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
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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ce17ee7-739c-4e84-bb58-c48dfc141b37%2Fcb3817f9-421f-43ae-a0b0-39792674d454%2Fktu6wjo_processed.jpeg&w=3840&q=75)
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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