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

(8) A referee has pointed out that the constraint in equation (1) should have [[phi].sub.i](n) rather than n. But both Deaton and Paxson (and Gan and Vernon 2003, in a comment on them) use n so we follow that presentation. Other aspects of the Barten model and Deaton and Paxson's specification of it can also be criticized but the aim here is to show how measurement error may affect their results, rather than to provide a critical test of the theory underlying their predictions. Thus, we treat their specification as a deus ex machina.

(9) By rewriting [beta] ln(x/[n.sup.1-[sigma]) as [beta] ln x - (1 - [sigma])[beta] ln n it is clear that [beta] ln(x/n) + [beta][sigma] ln n = [beta] ln(x/[n.sup.1-[sigma]).

(10) Once again, there is no intention to provide support for this atheoretical method by presenting these results. We simply want to see whether it suffers from sensitivity to measurement error in addition to its theoretical problems.

(11) The average gap is larger than Pradhan (2001) finds because households from urban Java are richer than the average household in the survey.

(12) Variables measuring literacy and gender composition, which may affect household income, show no difference in means between the two samples. Dwelling attributes, which may proxy for wealth, show few differences (the difference in the prevalence of earthen floors is weakly significant, at p < 0.10).

(13) The sampling scheme used the method of inter-penetrating subsamples. Within each of ten strata, four independent subsamples of villages were drawn. Each of these four subsamples is nationally representative. Two of the subsamples were surveyed in Round 1 and two in Round 2.

(14) This balance sheet was not present in previous versions of the survey carried out in 1993 and 1997.

(15) Just because the expenditure data match the income data more closely, it does not necessarily indicate greater accuracy in Round 2 of the survey. Because the income estimates come from the survey as well, they cannot serve as independent validations of the expenditure estimates.

(16) On an item basis, twenty out of the twenty-three food items in the consumption recall list had a statistically significant fall in the proportion of households reporting zero consumption between survey rounds.

(17) The added variable form of the Hausman test for equation (8) gives t = 0.28, while for equation (9) it gives [F.sub.(2.1430)] = 4.57.

(18) One concern with the instrumental variables estimate might be that attempting to reconcile household expenditure and income could introduce a common measurement error into the two, making it inappropriate to use income as the instrument. However, the estimate of [gamma] is almost unchanged if dwelling characteristics (floor area and quality of roof and floor materials) are used as the instrumental variables instead.

John Gibson is professor, Department of Economics, University of Waikato and Bonggeun Kim is assistant professor, College of Economics and Business, Hanyang University. Table 1. Monte Carlo Results for Food Share Model

Independent Measurement Errors

in Food Expenditures

v ~ N(0,

[[sigma].sup.2.sub.v]

No error [[sigma].sub.

v = 0.1 1a. E ([??]) -0.1379 -0.1344 1b. E ([??]) -0.0073 -0.0047 1c. E ([??]) 0.0518 0.0339

Food Expenditure Errors Correlated

with True Values

v = [phi] ln [x.sub.f] +

[epsilon], [epsilon] ~ N(0, 0.4)

No error [phi] = -0.1 2a. E ([??]) -0.1379 -0.1282 2b. E ([??]) -0.0073 -0.0383 2c. E ([??]) 0.0518 0.2986

Food Expenditure Errors Correlated

with Household Size

v = [lambda] ln n + [epsilon],

[epsilon] ~ N(0, 0.4)

No error [lambda] = -0.1 3a. E ([??]) -0.1379 -0.1263 3b. E ([??]) -0.0073 -0.0289 3c. E ([??]) 0.0518 0.2282

Food Expenditure Errors Correlated

with Household Siz

v = [lambda] ln n + [epsilon],

[epsilon] ~ N(0, 0.4)

Independent Measurement Errors in

Nonfood Expenditures

g ~ N(0, 0.4)

No error [lambda] = -0.1 4a. E ([??]) -0.1297 -0.1317 4b. E ([??]) -0.0024 -0.034 4c. E ([??]) 0.0173 0.2570

Food Expenditure Errors Correlated

with Household Size

v = [lambda] ln n + [epsilon],

[epsilon] ~ N(0, 0.4)

Nonfood Expenditure Errors Correlated

with Household Size

g = -0.2 ln n + [zeta], [zeta] ~ N(0, 0.4)

No error [lambda] = -0.1 5a. E ([??]) -0.1196 -0.1257 5b. E ([??]) 0.0398 0.0054 5c. E ([??]) -0.3354 -0.045

Independent Measurement Errors

in Food Expenditures

v ~ N(0,

[[sigma].sup.2.sub.v]

[[sigma].sub.v] [[sigma].sub.v]

= 0.2 = 0.3 1a. -0.1241 -0.1082 1b. 0.0030 0.0146 1c. -0.0254 -0.1377

Food Expenditure Errors Correlated

with True Values

v = [phi] ln [x.sub.f] +

[epsilon], [epsilon] ~ N(0, 0.4)

[phi] = -0.2 [phi] = -0.3 2a. -0.0940 -0.0560 2b. -0.0448 -0.0331 2c. 0.4763 0.5904

Food Expenditure Errors Correlated

with Household Size

v = [lambda] ln n + [epsilon],

[epsilon] ~ N(0, 0.4)

[lambda] = -0.2 [lambda] = -0.3 3a. -0.1262 -0.1242 3b. -0.0582 -0.0844 3c. 0.4603 0.6792

Food Expenditure Errors Correlated

with Household Size

v = [lambda] ln n + [epsilon],

[epsilon] ~ N(0, 0.4)

Independent Measurement Errors in

Nonfood Expenditures

g ~ N(0, 0.4)

[lambda] = -0.2 [lambda] = -0.3 4a. -0.1315 -0.1294 4b. -0.0629 -0.0895 4c. 0.4780 0.6908

Food Expenditure Errors Correlated

with Household Size

v = [lambda] ln n + [epsilon],

[epsilon] ~ N(0, 0.4)

Nonfood Expenditure Errors Correlated

with Household Size

g = -0.2 ln n + [zeta], [zeta] ~ N(0, 0.4)

[lambda] = -0.2 [lambda] = -0.3 5a. -0.1298 -0.1318 5b. -0.0281 -0.0608 5c. 0.2151 0.456 Notes: Results based on 10,000 replications of the model: [w.sub.f] = [alpha] + [beta] ln(x/n) + [gamma] ln n + u. The true values are [alpha] = 1.6, [beta] = -0.14, [gamma] = -0.007, and 1,000 [sigma] = [gamma] / [beta] = 0.05. Each series is 1,000 observations. Table 2. Comparison of the Core (Short Questionnaire) and Module (Long Questionnaire) SUSENAS Samples, Urban Java

Core Module t-Statistic on

Difference (a) Per capita expenditures 169.4 209.7 4.56 **

('000 Rupiah per month) (b) Food budget share 64.5 60.3 7.76 ** of households with main source 98.8 98.8 0.22

of lighting from electricity % of households whose dwelling 7.5 5.9 1.75 ***

has earthen floor Average floor area of dwelling 74.0 71.9 1.20 of the household who are male 48.8 49.0 0.56 of the households whose head is 90.7 91.2 0.79

literate Sample size 19,161 12,876 (a) Corrected for cluster structure of the samples. (b) Rp 8,730 per US$ at the time of the survey. ** = significant al 1% level, *** = significant at 10% level. Table 3. Comparison of Expenditure Estimates and Sample Characteristics for Two Rounds of the Cambodian Socio-Economic Survey

r-Statistic on

Round 1 Round 2 Difference (a) Per capita expenditures 61.9 74.0 3.48 **

('000 Riel per month) (b) Food budget share 66.0 67.3 1.50 % of households with main 16.1 17.3 0.50

source of lighting from

electricity of households whose dwelling 14.8 13.5 0.65