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Consider the linear model Yi = B₁ + B₂ dj + Ujr where y; is the subjective reported happiness of individual i, d; is a dummy variable which indicates whether individual i owns a dog (d; = 1) or not (d; = 0), and u, is an unobserved error term. Assume that E(u;) = 0 and E(u;d;) = 0. We observe an i.i.d. sample of (yi, di), i= 1, ... ,n, with sample size n = 100. In that sample we have no = (1 -d;) = 80 individuals with d; = 0, and n₁ = Σ₁ d = 20 individuals with d; = 1. The average reported happiness in the subpopulation with d = 0 is no¹ Σ(1 - d)yi = 3, and in the subpopulation with d = 1 is n₁¹ Σ=1 diyi 8. 1. Calculate the OLS estimator = (1, 72)' for the regression model Yi Yıdi +2(1-d₁) + ui. 2. Now also assume homoscedasticity, with Eu?|d;) = 4. Calculate the OLS stan- dard error of 32, and provide a 95% confidence interval for 3₂. (Hint: The 97.5% quantile of N(0, 1) is 1.96. The 95% quantile of N(0, 1) is 1.64.)

Consider the linear model Yi = B₁ + B₂ dj + Ujr where y; is the subjective reported happiness of individual i, d; is a dummy variable which indicates whether individual i owns a dog (d; = 1) or not (d; = 0), and u, is an unobserved error term. Assume that E(u;) = 0 and E(u;d;) = 0. We observe an i.i.d. sample of (yi, di), i= 1, ... ,n, with sample size n = 100. In that sample we have no = (1 -d;) = 80 individuals with d; = 0, and n₁ = Σ₁ d = 20 individuals with d; = 1. The average reported happiness in the subpopulation with d = 0 is no¹ Σ(1 - d)yi = 3, and in the subpopulation with d = 1 is n₁¹ Σ=1 diyi 8. 1. Calculate the OLS estimator = (1, 72)' for the regression model Yi Yıdi +2(1-d₁) + ui. 2. Now also assume homoscedasticity, with Eu?|d;) = 4. Calculate the OLS stan- dard error of 32, and provide a 95% confidence interval for 3₂. (Hint: The 97.5% quantile of N(0, 1) is 1.96. The 95% quantile of N(0, 1) is 1.64.)

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
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Consider the linear model Y; = B1 + B2 d; + U;, where y; is the subjective reported happiness of individual i, d; is a dummy variable which indicates whether individual i owns a dog (d; = 1) or not (d; = 0), and u; is an unobserved error term. Assume that E(u;) = 0 and E(u;d;) = 0. We observe an i.i.d. sample of (yi, d;), i = 1,..., n, with sample size n = 100. In that sample we have no =E(1 – di) = 80 individuals with d; = 0, and n1 E d; = 20 individuals with d; = 1. The average reported happiness in the subpopulation with d; = 0 is nɔ'E(1 – d;)y; = 3, and in the subpopulation with d; = 1 is n'D d:y; = 8. 1. Calculate the OLS estimator î = (î1, î2)'for the regression model Yi = Yıd; + 72(1 – d;) + ui. 2. Now also assume homoscedasticity, with E(u d;) = 4. Calculate the OLS stan- dard error of B, and provide a 95% confidence interval for B2. (Hint: The 97.5% %3| quantile of N(0, 1) is 1.96. The 95% quantile of N(0, 1) is 1.64.)
Transcribed Image Text:Consider the linear model Y; = B1 + B2 d; + U;, where y; is the subjective reported happiness of individual i, d; is a dummy variable which indicates whether individual i owns a dog (d; = 1) or not (d; = 0), and u; is an unobserved error term. Assume that E(u;) = 0 and E(u;d;) = 0. We observe an i.i.d. sample of (yi, d;), i = 1,..., n, with sample size n = 100. In that sample we have no =E(1 – di) = 80 individuals with d; = 0, and n1 E d; = 20 individuals with d; = 1. The average reported happiness in the subpopulation with d; = 0 is nɔ'E(1 – d;)y; = 3, and in the subpopulation with d; = 1 is n'D d:y; = 8. 1. Calculate the OLS estimator î = (î1, î2)'for the regression model Yi = Yıd; + 72(1 – d;) + ui. 2. Now also assume homoscedasticity, with E(u d;) = 4. Calculate the OLS stan- dard error of B, and provide a 95% confidence interval for B2. (Hint: The 97.5% %3| quantile of N(0, 1) is 1.96. The 95% quantile of N(0, 1) is 1.64.)
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