Is Poverty Reduction Over-Stated in Uganda? Evidence from Alternative Poverty Measures

Abstract

Uganda has experienced high economic growth rates over the past decade, averaging 5.4 % per year, while poverty rates have declined over 14 % points over 2002–2003 and 2009–2010. However, conventional wisdom is that the benefits of poverty reduction have not been distributed equally and some authors even question the large decline in poverty. This paper seeks to examine poverty trends across Uganda from 1995 to 2010 by using non-monetary indicators based on household assets, housing characteristics, and household size and composition. In a variation on poverty mapping methods, we select household characteristics that are available in four Demographic and Health Surveys (DHS) and the 2005–2006 Uganda National Household Survey (UNHS). Using the UNHS data, we estimate household per capita expenditure as a function of these characteristics. Finally, these estimated equations are applied to the same characteristics from the DHS data to generate estimates of per capita expenditure, which are then converted to estimates of the incidence of poverty. The results confirm that the overall incidence of poverty has declined in Uganda over the past 15 years, but they show less progress than official expenditure-based estimates of poverty. We explore several explanations for this discrepancy.

Appendix

Assuming that (1) the error term is homoscedastic (2) there is no spatial auto-correlation, and (3) there is no sampling error in the second stage (as when Census data are used), the variance of the estimated poverty headcount ratio can be calculated as follows:

$$\text{var} ({\text{P}}*) = \left( {\frac{{\partial {\text{P}}*}}{{\partial \hat{\upbeta }}}} \right)^{{\prime }} \text{var} (\hat{\upbeta })\frac{{\partial {\text{P}}*}}{{\partial \hat{\upbeta }}} + \left( {\frac{{\partial {\text{P}}*}}{{\partial \hat{\upsigma }^{2} }}} \right)^{2} \frac{{2\hat{\upsigma }^{4} }}{{{\text{n}} - {\text{k}} - 1}} + \sum\limits_{i = 1}^{\text{N}} {\frac{{{\text{m}}_{\text{i}}^{ 2} {\text{P}}_{\text{i}}^{ *} ( 1- {\text{P}}_{\text{i}}^{ *} )}}{{{\text{M}}^{ 2} }}}$$

(A1)

where P* is the estimated poverty rate, n is the sample size in the regression model, k is the number of regressors in the model, N is the sample size in the stage-two dataset (the DHS data in our model), mi is the size of household i in the stage-two dataset, and M is the number of people in the stage-two dataset. The partial derivatives of P* with respect to the estimated parameters can be calculated as follows:

$$\frac{{\partial {\text{P}}*}}{{\partial \hat{\upbeta }_{\text{j}} }} = \sum\limits_{\text{i = 1}}^{\text{N}} {\frac{{{\text{m}}_{\text{i}} }}{\text{M}}} \left( {\frac{{ - {\text{x}}_{\text{ij}} }}{{\hat{\upsigma }}}} \right)\upphi \left( {\frac{{\ln {\text{z}} - {\text{X}}_{\text{i}}^{{\prime }} \hat{\upbeta }}}{{\hat{\upsigma }}}} \right)$$

(A2)

$$\frac{{\partial {\text{P}}*}}{{\partial \hat{\upsigma }^{2} }} = - \frac{1}{2}\sum\limits_{i = 1}^{\text{N}} {\frac{{{\text{m}}_{\text{i}} }}{\text{M}}\left( {\frac{{\ln {\text{z}} - {\text{X}}_{\text{i}}^{{\prime }} \hat{\upbeta }}}{{\hat{\upsigma }^{3} }}} \right)} \phi \left( {\frac{{\ln {\text{z}} - {\text{X}}_{\text{i}}^{{\prime }} \hat{\upbeta }}}{{\hat{\upsigma }}}} \right)$$

(A3)

The first two terms in Eq. A1 represent the “model error”, which comes from the fact that there is uncertainty regarding the true value of β and σ in the regression analysis. This uncertainty is measured by the estimated covariance matrix of β and the estimated variance of σ², as well the effect of this variation on P*. The third term in Eq. A1 measures the “idiosyncratic error” which is related to the fact that, even if β and σ are measured exactly, household-specific factors will cause the actual expenditure to differ from predicted expenditure. These equations are described in more detail in Hentschel et al. (2000) and Elbers et al. (2003).

As noted above, Eq. A1 is valid only if there is no sampling error in the second stage, such as when Census data are used. In this study, we use DHS datasets in the second stage, so Eq. 1 must be modified as follows:

$$\text{var} ({\text{P}}*) = \left( {\frac{{\partial {\text{P}}*}}{{\partial \hat{\upbeta }}}} \right)^{{\prime }} \text{var} (\hat{\upbeta })\frac{{\partial {\text{P}}*}}{{\partial \hat{\upbeta }}} + \left( {\frac{{\partial {\text{P}}*}}{{\partial \hat{\upsigma }^{2} }}} \right)^{2} \frac{{2\hat{\upsigma }^{4} }}{{{\text{n}} - {\text{k}} - 1}} + \sum\limits_{\text{i = 1}}^{\text{N}} {\frac{{{\text{m}}_{\text{i}}^{ 2} {\text{P}}_{\text{i}}^{*} (1 - {\text{P}}_{\text{i}}^{*} )}}{{{\text{M}}^{2} }}} + {\text{V}}_{\text{s}}$$

(A4)

where V_s represents the variance associated with the sampling error in the DHS data. In this study, we use the statistical software Stata to calculate the variance associated with the sampling error, taking into account the design of the sample. This is accomplished with the “svymean” command. Stata calculates a linear approximation (a first-order Taylor expansion) of the sampling error variance based on information on the strata, the primary sampling unit, and the weighting factors.