resulting weights are used while drawing on the sentinel data to estimate a probit model of the association between HIV status and a set of individual, household and locational characteristics (with some of the latter coming from the census and other data linked-in using GIS). There is no attempt to estimate a causal model; rather the objective is to uncover the conditional correlation between HIV status and a set of “explanatory” variables that happen to have been collected in both the sentinel data as well as the household survey. Third, HIV status is imputed into the 2000 DHS household survey on the basis of parameter estimates from the probit model applied to identically defined individual, household and locational characteristics in the sentinel survey. HIV prevalence for each target woman in the DHS sample is estimated,<sup>7</sup> and then aggregation is performed to get the estimate of prevalence at the desired level (e.g., district).<sup>8</sup> In our example we predict HIV prevalence into the nationally representative DHS survey for 2000 that does not separately collect prevalence data. However, as mentioned above, in 2004 another DHS survey was fielded in Malawi that did collect prevalence data. In an effort to check the validity of our imputation procedure we compare districtlevel predicted prevalence in the 2000 DHS with observed prevalence at the district level from the 2004.9 Because there is a general perception that prevalence rates changed little during this time period we look to see whether the district level estimates we predict in the DHS 2000 are reasonably close to those that are directly estimated from the 2004 DHS survey.<sup>10</sup> ,<sup>11</sup>

> 7 In essence, this is an out-of-sample prediction.

> 8 Case studies using similar approach to predict welfare estimates show that the method provides unbiased estimates with relatively small standard errors, and are precise enough to allow for comparisons across geographic areas (Hentschel et al., 2000).

> 9 We anchor our estimates to the 2000 DHS because other data used (sentinel, census, GIS) have also been collected around that time. More discussion on this is provided later in the paper.

> 10 This validation using the 2004 DHS-based prevalence assumes that prevalence has not changed much between 2001 and 2004. Malawi National AIDS Commission and UNAIDS estimates indicate that indeed the prevalence rate in Malawi was stable during that period of time (National AIDS Commission, 2003; UNAIDS, 2006).

11 Elbers et al (2003), use bootstrap simulations to calculate the prediction error of the district-level estimate when estimating poverty rates after combining household survey data with population census data. This prediction error consists of three components: idiosyncratic error, which is the deviation of the actually observed prevalence from its expected value; model error, which is due to the variance in the parameter estimates; and computation error, which arises from the way the expected value of the prevalence is computed. We produce standard error calculations based on the same procedure, but these are partial only, as they do not reflect the additional contribution to the overall standard errors stemming from the fact that the DHS 2000 survey is a sample survey rather than population census.

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