Engel's law posits an inverse relationship between income and the proportion of income spent on food. This study examines the applicability of Engel's law within the South African context, a nation grappling with significant income inequality and diverse regional disparities. Understanding the dynamics of food expenditure is crucial for policymakers designing effective poverty reduction and food security strategies. The existing literature on South African household expenditure often overlooks the influence of district-level factors, potentially leading to biased estimates. This study employs multilevel modeling to address this gap and provide a more nuanced understanding of the relationship between income and food expenditure, explicitly incorporating contextual effects. The primary research question is whether Engel's law holds true in South Africa when considering both individual household characteristics and the broader district context. Secondary questions explore whether the relationship between income and food expenditure varies across different districts.

The literature on Engel's law and household expenditure patterns is extensive, with studies varying in methodology and geographical focus. Several studies have investigated Engel's law in South Africa, but often utilize single-level models that ignore the hierarchical nature of the data. Some research highlights the influence of household characteristics (age, gender, marital status, education) on consumption patterns. Other studies point to the importance of considering macroeconomic factors, regional variations, and the impact of social safety nets. This study builds on this body of work by integrating individual household characteristics with district-level context within a multilevel framework. This approach enables a more comprehensive and nuanced analysis of the income-food expenditure relationship in South Africa.

This study uses data from the fifth wave of the National Income Dynamics Study (NIDS), a longitudinal survey of South African households. The sample comprises 4,900 households after data cleaning. The dependent variable is the per capita household monthly food expenditure share, normalized for household size using a modified equivalent adult scale. The independent variable of primary interest is the logarithm of per capita household total monthly income. Control variables include the logarithm of the household head's age, gender, marital status, education level, ethnicity, and area of residence (urban/rural). A key methodological innovation is the inclusion of the district mean income as a level-2 variable to capture contextual effects. Several models are estimated: Ordinary Least Squares (OLS), Homogenous Least Squares Dummy Variable (Ho-LSDV), Random Intercept (RI), Heterogeneous Least Squares Dummy Variable (He-LSDV), and Random Effect (RE). Model selection is guided by likelihood ratio tests and Akaike Information Criterion (AIC) to determine the most appropriate model that accounts for the hierarchical structure of the data and the presence of contextual effects. The multilevel modeling approach addresses the issue of clustering within districts, providing more efficient and robust estimates than single-level models.

The OLS model, which does not account for data clustering, provides estimates similar to the multilevel models but overestimates the standard errors. The likelihood ratio test and AIC comparisons strongly support the use of multilevel models over OLS. The Random Intercept (RI) model is chosen as the most appropriate model based on the AIC. Results from the RI model confirm Engel's law: a one-rand increase in per capita monthly income is associated with a 2% decrease in the share of household expenditure allocated to food. The inclusion of district mean income as a level-2 variable is statistically significant, indicating the presence of contextual effects. The analysis suggests that the relationship between household income and food expenditure does not vary significantly across districts. Table 4 presents the results of the homogeneous models (OLS, Null, Ho-LSDV, RI), showing significant negative coefficients for income and other predictors. Table 4 also displays the results of the random-effects component, including residual variance and intercept variance. The Wald statistic is used to test the equality of coefficients for income and district mean income. Table 5 presents the results of heterogeneous models (He-LSDV and RE), with AIC used for model comparison.

The findings confirm the validity of Engel's law in the South African context, even when accounting for district-level contextual effects. The consistent negative relationship between income and the share of food expenditure highlights the importance of income as a determinant of food consumption patterns. The significant inclusion of district mean income suggests that unobserved district-level factors influence household food expenditure behavior. This highlights the value of multilevel modeling in capturing the interplay of individual and contextual effects on consumption choices. The study’s findings have implications for policymakers in designing targeted interventions to address food insecurity and improve the livelihoods of South African households.

This study confirms Engel's law in South Africa, demonstrating a negative relationship between income and the share of food expenditure. The use of multilevel modeling underscores the importance of considering contextual effects when analyzing household consumption behavior. Future research could explore the dynamic nature of this relationship over time, examining the impact of macroeconomic shocks and policy changes on food expenditure patterns. Further investigation into the specific district-level factors influencing food expenditure could provide valuable insights for policy development.

The study relies on cross-sectional data, limiting the ability to make causal inferences. The definition of household head in the NIDS is not explicitly stated, potentially impacting the interpretation of household characteristics. While the study accounts for various household characteristics, it may not capture all relevant factors influencing food expenditure.