Traducción y Pragmática: fenómenos de congruencia

The initial estimation of size economies revolved around Engel’s method. Engel’s method has been dominantly applied to the estimation of household size economies due to its simplicity, using food share as welfare indicator for different sized households (Deaton & Muellbauer, 1980b; Lanjouw & Ravallion, 1995). It required a single cross-sectional household

expenditure survey for a single demand equation estimation, with the food budget share of total expenditure as the dependent variable. The method is readily applicable without the need for price information, which is important as prices are generally absent in most household surveys.

Engel’s model was developed from empirical observation. There are two regularities and one assertion underlying the method. The first regularity is the famous Engel’s Law which states that the budget share devoted to food will fall when the household of a given size increases its income or expenditure. The second regularity states that there is a positive relationship

between food share and household size, holding total expenditure constant. Thus, Engel inferred that lower food shares indicate higher welfare. Engel asserted that the food share is a good indicator of welfare across households of different sizes and compositions, and that large and small households are equally well-off if they devote the same proportion of their expenditure to food.

The most influential functional form of the Engel curve parametric analysis is based on a model introduced by Working (1943) and endorsed by Leser (1963), postulating a linear relationship between the share of the budget on individual goods and the logarithm of total expenditure. The model was extended to include the household demographic composition. As asserted by Engel, the food budget share is a good welfare measurement. Lanjouw and

Ravallion (1995) (hereafter Lanjouw-Ravallion) adopted the Engel method in their estimation of household economies of scale for Pakistan using a Working-Leser model as follows:

u z a n x w R r r r f = + +

∑

where wf is the budget share for food (the ratio of food consumption in total expenditure); x

denotes total expenditure; n denotes household size; a_r= n_r/n is the proportion of persons in the household in the rth demographic group; z is a vector of the household characteristics

(region, adult employment rate); and u is an error term. Parameters to be estimated are

δ σ β

α, , , and η.

The parameter _{σ is an overall index of economies of scale, which is expected to be negative} in the Engel model. Lanjouw-Ravallion estimated _{σ to be 0.4, indicating that two adults} sharing can achieve the same welfare level as two single adults for 20.6 that is 1.52 times as much money. Deaton (1997) expressed concern over the large decrease in food expenditure per person for Pakistan where food accounts for more than half of the households’ budget. Lanjouw-Ravallion proved that the question of whether large households are poorer depends on the extent of dispersion in family sizes and the size elasticity of the equivalence scale. There is no distinction made between private and public goods. Applying the Engel method imposed several strict assumptions: size elasticity is independent of utility and prices are independent of household size. Thus, the model would underestimate the size elasticity if we assume that large households buy cheaper food through bulk discounts and the price elasticity of demand for food is less than unity. The existence of public goods would have substitution in favour of private goods, other than food. Household could be exactly compensated for an increase in household size. Thus, holding utility constant, food share will fall as household size increases. Consequently, the size elasticity of welfare would be underestimated.

The existence of household economies of scale would make a larger household better-off than a smaller household with the same per capita expenditure under Engel’s assumption and interpretation. Higher welfare was interpreted as lower food share. Hence, larger household would have a lower food share. Deaton and Paxson (1998) argued that this contradicts the scale economies model and public goods assumption. Engel’s method implied that a decline in the food share, holding per capita expenditure constant can only occur when there is a fall in food expenditure per capita. They argued that this contradicts what is expected when welfare increases due to an increase in household size with the presence of economies of scale. The increase in welfare due to the economies of scale would cause households to consume more food not less, as claimed by the Engel method.

Deaton (1997) tested the Engel method using a utility theoretic model; c (u, p, n) through two cost of living functions for household size n that achieve utility level u at prices p. The same food Engle curve is derived from both the functions but the estimated size elasticities of cost with respect to the household size differed. The result suggested that the true economies of scale were not captured by the Engel curve estimates, thus indicating the lack of

Deaton and Paxson (1998) draw from Barten’s model in their attempt to estimate the

household scale which makes sense but failed to prove its validity. Thus, they indicated that the Engel method works but makes no sense. In comparison to Lanjouw and Ravallion (1995) who estimated the size economies using Engel’s method, Deaton and Paxson (1998) showed different conclusions which questioned the applicability of Engel’s model in estimating the size economies. The differing conclusions of the estimations arouse from the underlying assumptions made. The controversial implications raised by Deaton and Paxson (1998) instigated several researchers to further analyse the theoretical models and their underlying assumptions. Gan and Vernon (2003) proved the applicability of Barten’s model in estimating the household economies through food share in food and other public goods as opposed to food share in total expenditure. Gibson (2002) demonstrated that the estimates of scale economies depended upon the method used to gather expenditure data. Thus, Gibson (2005) suggested that the Engel method should not be used for poverty measurement due to the conceptual and empirical problem using the method.

Kakwani and Son (2005) estimated the economies of scale for individual and overall goods consumed in households based on the assumption that the economies of scale exist in all goods with the highest degree displayed in public goods. Thus, their approach implicitly assumed that all goods consumed by households experience different degrees of economies of scale, as opposed to the uniform degree of economies scale assumed by Lanjouw and

Ravallion (1995).