Q5 IW 17 Problem 2] For the population of men who grew up with disadvantaged bac

Question

Q5 IW 17 Problem 2] For the population of men who grew up with disadvantaged backgrounds, let poverty be a dummy variable equal to one if a man is currently living below the poverty line, and zero otherwise. The variable age is age and educ is total years of schooling. Let vocat be an indicator equal to unity if a man's high school offered vocational training. Using a random sample of 850 men, you obtain P(poverty = lleduc, age, vocat)-A(. 453-01 6age-D87edu-049vocat) , where (z)-exp(z)/(1 + exp(z)] is the logistic function. For a 40-year-old man with 12 school on the probability of currently living in poverty? Is it a large effect?

Explanation / Answer

Here A(z) = Exp(z)/ [ 1+ exp(z)]

P(poverty = 1 l educ, age, vocat) = A (0.453 - 0.016 * age - 0.087 * edu - 0.049 * vocat)

so for age= 40 , edu = 12 years and Vocation training can be 0 or can be 1 .

so when there is no vocation training.

Z = 0.453 - 0.016 * 40 -0.087 * 12 = -1.231

A(Z) = exp(-1.231)/ [ 1 + exp(-1.231)] = 0.292/ ( 1 + 0.292) = 0.226

so P(poverty = 1 l educ = 12, age = 40, vocat = 0) = 0.226

When education = 12 ; age = 40 and vocation =1

Z = 0.453 - 0.016 * 40 -0.087 * 12 - 0.049 * 1 = -1.28

A(Z) = exp(-1.28)/ [ 1 + exp(-1.28)] = 0.278/ ( 1 + 0.278) = 0.2175

P(poverty = 1 l educ = 12, age = 40, vocat = 1) =0.2175

so that we see here that there is not any large impact of vocational training on poverty. As poverty probability when no vocational training is 0.226 and when there is vocational training, probability is 0.2175. So, there is not much difference is there.

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