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A Simple Poverty Scorecard for the Philippines - About the Philippines

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n2z= 2 ⋅⎛ ⎞⎜ ⎟ ˆp⎝ c ⎠*. (6)Still, ˆp*could be anything between 0–1, so (6) is not enough to compute samplesize. The estimate of ˆp*must be based on data available be<strong>for</strong>e baseline measurement.Suppose that <strong>the</strong> observed relationship between ˆp*and <strong>the</strong> variance of <strong>the</strong>baseline poverty rate p ( − )⋅ 1 is—as in Peru, see Schreiner (2008b)—close tobaselinep baseline[ ⋅ ( − )]pˆ *= 0.0085 + 0.206 ⋅ p baseline1 p baseline. Of course, pbaselineis not known be<strong>for</strong>e baselinemeasurement, but it is reasonable to use as its expected value a previously observedpoverty rate. Given this and a poverty line, a sample-size <strong>for</strong>mula <strong>for</strong> a single sampledirectly measured twice <strong>for</strong> <strong>the</strong> <strong>Philippines</strong> (once after July 2004 and <strong>the</strong>n again later)is:n2{ 0 0085 + 0 206 ⋅ [ p ⋅ ( 1 − )]}z= 2 ⋅⎛ ⎞⎜ ⎟ ⋅ . .2004p2004. (7)⎝ c ⎠As usual, (7) is multiplied by α to get scoring’s sample-size <strong>for</strong>mula:n2⎛ z ⎞= α ⋅ 2 ⋅ ⎜ ⎟ ⋅ { 0.0085 + 0.206 ⋅ [ p2004⋅ ( 1 − p2004)]}. (8)⎝ c ⎠The <strong>for</strong>mula <strong>for</strong> <strong>the</strong> standard error of scoring’s estimate of change in a single2 ⋅ α ⋅ { 0.0085 + 0.206 ⋅ [ˆ p ( pˆ2004⋅ 1 −2004)]}group’s poverty rate is <strong>the</strong>n σ =.nIn Peru (<strong>the</strong> only o<strong>the</strong>r country <strong>for</strong> which <strong>the</strong>re is an estimate, Schreiner, 2008b),<strong>the</strong> average α across years and poverty lines is about 1.8.39

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