Literature review

The demand for yogurt has been studied applying different theoretical frameworks and estimating various empirical models, depending on the nature of the respective analyses and on the data used. As exhibited in Table 1, various studies have focused primarily on yogurt without reference to Greek yogurt or to non-Greek yogurt. Additionally, past studies have considered the demand for yogurt by product forms, specifically refrigerated yogurt, frozen yogurt, drinkable yogurt, and flavored yogurt as well as by brand, particularly Chobani, Dannon, Yoplait, and private label. Without reference to brand, the demand for the aggregate category of yogurt has been estimated to be elastic, except for the studies by Boehm and Babb (Reference Boehm and Babb1975) and Chouinard et al. (Reference Chouinard, LaFrance, Davis and Perloff2010). The own-price elasticities for yogurt by brand have varied considerably as follows – Chobani (−2,64 to −6.84); Dannon (−0.35 to −5.48); Yoplait (−0.37 to −5.65); Private Label (−0.19 to −6.15). Most of the demand studies summarized in Table 1 were conducted using a demand systems approach.

Table 1. Selected prior studies from the economic literature dealing with yogurt

Notably, only a few prior studies have conducted separate demand analyses for Greek yogurt and non-Greek yogurt. Dharmasena et al. (Reference Dharmasena, Okrent and Capps2014) analyzed U.S. household demand for Greek yogurt and non-Greek yogurt along with other dairy products using the 2010 Nielsen Homescan Panel. Based on the estimation of a censored QUAIDS model involving 61,440 households, own-price elasticities for Greek yogurt and non-Greek yogurt were estimated to be −0.12 and −0.22, respectively. Their cross-price elasticities were positive, indicative of substitutes. The income elasticities for Greek yogurt and non-Greek yogurt were estimated to be 0.35 and 0.20, respectively, indicative of necessities. Key demographic factors affecting these demands were household income, age, and education of the female head of household, region, race, ethnicity, and presence/absence of children.

Keller (Reference Keller2018) estimated probit models only of household purchases of: (1) yogurt; (2) Greek yogurt only; (3) non-Greek yogurt only; and (4) both Greek and non-Greek yogurt. This research utilized the Nielsen Homescan Panel for calendar year 2015 only. Socio-demographic factors considered were household income, household size, region, age and presence of children, race, and education and age of the household head.

Gao and Capps (Reference Gao and Capps2023) investigated demand interrelationships for eight dairy categories, including Greek yogurt and non-Greek yogurt, as well as for margarine and plant-based milk alternatives using the QUAIDS and the Barten Synthetic Model, based on monthly data derived from Nielsen covering the period January 2010 to November 2015. Estimated own-price elasticities for non-Greek yogurt ranged from −1.42 and −1.63 and estimated own-price elasticities for Greek yogurt ranged from −1.97 to −2.25. Income elasticities for these products were estimated to be in the interval 0.23 to 0.50, indicative of necessities. Greek yogurt and non-Greek yogurt were revealed to be substitutes.

In sum, while there have been several research studies dealing with the demand for yogurt in the United States dating back to the 1970s, few studies have centered attention on partitioning yogurt into separate Greek and non-Greek yogurt categories. In our study, we use data acquired from Nielsen pertaining to 164,484 panel households across the United States for calendar years 2018 to 2020.Footnote ¹ Hence, our study reflects more recent market conditions of the yogurt category compared to previous studies. Additionally, we conduct separate analyses of Greek and non-Greek yogurt using a variation of the Heckman model to mitigate observed zero purchase values. We provide separate probit models dealing with the likelihood of purchasing Greek yogurt and non-Greek yogurt as well as separate conditional demand models for these distinct yogurt products. On this basis, our study subsequently adds to the literature concerning household demand for Greek yogurt and non-Greek yogurt. As such, we provide a comprehensive overview of the yogurt market in the United States.

Model development

Not all households purchase Greek or non-Greek yogurt in each calendar year of the sample period. For these households, the expenditures expressed in dollars and the quantities purchased expressed in ounces (with standardization) are zero. To deal with this censoring issue, we rely on the sample selection model of Heckman (Reference Heckman1976, Reference Heckman1979). Consistent with the first stage of Heckman two-step estimation procedure, we employ a probit model or selection equation (choice model) to develop profiles of U.S. households who purchase Greek or non-Greek yogurt.

The probit models in this analysis are binary choice models, where the dependent variables take on two values – 0 when no expenditure is made for Greek yogurt or non-Greek yogurt and 1 when any expenditure for these yogurt products is made by household i. Keller (Reference Keller2018) centered attention on the decision to purchase Greek yogurt only and non-Greek yogurt only as well as the decision to purchase both Greek yogurt and non-Greek yogurt. To differentiate our work from Keller (Reference Keller2018), we are concerned with the decision to purchase Greek yogurt or not and the decision to purchase non-Greek yogurt or not. Our sample covers calendar years 2018 to 2020, while the sample in Keller (Reference Keller2018) dealt with calendar year 2015 only.

We provide details of the probit model for yogurt product j (j = 1 for Greek yogurt and j = 2 for non-Greek yogurt) as follows:

(1) $$y_{ij}={{\boldsymbol{x}}}_{i}^{'}{{\boldsymbol{\beta}} }+{u_{1}}_{ij}$$

$$ y_{ij} = 1{\rm \ if\ }{\rm yogurt} \ {\rm product\ }{\rm purchase\ }{\rm j}\ {\rm was\ made\ by\ household\ }\mathit{i} $$

$$y_{ij}=0\ {\rm if\ no\ }{\rm yogurt} \ {\rm product\ }{\rm purchase\ }{\rm j}\ {\rm was\ made\ by\ household\ }\mathit{i}$$

and

(2) $$\Pr \left(y_{ij}=1 \,| \ \boldsymbol{x}_{i}^{'}\right)={\it{\Phi}} ({{\boldsymbol{x}}}_{i}^{'}\boldsymbol{\beta }),$$

where Φ is the cumulative distribution function (CDF) of the standard normal distribution; x _i ^′ is a column vector of explanatory variables, β is a vector of parameters associated with the explanatory variables, and e _i is the random error.

Socio-demographic factors were considered in previous studies of yogurt demand including household size, age, and education of the female head of household, the presence of children, race, region, and household income. Boehm and Babb (Reference Boehm and Babb1975) ascertained that regional differences were evident concerning yogurt consumption. Kepner, Knutson, and Nichols (Reference Kepner, Knutson and Nichols1978) noted that the typical yogurt consumer was female; college-educated; from the Pacific, Northeast, and Mid-Atlantic regions; resided in a household with relatively high income; and was between ages 13–19 or 35–44. Davis, Blayney et al. (Reference Davis, Blayney, Muhammad, Yen and Cooper2010a), Davis, Dong et al. (Reference Davis, Dong, Blayney and Owens2010b), and Davis et al. (Reference Davis, Yen, Dong and Blayney2011) analyzed the impacts of household size, education of the female head of household, region, race, ethnicity, presence of children, household income and marital status on the demand for refrigerated yogurt, frozen yogurt, and drinkable yogurt. As such, past research supports the contention that the influence of socio-demographic variables should be considered.

Additionally, Hill and Lynchehaun (Reference Hill and Lynchehaun2002), Peterson and Buse (Reference Peterson and Buse1975), and Dharmasena, Okrent, and Capps (Reference Dharmasena, Okrent and Capps2014) identified various cultural and socioeconomic factors influencing household preferences including age, ethnicity, household income, household size, education, presence of children, region, and race. We hypothesize that age is inversely related to the decision to purchase Greek and non-Greek yogurt, and households located in the Pacific, Northeast, and Mid-Atlantic regions are more likely to purchase Greek and non-Greek yogurt relative to other regions. Moreover, based on the work by Keller (Reference Keller2018), we expect household income to be positively linked to the decision to purchase Greek and non-Greek yogurt, but household size to be negatively related to the decision to purchase these yogurt products. Moreover, we expect the presence of children to be negatively associated with the likelihood of purchasing these yogurt products.

In agreement with Keller (Reference Keller2018), we expect key regions associated with the likelihood of purchasing Greek yogurt to be the New England, the Middle Atlantic, and the South Atlantic regions. Further, consistent with the finding of Kepner, Knutson, and Nichols (Reference Kepner, Knutson and Nichols1978) and because education level often is positively associated with health consciousness (Alviola and Capps, Reference Alviola and Capps2010), we hypothesize that college-educated households are more likely to purchase Greek and non-Greek yogurt relative to non-college-educated households. Finally, we hypothesize that prices of Greek yogurt and non-Greek yogurt also influence the purchase decision of these products.

Operationally, the decision to purchase either Greek or non-Greek yogurt is defined in equation (3) as:

(3) $$\eqalign{& {y_{ij}} = {f_{ij}}{\rm{(Ag}}{{\rm{e}}_{\rm{i}}}{{\rm{,}}_{\rm{,}}}{\rm{H}}{{\rm{S}}_{\rm{i}}}{\rm{,}}\,{\rm{H}}{{\rm{I}}_{\rm{i}}}{\rm{,}}\,{\rm{C}}{{\rm{D}}_{\rm{i}}}{\rm{, P}}{{\rm{C}}_{\rm{i}}}{\rm{,}}\,{\rm{B}}{{\rm{L}}_{\rm{i}}}{\rm{,}}\,{\rm{WC}}{{\rm{,}}_{\rm{,}}}{\rm{O}}{{\rm{R}}_{{\rm{i,}}}}{\rm{H}}{{\rm{C}}_{\rm{i}}}{{\rm{,}}_{\rm{,}}}{\rm{Pacifi}}{{\rm{c}}_{\rm{i}}}{\rm{, ES}}{{\rm{C}}_{\rm{i}}}{\rm{, M}}{{\rm{A}}_{\rm{i}}}{\rm{, M}}{{\rm{N}}_{\rm{i}}}{\rm{, N}}{{\rm{E}}_{{\rm{i,}}}}{\rm{S}}{{\rm{A}}_{\rm{i}}}{\rm{,}} \cr & {\rm{WN}}{{\rm{C}}_{\rm{i}}}{\rm{, WS}}{{\rm{C}}_{{\rm{i,}}}}{\rm{Panel\_Year\_201}}{{\rm{9}}_{\rm{i}}}{\rm{, Panel\_Year\_202}}{{\rm{0}}_{\rm{i}}}{\rm{, P}}{{\rm{G}}_{\rm{i}}}{\rm{, PN}}{{\rm{G}}_{{\rm{i,}}}}{\rm{DM}}{{\rm{A}}_{{\rm{ik}}}}{\rm{) + , }} u_{1ij},\cr}$$

where i = 1….164,484 households, j = 1 (Greek yogurt), j = 2 (non-Greek yogurt), and k = 1,…205 (designated market areas (DMAs)). The explanatory variables are explicitly listed as follows: (1) HS = Household_size_i; (2) HI = Household_income_i; (3) CD = College_degree_i, (4) PC = Presence_Children_i, (5) OR = Other_Races_i, (6) Bl = Black_i, (7) WC = White/Caucasian_i, (8) HC = Hispanic_i,_, (9) PC = Pacific_i, (10) ESC = East_South_Central_i, (11) MA = Mid_Atlantic_i, (12) MN = Mountain_i, (13) NE = New_England_i, (14) SA = South_Atlantic_i, (15) WNC = West_North_Central_i, (16) WSC = West_South_Central_i, (17) PG = Price_Greek_Yogurt_i, (18) PNG = Price_Non-Greek_Yogurt_i, and (19) DMA = Designated Market Areas.

DMAs are a group of counties and zip codes that form a particular geographic area. In this analysis, the number of DMAsFootnote ² was 205. Their use provides a more granular decomposition of geographical areas within the broader nine Census regions previously mentioned. We allow for the possibility that DMAs within the same region (or even the same state such as Texas) to have different preferences for Greek yogurt and non-Greek yogurt. Further, we add panel years as dummy variables in the analysis to isolate differences among the respective calendar years, particularly differences between 2018 and 2020 as well as between 2019 and 2020. The COVID pandemic was initiated in the United States in March 2020. Age of the household head, household size, household income, and the prices of the yogurt products are continuous variables, while the remaining explanatory variables are indicator or dummy variables.

To avoid the dummy variable trap, the reference categories for the indicator variables are Asian (race), East North Central (region), panel year 2018 (Panel Year), and New York city (DMA). Additionally, we use inflation-adjusted or real values of household income as well as prices of the respective yogurt products. The dependent variable and the explanatory variables in the probit specifications are defined explicitly in Table 2.

Table 2. Description and descriptive statistics of the dependent variables and explanatory variables included the analysis ¹

¹ Because of the large number of designated market areas (205), we do not report their means. This information is available from the authors upon request.

Marginal effects associated with the two probit models provide insight as to how changes in the right-hand side variables affect the probability of purchasing Greek yogurt and non-Greek yogurt. Because the marginal effects vary from observation to observation, they are calculated at the sample means for each of the explanatory variables in the probit model.

From the probit analysis, let Z _ij = 1 if household i purchases yogurt product j and 0 otherwise. Then, we can write the probability of purchasing Greek yogurt or non-Greek yogurt and the probability of not purchasing Greek yogurt or non-Greek yogurt as:

(4) $${\rm{Pr}}(Z_{ij}=1)={\it{\Phi}}({\boldsymbol{x}}_{ij}^{'}{\boldsymbol{\beta }}) \ {\rm{and}} \Pr \left(Z_{j}=0\right)=1-{\it{\Phi}} ({{\boldsymbol{x}}}_{ij}^{'}\boldsymbol{\beta }),$$

where i = 1,,.164,484; j = 1, 2, and x _ii ^′ is the vector of previously mentioned explanatory variables in equation (3). Following Heckman, we form the Inverse Mills Ratio (IMR), defined as

(5) $$\widehat{IMR_{ij}} = \left\{ {\matrix{ {{{\varphi \left( {{\boldsymbol{x}}_{ij}^{'}{\boldsymbol{\beta }} } \right)} \over {{\it{\Phi}} \left( {{\boldsymbol{x}}_i^{'}{\boldsymbol{\beta }} } \right)}},\;if\;{Z_{ij}} = 1} \cr {{{\varphi \left( {{\boldsymbol{x}}_{ij}^{'}{\boldsymbol{\beta }} } \right)} \over {1 - {\it{\Phi}} \left( {{\boldsymbol{x}}_{ij}^{'}{\boldsymbol{\beta }} } \right)}},\;if\;{Z_{ij}} = 0} \cr } } \right.$$

where ϕ is the probability density function (pf) of the standard normal distribution and Φ is the CDF of the standard normal distribution.

In the second stage of the Heckman model, let Q_ij denote the quantity of yogurt product j purchased (in ounces) by household i, and let ${{\boldsymbol{w}}}_{ij}^{'}$ correspond to the vector of explanatory variables in the model specification. The exclusion restriction in the Heckman model states that there must be at least one variable which appears with a non-zero coefficient in the selection (probit) equation but does not appear in the conditional demand equation (Puhani, Reference Puhani2000). In this study, we include DMAs in the first stage but not in the second stage to satisfy the exclusion restriction Otherwise, w _ij ^′and x _ij ^′ are the same set of explanatory variables. In the second stage, we only consider the conditional demands for Greek yogurt and for non-Greek yogurt. That is, we only use the non-zero amounts purchased of these products as the dependent variables. We then may write the household conditional demand functions as:

(6) $$E\left[Q_{ij}|Z_{ij}=1\right]={{\boldsymbol{w}}}_{ij}^{'}\gamma _{j}+\alpha {\varphi ({{\boldsymbol{x}}}_{ij}^{'}{\boldsymbol{\beta }}) \over {{\it{\Phi}}} ({{\boldsymbol{x}}}_{ij}^{'}\boldsymbol{\beta }))}={{\boldsymbol{w}}}_{i}^{'}\gamma _{j}+\alpha \widehat{IMR_{ij}} + u_{2ij}.$$

In equation 6, γ _j are parameters associated with the explanatory variables included in the conditional demand equations, β are parameters associated with the explanatory variables in the probit equations, and α is the parameter associated with the IMR included in the conditional demand functions. The existence/non-existence of sample selection bias rests on simply testing H ₀: α = 0.

We rely on the maximum likelihood (ML) estimator (also known as the full information maximum likelihood approach) in estimating the Heckman model. We estimate both the probit model and the conditional demand model for each type of yogurt simultaneously assuming that u _1ij ∼ N(0, σ _j ), u _2ij ∼ N(0, 1), and the correlation (u _1ij , u _2ij ) = ρ _j . The ML estimation procedure is done using Stata 15 (Stata Corp, 2017). σ _j and ρ _j are additional parameters to be estimated in conjunction with the ML procedure.

The ML procedure yields consistent and more efficient estimates than the two-step method especially if there is non-zero correlation between the error terms u _1ij and u _2ij . Previous empirical works such as those of Nelson (Reference Nelson1984), Stolzenberg and Relles (Reference Stolzenberg and Relles1990) and Nawata (Reference Nawata1993, Reference Nawata1994) provide evidence that the greater the correlation between u _1ij and u _2ij , the greater the superiority of the maximum likelihood estimator over the two-step estimator in terms of efficiency. With respect to the conditional demand functions, the number of observations is vastly different for Greek yogurt and for non-Greek yogurt. Consequently, we could not estimate the conditional demand functions jointly.

Following Saha et al. (Reference Saha, Capps and Byrne1997), the estimated marginal effect of a change in any explanatory variable k (discrete or non-discrete) for household i and yogurt product j in the conditional demand functions can be written as:

(7) $$\widehat{ME}_{ijk}={dE[log \,(Q_{ij})|Z_{i}j=1] \over dw_{ijk}}=\gamma _{jk}+\alpha {d \over dw_{ijk}}(\widehat{IMR_{ij}})$$

(8) $$\widehat{ME}_{ijk}=\gamma _{jk}-\alpha \hat{\boldsymbol{\beta }}_{jk}\left\{{{\boldsymbol{x}}_{ij}^{'}}{\boldsymbol{\beta}}\ {*}\ \widehat{IMR_{ij}}+\left(\widehat{IMR_{ij}}\right)^{2}\right\}$$

If $\alpha$ is not statistically different from zero, then no sample selection bias is evident, and γ _jk represents the appropriate marginal effect. Hence the significance, sign, and magnitude of the estimated parameter α embedded in equation (8) is very important in the calculation of appropriate marginal effects. To properly assess the impacts of explanatory variables, we implement equation (8) derived by Saha et al. (Reference Saha, Capps and Byrne1997).

We expect the own-price elasticities of Greek yogurt and non-Greek to be negative in accord with economic theory. We also expect the demand for these yogurt products to be elastic. This hypothesis is consistent with the findings of Gao and Capps (Reference Gao and Capps2023) but not with the findings of Dharmasena, Okrent, and Capps (Reference Dharmasena, Okrent and Capps2014). Consistent with past studies, we expect the cross-price elasticity of Greek yogurt with respect to non-Greek yogurt and vice versa to be positive, indicative of substitutes. As well, we expect the income elasticity of demand for the respective yogurt products to be positive and smaller than 1, suggesting that Greek yogurt and non-Greek yogurt are necessities. Additionally, we entertain similar hypotheses concerning the socio-demographic factors in the conditional demand functions as previously discussed with the respective probit models.

Data

As previously mentioned, the source of data for this analysis is the NielsenIQ, formerly known as the Nielsen Homescan Panel, pertaining to 164,484 households for calendar years 2018–2020. These data constitute a national panel of households wherein transactions of purchases from all retail outlets for the panel households are recorded daily over the calendar year. These data therefore provide information associated with expenditures (expressed in dollars) and quantities purchased (volume) of Greek and non-Greek yogurt (standardized as ounces) as well as socio-demographic characteristics of each household. Like Davis, Dong, Blayney, and Owens (Reference Davis, Dong, Blayney and Owens2010b) and Davis, Yen, Dong, and Blayney (Reference Davis, Yen, Dong and Blayney2011), the data are aggregated over each calendar year to determine annual expenditures and volume for each of the respective households. Importantly, the NielsenIQ data refer only to at-home purchases of Greek and non-Greek yogurt in the United States.

Prices of Greek and non-Greek yogurt are imputed as the ratio of expenditure to volume and are expressed as dollars per ounce. These unit value measures are considered as proxies for the prices of Greek and non-Greek yogurt. The construction of unit values is consistent with the methodology proposed by Deaton (Reference Deaton1987). Indeed, as pointed out by Deaton (Reference Deaton1988, Reference Deaton1990, Reference Deaton1997), bias associated with the use of unit values may occur. The bias is attributed to quality variation and reporting errors in expenditures and/or quantities (measurement errors). Deaton (Reference Deaton1988) suggested that the bias associated with quality variation makes the demand for a commodity appear to be more elastic, overstating the response of quantity to changes in price. We operate on the assumption that this bias is negligible.

For households not purchasing Greek and non-Greek yogurt, it is not possible to calculate their imputed values directly. Missing imputed values for those households who did not purchase these yogurt products are generated via auxiliary regressions in which observed unit values for each of the two respective products are regressed as a function of household income, household size, the region as well as the DMA where the household is located. In this analysis, we use dummy variables for 9 regions and 205 DMAs in the auxiliary regressions. Except for DMAs, these instrument variables have been used extensively in prior studies to not only obtain values of missing prices but also to deal with price endogeneity issues (Alviola and Capps, Reference Alviola and Capps2010; Dharmasena and Capps, Reference Dharmasena and Capps2012, Reference Dharmasena and Capps2014; Kyureghian et al., Reference Parmeter, Tsionas and Wang2011).

To ensure that the imputed prices of Greek and non-Greek yogurt are greater than zero, we employ a semi-logarithmic functional form. That is, the dependent variables in these auxiliary regressions correspond to the logarithm of observed Greek and non-Greek unit values. The parameters estimated from these auxiliary regressions are subsequently used to impute prices for observations associated with missing observations using the exponential transformation. Details associated with the auxiliary regressions for Greek and non-Greek yogurt are available from the authors upon request.

Across the sample of 164,484 households, on average, the price of Greek yogurt is 17.55 cents/ounce, and the price of non-Greek yogurt is 13.91 cents/ounce. As such, in our sample, the average price of Greek yogurt is 1.3 times the average price of non-Greek yogurt. The correlation between the respective prices is 0.1155. The number of households who purchase Greek and non-Greek yogurts during the three-year period is 41,120 and 127,042, respectively. Hence, the market penetration or percentage of households purchasing Greek and non-Greek yogurts is 25 and 77%, respectively. Of note, 21% of households purchase no yogurt at all, and 23% of households purchase both Greek and non-Greek yogurt.

In Table 2, we summarize the descriptive statistics (mean values only) for the sample of households included in our analysis. The average age of the household head in our sample is 60. On average, household size is 2.5, and household income is $65,745. About 46% of the sample earned a college degree, and slightly more than 7% are of Hispanic ethnicity. About 77% of our sample have no children living in the household. Further, roughly 80% of the sample is White/Caucasian, 11% are Black, and about 4% are Asian.

About 17% of the sample of households are located in the East North Central region (Illinois, Michigan, Ohio, and Wisconsin), 6% are located in the East South-Central region (Alabama, Kentucky, Mississippi, and Tennessee), 13% are located in the Mid-Atlantic region New Jersey, New York, and Pennsylvania), 7% are located in the Mountain region (Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah, and Wyoming), 5% are located in the New England region (Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont), 21% are located in the South Atlantic (Delaware, Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia, District of Columbia, and West Virginia), 8% are located in the West North Central region (Iowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota, and South Dakota), 11% are located in the West South-Central region (Arkansas, Louisiana, Oklahoma, and Texas), and 11% were located in the Pacific region (Alaska, California, Hawaii, Oregon, and Washington).

To demonstrate the representativeness of our sample to the U.S. population, as exhibited in Table 3, we compare the socio-demographic characteristics of our sample with population statistics provided by the U.S. Census Bureau for 2021 (U.S. Census Bureau, Current Population Survey, 2022 Annual Social and Economic Supplement). The median income for 2021 reported by the U.S. Census Bureau is $69,021, close to the median income of our study of $65, 000. As well, the average household size for 2021 as reported by the U.S. Census Bureau is 2.59, also very close to our average household size of 2.50. Further, similar percentages by race and region are evident. Moreover, the percentage of households whose head earned a college degree is 46% in our sample, close to 50% for 2021 as reported by the U.S. Census Bureau. However, the percentage of Hispanic households in our sample is 7.43%, less than the 12.50% for 2021 as reported by the U.S. Census Bureau. The percentage of households without children in our sample is 77.71%, more than the 67.20% of households without children as reported by the U.S. Census Bureau. The median age of the household head in our sample is 60, while the median age reported by the U.S. Census Bureau is 52. Nevertheless, we maintain our sample is representative of the socio-demographic and marketing landscape of the United States, lending to the external validity of this analysis.

Table 3. Representativeness of the 2018–2020 NielsenIQ Data to the U.S. Population According to the 2021 U.S. Census Bureau

Source: U.S. Census Bureau, Current Population Survey, 2022 Annual Social and Economic Supplement (CPS ASEC), https://www.census.gov/main/www/cprs.html.

Empirical results

For the probit models and the conditional demand function models, the level of statistical significance chosen is set at 0.05. We report the empirical results initially for Greek yogurt, and then for non-Greek yogurt. Specifically, we use the probit models to gain insight into the profile of households who purchase Greek yogurt and non-Greek. The maximum likelihood parameter estimates, standard errors, and associated p-values of the respective explanatory variables in the respective probit models are exhibited in Tables 4 and 5. Because of the numerous DMAs (205), we exclude this information to conform to space limitations. The details associated with these parameter estimates, standard errors, and p-values are available from the authors upon request. In addition, we report the marginal effects for the socio-demographic binary variables as well as for the continuous variables associated with the decision to purchase Greek yogurt and non-Greek yogurt for at-home consumption in Tables 4 and 5.

Table 4. Maximum Likelihood parameter estimates, standard errors, and p-values associated with the estimation of the probit model for Greek yogurt ¹

Note: Bold p-values indicate statistical significance at the 0.05 level. The sample size is 164,484 households.

Source: From the use of the econometric software package Stata 15.

¹ Because of the numerous DMAs (205), we exclude this information in Table 3 to conform to space limitation. The details associated with the parameter estimates, standard errors, and p-values of the DMA indicator variables are available from the authors upon request.

² These elasticities refer to the percentage change in the probability of purchasing Greek yogurt due to a one percent change in real household income, in the real price of Greek yogurt, and the real price of non-Greek yogurt.

Table 5. Maximum Likelihood parameter estimates, standard errors, and p-values associated with the estimation of the probit model for non-Greek yogurt ¹

Note: Bold p-values indicate statistical significance at the 0.05 level. The sample size is 164,484 households.

Source: From the use of the econometric software package Stata 15.

¹ Because of the numerous DMAs (205), we exclude this information in Table 5 to conform to space limitation. The details associated with the parameter estimates, standard errors, and p-values of the DMA indicator variables are available from the authors upon request.

² These elasticities refer to the percentage change in the probability of purchasing non-Greek yogurt due to a one percent change in real household income, in the real price of Greek yogurt, and the real price of non-Greek yogurt.

We also rely on prediction-success tables to validate the binary choices models for Greek and non-Greek yogurt. These tables are standard practice in the evaluation of binary choices models (Pindyck and Rubinfeld, Reference Pindyck and Rubinfeld1998). To formulate a prediction-success table, it is necessary to employ a decision rule for correct classifications of outcomes. Conventionally, if the predicted probability is ≤0.5, then the predicted outcome is Y_i = 0 (the household is predicted not to purchase). On the other hand, if the predicted probability is >0.5, then the predicted outcome is Y_i = 1 (the household is predicted to purchase). Maddala (Reference Maddala1983) and Pindyck and Rubinfeld (Reference Pindyck and Rubinfeld1998) support this contention. However, Park and Capps (Reference Park and Capps1997) point out that the appropriate cutoff may not necessarily be 0.5. Arguments have been made for the decision rule to be the ratio of the number of observations (households for which Y_i = 1) to the total number of observations. We adopt this decision rule in deriving the prediction-success tables.

Empirical results from the probit model for non-Greek yogurt

All estimated coefficients statistically different from zero are in bold. The factors affecting the decision to purchase non-Greek yogurt for at-home consumption are age, race, and education of the household head, presence of children, household size, real household income, region, and DMA in which the household is located, calendar year, and the real price of non-Greek yogurt. Hispanic origin and the real price of Greek yogurt are not statistically significant determinants of the decision to purchase non-Greek yogurt. From Keller (Reference Keller2018), statistically significant determinants of the decision to purchase non-Greek yogurt were household income, household size, region, race, and presence of children. Our results agree with Keller (Reference Keller2018) concerning household income, household size, and race only.

As the price of non-Greek yogurt increases, the likelihood of purchasing non-Greek yogurt for at-home consumption decreases as expected. Moreover, the decision to purchase non-Greek yogurt is positively linked to real household income and to household size. The older the head of household, the lower the likelihood of purchasing non-Greek yogurt, like the situation for Greek yogurt. Compared to Asian households, White/Caucasian households are more likely to purchase non-Greek yogurt, while Black households are less likely to do so.

Households whose head earned a college degree are more likely to purchase non-Greek yogurt relative to households whose heads do not have a college degree. As well, households with children are more likely to purchase non-Greek yogurt relative to households without children. Recall that the presence of children is not a factor in determining purchase of Greek yogurt. The likelihood of purchasing non-Greek yogurt is statistically the same for Hispanic and non-Hispanic households.

Relative to the East North Central region, households located in the Pacific and Mountain regions are more likely to purchase non-Greek yogurt. The likelihood of purchasing non-Greek yogurt is statistically the same for households located in East South-Central, Mid Atlantic, New England, South Atlantic, West North Central and West South-Central regions compared to households located in the East North Central region. Relative to calendar year 2018, households are less likely to purchase non-Greek yogurt in calendar years 2019 and 2020 just like the situation for Greek yogurt.

As the household head ages each year, the probability of purchasing non-Greek yogurt is lower by 0.13%. For household heads that earned a college degree, the probability of purchasing non-Greek yogurt is higher by 2.59% relative to household heads who did not earn a college degree. For each increase in household size, the likelihood of purchasing non-Greek yogurt for at-home consumption rises by 2.00%. Relative to Asians, the likelihood of purchasing non-Greek yogurt is lower by 4.59% for Black households, but higher by 3.86% for White/Caucasian households. Relative to households located in the East North Central region, households located in the Pacific and Mountain regions are more likely to purchase non-Greek yogurt by 17.15% and 8.46%, respectively. For households with children, the likelihood of purchasing non-Greek yogurt is higher by 4.22% relative to households without children. Relative to calendar year 2018, households are less likely to purchase non-Greek yogurt by 3.75% in calendar year 2019 and by 5.03% in calendar year 2020.

Calculated at the sample means, if household income increases by 1 percent, the probability of purchasing non-Greek yogurt for at-home consumption increases by nearly 0.04%. If the price of non-Greek yogurt changes by 1 percent, the probability of purchasing non-Greek yogurt changes by slightly less than 0.02% in the opposite direction. These elasticities concerning the probability of purchasing non-Greek yogurt are much lower than the corresponding elasticities for Greek yogurt.

Roughly 77% of the sample households purchase non-Greek yogurt for at-home consumption. Hence, in the derivation of the prediction-success of the probit model, the cutoff probability for classification purposes is 0.77. Using the cutoff probability, the probit model for non-Greek yogurt correctly classifies the decision to not make purchases with 64.57% accuracy (14,175 out of 37,442), and the probit model correctly classifies the decision to make purchases with 55.95% accuracy (71,080 out of 127,042). Overall, the model correctly classifies all decisions 95,255 out of 164,484 times, with 57.91% accuracy.

Subsequently, we rely on the conditional demand functions to determine the impact of socioeconomic determinants on the amount purchased of these yogurt products and to provide own-price, cross-price, and income elasticities of demand. As to specification, real household income, the real price of Greek yogurt and the real price of non-Greek also are expressed in logarithms. The maximum likelihood parameter estimates, standard errors, and associated p-values of the respective explanatory variables in the respective conditional demand models are exhibited in Table 6 and 7.

Table 6. Maximum Likelihood parameter estimates, standard errors, and p-values associated with the estimation of the conditional demand model for Greek yogurt

Note: Bold p-values indicate statistical significance at the 0.05 level. The sample size is 41,120 households.

Source: Use of the econometrics package Stata 15.

Table 7. Maximum Likelihood parameter estimates, standard errors, and p-values associated with the estimation of the conditional demand model for non-Greek yogurt

Note: Bold p-values indicate statistical significance at the 0.05 level. The sample size is 127.042 households.

Source: Use of the econometrics package Stata 15.

The sample of observations for the conditional demand function for Greek yogurt includes 41,120 households. On average, the number of ounces purchased of Greek yogurt for at-home consumption is 171.25. The sample of observations for the conditional demand function for non-Greek yogurt includes 127,042 households. On average, the number of ounces purchased of non-Greek yogurt for at-home consumption is 431.76 ounces.

The dependent variables in the conditional demand functions correspond to the logarithm of the number of ounces purchased by households of Greek yogurt and non-Greek yogurt over the period 2018 to 2020. Because the respective dependent variables entail a logarithmic transformation, the percentage change associated with the marginal effect for any dummy variable corresponding to a socio-demographic factor c is given as (exp(c)-1) *100, following Halvorsen and Palmquist (Reference Halvorsen and Palmquist1980).