Questions from Econometrics

Q: Consider the multiple regression of y on K variables X and an

Consider the multiple regression of y on K variables X and an additional variable z. Prove that under the assumptions A1 through A6 of the classical regression model, the true variance of the least sq...

Q: For the classical normal regression model y = Xβ +( with no

For the classical normal regression model y = Xβ +( with no constant term and K regressors, assuming that the true value of b is zero, what is the exact expected value of F[K, n - K] = (R2/K)/[(1 - R2...

Q: A multiple regression of y on a constant x1 and x2 produces

A multiple regression of y on a constant x1 and x2 produces the following results: yn = 4 + 0.4x1 + 0.9x2, R2 = 8/60, e'e = 520, n = 29, Test the hypothesis that the two slopes sum to 1.

Q: Show that in the multiple regression of y on a constant,

Show that in the multiple regression of y on a constant, x1 and x2 while imposing the restriction b1 + b2 = 1 leads to the regression of y - x1 on a constant and x2 - x1.

Q: Suppose the true regression model is given by (4-7

Suppose the true regression model is given by (4-7). The result in (4-9) shows that if pX.z is nonzero and g is nonzero, then regression of y on X alone produces a biased and inconsistent estimator of...

Q: The log likelihood function for the linear regression model with normally distributed

The log likelihood function for the linear regression model with normally distributed disturbances is shown in (14-39) in section 14.9.1. show that at the maximum likelihood estimators of b for B and...

Q: Show that the model of the alternative hypothesis in Example 5.

Show that the model of the alternative hypothesis in Example 5.7 can be written As such, it does appear that H0 is a restriction on H1. However, because there are an infinite number of constraints, th...

Q: The Grunfeld investment data in Appendix Table 10.4 constitute a

The Grunfeld investment data in Appendix Table 10.4 constitute a classic data set that has been used for decades to develop and demonstrate estimators for seemingly unrelated regressions.28 Although s...

Q: Using the results in Exercise 1, test the hypothesis that the

Using the results in Exercise 1, test the hypothesis that the slope on x1 is 0 by running the restricted regression and comparing the two sums of squared deviations.

Q: The regression model to be analyzed is y = X1B1 + X2B2

The regression model to be analyzed is y = X1B1 + X2B2 + E , where X1 and X2 have K1 and K2 columns, respectively. The restriction is B2 = 0. a. Using (5-23), prove that the restricted estimator is si...