Questions from Econometrics

Q: For the classical normal regression model y = Xβ + ( with

For the classical normal regression model y = Xβ + ( with no constant term and K regressors, what is plim /assuming that the true value of β is zero?

Q: Let ei be the ith residual in the ordinary least squares regression

Let ei be the ith residual in the ordinary least squares regression of y on X in the classical regression model, and let ei be the corresponding true disturbance. Prove that plim(ei - ei) = 0.

Q: For the simple regression model yi =  + i,

For the simple regression model yi =  + i, i ( N[0, 2], prove that the sample mean is consistent and asymptotically normally distributed. Now consider the alternative estimator mn = w y , w...

Q: Consider the simple regression yi = xi + i where

Consider the simple regression yi = xi + i where E[/x] = 0 and E[2 / x] = 2 a. What is the minimum mean squared e...

Q: Suppose that the classical regression model applies but that the true value

Suppose that the classical regression model applies but that the true value of the constant is zero. Compare the variance of the least squares slope estimator computed without a constant term with tha...

Q: Suppose that the regression model is yi =  + xi

Suppose that the regression model is yi =  + xi + i, where the disturbances i have f(i) = (1/) exp (-i/), i / . This model is rather peculiar in that all the disturbances are assumed to be...

Q: Continuing the analysis of Section 10.3.2, we

Continuing the analysis of Section 10.3.2, we find that a translog cost function for one output and three factor inputs that does not impose constant returns to scale is The factor share equations are...

Q: Prove that the least squares intercept estimator in the classical regression model

Prove that the least squares intercept estimator in the classical regression model is the minimum variance linear unbiased estimator.

Q: As a profit-maximizing monopolist, you face the demand curve

As a profit-maximizing monopolist, you face the demand curve Q =  + P + . In the past, you have set the following prices and sold the accompanying...

Q: The following sample moments for x = [1, x1,

The following sample moments for x = [1, x1, x2, x3] were computed from 100 observations produced using a random number generator: The true model underlying these data is y = x1 + x2 + x3 + e. a. Comp...