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4. Suppose the panel data model is given by: where Z, is not observed, i 1,, n and t - 1,2,3. In ...
4. Suppose the panel data model is given by: where Z, is not observed, i 1,, n and t - 1,2,3. In this model we have three waves or we have three cross-sectional data sets: Now we assign the weight 1/2, 1/3, 1/6 to wave 1, wave 2 and wave 3, respectively, i.e., the first wave receives a larger weight while the third wave gets less weight. Please propose a feasible "difference" type estimator for 3,
4. Suppose the panel...
7. Suppose the data consist of repeated observations (y;it, X), t = 1, -.. ,T, for each in- dividual i = 1,... ,n. Here...
7. Suppose the data consist of repeated observations (y;it, X), t = 1, -.. ,T, for each in- dividual i = 1,... ,n. Here yit is the response and xt is a covariate vector. A linear mixed-effects model for analysing the population-averaged and subject-specific effects of Xit is of the following form Z;B + W;b; + €;, yi = where y (yi1;* . ,ViT)T; Z; is a T x p design matrix built from {xji} for the fixed effects B;...
Question 1 1 pts Consider the simple, general model: Y = Bo + BX; + i....
Question 1 1 pts Consider the simple, general model: Y = Bo + BX; + i. A proposed instrumental variables, Zi, is relevant if Z and X are uncorrelated Z and u are correlated Z and u are uncorrelated Zand X are correlated
1.Which of the following assumptions is required to obtain a first-differenced estimator in a two-period panel...
1.Which of the following assumptions is required to obtain a first-differenced estimator in a two-period panel data analysis? a. The idiosyncratic error at each time period is uncorrelated with the explanatory variables in both time periods. b. The variance of the error term in the regression model is not constant. c. The explanatory variable does not change over time for any cross-sectional unit. d. The explanatory variable changes by the same amount in each time period. 2.A Chow test _____....
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...
Problem 3: Assume that 'nature' behaves according to the following linear additive model: Y = Bo...
Problem 3: Assume that 'nature' behaves according to the following linear additive model: Y = Bo + B1X +€, where ε is a Gaussian random variable N (0,02). Using this model, nature generates the following training dataset: D = {(Li, yi)}}–1 = {(–2, 47/2),(-1, -3), (0,0), (1,3), (2,7/2)}. Please, answer the questions below without the help of any computer software: a. Compute the estimates of Bo and @1 for a linear estimator û = Bo + 1X using the data...
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,......
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,... ,n. Let b1 = s^y/8r and bo = Y - b1 t be the least squared estimators of B1 and Bo, respectively. We showed in class, that N(B; 02/) Y~N(BoB1 T;o2/n) and bi ~ are uncorrelated, i.e. o{Y;b} We also showed in class that bi and Y 0. = (a) Show that bo is...
Suppose you want to estimate the model y Bo + βλη + β2T2 + u, with the data with the data: 10 1 1...
Suppose you want to estimate the model y Bo + βλη + β2T2 + u, with the data with the data: 10 1 1 -8 2 3 -6 3 5 -4 4 7 2 59 Can you estimate βο, βι, and β2? Why or why not?
Suppose you want to estimate the model y Bo + βλη + β2T2 + u, with the data with the data: 10 1 1 -8 2 3 -6 3 5 -4 4 7 2...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo +...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo + Bicite and the model satisfies the Gauss-Markov conditions. Answer the following questions: (a) What assumption in addition to the Gauss-Markov assumptions is required to estimate the model? (b) Show that in general, b is a biased estimator of B1. (c) Outline the special condition(s) under which b is an unbiased estimator of B1.
Consider the model, Y; = Bo + B1 X1,1 + B2 X2,1 + Uj, where you...
Consider the model, Y; = Bo + B1 X1,1 + B2 X2,1 + Uj, where you have sorted the residuals based on the X1, value in the Blue panel and based on the X2,; in the Red panel. Please indicate if you observe heteroskedasticity. Blue Panel Red Panel 3 3 2 2 . 1 1 50 50 -2 -3 0 0.2 0.4 0.6 0.8 1 0 0.5 1.5 2 2.5 3 3.5 4 X1 X2 A. Both panels B. Blue...
4. Suppose the panel data model is given by: where Z, is not observed, i 1,, n and t - 1,2,3. In this model we have three waves or we have three cross-sectional data sets: Now we assign the weight 1/2, 1/3, 1/6 to wave 1, wave 2 and wave 3, respectively, i.e., the first wave receives a larger weight while the third wave gets less weight. Please propose a feasible "difference" type estimator for 3,
4. Suppose the panel...
7. Suppose the data consist of repeated observations (y;it, X), t = 1, -.. ,T, for each in- dividual i = 1,... ,n. Here yit is the response and xt is a covariate vector. A linear mixed-effects model for analysing the population-averaged and subject-specific effects of Xit is of the following form Z;B + W;b; + €;, yi = where y (yi1;* . ,ViT)T; Z; is a T x p design matrix built from {xji} for the fixed effects B;...
Question 1 1 pts Consider the simple, general model: Y = Bo + BX; + i. A proposed instrumental variables, Zi, is relevant if Z and X are uncorrelated Z and u are correlated Z and u are uncorrelated Zand X are correlated
Problem 3: Assume that 'nature' behaves according to the following linear additive model: Y = Bo + B1X +€, where ε is a Gaussian random variable N (0,02). Using this model, nature generates the following training dataset: D = {(Li, yi)}}–1 = {(–2, 47/2),(-1, -3), (0,0), (1,3), (2,7/2)}. Please, answer the questions below without the help of any computer software: a. Compute the estimates of Bo and @1 for a linear estimator û = Bo + 1X using the data...
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,... ,n. Let b1 = s^y/8r and bo = Y - b1 t be the least squared estimators of B1 and Bo, respectively. We showed in class, that N(B; 02/) Y~N(BoB1 T;o2/n) and bi ~ are uncorrelated, i.e. o{Y;b} We also showed in class that bi and Y 0. = (a) Show that bo is...
Suppose you want to estimate the model y Bo + βλη + β2T2 + u, with the data with the data: 10 1 1 -8 2 3 -6 3 5 -4 4 7 2 59 Can you estimate βο, βι, and β2? Why or why not?
Suppose you want to estimate the model y Bo + βλη + β2T2 + u, with the data with the data: 10 1 1 -8 2 3 -6 3 5 -4 4 7 2...
Consider the following slope estimator: b=2i=1 Yi Suppose the true model is ki + Bo + Bicite and the model satisfies the Gauss-Markov conditions. Answer the following questions: (a) What assumption in addition to the Gauss-Markov assumptions is required to estimate the model? (b) Show that in general, b is a biased estimator of B1. (c) Outline the special condition(s) under which b is an unbiased estimator of B1.
Consider the model, Y; = Bo + B1 X1,1 + B2 X2,1 + Uj, where you have sorted the residuals based on the X1, value in the Blue panel and based on the X2,; in the Red panel. Please indicate if you observe heteroskedasticity. Blue Panel Red Panel 3 3 2 2 . 1 1 50 50 -2 -3 0 0.2 0.4 0.6 0.8 1 0 0.5 1.5 2 2.5 3 3.5 4 X1 X2 A. Both panels B. Blue...
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