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For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa. %3D

For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa. %3D

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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6. For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa. 7. In a linear regression model, if both dependent and explanatory variables are multiplied by the same constant c, then the OLS solution of the new transformed model is multiplied by c as well: 3 = c. Bold, where B is the OLS parameter estimate from the transformed model. i.i.d. 8. Consider a normal random variable X N(u, o?) and a corresponding random sample {x1, ..., xn}, where n = 1138. An estimator of the mean u = E1 x; is downward biased, however it is asymptotically unbiased. 9. In an Instrumental Variable regression we can check the assumption on instrument rele- vance by considering a first stage regression. In particular, we should regress the instru- ment on the endogenous variable and test the significance of the slope coefficient. If the slope coefficient is significantly different from zero, we conclude that the instrument is relevant. 10. Assume the population variance of a random variable is known, but the population mean is not. When using a sample to estimate the population mean, if the sample size is doubled then the variance of the distribution of the sample mean will be halved. 11. When testing for heteroscedasticity in a linear regression model it is preferable to use the Breusch-Pagan test, as it is able to detect non-linear forms of heteroscedasticity and has fewer parameters to estimate in the auxiliary regression, compared to the White test. 0 and E[f|2] = 0, then 12. In a bivariate regression model x; = d0 + d12i + Si, if cov(z, 5) = 0 and E[§|z] = 0, then the OLS estimator d is an unbiased and consistent estimator of d1.
Transcribed Image Text:6. For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa. 7. In a linear regression model, if both dependent and explanatory variables are multiplied by the same constant c, then the OLS solution of the new transformed model is multiplied by c as well: 3 = c. Bold, where B is the OLS parameter estimate from the transformed model. i.i.d. 8. Consider a normal random variable X N(u, o?) and a corresponding random sample {x1, ..., xn}, where n = 1138. An estimator of the mean u = E1 x; is downward biased, however it is asymptotically unbiased. 9. In an Instrumental Variable regression we can check the assumption on instrument rele- vance by considering a first stage regression. In particular, we should regress the instru- ment on the endogenous variable and test the significance of the slope coefficient. If the slope coefficient is significantly different from zero, we conclude that the instrument is relevant. 10. Assume the population variance of a random variable is known, but the population mean is not. When using a sample to estimate the population mean, if the sample size is doubled then the variance of the distribution of the sample mean will be halved. 11. When testing for heteroscedasticity in a linear regression model it is preferable to use the Breusch-Pagan test, as it is able to detect non-linear forms of heteroscedasticity and has fewer parameters to estimate in the auxiliary regression, compared to the White test. 0 and E[f|2] = 0, then 12. In a bivariate regression model x; = d0 + d12i + Si, if cov(z, 5) = 0 and E[§|z] = 0, then the OLS estimator d is an unbiased and consistent estimator of d1.
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