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n you show an example similar to this problem part A - but not this problem - of how to calculate an exact percentage change?

n you show an example similar to this problem part A - but not this problem - of how to calculate an exact percentage change?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Can you show an example similar to this problem part A - but not this problem - of how to calculate an exact percentage change?
Applied econometricians will sometimes regress log(y) on a explanatory variable x and interpret the coefficient as an approximation of the partial effect of a change in x on y in per- centage terms. This problem examines why the log-linear strategy may lead to a poor approx- imation of this effect when x is discrete (rather than continuous). Let educ be a continuous variable indicating the number of years of education and let married be a binary variable equal to 1 if the individual is married. Consider the population wage equation log(wage;)= Bo + B1married; + B₂educ; +Z₁Y+uj for which married is a binary indicator, educ is a continuous variable, and E[u, marriedį, educ₁, z₁] = 0. (a) Find the exact percentage change in wage from a change in educ (from educº to educ¹) using Elwage; marriedi,educ,zi-Elwage; marriedi,educ,zi] Elwage; married,,educ,z] (b) Find the exact percentage change in wage from a change in married (from married = 0 to married = 1) using Elwage, married₁=1,educ;,z₁] -E[wage, married;=0,educ;,z₁] Elwage, married;=0,educ;,z;] Is 3₁ a reliable approximation for this exact value?
Transcribed Image Text:Applied econometricians will sometimes regress log(y) on a explanatory variable x and interpret the coefficient as an approximation of the partial effect of a change in x on y in per- centage terms. This problem examines why the log-linear strategy may lead to a poor approx- imation of this effect when x is discrete (rather than continuous). Let educ be a continuous variable indicating the number of years of education and let married be a binary variable equal to 1 if the individual is married. Consider the population wage equation log(wage;)= Bo + B1married; + B₂educ; +Z₁Y+uj for which married is a binary indicator, educ is a continuous variable, and E[u, marriedį, educ₁, z₁] = 0. (a) Find the exact percentage change in wage from a change in educ (from educº to educ¹) using Elwage; marriedi,educ,zi-Elwage; marriedi,educ,zi] Elwage; married,,educ,z] (b) Find the exact percentage change in wage from a change in married (from married = 0 to married = 1) using Elwage, married₁=1,educ;,z₁] -E[wage, married;=0,educ;,z₁] Elwage, married;=0,educ;,z;] Is 3₁ a reliable approximation for this exact value?
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