vector of child-level variables, XI, a vector of household-level variables, X2, and a fixed effect at the level of the child's commune, _A.'_ Specifically, the model we estimate is' : We interpret eqn (9) as a reduced-form demand equation-rather than a production function-and estimate it using OLS.<sup>12</sup> In the _XI_ vector we include the child's age, age squared, and gender. Age entered nonlinearly allows for the fact that Vietnamese children start off in the early months being close to the US reference in terms of height-for-age, but gradually fall behind (Ponce et al. 1998). Including gender allows for the possibility of systematic differences in stunting by gender. The vector X2 includes household living standards, measured by, the log of per capita household consumption'<sup>3</sup> , dummy variables indicating whether or not the child's household had satisfactory drinking water and sanitation'<sup>4</sup> , and the years of schooling of the household head and the mother. These latter variables are fairly standard covariates in anthropometric regressions (Alderman 2000), and we expect all to reduce malnutrition.

'° We had hoped to be able to isolate the contribution of inequalities in different community-level variables, but. this proved impossible. Commune data were collected in both years, but only for communes in rural areas (and, ir, 1998, small towns). Furthermore, the 1993 community survey was rather limited in scope (Ponce et al. 1998). On top of this, health facility data were collected only for 1998, and even then were collected only for a limited set of facilities. and only in rural areas.

" We corrected standard errors both for heteroscedasticity and the effects of geographic clustering at tihe commune level (Deaton 1997). Sample weights were used in the model estimation for 1998 (they were not required fi)r the 1993 data).

12 The issue arises of whether household consumption-one of our X2 variables-is endogenous and therefore whether OLS is appropriate. There are various possible reasons why consumption might be endogenous, the most obvious being that mothers may base their work decisions in part on the health and nutritional status of their children, and that well-nourished children may be put to work (Ponce et al. 1998; Alderman 2000). Consumption may also **be** subject to measurement error that is correlated with the error term (Thomas et al. 1996; Appleton and Song 1999), Alderman 2000). Suppose one were to use instrumental variables (IV) instead of OLS. Then one would need to replace the concentration index of consumption in eqn (3) by the concentration index of _predicted_ consumption from the first stage of the IV procedure. Furthermore, in order for the decomposition to hold, one would need to re-rank children by their predicted consumption in the computation of _all_ concentration indices, including that of the malnutrition z-score. This would change the interpretation of the concentration index to be explained. In effect, one would be explaining inequalities purged of any simultaneity and measurement error. Arguably this might be a more interesting quantity TC) explain, but it is not _actual_ inequality. Our results below are therefore based on OLS, but we acknowledge that this is not an open-and-shut case.

13 The household consumption data were taken from the 2000 version of the VLSS data files. Consumptiorn aggregates were produced by VLSS staff using the standard aggregation procedures, and in the case of the 1993 data were converted by VLSS staff in June 2000 to 1998 prices using region-specific price indices.

**14** We have defined the drinking water and sanitation variables along the lines proposed by UNICEF (Govemmenl: of Vietnam 2000). Safe drinking water was defined as: tap or standpipe; deep dug well with pump; hand-dug well; **or** rain water. Satisfactory sanitation was defined as: flush toilet or latrine. Both differ slightly from the definitions used by UNICEF, because the categories in the VLSS data are somewhat different from those used by UNICEF.

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