After this paper, I am never going to look at a household Engel curve the same way
In the 1850s, Ernst Engel famously studied household budgets for 200 working class Belgian families, and found that the share devoted to food tends to decline with total household spending—a property that came to be known as Engel’s Law. Since then, “Engel curves” for budget shares have been widely used and much studied across the world, with near universal confirmation for Engel’s Law. Engel curves have found a wide range of applications, including in the assessment of policies related to agriculture, taxation, trade, industrial organization, housing, and in the measurement of poverty and inequality.
While there have been methodological and computational advances in the specification and estimation of Engel curves over the last 100 years or so, a common and persistent feature has been the reliance on household aggregates that Engel pioneered, along with a degree of imposed homogeneity in the Engel curves, allowing only limited variability in the parameters across and within households.
In a new paper, “Unpacking Household Engel Curves,” Philippe De Vreyer, Sylvie Lambert and myself have studied some neglected but potentially confounding sources of heterogeneity in standard household Engel curves. Three sources are postulated.
First, there can be latent household effects on individual demand behavior. Members of a given household are not autonomous individuals who happen to be living together, but rather they come together selectively, and then interact and influence each other’s behavior through the process of consuming (and often working) together. While we may reject the unitary model, it can be expected that there are aspects of the household, and shared local environment, that can have a powerful influence on individual choices. This can happen via individual preferences, which are to some extent formed within a household. Or it can stem from household- or location-specific aspects of the constraints on exercising personal preferences.
Second, there are differences in individual demand parameters within households. Engel’s Law may cease to hold at the household level when income gains are assigned to people with different consumption patterns and different preferences over how the extra money should be spent.
Third, there is heterogeneity in the extent of inequality within households. The existence of intra-household inequality is known to be a source of bias in the measurement of poverty and inequality. It is less well known that intra-household inequality can also bias estimates of empirical consumer demand functions, as invariably estimated from household aggregate data. Yet for many goods, and (hence) expenditures, there is a typically an unobserved individual assignment within the household, that may be a source of intra-household inequality, reflecting different reservation utilities outside the household. Furthermore, intra-household inequality can interact with individual parameter heterogeneity in influencing household demands, whereby greater intra-household inequality magnifies the effect of differences in preferences.
In our new paper, Philippe, Sylvie and I use an unusual survey for Senegal (which Philippe and Sylvie developed, in collaboration with others) that gives us a window on consumption distribution within the household. The families are typically multigenerational. Polygamous unions are common, with 25% of married men and 39% of married women engaged in such unions, which mostly comprise a husband and two wives.
Using these data, and with suitable modelling, we can unpack the traditional household Engel curve. In essence, what we do is estimate individual Engel curves (strictly, they are for sub-household units called “cells”) and then aggregate these up to the household level. We then compare the results we get this way with the traditional household Engel curve, pretending that we do not have the sub-household cell data.
We find that the traditional household Engel curve hides quite a lot about distribution within the household and preference heterogeneity, and these hidden factors are quite confounding about the true Engel curve. For example, intra-household inequality (not observed in standard data sets) surfaces in the error term of the traditional Engel curve. (To be more concrete, for those familiar with the literature on Engel curves, a form of the Theil index of intra-household inequality is found in the error term of the traditional Working-Leser household Engel curve.)
Two key lessons emerge. First, the (often-assumed) two-stage structure in bargaining-collective models of the household carries a testable implication with our data, namely that household spending should only matter to individual choices via the intra-household allocation of total spending. This exclusion restriction is generally consistent with our results. The exception is education spending, for which cell-specific budget shares are independently, and significantly, affected by the household’s overall standard of living. We suspect that this may be a “social effect” on cell Engel curves whereby the father exercises influence over the spouse(s) to spend more on his children’s schooling (including making conditional monetary transfers to), though some role may also be played by competition among the wives.
Second, our data reveal large biases in the standard household-level Engel curves. The sources of bias do not all go in the same direction; in particular, the bias associated with intra-household inequality tends to offset that due to latent heterogeneity in preferences. However, large net biases are indicated. For example, for the food share Engel curve, the coefficient on log total household spending is -0.11 using only household data but -0.28 when one estimates the Engel curve from the sub-household data and aggregates up to the household data. This is enough to reduce the income elasticity of demand for food (evaluated at mean food share) by one third, from 0.82 to 0.55.
In these data, we find that the bulk of the bias in standard household-level Engel curves is accountable to the influence of household fixed effects on sub-household Engel curves. The fact that the channel of bias via intra-household inequality partially offsets that due to the latent household effects in standard Engel curves implies that only adding controls to reflect intra-household inequality will tend to increase the bias in household-level Engel curves.
Given that we find that the bulk of the bias in standard household Engel curves is due to household effects on sub-household Engel curves, it may be expected that the most promising means of removing (or at least attenuating) the bias is to use longitudinal data, assuming that the confounding household effect in individual consumption behavior is time invariant. That conclusion is to be investigated further in future work.