Abstract
This paper uses small area estimation techniques to estimate the poverty indexes of Vietnam’s provinces and districts in 2009. We find that poverty rates have become more spatially concentrated over time, which is consistent with widely observed growth processes linked to agglomeration. We hypothesize that this makes geographic targeting of the poor more relevant as a means to rebalance growing welfare disparities between geographic areas. Simulations indicate that in both 1999 and 2009 geographic targeting for poverty alleviation improves upon a uniform lumpsum transfer and this becomes more evident the more spatially disaggregated the target populations.
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Notes
In Sect. 6 we note that caution must be exercised in comparing poverty between 1999 and 2009 as the underlying household survey data are not strictly comparable.
We do not present the full regression results to avoid the lengthy paper. However, readers can contact us to obtain these results. We conduct two exercises to shed light on the question how well the models do in predicting per capita expenditure. Firstly, within the 2010 VHLSS, we randomly split the six regions into two samples, and estimating the regional models in the first sample, we predicted expenditure in the second sample and compared the results to the actual per capita expenditure. We find that the observed poverty rates are in all regions’ subsamples similar to the predicted ones. Secondly, we also examine the sensitivity of the expenditure poverty rate of districts and provinces to different expenditure models. We estimate two expenditure models: one with a large number of explanatory variables and another with a smaller number of explanatory variables. Both models give very similar estimates of poverty indexes at the district and province level. For interpretation in this paper, we will use the estimates from the large model, which give lower standard errors of welfare estimates.
Which is different—usually lower—from the expenditure poverty line set by the General Statistics Office and The World Bank that is used by the international research community to study poverty.
Actually, comparing this noknowledge benchmark against the successfulness of the geographic targeting approach that Vietnam exercised a decade ago as assessed by Baulch and Minot (2002), it is not that extreme. They found that only 20 % of the poor were reached. If the total population gets distributed an equal part of the budget, 100 % the poor would be reached by definition. The only thing is that the amount received is probably so little in that scenario that it is questionable how many people would get lifted out of poverty.
We focus on the squared poverty gap because of its appealing properties from both a conceptual and technical point of view. The basic approach explored here would also work for other poverty measures, particularly FGT measures with values of parameter α greater than 1. However, with the headcount measure (the FGT measure with α = 0) welfare ‘optimization’ is not well defined and the approach taken here is thus less obviously applicable (see for example Ray 1998, pp 254–255).
Following Foster et al. (1984) the FGT class of poverty measures take the following form:
\(FGT(\alpha ) = \left( {\frac{1}{{\sum {w_{i} } }}} \right)\sum {w_{i} (1  (x_{i} /z))^{\alpha } }\)
where x_{i} is per capita expenditure for those individuals with weight w_{i} who are below the poverty line and zero for those above, z is the poverty line and \(\sum {w_{i} }\) is total population size. \(\alpha\) takes a value of 0 for the Headcount Index, 1 for the Poverty Gap and 2 for the Squared Poverty Gap. For further discussion, see Ravallion (1994).
The consumption distribution is constructed on the basis of the average, across r replications, of householdlevel predicted percapita consumption in the population census.
See for example the World Bank Policy Research Report, “Localizing Development: Does Participation Work?” (World Bank 2012).
Mont and Nguyen (2011) show a strong correlation between disability and poverty in Vietnam.
Other interpolation schemes are possible. For instance, if the poverty gap is given at table values zk/n an even simpler computation presents itself. Often the poverty mapping software will give percentiles of the expenditure distribution. These can also be used for interpolation, but the formulas are more cumbersome, since the percentiles are not equally spaced.
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Appendix: Simulating The Impact of “Optimal” Geographic Targeting
Appendix: Simulating The Impact of “Optimal” Geographic Targeting
As described in Elbers et al. (2007) and in the text, given our interest to minimize the FGT2, optimal geographic targeting implies that after transfers there is a group of locations all sharing the same (maximum) poverty gap in the country. We determine the level of transfers going to each location by first solving a different problem. Following the notation introduced in Section III consider the minimum budget S(G) needed to bring down all locations’ poverty gaps to at most the level G/z. This amounts to transferring an amount a _{ c } (G) to locations with beforetransfer poverty gaps above G/z, such that G _{ c }(a _{ c }(G)) = G. Once we know how to compute S(G), we simply adjust G until S(G) equals the originally given budget for transfers S. To implement this scheme we must solve the following equation for a _{ c }:
In what follows we drop the location index c for ease of notation. Using integration by parts it can be shown that
In other words we need to compute the surface under the expenditure distribution between expenditure levels y = 0 and y = z − t, for values of t up to z. Instead of computing G(t) exactly, we use a simple approximation. For this to work we split the interval [0,z] in n equal segments and assume that the ‘poverty mapping’ software has generated expected headcounts for poverty lines z k/n, where k = 0,…,n. In other words we have a table of F(z k/n). Using the table we approximate F(y) by linear interpolation for y between table values. With the approximated expenditure distribution it is easy to solve for transfers as a function of G (see below). In practice we find that n = 20 gives sufficiently precise results.^{Footnote 10}
The computational setup is as follows (note that the numbering we adopt means going from z in the direction of 0 rather than the other way around). Define b _{ 0 } = 0, and for k = 1,…,n, b _{ k } as the surface under the (approximated) expenditure distribution between zkz/n and z(k1)z/n, divided by z:
Let g _{ 0 } be the original poverty gap, or in terms of the discussion above, g _{ 0 } = G(0)/z. For k = 1,…,n, put
The g _{ k } are the poverty gaps of the approximated expenditure distribution for successively lower poverty lines z − kz/n. Let a _{ k } be the per capita transfer needed to bring down the poverty line to zkz/n:
We can now solve for per capita transfers as a function of the intended poverty gap g < g _{ 0 }:

1.
Find k such that g _{ k+1} ≤ g < g _{ k }.

2.
The per capita transfers resulting in poverty gap g are
$$a(g) = a_{k} + \frac{{g_{k}  g}}{{g_{k}  g_{k + 1} }} \cdot \frac{z}{n}.$$(9)
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Lanjouw, P., Marra, M. & Nguyen, C. Vietnam’s Evolving Poverty Index Map: Patterns and Implications for Policy. Soc Indic Res 133, 93–118 (2017). https://doi.org/10.1007/s1120501613559
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DOI: https://doi.org/10.1007/s1120501613559