Problem 3. Consider a very large random sample of (Yi, Xi, Zi, Qi), whereYi = Bo+ BıX+U,=and Z₁ and Q₁ are some variables. Suppose o = 4, 0²/2 3, o2 = 2, oxu = 0.9, σzx = 0.7,ozu = Y, for some number y, and Q₁ is independent of (Yi, Xi, Zi) (perhaps it was generatedrandomly on a computer without any connection to the data we have). Let us define a new variableRi= Zi + Qi.(a) Suppose we run OLS regression of Y; on X; and a constant. Will this result in a consistentestimator of B₁?(b) Suppose y = 0. Is Z, a valid instrumental variable?(c) Suppose y= 0. Is R₂ a valid instrumental variable?(d) Suppose y # 0. Let 3z denote the TSLS estimator of 3₁ that uses Z; as the instrumentalvariable. Let bz denote the probability limit of z, i.e., z →p bz as n → ∞. Using theinformation provided above, find bz. Hint: bz could depend on y.

Given: Consider a very large random sample of (Yi, Xi, Zi, Qi), where Y; = + 3X+Ui, and Zi and Qi…

Answered: Problem 3. Consider a very large random…

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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