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- QUESTION 1 Which one of the following assumptions is known as the spherical disturbance assumption? E(uu') = 0 E(uu') = XXxy1 E(uu') = =o²xy E(uu') = a2 All of the above. None of the above. QUESTION 2 If the error term covariance matrix is not spherical, but it is diagonal, then you have: O Autocorrelation, but no heteroskedasticity. O Heterskedasticity and autocorrelation. Heteroskedasticity, but no autocorrelation. Both heteroskedasticity and autocorrelation. Neither hetroskedasticity or autocorrelation. QUESTION 3 Which one of the following statements is true for a linear regression model with non-spherical disturbances (i.e. E(uu') = Q): The GLS estimator is inefficient. The OLS estimator is inefficient. The OLS estimator covariance matrix is diagonal. The GLS estimator covariance matrix is block-diagonal. All of the above. None of the above."In the regression model InY=b0+b1*InX+u, the coefficient b1 is interpreted as" O the intercept O A covariance O A regressor O An elasticityConsider a linear causal model Ya+BX+yW+u, with cov(X, W) > 0. Suppose we do not observe the variable W and have to omit it from the regression, then O OLS is expected to be larger than 3 in large samples. BOLS is expected to be equal to 3 in large samples. OLS is expected to be smaller than 3 in large samples. Since we do not know whether X and u are correlated and the sign of y, there is not enough information to compare OLS and B.
- 2 of 3 2. (a) Consider the generalized linear regression model Yt = a + Bxt + Et. 4 Assume Est = 0 and that we have no serial correlation among the disturbances but More var(t) = σ²x², where we assume that xt 0 for all t. Derive the feasible GLS estimator of a and B. Now consider the following regression, setting == / 7 It 1 Xt and estimate a and B again. How would the estimates differ from GLS. Explain. Yt =a Consider the ARMA(1.1) process : +B+ εi,Describe the important characteristics of the variance of a conditional distribution of an error term in a linear regression. What are the implicationsfor OLS estimation?In the December, 1969, American Economic Review (pp. 886-896), Nathanial Leff reports thefollowing least squares regression results for a cross section study of the effect of age composition onsavings in 74 countries in 1964:log S/Y = 7.3439 + 0.1596 log Y/N + 0.0254 log G - 1.3520 log D1 - 0.3990 log D2 (R2= 0.57)log S/N = 8.7851 + 1.1486 log Y/N + 0.0265 log G - 1.3438 log D1 - 0.3966 log D2 (R2= 0.96)where S/Y = domestic savings ratio, S/N = per capita savings, Y/N = per capita income, D1 = percentage ofthe population under 15, D2 = percentage of the population over 64, and G = growth rate of per capitaincome. Are these results correct? Explain..
- If two regressors are a linear combination of each other, what is the result if we run an OLS regressions with both of those regressors present? The regressors will cause the variance of the estimates to be higher but the estimates will still be unbiased. O a. We cannot run OLS because we have perfect multicollinearity. Ob. It will ensure our residuals are linear and not plagued by nonlinearity. OC. It will increase the power of our estimates since the two regressors are related. Od. None of these. Oe.Show that b ^β0 is an unbiased estimator of β0. (Hint: Use the fact that ^β1 isunbiased.If the error term covariance matrix is not spherical, but it is diagonal, then you have: Autocorrelation, but no heteroskedasticity. Heterskedasticity and autocorrelation. Heteroskedasticity, but no autocorrelation. Both heteroskedasticity and autocorrelation. Neither hetroskedasticity or autocorrelation.
- With Panel Data, if we assume that the individual effects vi are not correlated with the regressors Xit (i.e. E(vi|Xit) = 0), which one of the following statements is correct: The Fixed Effects estimator is not consistent. Both the OLS and the Random Effects estimators are not consistent. The OLS estimator is not consistent, but the Random Effects estimator is consistent. The OLS and the Random Effects estimator are consistent. All of the above. None of the aboveWhen positive autocorrelation is present, standard errors of OLS estimators become _____. Select one: a. smaller b. indeterminate c. larger d. zeroY 70 12 50 9 57 60 14 43 9 52 11 i. Find the estimators for Bi and B2 correct to decimal points and fit the regression equation for X and Y when X is the explanatory variable. Interpret the results from the obtained equation. calculate the sum of error squared. Find the variance of the sum square error ii. iii. iv. Find the standard error for B2 Find the coefficient of correlation and give its interpretation V. vi.