ESTIMATION OF THE LINEAR AND QUADRATIC EXPENDITURE SYSTEMS FOR COLOMBIAN HOUSEHOLDS
MARTIN, THOMAS LEE
Doctor of Philosophy
This study is an empirical analysis of household expenditure behavior using the Linear and Quadratic Expenditure Systems. The expenditure systems are estimated using data collected in 1972 by the Departmento Administrativo Nacional de Estadisticas (DANE) of Bogota, Colombia. The Linear Expenditure System(LES) has been estimated frequently since the initial work of Stone(1954), while the Quadratic Expenditure System(QES) is a relatively new system first estimated by Howe(1974). The LES is derived from the maximization of a modified Cobb-Douglas utility function, and the QES is derived from an indirect utility function through the application of Roy's(1941) Identity. The LES is a special case of the QES, and by estimating the more general QES, the validity of the restrictive assumptions of the LES can be tested. In the cross-section, the most severe restriction is that the income-consumption functions must be linear. Using the more flexible QES, consumption is a nonlinear function of income, which means that the marginal budget shares may vary for households at different income levels. The empirical results of this study indicate that the marginal budget shares do vary across income levels, and that the income-consumption functions are, in fact, nonlinear. For the 5219 households in the DANE survey, hundreds of expenditure items have been aggregated into the seven categories of food, housing, clothing, medical care, education, durable goods, and miscellaneous goods and services. The expenditure systems are estimated for the entire sample, for the sample divided according to income, urban/rural status, number of household members, and the education level of the household head. The empirical results confirm the superiority of the QES in most cases as judged by likelihood ratio tests. These results reinforce the conclusions of Howe(1974) and Pollak and Wales(1978a, 1978b) that the QES provides a statistically significant improvement over the LES. The empirical results of this study are useful to development planners in Colombia in order to more accurately predict the ultimate effects of income redistribution. In addition, the results help to evaluate the possibility of a leading sector of growth in the Colombian economy. Finally, the empirical results are compared with those from the Colombian study of Howe(1974) to test the sensitivity of the parameters to the data base which is used.