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A Simple Poverty Scorecard for the Philippines

A Simple Poverty Scorecard for the Philippines

A Simple Poverty Scorecard for the Philippines

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parents, it is less likely to own a refrigerator, one or more televisions, or have a salariedjob. Because scoring must assume that <strong>the</strong> future is exactly like <strong>the</strong> past, it cannotcapture such rapid change well.Under direct measurement, <strong>the</strong> sample-size <strong>for</strong>mula <strong>for</strong> <strong>the</strong> estimate of change inpoverty rates between two points in time with two independent samples. is:n2z= 2 ⋅⎛ ⎞⎜ ⎟ ⋅ pˆ⋅ ( 1 − pˆ), (3)⎝ c ⎠where z, c, and pˆ are defined as in (1). Be<strong>for</strong>e measurement, pˆ is assumed equal atboth baseline and follow-up. n is <strong>the</strong> sample size at both baseline and follow-up. 26The method developed in <strong>the</strong> previous section can be used again to derive asample-size <strong>for</strong>mula <strong>for</strong> indirect measurement via poverty scoring:n2z= α ⋅ 2 ⋅⎛ ⎞⎜ ⎟ ⋅ pˆ⋅ ( 1 − pˆ). (4)⎝ c ⎠The corresponding <strong>for</strong>mula <strong>for</strong> <strong>the</strong> standard error σ of scoring’s estimate of2 ⋅ α ⋅ pˆ⋅ ( 1 − pˆ)change in two independent group’s poverty rate is σ =.nAs be<strong>for</strong>e, α is <strong>the</strong> average across sample sizes ≥ 256 of <strong>the</strong> ratio between <strong>the</strong>empirical sample size required by scoring <strong>for</strong> a given precision and <strong>the</strong> <strong>the</strong>oreticalsample size required under direct measurement. For <strong>the</strong> <strong>Philippines</strong>’ scorecard, α ranges26This means that, <strong>for</strong> a given precision and with direct measurement, estimating <strong>the</strong>change in a poverty rate between two points in time requires four times as manymeasurements (not twice as many) as does estimating a poverty rate at a point in time.37

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