Problem 12 algebra, take the expectation treating x3 and rias nonrandom.]12 The following equation represents the effects of tax revenue mix on subsequent employment growthfor the population of counties in the United States:growthwhere growth is the percentage change in employment from 1980 to 1990, sharep is the share of prop-erty taxes in total tax revenue, share, is the share of income tax revenues, and shares is the share ofsales tax revenues. All of these variables are measured in 1980. The omitted share, share, includesfees and miscellaneous taxes. By definition, the four shares add up to one. Other factors would includeexpenditures on education, infrastructure, and so on (all measured in 1980).Why must we omit one of the tax share variables from the equation?Give a careful interpretation of B₁.(i)(ii)13 (1)=Bo + Bisharep + B₂share, + B3shares + other factors,Consider the simple regression model y = ßo + B₁x + u under the first four Gauss-Markovassumptions. For some function g(x), for example g(x) = x² or g(x) = log(1 + x²), defineZ₁ = g(x). Define a slope estimator asB₁ (2₁ –2)y.)/(2(2₁ - 2)x₁).Show that B₁ is linear and unbiased. Remember, because E(ulx) = 0, you can treat both x; and zias nonrandom in your derivation.(ii) Add the homoskedasticity assumption, MLR.5. Show thatVar(B₁) = ²(2(2, - 2)²)/(2(2₁ - 2).x.).(Zii=1(iii) Show directly that, under the Gauss-Markov assumptions, Var(8₁) ≤ Var(B₁), where B, is theOLS estimator. [Hint: The Cauchy-Schwartz inequality in Math Refresher B implies that(n-¹2 (2,-2)(x,-3))' = (1-¹2 (2, - 2)²)(n-¹ (x₁ - 3)²);2n

The given model is: growth=β0+β1sharep+β2share1+β3shares+other factors

Answered: The following equation represents the…

The following equation represents the effects of tax revenue mix on subsequent employment growth United States: for the population of counties in the

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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