Can you explain what it means for a coefficient to be "consistently estimated" in a first difference equation? Aftering differencing, im left with alpha2, gamma2*female and Beta coefficients. Can time invariant coefficients be consistently esimtated in a differenced equation? Do the coefficients in the differenced equation represent the same thing as if it were a simple cross-sectional model, only within the same time period? (see attached image)
Can you explain what it means for a coefficient to be "consistently estimated" in a first difference equation? Aftering differencing, im left with alpha2, gamma2*female and Beta coefficients. Can time invariant coefficients be consistently esimtated in a differenced equation? Do the coefficients in the differenced equation represent the same thing as if it were a simple cross-sectional model, only within the same time period? (see attached image)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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Can you explain what it means for a coefficient to be "consistently estimated" in a first difference equation? Aftering differencing, im left with alpha2, gamma2*female and Beta coefficients. Can time invariant coefficients be consistently esimtated in a differenced equation? Do the coefficients in the differenced equation represent the same thing as if it were a simple cross-sectional model, only within the same time period? (see attached image)
![Suppose that you have a balanced panel of n working individuals over two time periods.
Consider the population model
log(wage it) = a₁ + a₂ · 1[t=2] + Zitß + ₁ female; +72 1[t=2]· female; +ci+ Uit
where 1[t = 2] is a dummy variable equal to one if t=2 and c; is correlated with zit and
female;. Write the log (wage) equation for each of the two time periods and subtract one from
the other. Which coefficients in this differenced log(wage) equation can be consistently esti-
mated? Interpret those coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ce17ee7-739c-4e84-bb58-c48dfc141b37%2F0faf2d8e-e215-4e51-a5ab-1200d73f36bb%2F58unyow_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that you have a balanced panel of n working individuals over two time periods.
Consider the population model
log(wage it) = a₁ + a₂ · 1[t=2] + Zitß + ₁ female; +72 1[t=2]· female; +ci+ Uit
where 1[t = 2] is a dummy variable equal to one if t=2 and c; is correlated with zit and
female;. Write the log (wage) equation for each of the two time periods and subtract one from
the other. Which coefficients in this differenced log(wage) equation can be consistently esti-
mated? Interpret those coefficients.
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