Questions from Econometrics

Q: For the model in Application 1, test the hypothesis that =

For the model in Application 1, test the hypothesis that = 0 using a Wald test and a Lagrange multiplier test. Note that the restricted model is the cobb–Douglas log linear model. The LM test statis...

Q: The model / satisfies all the assumptions of the seemingly

The model satisfies all the assumptions of the seemingly unrelated regressions model. All variables have zero means. The following sample second-moment matrix is obtained from a sample of 20 observati...

Q: Prove that in the model / generalized least squares

Prove that in the model generalized least squares is equivalent to equation-by-equation ordinary least squares if X1 = X2. The general case is considered in Exercise 14.

Q: Consider the two-equation system / Assume that the

Consider the two-equation system Assume that the disturbance variances and covariance are known. Now suppose that the analyst of this model applies GLS but erroneously omits x3 from the second equatio...

Q: Consider the system / The disturbances are freely correlated.

Consider the system The disturbances are freely correlated. Prove that GLS applied to the system leads to the OLS estimates of 1 and 2 but to a mixture of the lea...

Q: For the model / Assume that yi2 + yi3

For the model Assume that yi2 + yi3 = 1 at every observation. Prove that the sample covariance matrix of the least squares residuals from the three equations will be singular, thereby precluding comp...

Q: Consider the following two-equation model: / a

Consider the following two-equation model: a. Verify that, as stated, neither equation is identified. b. Establish whether or not the following restrictions are sufficient to identify (or partially id...

Q: Obtain the reduced form for the model in Exercise 8 under each

Obtain the reduced form for the model in Exercise 8 under each of the assumptions made in parts a and in parts b(1) and b(9).

Q: The following is a panel of data on investment (y)

The following is a panel of data on investment (y) and profit (x) for n = 3 firms over T = 10 periods. a. Pool the data and compute the least squares regression coefficients of the model b. Estimate...

Q: Suppose that the fixed effects model is formulated with an overall constant

Suppose that the fixed effects model is formulated with an overall constant term and n - 1 dummy variables (dropping, say, the last one). Investigate the effect that this supposition has on the set of...