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One is interested in the ceteris paribus relationship between the dependent variable y; and the explanatory variable ₁1. For this, one collects data on two control variables 2 and 3 and runs two LS regressions. Regression 1: yi = Buil+ui Regression 2: yi = B1x1 + B₂x2 + 3x i3 + Ei Let B₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁ in Regression 2. Assume that the true model is given by Regression 2 and that all variables are centered. b) would you expect a difference between ₁ and 3₁ when ₁₁ has almost no correlation with Xi2 and and 3 are highly correlated? but 2 Xiz a) Would you expect a difference between ₁ and ₁ when ₁₁ is highly correlated with 2 and 3 and the partial effects of xi2 and is on y, are also high?

One is interested in the ceteris paribus relationship between the dependent variable y; and the explanatory variable ₁1. For this, one collects data on two control variables 2 and 3 and runs two LS regressions. Regression 1: yi = Buil+ui Regression 2: yi = B1x1 + B₂x2 + 3x i3 + Ei Let B₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁ in Regression 2. Assume that the true model is given by Regression 2 and that all variables are centered. b) would you expect a difference between ₁ and 3₁ when ₁₁ has almost no correlation with Xi2 and and 3 are highly correlated? but 2 Xiz a) Would you expect a difference between ₁ and ₁ when ₁₁ is highly correlated with 2 and 3 and the partial effects of xi2 and is on y, are also high?

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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One is interested in the ceteris paribus relationship between the dependent variable y, and the explanatory variable ₁1. For this, one collects data on two control variables Xi2 and Xiz and runs two LS regressions. Regression 1: yi = B₁x₁1 + Ui Regression 2: y = B₁xil+ B₂x₁2 + B3x13 + Ei Let ₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁ in Regression 2. Assume that the true model is given by Regression 2 and that all variables are centered. a) Would you expect a difference between ₁ and ₁ when is highly correlated with 2 and 3 and the partial effects of xi2 and xi3 on yi are also high? b) Would you expect a difference between ₁ and 3₁ when ₁ has almost no correlation with and Xi3 but X2 and 3 are highly correlated? Xi2 c) Which of the two estimators is more efficient if x₁1 is highly correlated with 2 and 13, and Xiz have small partial effects on yi? but i2 d) Which of the two estimators is more efficient if x₁1 is almost uncorrelated with 2 and 13, wherein ₁2 and 13 have large partial effects on yi and xi2 and is are highly correlated?
Transcribed Image Text:One is interested in the ceteris paribus relationship between the dependent variable y, and the explanatory variable ₁1. For this, one collects data on two control variables Xi2 and Xiz and runs two LS regressions. Regression 1: yi = B₁x₁1 + Ui Regression 2: y = B₁xil+ B₂x₁2 + B3x13 + Ei Let ₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁ in Regression 2. Assume that the true model is given by Regression 2 and that all variables are centered. a) Would you expect a difference between ₁ and ₁ when is highly correlated with 2 and 3 and the partial effects of xi2 and xi3 on yi are also high? b) Would you expect a difference between ₁ and 3₁ when ₁ has almost no correlation with and Xi3 but X2 and 3 are highly correlated? Xi2 c) Which of the two estimators is more efficient if x₁1 is highly correlated with 2 and 13, and Xiz have small partial effects on yi? but i2 d) Which of the two estimators is more efficient if x₁1 is almost uncorrelated with 2 and 13, wherein ₁2 and 13 have large partial effects on yi and xi2 and is are highly correlated?
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