ABSTRACT
As introduced in Chapter 12, the most widely used method for small area poverty mapping is the so-called ELL method. In its simplest form, and assuming a non-informative sampling design, the ELL method assumes a nested error regression model on the logarithmically transformed values of yij,
, . (15.1)
MSE [ Z;"B ( a, t ) ] = L-I I [ ztB(I) ( a, t ) - E ( zjWB ( a, t )) ] I~ I
For notational simplicity we sometimes refer to yij as the income variable or the logarithm of the income variable. The method starts by estimating (15.1) using the sample data. Once estimates of the fixed effects, , of the variance components, σˆ 2u, σˆ 2ε, and of the area random effects, ûj, have been obtained, the ELL method uses the following bootstrap population model to generate L synthetic Censuses,
, . (15.2)
The exact steps of the Monte-Carlo simulation are as follows. Start by estimating (15.1) using the sample data; draw L population vectors of using (15.2); using the synthetic values of the welfare variable, , compute the ELL estimate from the 1th synthetic Census, ; last, average the results over L Monte Carlo simulations. Using the bootstrap population model (15.2), one can further compute the MSE of the estimated poverty indicators,
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