The influence of demand model selection on household welfare estimates: An application to South African food expenditures

This study analyzes food expenditure patterns in South Africa, taking into account differences in demand behavior across rural and urban households, as well as across income groups. The study makes three main contributions from this study. First, it develops a Lagrange Multiplier (LM) test that can be used to determine whether the demand model should be specified with a quadratic or a linear expenditure term. The advantage of this test over the Wald test, which is based on the significance of the quadratic expenditure term in the demand model, is that it can be conducted without having to explicitly estimate the quadratic (in expenditure) demand model, which tends to be highly nonlinear. Second, the study examines the effects on household welfare of an indirect food tax reform, and evaluates the magnitude of the biases in the welfare estimates due to demand model is misspecification. The tax reform evaluated is the zero-rating of value-added tax (VAT) on meat products. Lastly, this study examines the differences in the consumption patterns between rural and urban households, and across households in different income groups. The study makes use of panel data on household food consumption in South Africa, collected as part of the KwaZulu-Natal Income Dynamics Study.; Results from both the LM and the Wald tests support the inclusion of the quadratic expenditure term. The implication of this finding is that popular functional forms such as the almost ideal demand system (AIDS), which have Engel curves that are linear in expenditure, would not give an accurate picture of demand behavior of the households considered in this study. Given these findings, this study estimates the quadratic almost ideal demand system (QUAIDS), which a generalization of AIDS that allows for a quadratic relationship between budget shares and expenditure. The QUAIDS model is used to estimate demand functions for seven food groups---grains, meat and fish, fruits and vegetables, dairy, oils and fats, sugar, and other foods. The endogeneity of expenditure in the demand model is explicitly tested and, where necessary, corrected for using the control function approach. The model is also adjusted to account for a large fraction of observed zero expenditures using a two-step procedure appropriate for equation system estimation.; Five of the seven food groups were found to be expenditure elastic, the exceptions being meat and fish and other foods. Demand behavior differs significantly between rural and urban households, as well as across income groups, implying that an accurate analysis of expenditure patterns in South Africa requires a disaggregated analysis that takes into account this heterogeneity in demand behavior. All households gain from the removal of VAT on meat, with welfare gains being larger for high-income households. On average, the AIDS expenditure elasticity estimates tend to be larger than the estimates based on QUAIDS. The AIDS model was also found to systematically overstate the welfare gains of the tax reform considered on this study, particularly for households with large expenditure levels.