Using sparse categorical principal components to estimate asset indices: new methods with an application to rural southeast asia

• DOI: http://doi.org/10.1111/rode.12568
• Published date: 01 May 2019
• Author: Giovanni Maria Merola,Bob Baulch
• Date: 01 May 2019

REGULAR ARTICLE

Using sparse categorical principal components to

estimate asset indices: new methods with an

application to rural southeast asia

Giovanni Maria Merola

1

|

Bob Baulch

2

1

Xi’an Jioatong Liverpool University,

Suzhou Dushu Lake Science and

Education Innovation District, Suzhou

Industrial Park, 111 Ren’ai Road,

Suzhou, Jangsu, P R China

2

International Food Policy Research

Institute, 2033 K Street NW, Washington

DC, USA

Correspondence

Giovanni Merola, Xi’an Jioatong

Liverpool University, 111 Ren’ai Road

Suzhou, Suzhou Dushu Lake Science and

Education Innovation District, Suzhou

Industrial Park, Suzhou, P. R. China.

Email: giovanni.merola@xjtlu.edu.cn

Abstract

Asset indices have been used since the late 1990s to mea-

sure wealth in developing countries. We extend the stan-

dard methodology for estimating asset indices using

principal component analysis in two ways: by introducing

constraints that force the indices to have increasing value

as the number of assets owned increases, and by estimat-

ing sparse indices with a few key assets. This is achieved

by combining categorical and sparse principal component

analysis. We also apply this methodology to the estima-

tion of per capita level asset indices. Using household

survey data from northwest Vietnam and northeast Laos,

we show that the resulting asset indices improve the pre-

diction and ranking of income both at household and per

capita level.

1

|

INTRODUCTION

Since the late 1990s, researchers have used asset indices (AIs) as a relatively simple way to

measure households’long-term wealth or socioeconomic status in developing countries. The

reason for using AIs as a proxy for household income or expenditure stems from the well-

known difficulties associated with collecting comprehensive and reliable data on household

income or expenditures (Deaton, 1997; Grosh and Glewwe, 2000), a desire in surveys focused

on health or other issues to have “quick”measure of household wealth (Gwatkin et al., 2007;

Filmer and Pritchett, 2001), and the reduction of poverty and income dynamics due to mea-

surement error (Carter and Barrett, 2006; Deaton, 1997; McKay and Perge, 2013). A recent

review by Filmer and Scott (2012) analyzed the results of a number of applications of AIs and

concluded that they are useful for the analysis of differences in health, education, fertility, and

child mortality.

DOI: 10.1111/rode.12568

640

|

© 2018 John Wiley & Sons Ltd wileyonlinelibrary.com/journal/rode Rev Dev Econ. 2019;23:640–662.

In most applications AIs are estimated by adapting methods designed for summarizing continu-

ous data into the categorical asset ownership and housing characteristic observed in household sur-

veys. The most popular approach is to is to apply principal component analysis (PCA) to dummy

variables representing asset ownership, as originally proposed by Filmer and Pritchett (2001).

Other methods used to compute AIs include factor analysis (Sahn and Stifel, 2000, 2003; Balen et

al., 2010; Smits and Steendijk, 2015), polychoric PCA (Kolenikov and Angeles, 2004; Moser and

Felton, 2007), and multiple correspondence analysis (MCA) (Booysen et al., 2005; Smits and

Steendijk, 2015).

Despite the widespread adoption of AIs, concerns remain about both the statistical validity of

the way AIs are constructed and the interpretability of the results generated. One of the major

drawbacks of AIs computed from dummy variables is that the intrinsic ordering of counts of assets

cannot be retained. Therefore, the coefficients corresponding to owning a large amount of an asset

may be smaller than the coefficients corresponding to owning a smaller amount of the same asset.

This is both counter-intuitive and troubling for the use of AIs as a measure of wealth. A similar

argument can be made for housing characteristics which, when used for estimating wealth, can be

made more informative by ordering their categories by their quality or cost.

Another drawback of AIs is that they lack parsimony: they are often defined by hundreds of

coefficients, one for each number of the assets owned and each type of housing characteristic.

Therefore, the contribution of an individual asset to the index cannot be determined. Understanding

which assets and housing characteristics are the major drivers for the variation of wealth across

households could be of great importance for studying its socioeconomic fabric, designing future

surveys and cross-country comparisons.

This paper proposes an improvement on Filmer and Pritchett's approach to compu ting AIs by

including monotonicity constraints which force the coefficients of dummy variables to respect the

ordering of their corresponding categories. This can be readily done by applying categorical PCA

(CATPCA: Gifi, 1990; Michailidis and de Leeuw, 1998) to household surveys data. CATPCA is

analogous to MCA with the addition of monotonicity constraints. In this paper we compute the

CATPCA components by applying PCA to categorical variables scaled using aspect analysis (Mair

and De Leeuw, 2010).

We also apply least squares sparse PCA (SPCA: Merola, 2015) to the aspect scaled categorical

variables to derive sparse principal components, which show the key drivers of variation across

households using only a limited number of variables. This involves only a small loss of optimality

while retaining the monotonicity constraints. Interpreting sparse AIs is much simpler than interpret-

ing AIs defined as combinations of all the variables, because a few key variables that explain the

most variance of the dataset can be quickly identified. As far as we are aware, this is the first time

that CATPCA and SPCA have been used together to compute sparse components for categorical

variables.

Finally, we use the scaled categorical variables to compute individual (per capita) level AIs

from the asset counts for each household and aspect scaled housing categories divided by house-

hold sizes. We show that these AIs are superior to the standard ones both in predicting income

and in classifying income quintiles.

The paper is organized as follows. In Section 2 we give a brief methodological overview of the

statistical techniques used for estimating AIs, including PCA, CATPCA and SPCA: In Section 3

we illustrate the estimation of AIs using CATPCA and SPCA using household survey data from

northwest Vietnam and northeast Laos. Finally, in Section 4, we provide some concluding remarks

and suggestions for future research.

MEROLA AND BAULCH

|

641