Literature Review

Empirical Model and Estimation Procedure

Generally speaking, not all households (or individuals) purchase all food types during the sampling period, resulting in zero expenditure levels (and quantities) reported for some foods under consideration (also known as the data censoring problem). The application of ordinary least squares (OLS) to estimate a regression with a censored dependent variable can result in biased estimates (Kennedy 2003). Dropping the observations with zero reported expenditures would result in sample selection bias. Therefore, to account for zero instances (or censored data) of fiber intake, we adopt a Heckman two-step sample selection procedure (Heckman Reference Heckman1979). To account for the panel nature of the data, a random effects panel model is used in the second step to estimate the demand for particular foods rich in dietary fiber. The households in the panel are likely to differ in culture, tastes, and other unobservable factors. Thus, it is reasonable to assume that the differences among them are randomly distributed.

The first stage involves the decision to purchase a food product. Let $Z_{it}^\ast$ be a latent selection variable described by equation (1):

(1)$$z_{it} ^{\ast} = {\bi x}_{it}\; \gamma + \; \varepsilon _{it}\comma \; $$

where the latent selection variable is described as j, y _ij,

(2)$$z_{it} = \; \left\{{\matrix{ {z_{it}^{\ast} = {\bi x}_{it}\; \gamma_i + \; \varepsilon_{it}\comma \; \; \; \; if\; \; z_{it}^{\ast} \gt 0\; } \cr \!\!{0\comma \;\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; if \; \; z_{it}^{\ast} \le 0} \cr}} \right.\;. $$

for i = 1,2,…,N, t = 1,2,…,T. For equation (1), x_it is the vector of explanatory variables for household i (e.g., prices and demographics), γ is the vector of coefficients to estimate, and ε_it are the error terms which are assumed to be identically and independently distributed (i.i.d). ${\rm {\cal N}}\lpar 0\comma \; {\rm \sigma} _{\rm e}^2$). The decision to purchase a food product is modeled through the use of a probit model. The estimation of this model leads to an inverse Mills Ratio (IMR) (calculated as a ratio between the probability density function and cumulative distribution of probabilities derived from the standard normal distribution assumed in the probit model) that is included in the second stage regression to account for sample selection bias due to non-purchase events.

The second stage with panel-level random effects is described as:

(3)$$y_{itk}^{\ast} = {\bi x}_{itk}\; \beta _{ik} + \alpha _{ik}\lambda _{itk} + v_{ik} + \; \varepsilon _{itk}\comma \; $$

where $y_{itk}^ \ast$ denotes the amount of dietary fiber derived from food product k for household i in time period t, x_itk is the vector of explanatory variables for household i (e.g., prices and demographics) and product k in time period t, λ _itk is the IMR, β is the vector of coefficients to estimate for product k, v _ik are the random effects which are independently and identically distributed (i.i.d.)${\rm {\cal N}}\lpar {0\comma \; {\rm \sigma}_{\rm v}^2} \rpar$, and ε_itk are the error terms which are i.i.d. ${\rm {\cal N}}\lpar {0\comma \; {\rm \sigma}_{\rm e}^2} \rpar$ and independent ofv _ik.

Given that regressors appear in both the first and second stage regressions, we employ the calculation of Saha, Capps, and Byrne (Reference Saha, Capps and Byrne1997) to derive the appropriate marginal effects. This calculation takes the form:

(4)$$\widehat{{ME_{\,jk}}} = \widehat{{\beta _{\,jk}}}-\widehat{{\alpha _k}}\widehat{{\gamma _j}}\lcub {\lpar {{\bi x}_{\,jk}\widehat{{\; \gamma_{\,jk}}}} \rpar \widehat{{\lambda_{\,jk}}} + \widehat{{\lambda_{\,jk}^2}}} \rcub \comma \; $$

where $\widehat{{\beta _{jk}}}$ is the estimated coefficient for the jth explanatory variable for product k from the second stage, $\widehat{{\alpha _k}}$ is the estimated parameter associated with the IMR, $\widehat{{\gamma _{jk}}}$ is the estimated coefficient for the jth explanatory variable from the first stage, ${\bi x}_{jk}\widehat{{\; \gamma _{jk}}}$ is the predicted value from the first stage for product k, and $\widehat{{\lambda _{jk}}}$ is the estimated IMR from the first stage for the product k. We estimate the model parameters, standard errors, and marginal effects using Stata 14 (STATA, 2015).Footnote ²

The panel-level random effects models for the respective food products represented by (3) are estimated independently as separate equations for each of the nine aforementioned food categories. We chose not to use a demand system approach largely because the theorized restrictions of homogeneity and symmetry are often rejected when tested empirically. As well, an unconstrained approach may be more suitable because of the numerous zero expenditure observations. Finally, because the pairwise correlations of the error terms between the single equation models are negligible, a systems approach is not warranted.

In order to investigate the effect of a proposed subsidy, we begin by finding a baseline intake of dietary fiber as an average of the last four quarters of the data for each household. Then for each dietary fiber intake category, we increase or decrease this baseline amount based on the corresponding estimated conditional own-price and cross-price elasticities. This procedure assumes that any change in fiber intake will be met by a change in supply at the current price. This assumption is reasonable since the current intake of dietary fiber is 16 grams per person per day and the current U.S. food supply provides around 25 grams per person per day for a 2,000 kcal diet (Hoy and Goldman, Reference Hoy and Goldman2010; Economic Research Service 2015). This situation corresponds to a relatively inelastic demand curve and a perfectly elastic supply curve, which means a 100 percent pass through of the price reduction to consumers. Different scenarios are analyzed for the 20 percent reduction in price due to the subsidy: (1) all fruit and vegetables, (2) canned fruit and vegetables only, and (3) fresh fruit and vegetables only.

Data

Data are obtained from the Nielsen Homescan Panel (Nielsen Reference Nielsen2018) over the period 2004 through 2014.Footnote ³ We create a quarterly panel of households for the years 2004 through 2014 (44 quarters) consisting of 9,896 households across the United States totaling 435,424 observations.Footnote ⁴ In this sample, 90 percent of households report a positive intake of dietary fiber based on the food categories selected for analysis. Each participating household is given a scanner to read Universal Product Codes (UPCs) of products purchased at stores. Nielsen matches the scanned UPC with product characteristics in their database. The household is also asked to enter quantity, expenditure, and any coupon information about the products purchased.

The quantity of each food product, the fiber quantities derived from these products, and demographic characteristics of the household are obtained. The food products selected for study are bread, pasta, tortillas, fresh fruit, fresh vegetables and beans, frozen fruit, frozen vegetables and beans, canned fruit, canned vegetables and beans. Each product in the dataset is recorded based on its associated Universal Product Code (UPC) as well as an abbreviated product description. For each product, an estimate is made of the fiber content by utilizing a keyword search over the abbreviated product descriptions.Footnote ⁵

We only include products with a UPC and do not include information about random weight produce. We are not able to adequately estimate the dietary content for a broad category of random weight fruit or vegetable purchases. Thus, it was necessary to exclude random weight items from our analysis. We do not believe the lack of random weight purchases will have a major effect on our results. This issue is not unique when analyzing Nielsen data. Dettmann and Dimitri (Reference Dettmann and Dimitri2009) found that random weight vegetable purchases comprised 11 percent of their sample when justifying dropping random weight items from their analysis. Piernas et al. (Reference Piernas, Mendez, Ng, Gordon-Larsen and Popkin2013) also dropped random weight products from their analysis and found it justified because packaged foods constitute a higher contribution to total energy intake. We believe that the Nielsen data are a sufficiently strong source of fiber purchase information which is recorded and is better than dietary recall data.

We were able to identify around 154,000 products across the aforementioned nine food categories. Subsequently, the fiber content for each category is summed to create the total fiber intake for the household in that quarter for each of the nine categories. This total for each category is then divided by the number of members of the household to create an approximation of daily dietary fiber intake per person.Footnote ⁶ Dividing by household size to derive the intra-household allocations is not unique. For example, this approach is taken in Dharmasena, Capps, and Clauson (Reference Dharmasena, Capps and Clauson2011) and Zhen et al. (Reference Zhen, Finkelstein, Nonnemaker, Karns and Todd2013).

Summary statistics of the dependent variables are listed in Table 1. The means presented are conditional on a positive intake in that category. The largest sources of fiber based on the conditional means are bread, canned vegetables, and fresh vegetables. It is important to note the large number of zero observations for some of the categories. Across all food products, 8,864 of the 9,964 households report a non-zero per person fiber intake.

Table 1. Summary Statistics for Fiber Intake Derived from Various Food Categories (Grams per Person per Day)

Note: This table lists summary statistics conditional on purchasing in that category.

Source: Calculations by the authors.

In Figure 1, a histogram for the daily fiber intake per person is shown. The average daily fiber intake per person of our sample is 4.38 grams. This level falls far short of the USDA target of 25 grams per person per day for a 2,000 kcal diet. The majority of our sample is not meeting the USDA guidelines. The USDA (2010, pg. 46) estimates the typical American diet provides 40 percent of needed fiber. Our sample average shows participants meeting slightly less than 20 percent of the recommended target of 25 grams per person. King, Mainous, and Lambourne (Reference King, Mainous and Lambourne2012), using data from the National Health and Nutrition Examination Survey (NHANES), found that mean dietary fiber intakes over the period 1999 to 2008 were in the interval of 15.5 grams/day to 16.1 grams/day. Recall that the dietary fiber intake in our study is derived from only nine food products purchased for at-home consumption, and random weight produce purchases are excluded from this analysis. As such, other possible dietary fiber sources are not included in this research.Footnote ⁷

Note: For the above distribution, the sample average daily dietary fiber intake is 4.38 grams per person.Source: Calculation by the authors.

Figure 1. Distribution of Intake of Dietary Fiber per Person from the Nielsen Panel 2004–2014

For the explanatory variables, unit values (proxy for prices) are calculated by taking the total expenditure in a category and dividing by the total weight (grams) purchased for that category. We observe no unit value or price for the transactions with zero quantities and hence zero expenditures (due to censored nature of these observations). Missing prices are imputed using an auxiliary regression of quantity purchased based on household income, household size, location, and time variables. The variable for income controls for different levels of quality, while the other variables account for price differences associated with regional differences, demographic variability, and time effects. The use of such imputed prices in the regression model also helps deal with potential endogeneity in the price variable. This approach is not without precedent and is standard procedure in the price imputation literature (Capps et al. Reference Capps, Tsai, Kirby and Williams1994; Alviola and Capps Reference Alviola and Capps2010; Kyureghian, Capps, and Nayga Reference Kyureghian, Capps and Nayga2011; Dharmasena and Capps Reference Dharmasena and Capps2014).Footnote ⁸ In Table 2, we present summary statistics for observed prices and imputed prices for each of the product categories. The table shows that the means of the imputed prices are close to the means of the observed prices, confirming the consistency of the observed and imputed prices.

Table 2. Summary Statistics for Observed and Imputed Prices for Each of the Food Products

Note: Imputed prices were calculated with an auxiliary regression that included household income, household size, location, and time as explanatory variables. The number of observed prices is out of a possible 435,424 observations.

Source: Calculations by the authors.

A range of standard demographics to uncover the effect of various household characteristics affecting the demand for fiber intake derived from consumption of various foods is exhibited in Table 3. The age variable was constructed to consider only the age of the oldest head of the household. The average age of the head of household in our sample in 2005 in the first quarter is 56 years.Footnote ⁹ Further, this sample has 5 percent of respondents identified as being of Hispanic origin. Controlling for Hispanic origin (ethnicity) and race is important because such respondents may have different preferences concerning purchases of the respective categories based on sociocultural factors (e.g., tortillas).

Table 3. Summary Statistics Associated with the Set of Explanatory Variables in the Panel Regressions

¹ Average age at the first quarter of calendar year 2005.

Note: This table lists summary statistics for the explanatory variables in the panel regressions. Except for income, age, and household size, the respective factors are indicator variables. The total number of households is 9,896.

Source: Calculations by the authors.

We construct an indicator variable for the presence of children in the households. This variable indicates if there is at least one child present in the household. This variable may be important as the presence of children may change the nutritional mix of food purchased. Parents may focus on purchases of a different food mix when children are present in the household.

Household income is included in the set of explanatory variables in the probit models. Nielsen provides only categorical income information. The income variable is constructed as the natural log of the midpoint of the categorical yearly income variable and adjusted for inflation using the Consumer Price Index (CPI). The average real income in our sample is $27,100. The poverty dummy variables indicate whether household income is at or below 130 percent of the federal poverty level and whether household income is between 130 percent and 185 percent of the federal poverty level. These variables are calculated using household income and household size. As such, in the second-stage equations, household income and household size do not appear explicitly as explanatory variables in the estimated panel regressions.

The place of residence dummies corresponds to the four major U.S. Census Bureau designated divisions (the Northeast, the Midwest, the South, and the West). These are used to control for possible differences in the characteristics of the food environment. These differences may include the availability of grocery stores and other food outlets or possible geographical differences associated with food tastes and preferences.