(i) The Data The study used the micro-level cross section data containing 638 households from four villages of Dinajpur sadar upazila. The data were collected in 2005-2006, adopting a two-stage sampling method. The upazila of Dinajpur sadar was selected purposively, then two unions (out of ten), namely Chehelgazi (with 33552 population) and Kamalpur (with 20075 population*) were selected randomly (BBS, 2005). The number of households as recorded in the government mouza lists was used for determining the households. A revenue village with a jurisdiction list number and defined area is called mouza. A mouza may be same as a village or there may be more than one villege in a mouza. After selecting the unions, two villages were chosen randomly from each selected union and all the households of the selected villages are considered for the study. Data were aggregated into the following 7 categories: (a) cereals, (b) roots and pulses, (c) vegetables, (d) fish, (e) meat and egg, (f) milk and sugar, (g) oil and spices. Monthly total expenditure and budget shares of the selected food categories were calculated for the sampled households.
(iv) Model Specification In many developing countries (e.g. Bangladesh, India, Pakistan, etc.), consumers usually have the tendency to provide wrong information regarding their income. This leads to the researcher to consider per capita total monthly expenditure instead of income (y) as the explanatory variable and (iv) Model Specification In many developing countries (e.g. Bangladesh, India, Pakistan, etc.), consumers usually have the tendency to provide wrong information regarding their income. This leads to the researcher to consider per capita total monthly expenditure instead of income (y) as the explanatory variable and x = X / z.
Where, X denotes total monthly expenditure of households and z, the household size. However, the literature review of some previous studies with Engel models ( Ferdous, 1997 ; Khanam and Ferdous, 2000 ; Mullah and Ferdous, 2006 etc.) has shown that a model in which budget shares are considered related to per capita total expenditure provides an excellent fit to the data. As a consequence, we have used budget share ( Wi ) as the dependent variable rather than quantity demanded for ith commodity ( q i ).
(vi) Estimation In dealing with household expenditure data, a careful attention is needed in the estimation of a possibly heteroscedastic demand system subject to cross equations or non-liner restrictions. In the present study, the Engel models have been estimated by Ordinary Least Squares (OLS) procedure using SPSS version 12.0 (SPSS, Inc) in the absence of cross equation or non-liner restrictions. The usual mean-variance assumptions are made regarding the random error term. However, using R software version 2.7.1 (R, 2008) the Breusch-Pagan-Godfrey (BPG) test has been performed which confirmed the presence of heteroscedasticity in the data set. In order to solve this problem, it is assumed that the error variance is proportional to the per capita total monthly expenditure (x),