CHAPTER 12: Vulnerability to Poverty
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enough to allow us to measure a household’s vulnerability to poverty. The required pieces of information are as follows: • The household’s expected level of consumption per capita in the next period, given by E(ct+1) • The variance of the household’s expected level of consumption per capita in the next period, σ2 • The poverty line, z. To this we add the assumption that the expected level of consumption follows a known distribution such as the normal (Gaussian) distribution. Then we may proceed as set out in this example: Example: Suppose what we expect the per capita consumption of a household to be 50 next year. This is only an estimate, and we believe that the standard deviation of this estimate is 12 (that is, the variance is 144). The poverty line is 40. What is the probability that this household will be poor next year? Assuming that the shocks to per capita consumption are normally distributed, then the probability that this household will be poor next year (that is, its vulnerability) is 0.202.3 In other words, given the expected consumption per capita and its associate variance, there is a 20.2 percent probability that this household will in fact find itself below the poverty line. This is illustrated by the shaded area in figure 12.1.
Figure 12.1 Illustrating the Probability of Poverty for a Household
Source: Authors. Note: Poverty line is 40, Expected income per capita is 50; standard deviation of expected income is 12.
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