Measurement error in recall surveys and the relationship between household size and food demand.

The results of the Monte Carlo experiments are reported in table 1, in the form of the mean values of three parameters: [??}, [??], and the scale elasticity [??} = [??]/[??} under the assumptions of the Engel method. (10) The results confirm the finding from equation (15), that errors in measuring food expenditures that are negatively correlated with either household size (row 3b) or with the true value of food expenditures (row 2b) could cause negative bias in estimates of [gamma]. Also, if measurement errors in food expenditures are correlated with the true value of expenditures, the coefficient on ln(x/n), [??] will suffer attenuation bias (i.e., toward zero) but if errors are correlated with household size, there will be no effect on (see rows 2a and 3a). It is also apparent that errors in measuring food expenditures that are negatively correlated with either true values (row 2c) or with household size (row 3c) can cause [??} to be biased upwards. The results when nonfood is also measured with error can be summarized by the following two points: if the errors in nonfood expenditures are independent, i.e., ln [[??].sub.nf] = ln [x.sub.nf] + g where g ~ N(0, 0.4), the effect of food expenditure errors is amplified slightly (row 4b). If the errors in nonfood expenditures vary negatively with household size, g = -0.2 ln n + [xi] where [xi] ~ N(0, 0.4) and the food expenditure errors are at least as strongly correlated with household size ([lambda] [less than or equal to] -0.2), [??] is negatively biased and moves into the range -0.06 [less than or equal to] [gamma] [less than or equal to] -0.03 (row 5b).

The results of the Monte Carlo experiments suggest that one way to empirically observe the effect of correlated measurement errors is to estimate a food Engel curve with an interaction term between household size and a dummy variable, D for differences in household survey methods. For example, if it is assumed that reporting errors are less likely when households have their expenditures measured with a long, detailed recall questionnaire rather than with a shorter recall, the effect of errors correlated with household size may be observed from:

(17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [D.sub.i] = 1 if the household expenditures are measured with the long recall and [D.sub.i] = 0 if the short recall is used. If [[??].sub.1] > 0 it would imply that reporting errors in shorter, less detailed surveys are correlated with household size, where such a correlation could occur because of the greater number of food purchases to recall in larger households (Gibson 2002).

In contrast, if errors are negatively correlated with the true value of food expenditures, the bias will affect not only [??} but also [??} (see row 2a, table 1). Consequently, other variables may also need to be interacted with D, giving the more general model:

(18) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In equation (18), [[kappa].sub.2] > 0 and [[kappa].sub.1] > 0 would be consistent with reporting errors that are negatively correlated with the true value of food expenditures. On the other hand, errors that are correlated with household size would imply [[kappa].sub.2] > 0 and [[kappa].sub.1] = 0.

Data

To estimate equations (17) and (18), data from household surveys carried out in 1999 in two developing countries, Cambodia and Indonesia, are used. Both surveys feature random variation in the methods and practices used within each country. By relying on within-rather than between-country variation, most of the other factors listed as possible explanations by Deaton and Paxson should be held constant. If estimated food demand parameters then differ between two randomly selected groups of households in the same setting whose expenditures were measured in different ways, measurement error is one plausible explanation.

Indonesia

The annual SUSENAS (National Socio-Economic Household Survey) Core questionnaire asks respondents about their household's consumption of fifteen food groups over the previous week and eight nonfood groups over both the previous month and previous year. Once every three years, a randomly selected subsample receives a detailed consumption questionnaire (the Module). The Module has 218 categories of food and 102 of nonfood, and uses the same reference periods as the Core. The Module questionnaire is nested in the Core, which covers the same items but more broadly. Households given the Module are not also asked the Core questions, instead interviewers add up consumption within each subgroup of the Module and copy these into the Core. Thus, we cannot compare Core and Module results for the same household, but we can make comparisons between the group given the Module and those given just the Core.

Pradhan (2001) has analyzed this large, repeated, experiment in survey design and found that the shorter, Core questionnaire gives average consumption that is 12% to 20% below the more detailed Module (Pradhan 2001). The trade-off for survey authorities is that use of the Module almost doubles the average interview time, raising it from fifty to eighty minutes per household. The underestimation varies from year to year (highest in 1996), is worst for nonfood, and appears to vary systematically with the true level of consumption (i.e., a correlated measurement error). Pradhan does not test whether the underestimation varies by household size, which would also show up as a correlation with total consumption.

We use data from the 1999 survey, mainly for urban areas on Java, because household wage income is used as an instrument and wage earning is much more prevalent in urban areas. Almost 13,000 of these households were given the detailed consumption Module and 19,000 were given the Core. In this sample, the households given the longer Module questionnaire have measured per capita consumption expenditures almost one quarter higher than the average for those given the shorter Core questionnaire (table 2). (11) The food budget share is also lower, suggesting that nonfood expenditures are raised most by using the more detailed questionnaire, corroborating results reported by Pradhan (2001). Except for these questionnaire effects, there is no evidence that the two samples of households differ in any significant way. (12)

It is likely that the questionnaire effects also vary with household size. For example, a simple nonparametric description of the Core and Module data shows that measured food expenditures rise much more strongly with increases in household size when the longer Module questionnaire is used (figure 1). Approximating these nonparametric curves by linear functions, with the Core, an additional person is associated with a 15.2% increase in food expenditure but with the Module, each additional person is associated with an 18.3% rise in additional food expenditure (the difference is statistically significant at p < 0.001).

[FIGURE 1 OMITTED]

Cambodia

The 1999 Cambodia Socio-Economic Survey (CSES) used a consumption recall with twenty-three foods and thirteen nonfoods specified. It did not aim to apply different procedures to different groups in the population but variation in interviewer practice appears to have produced the same effects. This variation is apparent because the sample was randomly split, with half of the households interviewed between January and March (Round 1), and the remainder interviewed between June and September (Round 2). (13) Between the two rounds, interviewers were retrained, where it was emphasized that estimates of household consumption should be "reasonable" given the estimate of household income. To facilitate these income-expenditure comparisons the questionnaires included a Household Income and Expenditure Balance Sheet. (14) Consistent with a greater effort made to reconcile household total income, y and total expenditure, x there is a much closer relationship between the two variables in Round 2 of the survey than there was in Round 1: Round 1 Round 2 ln x = 3.25 + 0.777 ln y ln x = 2.01 + 0.862 ln y [R.sup.2] = 0.60 [R.sup.2] = 0.80

The rise in the estimated income elasticity of expenditure between the two survey rounds is statistically significant (p < 0.02). As a result of the extra effort to match expenditure and income, there is a 20% rise in measured expenditures between the two survey rounds (table 3). (15)

One possible cause for different expenditure estimates between the survey rounds is that the sample splitting was not random. However, comparisons between the two groups of households in terms of dwelling characteristics (as proxies for wealth) and literacy (as a proxy for income) reveal no evidence that the subsamples differ in any systematic way (table 3). Also, if one subsample was significantly better off, it would also be expected to alter the food budget share (according to Engel's Law) but the average food share is almost the same across survey rounds, and if anything, indicates that the households in Round 2 are worse off.