ˆ _d_ where _wk_ is the coefficient estimate for housing characteristic _k_ for spatial domain _d_ from the hedonic regression, and _hk_ are housing characteristics.

# **_Asset Index_**

The standard approach to constructing an asset index is to define it as the weighted sum of household assets (and other characteristics), where the weights are derived from principal components analysis (Filmer and Pritchett 1998).<sup>14</sup> Principal components analysis seeks to describe the variation of a set of multivariate data in terms of a set of uncorrelated linear combination of the original variables, where each consecutive linear combination is derived to explain as much as possible of the variation in the original data, while being uncorrelated with other linear combinations. The asset index for individual _i_ is defined as the first principal component: where _fn_ and _fk_ is the factor loading for asset and housing characteristics, _an_ and _hk_ are asset dummies and housing characteristics, _~~a~~ n_ and<sup>_h_</sup> _k_<sup>are sample means, and the sample mean</sup> is the value of the asset for household _i_ ,<sup>_~~a~~_</sup> _k_<sup>is the sample mean, and</sup><sup>_s_</sup> _na_<sup>and</sup><sup>_s_</sup> _kh_<sup>represent</sup> standard deviation.

# **_Relationship between Consumption and the Asset Index_**

At a conceptual level, there are important differences between consumption and the asset index as a measure of living standards. In particular, asset data are likely to be less prone to fluctuation than consumption, and may therefore be considered a better measure of long-term household welfare or wealth.<sup>15</sup> At an empirical level, the correlation between 14 In contrast to the principal components approach proposed by Filmer and Pritchett (1998, 1999), Sahn and Stifel (2000) construct a welfare index on the basis of factor analysis. They argue that factor analysis is preferable to the principal component method because it does not force all of the components to accurately and completely explain the correlation structure between the assets. Despite the perceived advantages, they note that the Spearman rank correlation between the principal components and factor analysis asset indices is about 0.98 for each of the samples considered. In addition to the principal component and factor analysis, there are two other approaches to constructing welfare indices. First, some studies have used what may be referred to as “naïve” indices to proxy or control for living standards, often constructed as the sum of the indicator or dummy variables for whether a household possesses certain assets (see Montgomery and others 2000, Falkingham and Namazie 2002, and Morris and others 2000 for a discussion). In cases where complementary consumption data are available from a past or parallel survey, a living standard index can be constructed with weights derived from a “consumption regression.” This approach draws on the techniques from the targeting literature, which seeks to identify a set of variables that predict consumption (Ahmed and Bouis 2001; Grosh and Baker 1995).

15 A household’s wealth at any given time can be defined as the difference between its stock of assets and its stock of liabilities. Unlike the flows of income, consumption and saving, wealth or “net worth” is a stock figure. It changes over time by being added to through saving and capital transfers. It may also be depleted by incurring liabilities, by liquidating assets to finance consumption, or by transferring assets to another entity. Wealth is likely to be an important determinant of consumption, although the relationship will vary depending on life-cycle considerations, the nature of asset and credit markets, and other factors (Deaton 7