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Answer each question by writing TRUE or FALSE 1. For OLS estimators to be linear the...
Answer each question by writing T or F When selecting models using the Akaike Information Criterion...
Answer each question by writing T or F When selecting models using the Akaike Information Criterion (AIC) we select the model that minimises the statistic. 1. 2. When imperfect multicollinearity exists among two or more explanatory variables, and 3. The Breusch-Pagan LM test statistic follows the F-distribution. 4. If a regression model suffers from autocorrelation the OLS estimators are inefficient and 5. If we include a non-influential variable in an equation the OLS estimators will be biased 6. We can...
(a) Distinguish between autocorrelation and heteroscedasticity and explain their implications for...
(a) Distinguish between autocorrelation and heteroscedasticity and explain their implications for the OLS estimators. (b) Briefly discuss the alternative tests, at least two in case, employed to detect the problems of autocorrelation and heteroscedasticity in the estimated regression model. (c) Using the data on consumer prices, broad money (M2) and Treasury bill rate, as given in question (1), test the quantity theory of money (QTM) as represented by: pt=β0+β1mt+β1yt+ut such that β0>;β1>0;β2<0;β1=1;β2=-1 Show the estimated regression model, together with all...
4. Consider the regression model, y1B22+ BKiK+ei -.. where errors may be heteroskedastic. Choose the most incorrect sta...
4. Consider the regression model, y1B22+ BKiK+ei -.. where errors may be heteroskedastic. Choose the most incorrect statement (a) The OLS estimators are consistent and unbiased (b) We should report the OLS estimates with the robust standard errors (c) The Gauss-Markov theorem may not apply (d) The GLS cannot be used because we do not know the error variances in practice (e) We should take care of heteroskedasticity only if homoskedasticity is rejected Consider the regression model, +BKIK+et e pet-1+...
1. Consider a linear regression model of y on K regressors and an intercept. (i) Describe...
1. Consider a linear regression model of y on K regressors and an intercept. (i) Describe the Breusch-Pagan test of heteroskedasticity. (ii) What are the consequences for OLS estimation and testing of rejecting the null hypothesis of the BP test? (iii)What can you say about the form of Heteroskedasticity function implied by BP? What if it is wrong? (iv) Describe the test of heteroskedasticity proposed by White. (v) When there is only one regressor (K=1), give the expression for White’s...
1. Carefully go through each statement. Answer true or false with explanation (only answers with an...
1. Carefully go through each statement. Answer true or false with explanation (only answers with an explanation will gain credit). (a) In a regression model, a stochastic regressor is an explanatory variable that has a random component (4 marks] (b) When a stochastic regressor is used in a regression model, OLS regression estimates will be biased. [4 marks] (c) Heteroscedasticity occurs when the disturbance term in a regression model is correlated with one of the explanatory variables. [4 marks] (d)...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. th...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. they are approximately normally distributed in samples with less than 10 observations large enough sample sizes c. they have a constant mean equal to zero and variance equal to d. they have a constant mean equal to one and variance equal to o 2 In a multiple regression model, the OLS estimator is consistent if a. there is no correlation between the dependent...
1. Autocorrelation test Given the model Consumption, = a + B.Year + B Disposible Income, +E,...
1. Autocorrelation test Given the model Consumption, = a + B.Year + B Disposible Income, +E, and the estimated model: Model 1: OLS, using observations 1959-1995 (T = 37) Dependent variable: c t-ratio p-value const time Disposable Income Coefficient Std. Error 2707.84 385.254 80.9122 13.6539 0.508123 0.0460444 Mean dependent var Sum squared resid R-squared F(2, 34) Log-likelihood Schwarz criterion rho 11328.65 304975.4 0.998650 12577.63 -219.3165 449.4657 0.551018 S.D. dependent var S.E. of regression Adjusted R-squared P-value(F) Akaike criterion Hannan-Quinn Durbin-Watson...
Question 3 True/False/Explain 1. The variance of the OLS estimator of the coefficient of a certain...
Question 3 True/False/Explain 1. The variance of the OLS estimator of the coefficient of a certain variable X; in a regression is higher, the higher is the degree of collinearity between that variable and the other regressors included in the model 2. Suppose that we estimated the following hourly wage equation n(wage) .092educ + .0041ехреr + (007) 022tenure 284 (0017) (.104) (003) where the numbers in parentheses are estimated standard errors. Assuming that the classical normal linear regression model holds,...
Consider the following regression equation with the ususal assumptions of the Linear Regression Model. State whether the following are True or False. Give reasons for your answer. The OLS Sample regression equation passes through the point of sample mean
Consider the following regression equation with the ususal assumptions of the Linear Regression Model. State whether the following are True or False. Give reasons for your answer.i) The OLS Sample regression equation passes through the point of sample means ii) The sum of the estimated () equals the sum of the observed ; or the sample mean of the estimated () equals the sample mean of the observed .iii) The OLS residuals (i = 1, …, N) are uncorrelated with...
Answer each question by writing T or F When selecting models using the Akaike Information Criterion (AIC) we select the model that minimises the statistic. 1. 2. When imperfect multicollinearity exists among two or more explanatory variables, and 3. The Breusch-Pagan LM test statistic follows the F-distribution. 4. If a regression model suffers from autocorrelation the OLS estimators are inefficient and 5. If we include a non-influential variable in an equation the OLS estimators will be biased 6. We can...
4. Consider the regression model, y1B22+ BKiK+ei -.. where errors may be heteroskedastic. Choose the most incorrect statement (a) The OLS estimators are consistent and unbiased (b) We should report the OLS estimates with the robust standard errors (c) The Gauss-Markov theorem may not apply (d) The GLS cannot be used because we do not know the error variances in practice (e) We should take care of heteroskedasticity only if homoskedasticity is rejected Consider the regression model, +BKIK+et e pet-1+...
1. Carefully go through each statement. Answer true or false with explanation (only answers with an explanation will gain credit). (a) In a regression model, a stochastic regressor is an explanatory variable that has a random component (4 marks] (b) When a stochastic regressor is used in a regression model, OLS regression estimates will be biased. [4 marks] (c) Heteroscedasticity occurs when the disturbance term in a regression model is correlated with one of the explanatory variables. [4 marks] (d)...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. they are approximately normally distributed in samples with less than 10 observations large enough sample sizes c. they have a constant mean equal to zero and variance equal to d. they have a constant mean equal to one and variance equal to o 2 In a multiple regression model, the OLS estimator is consistent if a. there is no correlation between the dependent...
1. Autocorrelation test Given the model Consumption, = a + B.Year + B Disposible Income, +E, and the estimated model: Model 1: OLS, using observations 1959-1995 (T = 37) Dependent variable: c t-ratio p-value const time Disposable Income Coefficient Std. Error 2707.84 385.254 80.9122 13.6539 0.508123 0.0460444 Mean dependent var Sum squared resid R-squared F(2, 34) Log-likelihood Schwarz criterion rho 11328.65 304975.4 0.998650 12577.63 -219.3165 449.4657 0.551018 S.D. dependent var S.E. of regression Adjusted R-squared P-value(F) Akaike criterion Hannan-Quinn Durbin-Watson...
Question 3 True/False/Explain 1. The variance of the OLS estimator of the coefficient of a certain variable X; in a regression is higher, the higher is the degree of collinearity between that variable and the other regressors included in the model 2. Suppose that we estimated the following hourly wage equation n(wage) .092educ + .0041ехреr + (007) 022tenure 284 (0017) (.104) (003) where the numbers in parentheses are estimated standard errors. Assuming that the classical normal linear regression model holds,...
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