (0.11)(0.11) (0.07)(0.07)Other canned0.07 0.07 –0.11 0.06 0.09 0.00–0.79***0.38***fish(0.09) (0.07) (0.09) (0.11) (0.10) (0.06)(0.05)(0.04)Note: Asymptotic standard errors in parentheses. Levels of statistical significance: *** = 1%, ** = 5%, * = 10%.39Table 5. Compensated Price Elasticities: Low-Income HouseholdsVariableGroundBeef SteaksOtherBeef PorkBonelessPoultryOtherPoultryOtherMeatGround beef–0.94*** –0.17*** 0.08* 0.16*** 0.18*** 0.15*** 0.20***(0.06) (0.04) (0.04) (0.04) (0.04) (0.03) (0.04)Steaks –0.10***–0.61*** –0.09*** 0.19*** 0.04 0.07*** 0.28***(0.04)(0.05) (0.03) (0.03) (0.04) (0.03) (0.04)Other beef 0.16*** –0.13***–0.81*** 0.10*** 0.16*** –0.04 0.23***(0.05) (0.04)(0.05) (0.04) (0.04) (0.03) (0.05)Pork 0.15*** 0.09*** 0.03–0.95*** 0.19*** 0.02 0.15***(0.03) (0.03) (0.03)(0.04) (0.03) (0.03) (0.03)Boneless poultry 0.32*** 0.04 0.17*** 0.37***–1.28*** 0.14*** 0.31***(0.05) (0.05) (0.05) (0.05)(0.07) (0.04) (0.05)Other poultry 0.24*** 0.07* –0.03 0.08*** 0.11***–1.01*** 0.28***(0.03) (0.03) (0.03) (0.03) (0.03)(0.04) (0.04)Other meat 0.08*** 0.04* 0.03 0.05*** 0.05* 0.05***–0.59***(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)(0.03)Shrimp 0.17* 0.07 0.06 0.12* –0.06 0.03 0.38***(0.08) (0.07) (0.07) (0.07) (0.07) (0.06) (0.08)Other shellfish 0.24*** 0.27*** 0.15* 0.07 –0.03 –0.09 0.23***(0.08) (0.07) (0.07) (0.07) (0.08) (0.06) (0.09)Freshwater0.33*** –0.01 0.11 0.02 0.15* –0.06 0.46***finfish(0.10) (0.09) (0.08) (0.09) (0.09) (0.08) (0.10)Salmon0.20* –0.20* –0.04 0.29*** –0.02 0.19*** 0.32***(0.11) (0.09) (0.09) (0.09) (0.10) (0.08) (0.11)Other saltwater0.29* –0.06 0.11 0.34*** –0.10 0.13 0.06finfish(0.13) (0.11) (0.11) (0.11) (0.11) (0.09) (0.13)Canned tuna0.03 0.09 –0.03 0.25*** –0.22* 0.07 0.22*(0.11) (0.09) (0.09) (0.10) (0.10) (0.08) (0.11)Other canned0.17* 0.04 0.20*** 0.30*** –0.45 0.05 0.20*fish(0.09) (0.08) (0.08) (0.08) (0.08) (0.06) (0.09)40Table 5 continued.VariableShrimpOtherShellfishFreshwaterFinfish SalmonOther Saltwater FinfishCannedTunaOtherCanned FishGround beef 0.04 0.07 0.18*** 0.14* 0.15* –0.01 –0.25***(0.05) (0.04) (0.05) (0.06) (0.08) (0.03) (0.08)Steaks 0.03 0.11*** 0.08 –0.02 0.06 0.03 –0.05(0.05) (0.04) (0.05) (0.06) (0.08) (0.03) (0.10)Other beef 0.03 0.08 0.13*** 0.05 0.12 –0.02 –0.06(0.05) (0.05) (0.05) (0.07) (0.08) (0.04) (0.09)Pork 0.02 0.00 0.06 0.17*** 0.16* 0.04 –0.14(0.04) (0.04) (0.04) (0.05) (0.07) (0.03) (0.09)Boneless poultry –0.06 –0.01 0.16*** 0.06 0.03 –0.09* –0.17*(0.06) (0.05) (0.06) (0.08) (0.08) (0.04) (0.09)Other poultry 0.00 –0.04 0.05 0.18*** 0.12* 0.02 –0.08(0.04) (0.04) (0.05) (0.06) (0.07) (0.03) (0.09)Other meat 0.04 0.01 0.13*** 0.11*** 0.06 0.00 –0.07(0.03) (0.03) (0.03) (0.04) (0.06) (0.02) (0.07)Shrimp–1.08*** –0.09 0.03 0.20* 0.05 –0.03 0.15(0.12) (0.07) (0.08) (0.10) (0.10) (0.06) (0.10)Other shellfish –0.13–1.07*** 0.17* 0.03 0.21* –0.05 –0.01(0.09)(0.09) (0.08) (0.10) (0.10) (0.06) (0.10)Freshwater–0.08 0.09–1.78*** 0.33*** –0.01 0.12* 0.32***finfish(0.10) (0.08)(0.13) (0.12) (0.11) (0.07) (0.11)Salmon0.13 –0.04 0.29***–1.62*** 0.32*** 0.01 0.18*(0.11) (0.08) (0.10)(0.17) (0.12) (0.08) (0.11)Other saltwater–0.05 0.16* –0.02 0.42***–1.24*** –0.09 0.03finfish(0.14) (0.10) (0.12) (0.16)(0.18) (0.10) (0.12)Canned tuna–0.06 –0.06 0.25* 0.10 –0.02–0.63*** 0.00(0.11) (0.09) (0.11) (0.13) (0.12)(0.11) (0.07)Other canned0.08 0.08 –0.07 0.10 0.12 0.01–0.82***fish(0.10) (0.07) (0.09) (0.11) (0.11) (0.07)(0.06)Note: Asymptotic standard errors in parentheses. Levels of statistical significance: *** = 1%, ** = 5%, * = 10%.41Table 6. Uncompensated Price and Total Meat Expenditure Elasticities: High-Income HouseholdsVariableGroundBeef SteaksOtherBeef PorkBonelessPoultryOtherPoultryOtherMeatGround beef–0.77*** –0.16*** –0.09** 0.15*** 0.10** 0.00 –0.18***(0.06) (0.04) (0.04) (0.04) (0.04) (0.03) (0.04)Steaks –0.14***–0.33*** –0.14*** –0.06** –0.15*** –0.07*** –0.16***(0.03)(0.04) (0.03) (0.03) (0.03) (0.02) (0.03)Other beef –0.11*** –0.19***–0.43*** –0.14*** –0.01 –0.07** –0.16***(0.04) (0.04)(0.05) (0.04) (0.04) (0.03) (0.04)Pork 0.10*** –0.03 –0.10***–0.91*** 0.07** –0.09*** –0.18***(0.03) (0.03) (0.03)(0.04) (0.03) (0.02) (0.03)Boneless poultry 0.11** –0.21*** 0.00 0.11***–0.78*** 0.09** 0.03(0.05) (0.05) (0.04) (0.05)(0.07) (0.04) (0.05)Other poultry 0.00 –0.07** –0.05* –0.11*** 0.08**–0.94*** 0.05(0.03) (0.03) (0.03) (0.03) (0.03)(0.03) (0.04)Other meat –0.05 –0.04** –0.03* –0.05*** 0.02 0.04***–0.79***(0.02) (0.02) (0.02) (0.02) (0.02) (0.01)(0.03)Shrimp –0.03 0.09 –0.12** 0.02 –0.21*** –0.05 0.12*(0.07) (0.06) (0.06) (0.06) (0.07) (0.05) (0.07)Other shellfish –0.02 0.15*** 0.05 –0.10* –0.06 –0.11** –0.18***(0.06) (0.06) (0.05) (0.06) (0.06) (0.05) (0.07)Freshwater0.07 –0.02 –0.05 –0.10 –0.09 –0.10* 0.15**finfish(0.07) (0.07) (0.06) (0.07) (0.07) (0.06) (0.08)Salmon0.01 –0.21*** 0.06 0.06 –0.23*** 0.10* 0.15**(0.07) (0.07) (0.06) (0.07) (0.07) (0.05) (0.08)Other saltwater0.08 –0.46*** –0.02 0.27** 0.27** –0.04 –0.17finfish(0.14) (0.12) (0.12) (0.12) (0.13) (0.10) (0.14)Canned tuna–0.08 –0.19*** –0.01 0.01 0.01 0.02 0.02(0.08) (0.08) (0.07) (0.08) (0.08) (0.06) (0.09)Other canned–0.03 –0.05 0.26*** 0.26*** –0.41*** 0.12** –0.12fish(0.09) (0.08) (0.08) (0.08) (0.09) (0.06) (0.10)42Table 6 continued.VariableShrimpOtherShellfishFreshwaterFinfish SalmonOther Saltwater FinfishCannedTunaOtherCanned FishTotal MeatExpenditureGround beef –0.01 0.00 0.05 0.01 0.03 –0.05 –0.13***1.04***(0.05) (0.03) (0.04) (0.05) (0.05) (0.03) (0.03)(0.02)Steaks 0.05 0.08*** –0.01 –0.10*** –0.14*** –0.06*** –0.041.26***(0.03) (0.03) (0.03) (0.03) (0.03) (0.02) (0.02)(0.02)Other beef –0.08* 0.05 –0.03 0.04 –0.02 –0.01 –0.011.19***(0.04) (0.03) (0.04) (0.05) (0.04) (0.03) (0.03)(0.02)Pork 0.02 –0.03 –0.04 0.03 0.06* –0.01 –0.06***1.17***(0.03) (0.03) (0.03) (0.03) (0.03) (0.02) (0.02)(0.01)Boneless –0.16*** –0.03 –0.05 –0.17*** 0.10** 0.00 –0.07**1.06***poultry (0.05) (0.04) (0.05) (0.06) (0.05) (0.04) (0.03)(0.02)Other poultry –0.03 –0.06** –0.05 0.07* –0.02 –0.01 0.07***1.07***(0.03) (0.03) (0.03) (0.04) (0.03) (0.02) (0.02)(0.02)Other meat 0.03 –0.04** 0.05*** 0.04** 0.00 –0.02 –0.010.84***(0.02) (0.02) (0.02) (0.02) (0.02) (0.01) (0.02)(0.01)Shrimp–0.26** 0.06 –0.31*** –0.34*** –0.05 –0.03 0.09*1.03***(0.11) (0.06) (0.06) (0.08) (0.07) (0.05) (0.05)(0.03)Other shellfish 0.07–0.59*** –0.05 –0.36*** –0.03 –0.05 0.13***1.17***(0.07)(0.08) (0.06) (0.07) (0.06) (0.05) (0.05)(0.03)Freshwater–0.37*** –0.04–0.55*** 0.14* –0.52*** 0.06 0.25***1.16***finfish(0.08) (0.06)(0.10) (0.08) (0.07) (0.05) (0.05)(0.03)Salmon–0.35*** –0.31*** 0.12*–0.73*** 0.18** –0.03 0.12**1.07***(0.08) (0.06) (0.07)(0.11) (0.08) (0.05) (0.05)(0.03)Other saltwa-–0.08 –0.01 –0.85*** 0.36**–0.71*** 0.19** 0.031.15***ter finfish(0.14) (0.10) (0.13) (0.16)(0.20) (0.10) (0.08)(0.05)Canned tuna–0.07 –0.10 0.09 –0.05 0.21***–0.34*** –0.070.54***(0.09) (0.07) (0.08) (0.09) (0.09)(0.09) (0.05)(0.05)Other canned–0.08 0.26*** 0.02 0.19* 0.08 –0.01–0.64***0.15***fish(0.10) (0.07) (0.09) (0.10) (0.11) (0.06)(0.06)(0.06)Note: Asymptotic standard errors in parentheses. Levels of statistical significance: *** = 1%, ** = 5%, * = 10%.43Table 7. Compensated Price Elasticities: High-Income HouseholdsVariableGroundBeef SteaksOtherBeef PorkBonelessPoultryOtherPoultryOtherMeatGround beef–0.66*** –0.12*** –0.03 0.27*** 0.14*** 0.08*** 0.11**(0.06) (0.04) (0.04) (0.04) (0.04) (0.03) (0.04)Steaks –0.01–0.28*** –0.07*** 0.09*** –0.10*** 0.03 0.18***(0.03)(0.04) (0.03) (0.03) (0.03) (0.02) (0.03)Other beef 0.01 –0.15–0.36*** 0.00 0.04 0.02 0.17***(0.04) (0.04)(0.05) (0.04) (0.04) (0.03) (0.04)Pork 0.22*** 0.01 –0.03–0.77*** 0.12*** 0.00 0.14***(0.03) (0.03) (0.03)(0.04) (0.03) (0.02) (0.03)Boneless 0.22*** –0.17*** 0.06 0.24***–0.74*** 0.17*** 0.32***poultry (0.05) (0.05) (0.04) (0.05)(0.07) (0.04) (0.05)Other poultry 0.10*** –0.03 0.01 0.02 0.12***–0.86*** 0.34***(0.03) (0.03) (0.03) (0.03) (0.03)(0.04) (0.04)Other meat 0.03* –0.01 0.02 0.05*** 0.06*** 0.10***–0.56***(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)(0.03)Shrimp 0.08 0.12** –0.06 0.14** –0.17*** 0.03 0.40***(0.07) (0.06) (0.06) (0.06) (0.07) (0.05) (0.07)Other shellfish 0.10* 0.19 0.12** 0.03 –0.01 –0.02 0.14**(0.06) (0.06) (0.05) (0.06) (0.06) (0.05) (0.07)Freshwater0.19*** 0.03 0.01 0.04 –0.04 –0.01 0.47***finfish(0.07) (0.07) (0.06) (0.07) (0.07) (0.06) (0.08)Salmon0.12* –0.17*** 0.12* 0.19*** –0.19*** 0.18*** 0.44***(0.07) (0.07) (0.06) (0.07) (0.07) (0.05) (0.08)Other saltwa-0.19 –0.41*** 0.04 0.41*** 0.31** 0.05 0.14ter finfish(0.14) (0.12) (0.12) (0.12) (0.13) (0.10) (0.14)Canned tuna–0.02 –0.17* 0.02 0.08 0.03 0.06 0.17**(0.08) (0.08) (0.07) (0.08) (0.08) (0.06) (0.09)Other canned–0.01 –0.04 0.27*** 0.27*** –0.41*** 0.14** –0.08fish(0.09) (0.08) (0.08) (0.08) (0.09) (0.06) (0.10)44Table 7 continued.VariableShrimpOtherShellfishFreshwaterFinfish SalmonOther Saltwater FinfishCannedTunaOtherCanned FishGround beef –0.04 –0.05 0.07 0.01 0.13** –0.05 0.14**(0.05) (0.04) (0.05) (0.05) (0.07) (0.03) (0.06)Steaks 0.02 0.02 0.02 –0.10*** –0.01 –0.06*** 0.28***(0.04) (0.03) (0.03) (0.04) (0.06) (0.02) (0.07)Other beef –0.11** –0.01 –0.01 0.05 0.09 –0.02 0.29***(0.05) (0.04) (0.04) (0.05) (0.07) (0.03) (0.07)Pork –0.01 –0.09*** –0.01 0.04 0.18*** –0.02 0.23***(0.04) (0.03) (0.04) (0.04) (0.06) (0.03) (0.06)Boneless –0.19*** –0.09* –0.03 –0.17*** 0.20*** –0.01 0.20***poultry (0.06) (0.05) (0.05) (0.06) (0.07) (0.04) (0.06)Other poultry –0.06 –0.11*** –0.03 0.07* 0.09 –0.01 0.34***(0.04) (0.03) (0.04) (0.04) (0.06) (0.03) (0.06)Other meat 0.01 –0.08*** 0.07*** 0.05* 0.08* –0.02 0.20***(0.03) (0.03) (0.02) (0.03) (0.05) (0.02) (0.05)Shrimp–0.29*** 0.00 –0.29*** –0.34*** 0.06 –0.04 0.35***(0.11) (0.06) (0.07) (0.08) (0.08) (0.05) (0.07)Other shellfish 0.04–0.65*** –0.03 –0.36*** 0.09 –0.05 0.42***(0.07)(0.08) (0.06) (0.07) (0.08) (0.05) (0.08)Freshwater–0.40*** –0.10*–0.52*** 0.14** –0.40*** 0.05 0.54***finfish(0.08) (0.06)(0.10) (0.08) (0.09) (0.05) (0.08)Salmon–0.38*** –0.37*** 0.14**–0.72*** 0.28*** –0.03 0.39***(0.08) (0.06) (0.07)(0.11) (0.09) (0.05) (0.08)Other saltwa-–0.11 –0.07 –0.83*** 0.36**–0.60*** 0.18** 0.32***ter finfish(0.14) (0.10) (0.14) (0.16)(0.20) (0.10) (0.11)Canned tuna–0.08 –0.13* 0.11 –0.05 0.27***–0.34*** 0.06(0.09) (0.07) (0.08) (0.09) (0.09)(0.09) (0.07)Other canned–0.09 0.25*** 0.03 0.19* 0.10 –0.01–0.60***fish(0.10) (0.07) (0.09) (0.10) (0.11) (0.06)(0.06)Note: Asymptotic standard errors in parentheses. Levels of statistical significance: *** = 1%, ** = 5%, * = 10%.45