Literature review

The literature review is divided into two sections. First, we review the literature that has analyzed differences in estimates obtained using consumption versus expenditure (sometimes called acquisition surveys), while the second section reviews the literature on estimating meat demand in Nigeria.

A body of literature has already evaluated differences in estimates of nutritional status (caloric counts) using consumption versus acquisition surveys (e.g., Smith, Alderman, and Aduayom Reference Smith, Alderman and Aduayom2006; Kaara and Ramasawmy Reference Kaara and Ramasawmy2008; Conforti, Grunberger, and Troubat Reference Conforti, Grünberger and Troubat2017; Fiedler and Mwangi Reference Fiedler and Mwangi2016). These studies focus on population-wide estimates of per capita Dietary Energy Consumption (DEC) and their variability. For example, Conforti, Grunberger, and Troubat (Reference Conforti, Grünberger and Troubat2017) compared DEC estimates from consumption versus acquisition data using 81 surveys from several countries. They found that acquisition surveys provided higher estimates (about 10% larger) of DEC than consumption surveys with larger relative variability (i.e., coefficient of variation).

In addition to population-wide estimates of nutritional status, food and policy analyses also require other information generated from survey data, such as income and price elasticities of demand (Piggot and Marsh Reference Piggott and Marsh2011). Two groups of studies evaluate the effect of measurement error on demand estimation. The first group compares demand estimates obtained using alternative survey designs (Gibson Reference Gibson2002; Gibson et al. Reference Gibson, Beegle, De Weerdt and Friedman2015; Gibson and Kim Reference Gibson and Kim2007). The second group evaluates econometric procedures that account for the measurement error problem due to infrequency of purchases (e.g., Deaton and Irish Reference Deaton and Irish1984; Kay, Keen, and Morris Reference Kay, Keen and Morris1984; Keen Reference Keen1986; Blundell and Meghir Reference Blundell and Meghir1987).

For example, within the first group of studies, Gibson et al. (Reference Gibson, Beegle, De Weerdt and Friedman2015) assess the effect of alternative consumption survey designs on Engel demand estimation. The survey designs differed by the method of data capturing (diary versus recall), respondent type (individual versus household reporting), recall period (7-day, 14-day, and one month), and the number of items in the recall list. The authors find that the survey design affects estimated income effects, but not household size effects. However, studies comparing estimates obtained from consumption and expenditure data from the same household are less common (e.g., Gibson and Kim Reference Gibson and Kim2011).

Gibson and Kim (Reference Gibson and Kim2011) measured hidden consumption from food stocks using an unusual household survey that observed food stock changes during the survey period directly. Based upon the bounded recall methodology used in the 1996 Papua New Guinea Household Survey, the authors identified hidden consumption. During the first interview, enumerators weighed household food stocks of 18 major foods and reweighed the stocks of the same foods again in the second interview. This made it possible to measure starting and ending food stocks and observe their hidden consumption. They compared parameter estimates obtained directly from measuring consumption of pre-existing food stocks (i.e., hidden consumption) with estimates obtained from infrequent purchase models (IPM) – models that attempt to account for this hidden consumption indirectly through statistical analysis.Footnote ² The authors found that IPMs produced substantially biased income elasticity estimates. In contrast to their approach to testing the IPMs’ performance using acquired consumption relative to a model that uses measured consumption, we compare demand estimation results using the same econometric procedure but two different data sources: consumption and expenditures. Moreover, Gibson and Kim’s (Reference Gibson and Kim2011) study focused only on estimating income elasticity, while we studied both price and expenditure elasticities.

A related literature has evaluated data quality and focused on assessing the quality of Homescan datasets versus Consumer Expenditure Survey datasets (e.g., Boonsaeng and Carpio Reference Boonsaeng and Carpio2019; Sweitzer et al. Reference Sweitzer, Brown, Karns, Muth, Siegel and Zhen2017). In contrast, our study evaluates the demand estimation results using consumption and expenditure data from the same survey.

The literature review identified only a small number of studies that examined Nigerian consumers’ demand for meat products; however, none used nationally representative country samples, and most used small cross-sectional samples (Igwe and Onyekwere Reference Igwe and Onyekwere2007; Alimi Reference Alimi2013; Ogundari Reference Ogundari2012). The most extensive study was conducted using data from urban households in 3 cities in Northern Nigeria (Ezedinma, Kormawa, and Chianu Reference Ezedinma, Kormawa and Chianu2006), in which 960 households’ expenditures on beef, mutton/goat, chicken, fish, eggs, and milk were evaluated. The authors found that urban households’ meat demand increased as their income increased. More affluent households consumed primarily chicken, eggs, and milk, while poorer households consumed more fish and beef. Beef was found to be the meat product mainly consumed by 77% of households, followed by fish (68%), milk (47%), eggs (45%), chicken (22%), and mutton and goat meat (15%). Own-price elasticities indicated that beef, mutton/goat, chicken, fish, eggs, and milk are highly elastic, and all the meat products were found to be complements. Relative to the previous studies that have analyzed meat demand in Nigeria, this study uses a sample of households observed during several periods and drawn from around the country.

Data

The data for this study was derived from the 2010–2015 Nigerian General Household Survey Panel component of the annual GHS. The survey began in 2010/2011 and resulted from a partnership between local and international organizations (National Bureau of Statistics 2016).

Fisher ideal price index

We constructed Fisher-price indices for the demand model using a three-step procedure: (1) the unit values for each meat product are determined; (2) quality-corrected prices are specified; and (3) price indices for the commodity groups are constructed.

Following Boonsaeng and Carpio (Reference Boonsaeng and Carpio2019), the first step involved defining a single unit value $\left(UV_{si}^h\right)$ Footnote ⁷ for each product $s$ in meat group $i$ (Table 1) for household $h$ as:

(1) $$UV_{si}^h = {{{m_s}} \over {{q_s}}}$$

in which ${m_s}$ is the household’s expenditure on meat product $s$ in the past 7 days (household’s response to question (3) above), and ${q_s}$ is the amount of meat product $s$ purchased (household’s response to question (2) above).

Table 1. Average budget shares, amounts and expenditures, and percentage differences (consumption data–expenditures data)

^a St. Dev. denotes standard deviation.

^b 1 US$ = 415.42 ₦, March 19, 2022.

^c [(average share consumption data – average share expenditures data)/average share expenditures data]*100%.

^d [(average quantity consumption data – average quantity expenditures data)/average quantity expenditures data]*100%.

^f [average expenditure consumption data – average expenditure expenditures data)/average expenditure expenditures data]*100%.

^g p-values reported correspond to paired t-tests of the variables.

In the second step, we specified quality-corrected pricesFootnote ⁸ to derive an approximation of prices that accounted for quality and measurement error (Alfonzo and Peterson Reference Alfonzo and Peterson2006). The first stage of this quality correction involved an OLS regression of the form:

(2) $$lnUV_{si}^h = {\alpha _s} + {\beta _s}lnx + \mathop \sum \limits_{l = 1}^L {\theta _{sl}}{z_l} + \mathop \sum \limits_{c = 1}^{C - 1} {\varphi _{sc}}{D_c} + {\varepsilon _{s\;}}$$

in which $UV_{si}^h$ is the unit value of product $s$ in meat group $i$ for household $h$ , $x$ is household income, $z$ corresponds to household characteristics, ${D_c},\;c = 1,\;.\;.\;.,\;C,\;\;$ are dummy variables that indicate the enumeration areas (clusters) to which the household belongs, ${\alpha _s}$ , ${\beta _s}$ , ${\theta _{sl}}$ , and ${\varphi _{sc}}\;$ are parameters, and ${\varepsilon _s}$ is a vector of error terms. Note that these individual regressions only use data from individuals with observed purchases. In the second stage, we define an approximation of the price as:

(3) $$ln{\hat P_{si}} = {\hat \alpha _s} + {\rm{\;}}\mathop \sum \limits_{c = 1}^{C - 1} {\hat \varphi _{sc}}{D_{c\;}}$$

in which ${\hat P_{si}}$ is the approximated price of meat product $s\;$ in meat group $i$ , and ${\hat \alpha _s}$ and ${\hat \varphi _s}$ are OLS estimates of ${\alpha _s}$ and ${\varphi _s}$ , respectively. This price approximation is independent of household-specific choices, reflects region, time, and seasonal variations, and allows us to estimate price-quantity relations accurately. Moreover, this procedure enables the estimation of prices for households, even if they do not report expenditures (Alfonzo and Peterson Reference Alfonzo and Peterson2006; Meghir and Robin Reference Meghir and Robin1992; Zhen et al. Reference Zhen, Wohlgenant, Karns and Kaufman2011).

In the third step, we combined quality-corrected meat product prices, ${\hat P_{si}}$ , into an index that represented the meat group price. The Fisher-price index for household $h$ ’s meat group $i$ is:

(4) $$p_i^h = \sqrt {P_{Pi}^hP_{Li}^h\;} $$

in which $P_{Pi}^h = {{\sum {\hat P_{si}^h} q_{si}^h} \over {\sum {{\hat{ \bar P}_{si}}} q_{si}^h}}$ ; $P_{Li}^h = {{\sum \hat P_{si}^h{q_{si}}} \over {\sum {\hat{\bar P}_{si}}{q_{si}}}}$ , $P_{Pi}^h$ and $P_{Li}^h$ are household $h$ ’s Paasche and Laspeyres indices for meat group $i$ , respectively, $q_{si}^h$ is the amount of product $s$ in meat group $i$ that household $h$ purchased, ${q_{si}}$ is the average amount of product $s$ in meat group $i$ , $\hat p_{si}^h$ is the price of product $s$ in meat group $i$ for household $h$ , and ${\widehat {\bar P}_{si}}$ is the average price of product $s$ in meat group $i$ . The Fisher-price index obtained using expenditure data was also used for the demand models of consumption data. Thus, we assume that the value per unit (i.e., price) of households’ consumption is the same as the price of goods purchased. In other words, the price of food consumed is the same as its estimated market price.

Model for unbalanced panel demand system

The demand model used in this study is the Exact Affine Stone Index (EASI) demand system (Lewbel and Pendakur Reference Lewbel and Pendakur2009). We use the EASI model’s approximate linear version, which has been shown to provide similar results (Lewbel and Pendakur Reference Lewbel and Pendakur2009). Further, we use a more parsimonious version of the original EASI model that excludes the interaction terms between prices and demographic characteristics and between prices and actual total expenditures. The EASI budget share demand for commodity $i$ for household $h$ can be modified as:

(5) $$w_i^h = \mathop \sum \nolimits_{r = 0}^4 {b_{ri}}{\left( {ln{x^h}} \right)^r} + \mathop \sum \nolimits_{j = 1} {A_{ji}}lnp_j^h + \mathop \sum \nolimits_{k = 1} {C_{ki}}z_k^h + {\varepsilon _{it}},\; i = 1,2, \ldots, n$$

in which $w_i^h$ is the budget share allocated to the $ih$ meat group for household $h$ (i.e. $w_i^h = p_i^hq_i^h/{Y^h}$ ), ${Y^h}$ is the total expenditures in meats for household h, $p_j^h$ is the Fisher-price index of meat group $j$ for household $h$ , and $ln{x^h}\;$ is the natural log of household $h$ ’s actual total expenditures on all meats ( $ln{x^h} = ln{Y^h} - \mathop \sum \nolimits_{i = 1}^n lnp_i^h{\bar w_i},\;$ in which ${\bar w_i}$ is all households’ average budget (Lewbel and Pendakur Reference Lewbel and Pendakur2009)). The explanatory variables in this model include K different demographic characteristics $\left( {{z_k}'s} \right)$ . The estimated model used a fourth order polynomial in $\;ln{x^h}$ (see Lewbel and Pendakur Reference Lewbel and Pendakur2009).

For the demand system that used expenditure data, the $w_i^h$ variable was constructed using the reported expenditures on each meat group ( $E_i^h = p_i^hq_i^h$ ). For the demand system that used consumption data, the $w_i^h$ variable was constructed using the $q_i^h$ reported and the price predicted in Equation (3). Compensated, uncompensated, and expenditure elasticities were calculated using the parameters in Equation (5) (Lewbel and Pendakur Reference Lewbel and Pendakur2009; Boonsaeng and Carpio Reference Boonsaeng and Carpio2020). The demand system was estimated by imposing homogeneity and symmetry restrictions. The last equation is dropped from the demand system, and its parameters are recovered using the adding-up constraint (Lewbel and Pendakur Reference Lewbel and Pendakur2009). Whereas there are several recommended approaches to account for censoring issues in demand estimation (e.g., Shonkwiler and Yen Reference Shonkwiler and Yen1999; Meyerhoefer, Ranney, and Sahn Reference Meyerhoefer, Ranney and Sahn2005; McCullough et al. Reference McCullough, Zhen, Shin, Lu and Arsenault2022), we used simple linear regression models, as the main objective of this study is to estimate prices and income effects on average demand (Deaton Reference Deaton1997, p. 92).

The Wooldridge-Chamberlain-Mundlak approach (Wooldridge Reference Wooldridge2019) to estimate fixed effects models in unbalanced panel data is used for econometric estimation. The fixed effects estimator is chosen since it is robust to potential endogeneity due to the correlation between explanatory variables and unobserved time-invariant factors (Wooldridge Reference Wooldridge2002). Following this approach, the fixed effects demand system can be computed as the original demand system with the covariates’ time averages added as additional explanatory variables. Hence, the econometric model for the EASI demand system in Equation (5) for meat group $i\;$ for household $h$ and time period $t$ is as follows:

$$\eqalign{ & w_{it}^h = \sum\nolimits_{r = 0}^4 {{b_{ri}}} {\left( {lnx_t^h} \right)^r} + \sum\nolimits_{j = 1} {{A_{ji}}} lnp_{jt}^h + \sum\nolimits_{k = 1} {{C_{ki}}} z_{kt}^h + \sum\nolimits_{r = 0}^4 {{f_{ri}}} {\left( {\overline {lnx} _t^h} \right)^r} \cr & \quad \quad + \sum\nolimits_{j = 1} {{B_{ji}}} \overline {lnp} _{jt}^h + {\varepsilon _{it}} \cr} $$

(6) $$\hskip-71pti = 1,2, \ldots, n, t = 1,2, \ldots, {\rm{\;}}T, {\rm and}\; h = 1,2,{\rm{\;}} \ldots, {\rm{\;}}H$$

in which $n$ is the total number of meat groups, $H$ is the total number of households, and $T$ is the total number of time periods. The $\overline {lnx} _t^h$ and $\overline {lnp} _{jt}^h$ are additional explanatory variables, in which $\overline {lnx} _t^h = T_h^{ - 1}\mathop \sum \nolimits_{t = 1}^{{T_h}} lnx_t^h\;$ and $\overline {lnp} _{jt}^h = T_h^{ - 1}\mathop \sum \nolimits_{t = 1}^{{T_h}} lnp_{jt}^h$ . ${T_h}$ is the number of times that household $h$ is observed in the unbalanced panel data, $\overline {lnx} _t^h$ is the average of the natural log of actual total expenditures on $n$ goods for household $h$ , and $\overline {lnp} _{jt}^h$ is the average price of meat group $j$ for household $h.$ The model does not include average values of the $z_{kt}^h$ , as there is little or no variability over time (see Table 2). Income and all expenditure values (including unit values) were deflated using the Nigerian composite consumer price index reported by the National Bureau of Statistics (Reference McCullough, Zhen, Shin, Lu and Arsenault2022).

Table 2. Household composition variables and demographic characteristics

^a This value corresponds to the median household income, as income has a highly skewed distribution. Mean household income was ₦225,648.20 (1 US$ = 415.42 ₦, March 19, 2022).

An additional problem with the demand system estimation of Equation (6) is the potential endogeneity of total expenditures. To account for this problem, we used Blundell and Robin’s (Reference Blundell and Robin2000) control function approach. The procedure involves two steps. The first step requires the estimation of a linear regression model with $lnx_t^h$ as the dependent variable, and as explanatory variables, all the other explanatory variables included in the share models $lnp_{jt}^{h'}s\;{\rm and} \;z_{kt}^{h'}s$ as well as the natural log of household income, its square, cube, and fourth power (these serve as instruments). Similar to the budget share models, model estimation used the Wooldridge-Chamberlain-Mundlak approach, with the average values of explanatory variables across time for each household included as controls. In the second step, the predicted errors of the first-step regression model are used as an explanatory variable in Equation (6) to account for endogeneity Blundell and Robin (2000).

Comparison of elasticities between consumption and expenditure data

In addition to the comparison of the magnitudes of the elasticities obtained using consumption and expenditure data, the null hypothesis of no differences between these elasticities was tested using a two-sample T² statistic (Gupta et al., Reference Gupta, Chintagunta, Kaul and Wittink1996):

(7) $${T^2} = {{{N_1}{N_2}} \over {\left( {{N_1} + {N_2}} \right)}}\left( {{{\hat E}_1} - {{\hat E}_2}} \right){\hat W^{ - 1}}{\left( {{{\hat E}_1} - {{\hat E}_2}} \right)^\prime },$$

in which $\hat W$ is the pooled covariance matrix obtained from the two covariance matrices, ${N_1}$ and ${N_2}$ are the number of observations, and ${\hat E_1}$ and ${\hat E_2}$ are the vectors of estimated elasticities of Models 1 and 2, respectively. The test has an F distribution, with degrees of freedom $p$ and ${N_1} + {N_2} - p - 1$ :

(8) $$F = {{{N_1} + {N_2} - p - 1} \over {\left( {{N_1} + {N_2} - 2} \right)p}}{T^2}$$

in which $p$ is the size of the elasticity vectors $\left( {{{\hat E}_1}\;{\rm{and}}\;{{\hat E}_2}} \right)$ .