Where y is the log of per capita consumption expenditure of household h residing in
cluster c, X are the household characteristics that are observable in both the survey
and census data sets, and β is a coefficient vector. In our household survey, the clustering
is done at regional (disaggregated into rural and urban) areas. The error term
is composed of two parts. On the one hand, ηc (Z) applies to all households within
a given cluster (location effect), which depends on the biomass conditions Z. On the
other hand, ∈ch is household specific component of the error term (heteroscedasticity).
These two error components are uncorrelated with one another and independent
of the regressors. This specification of the error term allows for heteroscedasticity
of the household specific error component. It also allows for the possibility of spatial
autocorrelation. That is, location specific effects that are common to all households
within a cluster.