2.7 Watts poverty measure (svywatts, svywattsdec)

The measure proposed in Watts (1968Watts, Harold W. 1968. “An Economic Definition of Poverty.” Discussion Papers 5. Institute For Research on Poverty. https://www.irp.wisc.edu/publications/dps/pdfs/dp568.pdf.) satisfies a number of desirable poverty measurement axioms and is known to be one of the first distribution-sensitive poverty measures, as noted by Haughton and Khandker (2009Haughton, Jonathan, and Shahidur Khandker. 2009. Handbook on Poverty and Inequality. World Bank Training Series. World Bank Publications. https://openknowledge.worldbank.org/bitstream/handle/10986/11985/9780821376133.pdf.). It is defined as

\[ Watts = \frac{1}{N} \sum_{i \in U} \log{ \bigg( \frac{y_i}{\theta} \bigg) \delta ( y_i \leqslant \theta) }. \]

Morduch (1998Morduch, Jonathan. 1998. “Poverty, Economic Growth, and Average Exit Time.” Economics Letters 59 (3): 385–90. doi:https://doi.org/10.1016/S0165-1765(98)00070-6.) points out that the Watts poverty index can provide an estimate of the expected time to exit poverty. Given the expected growth rate of income per capita among the poor, \(g\), the expected time taken to exit poverty \(T_\theta\) would be

\[ T_\theta = \frac{Watts}{g}. \]

The Watts poverty index also has interesting decomposition properties. Blackburn (1989Blackburn, McKinley L. 1989. “Poverty Measurement: An Index Related to a Theil Measure of Inequality.” Journal of Business & Economic Statistics 7 (4): 475–81. doi:10.1080/07350015.1989.10509760.) proposed a decomposition for the Watts poverty index, rewriting it in terms of the headcount ratio, the Watts poverty gap ratio and the mean log deviaton of poor incomes2 The mean log deviation (also known as Theil-L or Bourguignon-Theil index) is an inequality measure of the generalized entropy class. The family of generalized entropy indices is discussed in the next chapter.. Mathematically,

\[ Watts = FGT_0 \big( I_w + L_* \big) \]

where \(I_w = \log(\theta/\mu_*)\) is the Watts poverty gap ratio3 \(\mu_*\) stands for the average income among the poor. and \(L_*\) is the mean log deviation of incomes among the poor. This can be estimated using the svywattsdec function.

This result can also be interpreted as a decomposition of the time taken to exit poverty, since

\[ \begin{aligned} T_\theta &= \frac{Watts}{g} \\ &= \frac{FGT_0}{g} \big( I_w + L_* \big) \end{aligned} \]

As Morduch (1998Morduch, Jonathan. 1998. “Poverty, Economic Growth, and Average Exit Time.” Economics Letters 59 (3): 385–90. doi:https://doi.org/10.1016/S0165-1765(98)00070-6.) points out, if the income among the poor is equally distributed (i.e., \(L_*=0\)), the time taken to exit poverty is simply \(FGT_0 I_w / g\). Therefore, \(FGT_0 L_* / g\) can be seen as the additional time needed to exit poverty as a result of the inequality among the poor.