Calculating the Change in PCEXP Needed to Reach Your Poverty Reduction Target

Revised Target Setting Guidance – Issued April 12, 203

Goal: Based on the results of your baseline survey, calculate the percentage increase in per-capita expenditures (PCEXP) needed to reach the $1.25/day extreme poverty target for your ZOI.

Background: The baseline household survey conducted within your ZOI collected a lot of information, but from the standpoint of estimating the prevalence of poverty, only two pieces of that information are important: the column showing each household’s per-capita expenditure (HHPCEXP), calculated by dividing total household expenditure by the number of household members; and the column showing the number of people (household members) in each household (HHSIZE).[1] Those two columns of numbers contain all the available information on the distribution of household wellbeing within your ZOI.

Problem: To calculate what percentage increase in each household’s PCEXP is needed to reduce the prevalence of poverty in your ZOI from the level identified in the baseline survey to the target level for your country. The initial assumption is that each household will experience the same percentage increase in PCEXP—a reasonable assumption given international experience.

Suggested approach: An iterativeapproach, which is simply a fancy label for “guess, check, adjust, and check again—and keep repeating until done.” To keep the explanation simple, we’ll assume that you (the M&E Contractor or other user) already have a valid method for calculating the prevalence of poverty based on the information gathered in the baseline survey.[2]

The logical steps include:

  1. Using the data from the baseline survey, estimate the prevalence of poverty in the ZOI.
  2. Multiply each household’s PCEXP by a number equal to 1 plus an initial guesstimate of the percentage increase in PCEXP needed to reach the poverty target.
  3. Re-estimate the prevalence of poverty based on the new set of PCEXPs.
  4. Depending on whether the new estimated poverty prevalence is higher or lower than the target rate, increase or decrease the percentage increase in PCEXP and check again.
  5. Repeat steps 1-4 until you identify the percentage increase in PCEXP that will yield the targeted prevalence of poverty.

Example: Let’s assume that your baseline survey gathered data from 1,000 households. After a lot of calculations, the Contractor has come up with a column of 1,000 numbers, each representing an estimate of a particular household’s PCEXP.[3] Let’s call that whole column of numbers PCEXPbase. The Contractor uses PCEXPbase (and HHSIZE) to estimate the initial share of the population living below the $1.25 poverty line. Let’s assume that that initial prevalence of $1.25/day poverty was 40%. Meanwhile, your mission has selected a target of reducing $1.25/day poverty in the ZOI by 25% over the 5-year FTF window, meaning that you need to reach a target prevalence of $1.25 poverty of 30%.

The recommended procedure is simply to generate a set of new PCEXP columns, each a simple multiple of column PCEXPbase. For example, PCEXP30 is produced by multiplying each number in the column PCEXPbase by 1.30 (that is, 1 plus 30%). The Contractor uses PCEXP30 to estimate the prevalence of poverty if each household’s consumption expenditures increased by 30%. Depending on whether this estimate falls short of the poverty target or exceeds it, the multiple is increased or reduced a bit, and the process repeated. A few iterations should be sufficient to narrow in on the percentage multiple of PCEXPbase needed to reach the poverty target.

To get to the solution a bit faster, you can take advantage of the “poverty elasticity” used in the poverty target-setting exercise. For example, the poverty elasticity might be 0.8, meaning that (based on a previous national household survey) a 10% increase in each household’s consumption is estimated to reduce the poverty headcount ratio by 8%. In that case, you can divide the targeted proportional reduction in the poverty headcount ratio (in this example 25%) by the elasticity to come up with your initial estimate of how much PCEXP needs to increase to reach the poverty target: 0.25/0.8=0.3125. In that case, your first guesstimate would be that each household’s PCEXP needs to increase by 31.25%, so you multiply PCEXPbase by 1.3125to come up with a new column PCEXP31.25. You then calculate a new estimate of the prevalence of poverty, which will be higher or lower than the target.

Depending on how close your last guesstimate came to the poverty target, the next one should be adjusted by a little or a lot in the appropriate direction. In general, you’ll want to choose values that progressively narrow the range of values of PCEXP needed to reach the poverty target. Paying attention to the pattern of poverty estimates produced with each iteration should allow you to narrow this range more quickly: for example, if you tried PCEXP30 and PCEXP40 and found that the former produced a prevalence of poverty slightly above the target while the latter produced a prevalence of poverty well below the target, your next guess would be a value closer to 30 than to 40.[4]

Isn’t this a lot of work? Actually, it’s a lot more difficult to describe this procedure than it is to actually do it. Computers are very good at this kind of thing. Generating each new column of PCEXPxx takes a couple of seconds. Recalculating the prevalence of poverty or feeding the column back into the poverty software package might take a minute or two. Observing the results from each iteration and deciding on the next guesstimated PCEXP adds another minute or two. If the whole procedure takes your M&E Contractor more than an hour in total, you’ve probably got the wrong contractor.

[1] Actually a third column is important as well—the household weights that reflect the sampling method. However, those don’t change in the approach suggested, so we’ll ignore them for the sake of simplicity.

[2]That method might be programmed into the data management/statistical package you’re using (e.g. Stata, SPSS), or may rely on a separate software tool (such as the World Bank’s freely downloadable ADePT poverty tool). In either case, the PCEXP andHHSIZE variables should be used to calculate the share of the population living below the poverty line—the prevalence of poverty (also known as the poverty headcount ratio.)

[3] As noted above, the column containing the size of each household plays an important role in calculating the poverty headcount, but for our purposes we’re assuming that that column remains the same and so ignore it.

[4] If you or your M&E Contractor are using ADePT to do the poverty calculations, you can save time by first generating all the relevant multiples of PCEXP in Stata, saving the dataset under a new file name, and then feeding the expanded dataset into ADePT. For example, if your PCEXP variable is called pc_exp, you would first generate a set of 1-digit changes to pc_exp: gen pc_exp10=pc_exp*1.1, gen pc_exp_20=pc_exp*1.2, gen pc_exp30=pc_exp*1.3, and so on over some reasonable range. You would then pull the dataset containing those new variables into ADePT, and start testing them. If you find that pc_exp10 implies a poverty headcount higher than your target, while pc_exp20 implies a poverty headcount below the target, you would go back to Stata and generate a new set of pc_exp’s at the 2-digit level, between pc_exp10 and pc_exp20: gen pc_exp11=pc_exp*1.11, gen pc_exp12=pc_exp*1.12, etc up to gen pc_exp19=pc_exp*1.19. Now go back into ADePT and find the pair of 2-digit changes in PCEXP that bracket the poverty target. Finally, generate a set of 3-digit multiples within that range: pc_exp121=pc_exp*1.121, etc. Testing each of these in ADePT will pinpoint the percentage change in PCEXP needed to reach the poverty goal.