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CPS2010 Rodrigo L. et al.
appropriate weights to each of them. If we consider weights wi and wealth
indicators xi, the index is defined as:

= ′ = + + ⋯ +
1 1
2 2
9 9

We use two alternative approaches to calculate the weights for this
household wealth measure. First, we calculate the weights through principal
component analysis (PCA). This data-reduction technique produces weights
by identifying the directions of larger data variability. PCA is applied to a
pooled dataset including all census samples, so that each indicator receives
the same weights across countries and years (similar to Booysen et al, 2008,
Sahn and Stifel, 2000). The household wealth index is then created from the
first principal component of the data. Given the variance-covariance matrix of
the data ∑, then PCA derives the weights wj from the following optimization
problem:
( ) = ∑
′
′

′ = 1

Second, weights are also produced by estimating a model for household
expenditures, where we use each of the nine indicators as explanatory
variables. For this purpose, we rely on household surveys that are
contemporary with the most recent census year as an additional data source,
given that expenditures or income are rarely included in census microdata.
Therefore, in order to carry out this analysis, the supplementary data source
must include the same set of variables and household expenditures. Given
household expenditures E, the weights wi are estimated using the regression
equation below. The household wealth index corresponds to predicted
expenditures using these estimated weights.

= + + + ⋯ + +
2 2
0
9 9
1 1

Based on each of these two alternative wealth indices, we examine changes
in poverty. Two definitions of poverty are operationalized with the data. First,
households are considered poor if they are at the bottom 40% of the wealth
distribution, based on the pooled data for a specific country. Second, we
identify a set of minimum household characteristics that would be necessary
to achieve a predicted expenditure equivalent to the poverty line used by the
country. By using these two definitions, we identify whether poverty increased
or decreased over time, and how it was spatially distributed.
The spatial component of the analysis faces a major challenge posed by
changes in administrative boundaries over time. Researchers interested in

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