Evidence of Changes in Preferences Among Beef Cuts Varieties: An Application of Poisson Regressions. Authors

Transcription

1 Evdence of Changes n Preferences Among Beef Cuts Varetes: An Applcaton of Posson Regressons Authors Oscar Ferrara and Ronald W. Ward Contact: rward@ufl.edu Unversty of Florda (Trackng No ) Selected Paper prepared for presentaton at the Amercan Agrcultural Economcs Assocaton Annual Meetngs, Portland, OR, July 29-August 1, 2007 Copyrght 2007 by Oscar Ferrara and Ronald W. Ward. All rghts reserved. Reader may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes.

2 Evdence of Changes n Preferences Among Beef Cuts Varetes: An Applcaton of Posson Regressons Oscar Ferrara and Ronald W. Ward The U.S. beef ndustry has focused much of ther marketng efforts n provdng a wde range of mprovements n terms of varety, qualty, convenence, and product consstency. Often ths occurs through efforts to acheve some dfferentaton by marketng base on specfc product attrbutes (e.g., Coleman Natural Beef, Harrs Ranch Beef, Angus Beef, etc). Clearly, consumers must understand these attrbutes. Meat products n general, and n our case beef cuts, can be dfferentated accordng to how consumers perceve product attrbutes, how these attrbutes affects the product s performance, and how mportant these attrbutes are to potental consumers. Demand for convenence, nutrton, and varety should be reflected through both total consumpton and the number of beef cuts purchased n any one buyng occason. That s, the number of beef cuts (e.g., hamburgers, steaks, roast, etc.) purchased n a food shoppng experence provdes one ndcator of consumers preference set for beef n ts wdenng range of forms (Van Osselaer and Alba, 2000). Whle recognzng that the number of cuts s but one of several measures of consumers meat preference, ths study specfcally focuses on the desre for varety through measurng the number of beef cuts actually purchased n each buyng event. As an ntal step, we have lmted ths part of the research just to measurng the lkelhood of buyng one, two, three, or more numbers of cuts n each settng wthout dealng wth the type of cuts and the pounds. Clearly, after measurng the desre for varety; the next step s to determne what fulflls that desre (.e., beef form) and how much. Prevous studes have shown that demographcs and health concerns are mportant demand drvers along wth prces, competng foods, and nformaton (Economc Research Servces, 1994; Ward, 2004). For example, f health s an mportant ssue for the consumer whle shoppng for 2

3 beef products, he or she wll more lkely make a purchase dependng on how the attrbutes of the avalable beef cuts are assocated wth the nutrtonal consderatons. Lkewse, any reducton n searchng costs by offerng greater varetes should contrbute to a greater number of beef cuts purchased. Martnez and Stewart (2003) suggest that tme-pressed consumers purchase more on convenence, whle lookng for qualty, varety, and value. Barkema (2001) ndcated that consumer demand for food s shftng toward products that are easy to prepare whle also promsng safe eatng, mproved nutrton, and greater consstency. Are consumers purchasng habts for beef consstent wth the expectaton of desrng more convenence, havng more optons, and havng the ablty to match the products wth specfc health concerns? Usng a sample selecton model, consumers preferences for beef cuts are measured usng a combnaton of lmted dependent varable models. In an ntal step, a logt model s specfed to generate a sample that ncludes only meat consumers. Then, n the second step, Posson regresson models are ntroduced to calculate the probabltes of the number of purchases. Step one generates the regme choce as a bnary outcome, whle n the other generates the count varable, whch represents levels of consumpton among beef cuts (Green, 1994). Household Consumpton Dares Usng household consumpton dares from a database mantaned and marketng by the Natonal Panel Dary Group (NPD), a total of 95,559 households reported ther meat consumpton actvtes on a two-week (wave) purchasng cycle coverng the perods from September 1992 through August NPD s a prvate data management system where households are moved n and out of the sample n order to mantan a demographcally representatve sample. Snce households move n and out of the base, the household demographcs are the dfferentatng characterstcs among households, not the specfc 3

4 household dentty. That s, we are not poolng cross sectons over tme snce the cross sectons change frequently wthn the data set. Fgure 1 llustrates the dstrbuton of consumer beef cuts purchased among the 95,559 households reportng snce An estmated 14.1 percent of the households ndcated no beef consumpton durng a reportng wave. Among those average households consumng some beef, 27.1 percent only purchased one beef cut n a buyng occason and 26.6 percent purchased two types of cuts. As would be expected, the remanng percentages drop off rapdly. The average dstrbutons should dffer across households, possbly over seasons and over tme. Therefore, dentfyng and measurng the effects of household demographcs and tme s of prmary nterest. For example, are changes n the varetes of beef reflected wth changes n the dstrbuton shown n Fgure 1?. In the left columns of Table 1 we have dentfed several varables that profle the household characterstcs and measure the change through tme. DCUT represents the number of beef cuts purchased. Income (INC), household sze (HWZ), age of the respondent (AGE), presence of chldren (CHD), educaton level (EDU), and occupaton (OCC) correspond to a set of explanatory terms representng household demographcs. Geographc characterstcs of the respondent and adjustments across tme are captured wth the regon of the country (STA), market sze (MSZ), seasons (MTH) and years (YRS). All these varables are bnary and are ncluded n the subsequent models usng the restrctons that the sum of the coeffcents for each dummy equals zero to deal wth the sngularty ssue wth dummy varables (Ward and Ferrara, 2005). Estmatng Purchasng Frequences Purchase processes are generally assumed to be a renewal process. Varables that report a frequency are often treated usng count data models (Long, 1997). Count data models have been appled n varous research dscplnes such as agrcultural economcs, poltcal scence, and 4

5 medcal scences. Examples nclude the number of tmes that shoppers decde to purchase rradated meat products (Rmal et al, 1999), modelng household purchases (Pelzer et al, 1991), and estmaton food expendtures on bulk purchases (Peña and Ruz, 1998). Such studes nvolve truncated data sets because only those who consume beef at least once are ncluded n the analyss (Okoruwa et al, 1998). In contrast to these studes, the current database ncludes those households who also dd not purchase beef n a partcular buyng occason. The objectve of ths research s to estmate the demand for beef cut varetes usng a lmted dependent varable model that accounts for both partcpaton and consumpton decsons. For ths purpose, t s useful to consder the process as two separate choce events: frst, the decson of whether or not to consume meat products and second, condtonal on consumpton, the decson of the number of beef purchases durng that partcular perod. For ths research, a count-dentfcaton model for beef consumpton s estmated jontly usng a zero-nflated Posson regresson (ZIP) for the frequences and usng a truncated logt regresson for the consumpton of beef products. The jont modelng s accomplshed by assumng that condtonal on ndependent varables ( x ' s) the dependent varables ( y ' s) are stochastcally dfferent. Under ths scenaro, the dependency (beef consumer) s captured through the ( x s), and the jont-lkelhood factors provde a component for consumpton and another for ' count or number of purchases (Cameron and Trved, 1998). A major objectve n the analyses of truncated data s to estmate the underlyng (latent) populaton demand for beef cut products. Followng Green (2003), the analyss ncludes a logt model that determnes whether a zero or a nonzero consumpton outcome occurs and t s gven by usng to denote the observatons: y f ( x ) * u (1) 5

6 Let y * ( Pounds ) be the count varable of nterest and defne the ndcator varable for the Posson regresson as: DCUT y 0 f f y y * * 0 0. and DDCUT 1 0 f f DCUT DCUT 0 0 (2) where x s a row vector that represents the full set of demographc and non-demographc varables that mght affect the frequency of purchase (see Table 1); s a vector of parameters, and u s the resdual term (Gujarat, 2003). The response varable s qualtatve n nature and can take only two values: 1 or 0 thus, consumpton s only observed f * ( Pounds ) s greater than zero. Once the sample selecton s performed, the Posson regresson model s used to examne the non-lnear relatonshp between the frequency of purchase, the varety of purchase, and the factors that may nfluence consumers preferences. In general, the probablty of an ndvdual not consumng beef; and consequently not buyng one or more beef cut varetes s: exp( x ) Pr [ DDCUT 1]. (3) 1 exp( x ) Usng a more detaled specfcaton proposed by Cameron and Trved (1998) and Greene (2003), the number of beef cuts purchased and the probablty dstrbuton can be formulated as follows: y e ( ) Pr( DCUT y x ), y 1,2,... k (4) y! where exp( x ) lettng y denote the number of cuts DCUT. y To be more specfc, we assume that ndvdual quantty demanded y s a random draw from a Posson dstrbuton wth a mean whch n turn, s assumed to be a functon of parameters and a vector of ndvdual specfc explanatory varables x (Haab and McConnell, 1996). In 6

7 equaton (4) the equaton k ln corresponds to a set of dummy varables wth ther j 0 x j j respectve coeffcents along wth the ntercept. Gven the lmted space, Table 1 ncludes the Posson coeffcents for the second stage of the model along wth the supportng t-values. Almost all varables are statstcally sgnfcant and have the expected sgns (.e., when the sgns could by hypotheszed). Snce, the varables can be statstcally sgnfcant but numercally unmportant, we wll use the results from Table 1 to concentrate on the probabltes of each level of beef purchases (.e., counts) and express the response to each varable relatve to the average. The estmaton of the mean predcted probablty s of partcular mportance n order to compare the observed proportons of the sample at each count, and summarze the predctons of the model. The predcted probabltes for the average consumer can be computed for each observaton and for each count (DCUT) that s of nterest (Long, 1997) as follows: y 1 1 exp( ˆ ) ˆ Pr ( y DCUT) (5) K K K Pˆr( y DCUT x ) 1 K 1 y! Posson regresson models show a very restrctve but convenent theoretcal characterstc, that s, ts condtonal mean s equal to ts condtonal varance whch represents the man property of the model. As a result, the condtonal mean of ( y ) measures the average consumpton gven the probablty of observng a postve consumpton, ( E [ y x ]) = Var [ y x ]) =. (6) ( However, many tmes ths assumpton s not satsfed and the varance s greater than the mean, whch s often the case when zero event counts are domnant or represent a large number of observatons of the sample set. Indvduals show unobserved heterogenety when expressng ther experences regardng an event n partcular, and ths heterogenety leads to overdsperson; that s, the actual varance of the process exceeds the nomnal Posson varance even after regressors are ntroduced (Cameron and Trved, 1998). To account for the over-dsperson, we 7

8 can use a Negatve Bnomal as a Gamma mxture of Posson random varable that accounts for over-dsperson by addng a parameter alpha. The negatve bnomal dstrbuton adds a quadratc 2 term ( ) to the varance functon ( ) representng the overdsperson. As such, the key to modelng the effect s to ntroduce the unobservable nto the model whch, n the case of the negatve bnomal arses f t s assumed that the unobserved heterogenety,, has log gamma dstrbuton. Selectvty would arse f the unobserved heterogenety n ths condtonal mean s correlated wth the unobservable n the sample selecton mechansm (Green, 2006). Followng Cameron and Trved, 1998, the negatve bnomal model takes the form: 1 1 ( y1 ) Pr( DCUT y, ) ( ) y! 1 y, 0, y 1,2,... k (7) Ths reduces to the Posson f 0. The larger the value of the more varablty s n the data that s assocated wth the mean. Whle the full results are not reported n Table 1, a negatve bnomal ( ) coeffcent was ncluded showng an alpha ( ) parameter consstent (almost zero) wth the Poson regressors, hence the negatve bnomal parameter estmated equals the Posson estmates ( ) and the LR test statstc take a value equal to zero. As a result, the condtonal mean s correctly specfed and there s not overdsperson (see Table 1). Poson estmates yeld consstent parameter estmates, wth nearly all t-values showng hghly sgnfcant results whch, ndcatng the statstcal mportance of each of the varables ncluded n the model. Posson Beef Cuts Model Estmates Whle almost all demographc varables n Table 1 show statstcally sgnfcant mpacts, numercally not all of them are expected to have an mportant effect on the lkelhood of buyng one or more beef cuts. The large sample sze allows hgh levels of sgnfcance among 8

9 coeffcents wth almost 65% of them beng sgnfcant at the 5% level or lower. Estmates also show a small R 2 coeffcent, whch doesn t represent a concern n ths model consderng the number of observatons. The log lkelhood value for frequency of purchase (-118,569) lead to the nference of a sgnfcant systematc relatonshp between the ndependent varables and the number of beef cuts purchased (DCUT), and consstent wth the LR test, all coeffcents are sgnfcantly dfferent from zero at the 0.05 sgnfcance level. The sgnfcance and numercal effect of parameter estmates from the models used n ths study are partcularly noteworthy, and tend to confrm that there s no evdence of change n consumers apttudes or preferences toward purchasng one or more beef cuts over tme. As parameters coeffcents ndcate, the quantty of cuts purchased among beef consumers are more lkely to be affected by factors related to the number of people lvng n the household, the professon of the respondent, hs/her age and educaton. For nstance, at lower levels of educaton coeffcents clearly show the negatve effect on the number of cuts purchased whch, mght sgnalze the strong effect of ncome-educaton on the qualty and quantty of beef purchased, assumng that people wth hgher levels of educaton have hgher ncome levels and assumng that more beef varetes mplctly refer to dfferent qualty levels. These results also ndcate that a sngle respondents or couples have a negatve propensty to purchase more than one varety. Conversely, estmated coeffcents on household sze of more than three are postve and statstcally sgnfcant, suggestng that n the case of large famles, the household s head mght be nterested n large number of beef cuts to satsfy the preferences n terms of varety, convenence, and qualty. On the other hand, the effects of the respondent s age are consstent and ndcate that the mpact of people aged 40 years and younger s small when purchasng for more than one beef cut. However, the estmated coeffcents on age for respondents aged 40 years and older have a postve sgn, ndcatng a strong relaton between age and the number of cuts (.e., two or more 9

10 cuts). Outputs from all other varables ncluded n ths research ndcate that almost all of them have a sgnfcant mpact on the frequency of buyng beef products but, consderng ther small numercal value, they are not dscussed n detal. In general, the estmates reported here are very revealng n terms of lfe styles and mght explan the tendency among beef consumers to relate a partcular beef product wth certan attrbutes that are expected whle shoppng beef cuts for a partcular occason. Probablty of Beef Cuts Purchase Results from equaton (5) show the predcted change n the condtonal mean f the regressor changes by one unt. Thus, for the average consumer, the lkelhood of buyng beef products s more than 85 percent ( probablty of zero consumpton s 14.1 percent) and that the probablty of buyng one, two, three, four, or fve beef cut varetes are 27.1 %, 26.6 %, 17.7 %, 9%, and 3.7 % respectvely (Fgure 1). In order to show the mpact of each varable ncluded n Table 1 and equaton (5), a useful approach s to express the lkelhoods for each beef cut relatve to the average probablty for each category n order to nterpret the range and extenson of the response (Ward and Ferrara 2005). To facltate the nterpretaton of the probabltes, a rankng of the mpacts of each varable s presented n Fgures 2 and 3 showng the dfferences between the most negatve effect and the most postve effect of each varable whle holdng all other varables to ther mean values. The dfferences were then sorted n descendng absolute magntude, thus gvng a quck way to rank the mpacts of each varable ncluded n the Posson regresson thus showng the varables creatng the largest mpacts on beef buyng to those varables wth the least mpact. At ths pont of the analyss t s mportant to reterate that even the fact that almost all the varables ncluded n the model showed statstcally sgnfcant mpacts, numercally the range of effects on the lkelhood of the number of cuts purchased were qute small relatve to the average probablty. However, results clearly show the mportance of the household sze, occupaton th k 10

11 (professon), and age n terms of purchase probabltes. In the case of two cuts purchase, ths sequence s altered due to the larger effect of educaton comparng to the age of the respondent but, n general the numercal effect of ths demographc s almost mperceptble. Readng the fgures, the number of people n the household s ranked frst (most lkely to nfluence) n all categores wth ranges fluctuatng wthn 8 percentage ponts, as n the case of one beef cut, to 1 percentage pont n the two beef cut category. These results are somehow expected because of the dfference n preferences among household members and n partcular when young and older people coexst. Next, occupaton of the respondent can mpact the lkelhood of purchasng from 1 to 5 percentage ponts, dependng on the number of cuts consdered. For one cut, ths range s fve ponts; for three and four cuts, 3 ponts; and for two and fve cuts, one pont. Note that respondents wth hgher level of responsblty (manager and propretors) and more educaton (professonals and students) are more lkely to purchase less varety whch, mght ental an nclnaton for a partcular beef cut that contan the attrbutes to satsfy ther expectatons n terms of health and safety. Age of the respondent present relatve low sgnfcance when buyng one or more beef cuts yet, t mght mply that older people have a postve tendency to purchase more varety, n partcular cuts wth characterstc of convenence and lower fat levels. Indvduals over 40 years of age have an ncreasng probablty of purchasng more than one varety. A study by Capps et al n 1988, suggest that consumers older than 30 years of age are more lkely to try lean meat products than consumers from 20 to 29 years of age. Therefore, consstent wth our results, older people seem to be more health conscous n ther eatng habts than younger people. Regardng the effects of occupaton, the results nterestngly suggest some consstency n the probablty of buyng more beef cuts for respondents n low sklled professons. The estmated coeffcents on these categores have a postve sgn and coeffcents 11

12 are hghly sgnfcant. In contrast, respondents n professons that requre more tranng and educaton show negatve effect on the probablty of buyng more than one beef cut. Beyond educaton, the mpact of all other demographcs and seasonal changes s relatvely low wth an average range between 1 and 2 unts, and n the extreme case of the category for two beef cuts ths range s almost zero. Total effects of household sze and occupaton of the respondent varables on probabltes of purchasng beef cut varetes s clearly shown n Fgure 4. As expected, n the case of household sze, as the number of household members ncrease the probablty of purchasng ncrease almost ten percentage ponts, whle for household head occupaton the overall probablty to affect the number of beef cut purchases vares between 83 percent (sales professonals) and 87 percent (retred respondents). Fnally, t s possble to compare the effect of those two varables across the fve types of beef cuts by comparng the full range of probablty change as llustrated n Fgures 5 and 6. In the case of household sze, wth the excepton of one beef cut, the probabltes of buyng two or more cuts ncrease as the number of people lvng n the house ncrease. Whle, the lkelhood of buyng one beef cut shows a decrease of a 10 percentage pont range across households categores, Fgure 5 clearly llustrates an ncrease of 4 to 11 percentage ponts when consderng the lkelhood of purchasng two or more beef cuts. In Fgure 6 the effect of occupaton presents a dfferent trend n terms of the drecton of the change n probabltes. In ths case, retred respondents show the hghest probablty of buyng two or more beef cut varetes and sales professonals the lowest, whle ths tendency s reverse for one beef cut purchase. Concludng Remarks What do these results mean for the beef ndustry and for consumers demand for varety wthn the context of the beef ndustry? Consderable efforts to provde varety wthn the 12

13 product category s one way to potentally nfluence demand for the category such as beef. In the beef ndustry even the ncreasng role of brands s apparent where brandng has almost doubled (Ward and Ferrara, 2006). As ntally shown n Fgure 1 the sngle cut s only around one-fourth of the total, thus pontng to the propensty to buy more than one cut n a buyng occason. Yet, the tme dmenson to the model ponts to lttle change n the probabltes across the decade of the 90 s and, n fact, the probabltes of not buyng beef even ncreased slghtly. Furthermore, among those buyng some beef the lkelhood of buyng just one cut actually ncreased although by a very small amount. The man story, however, s that the models pont to very lttle change over tme n terms of the dstrbutons of count or number of cuts, and equally mportant s the fact that the mpact of all the demographcs on buyng beef cut varetes s small. Ths s surprsng gven the growth wth brands wthn the beef category and gven the fundamental dfferences among consumers as reflected wth age and ncome. Achevng growth n demand through varyng the number of cuts appears to be qute lmted to the extent that growth and the number of cuts are correlated. Agan, we emphasze that the measure does not account for the pounds nor the type of cuts, just the numbers of cuts. Clearly, that s a logcal extenson to the analyss. References Barkema, Alan, Mark Dranbenstott, and Nancy Novack;. "The New U.S. Meat Industry." Economc Revew (Federal Reserve Bank of Kansas Cty); 86, no. 2 (2001): 24. Cameron, A. Coln, and Trved, P. K. Regresson Analyss of Count Data. Cambrdge Unversty Press, New York, Capps, Oral Jr., D.S. Moen and R. E. Branson. "Consumer Characterstcs Assocated wth the Selecton of Lean Meat Products." Agrbusness ( ) 4, no. 6 (1988): Economc Research Servce, USDA. Per Capta Food Consumpton Data System. Economc Research Servces, Unted States Department of Agrculture -, 2004 [cted February 08, 2007]. Avalable from: 13

14 Greene, Wllam H. Accountng for Excess Zeros and Sample Selecton n Posson and Negatve Bnomal Regresson Models. Department of Economcs, Stern School of Busness, New York Unversty. New York, NY. (1994):1-37. Greene, Wllam H. Econometrc Analyss. 5th ed. Upper Saddle Rver, NJ: Prentce Hall, Gujarat, Deodar N. Basc Econometrcs. 4th ed. New York, NY: McGraw-Hll/Irwn, Long, J. Scott. Regresson Models for Categorcal and Lmted Dependent Varables. Vol. 7, Advanced Quanttatve Technques n the Socal Scences Seres. Thousand Oaks, CA: Sage Publcatons, Haab, T. C., and McConnell, K. E. Count Data Models and the Problem of Zeros n Recreaton Demand Analyss. Amercan Journal of Agrcultural Economcs, Vol 78, no.1 (1996): Martnez, Stephen and Hayden Stewart. "From Supply Push to Demand Pull: Agrbusness Strateges for Today's Consumers." Amber Waves (2003): 1-8. McFadden, D. "Condtonal Logt Analyss of Qualtatve Choce Behavor." In P. Zarembka, (Ed.) Fronter of Econometrcs, New York: Academc Press. (1973): Natonal Panel Dary Group (NPD). "The Natonal Eatng Survey." Natonal Panel Dary Group, Inc. Chcago, Illnos Okoruwa, A. Ason, J.V.Terza, and H.O.Nourse."Estmatng patronzaton shares for urban retal centers: An extenson of the Posson gravty model." Journal of Urban Economcs, vol. 24(3). (1988): Pelzer, Perre M.L., Dale J. Menkhaus, Glen D. Whpple, Ray A. Feld, and Shawn W. Moore. "Factors Influencng Consumer Rankngs of Alternatve Retal Beef Packagng." Agrbusness ( ) 7, no. 3 (1991): 253. Peña, Danel and Ruz-Castllo, J. The Estmaton of Food Expendtures from Household Budget Data n Presence of Bulk Purchases. Journal of Busness and Economc Statstcs, Vol 16, no. 3 (1998): Rmal, Arbndra., Fletcher, P., McWatters, K. H. Nutrton consderatons n food selecton. Internatonal Food and Agrbusness Management Revew. Vol 3; no. 1 (2000): Van Osselaer, Stjn J. and Joseph W. Alba. "Consumer Learnng and Brand Equty." Journal of Consumer Research 27, no. 1 (2000): 16. Ward, Ronald W. "Advertsng and Promotons." In Agro-Food Marketng, edted by Danel. I. Padberg, : CAB Internatonal, Ward, Ronald W. and Oscar Ferrara. "Measurng Brand Preferences Among U.S. Meat Consumers wth Probt Models." Paper presented at the 2005 Amercan Agrcultural Economcs Assocaton, Provdence, RI. July 24-27,

15 Table 1: Demographc characterstcs and coeffcent estmates Descrpton Varable Name / Range Posson Coef. t-value (Frequency) Intercept INC: ncome per household (dollars) HWZ: household sze (Number of members) AGF: age of female head (years) CHD: presence of chldren(<18) EDF: female head educaton level OCC: occupaton householder STA: Regons (based on census) MSZ: Market Sze (number of people) MTH: months YRS: Years (1992: 2000) INC1 INC2 INC3 INC4 HWZ1 HWZ2 HWZ3 HWZ4 AGF1 AGF2 AGF3 AGF4 CHD1 CHD2 EDF1 EDF2 EDF3 EDF4 OCC1 OCC2 OCC3 OCC4 OCC5 OCC6 OCC7 OCC8 OCC9 OCC10 OCC11 OCC12 STA1 STA2 STA3 STA4 STA5 STA6 STA7 STA8 STA9 MSZ1 MSZ2 MSZ3 MSZ4 MSZ5 MSZ6 MTH1 MTH2 MTH3 MTH4 MTH5 MTH6 MTH7 MTH8 MTH9 MTH10 MTH11 MTH12 YRS1 YRS2 YRS3 YRS4 YRS5 YRS6 YRS7 YRS8 YRS9 0-24,999 25,000-49,999 over 75,000 50,000-74,999* or more* Under to to 65 Over 65* Yes None < 18* Hgh school or less Post graduate College graduate Some college* Professonal Propretor, manager Clercal Sales Craftsman Operatve Mltary Servce worker Farm related jobs Student employed Laborers Retres, unemployed* New England Mddle Atlantc East North Central Pacfc South Atlantc East South Central West South Central Mountan West North Central* 50, , , , , ,999 2,500,000 or more 1,000,000-2,499,999 Non market sze* Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec* * alpha (α): Negatve bnomal coeffcent *Normalzed on the last category of each explanatory varable Perod: 1992:9-2001:8 N. of obs. = 95,559 N. pos. obs. = 80,839 % Postve obs. = R-squared = Scaled R-squared = Overdsperson test = Log lkelhood = LR =

16 Probabty of a number Number of beef cut purchases Fgure 1: Average probablty of buyng one or more beef cuts across ncome categores. No Beef Cuts One Beef Cut Two Beef Cuts Housesze Housesze Housesze 0.26 Occupaton Occupaton Occupaton 0.26 Age Age Educaton 0.26 Educaton Educaton Age Months Months Chldren 0.26 Market Sze Market Sze Market Sze Regon Regon Months Years Years Regon Income Income 0.28 Years Chldren Chldren 0.28 Income Probablty of No Cut Probablty of One Cut Probablty of Two Cuts Fgure-2: Range from the average probablty of zero, one or two beef cut purchases 16

17 Three Beef Cuts Four Beef Cuts Fve Beef Cuts Housesze Housesze Housesze Occupaton Occupaton Occupaton Age Age Age Educaton Educaton Educaton Months Months Months Market Sze Market Sze Market Sze Regon Regon Regon Years Years Years Income Income Income Chldren Chldren Chldren Probablty of Three Cuts Probablty of Four Cuts Probablty of Fve Cuts Fgure-3: Range from the average probablty of more than two beef cut purchases Hw dsze 1 Hw dsze 2 Hw dsze 3 Hw dsze Retr Other Oper Prof Mlt Farm Clerc Serv Skll Manag. Labor Sales Fgure 4: Overall effect of household sze and occupaton on the probablty of buyng beef cut varetes 17

18 Fgure-5: Probabltes of buyng one or more beef cuts based household sze. Fgure-6: Probabltes of buyng one or more beef cuts based on occupatons. 18