Homework Answers
1.) d. ( The F statistic is more flexible them the t statistic)
2.) c. (2/3)
3.) a,c,e ( .in a multiple regression
. Both the almost all option
4.) d. Converges the single point Bita 1
5.) c. Equls to zero and variance eqaul to siqma ^2
6.) a , b ,d.
7.) a , c , f
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Which of the following statements is true? (a) If the calculated value of F statistic is...
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...
15. Suppose that the population model is y-βο + Ax + u Another way to deal...
15. Suppose that the population model is y-βο + Ax + u Another way to deal with endogeneity ofr s to employ the Two-stage Least Squared Estimator. In the first stage, we estimate x = π。+ π12+ u and obtain its prediction x and run the regression y = β° + Ax + u in the second stage. Which of the following is correct regarding therelationship between the 2SLS and IV estimators? (a) The 2SLS estimator is exactly the same...
1. Select all true statements about sample mean and sample median. A) When the population distribution...
1. Select all true statements about sample mean and sample median. A) When the population distribution is skewed, sample mean is biased but sample median is an unbiased estimator of population mean. B) When the population distribution is symmetric, both mean and sample median are unbiased estimators of population mean. C) Sampling distribution of sample mean has a smaller standard error than sample median when population distribution is normal. D) Both mean and median are unbiased estimators of population mean...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a and b. Answer the following questions. (a) Suppose we multiply X, by 1/2 for all i and do the OLS estimation again using X as the regressor (the independent variable). What will be your new estimators, denoted by ă (intercept) and b (slope)? Compare them with the original OLS estimators a and b, respectively (b) Compare Var[b] and Var[b]. Are they the same or...
1.Given the Multiple Linear regression model as Y-Po + β.X1 + β2X2 + β3Xs + which in matrix notation is written asy-xß +ε where -έ has a N(0,a21) distribution + + ßpXo +ε A. Show that the OLS estimat...
1.Given the Multiple Linear regression model as Y-Po + β.X1 + β2X2 + β3Xs + which in matrix notation is written asy-xß +ε where -έ has a N(0,a21) distribution + + ßpXo +ε A. Show that the OLS estimator of the parameter vector B is given by B. Show that the OLS in A above is an unbiased estimator of β Hint: E(β)-β C. Show that the variance of the estimator is Var(B)-o(Xx)-1 D. What is the distribution o the...
7. True/False a. If Cov(x,u)>0, then the OLS estimator βι will then to be higher than...
7. True/False a. If Cov(x,u)>0, then the OLS estimator βι will then to be higher than β b. Suppose you run a regression and obtain the estimate B1 - 3.4. Stata tells you that the test statistic for the null hypothesis that B12 is equal to 2. This implies that the standard error of the slope coefficient is also equal to 2.
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we ca...
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we call it regression through the origin. Consider a population model Y- Au + βίχ + u and we estimate an OLS regression model through the origin: Y-β¡XHi (note that the true intercept parameter Bo is not necessarily zero). (i) Under assumptions SLR.1-SLR.4, either use the method of moments or minimize the SSR to show that the βί-1-- ie1 (2) Find E(%) in terms...
Which of the following statements are true or false ? Give reasons for your answer. 5x2-10 (a) There is no difference between qualitative and quantitative variables. (b) For a standard exponential di...
Which of the following statements are true or false ? Give reasons for your answer. 5x2-10 (a) There is no difference between qualitative and quantitative variables. (b) For a standard exponential distribution, mean is 0 and variance is 1. If T is an unbiased estimator for θ, then T"is (c) 2 an unbiased estimator for θ 6 (d) Geometric distribution is a particular distribution obtained from Binomial distribution. If the mg.f. of X is M,(t) = exp (32t2), then (e)...
Answer each question by writing TRUE or FALSE 1. For OLS estimators to be linear the...
Answer each question by writing TRUE or FALSE 1. For OLS estimators to be linear the explanatory variables must be variable, non- stochastic and fixed in repeated samples. Under the conditions of perfect multicollinearity, the OLS estimators are not unique. The presence of heteroskedasticity causes the OLS method to overestimate the variances 2. 3. of the parameters. The Breusch-Godfrey LM test is applicable when a lagged dependent variable is used. If we include a non-influential variable in an equation the...
Question 2 (10 points) You are given the following model y-put ei. Consider two alternative estimators of β, b2xvix? and b = Zy/X 1. Which estimator would you choose and why if the model satisfies al...
Question 2 (10 points) You are given the following model y-put ei. Consider two alternative estimators of β, b2xvix? and b = Zy/X 1. Which estimator would you choose and why if the model satisfies all the assumptions of classical regression? Prove your results. (4 points) 2. Now suppose that var(y)-hxi, where h is a positive constant (a) Obtain the correct variance of the OLS estimator. (2 points) (b) Show that the BLU estimator is now 6. Derive its variance....
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...
15. Suppose that the population model is y-βο + Ax + u Another way to deal with endogeneity ofr s to employ the Two-stage Least Squared Estimator. In the first stage, we estimate x = π。+ π12+ u and obtain its prediction x and run the regression y = β° + Ax + u in the second stage. Which of the following is correct regarding therelationship between the 2SLS and IV estimators? (a) The 2SLS estimator is exactly the same...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a and b. Answer the following questions. (a) Suppose we multiply X, by 1/2 for all i and do the OLS estimation again using X as the regressor (the independent variable). What will be your new estimators, denoted by ă (intercept) and b (slope)? Compare them with the original OLS estimators a and b, respectively (b) Compare Var[b] and Var[b]. Are they the same or...
1.Given the Multiple Linear regression model as Y-Po + β.X1 + β2X2 + β3Xs + which in matrix notation is written asy-xß +ε where -έ has a N(0,a21) distribution + + ßpXo +ε A. Show that the OLS estimator of the parameter vector B is given by B. Show that the OLS in A above is an unbiased estimator of β Hint: E(β)-β C. Show that the variance of the estimator is Var(B)-o(Xx)-1 D. What is the distribution o the...
7. True/False a. If Cov(x,u)>0, then the OLS estimator βι will then to be higher than β b. Suppose you run a regression and obtain the estimate B1 - 3.4. Stata tells you that the test statistic for the null hypothesis that B12 is equal to 2. This implies that the standard error of the slope coefficient is also equal to 2.
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we call it regression through the origin. Consider a population model Y- Au + βίχ + u and we estimate an OLS regression model through the origin: Y-β¡XHi (note that the true intercept parameter Bo is not necessarily zero). (i) Under assumptions SLR.1-SLR.4, either use the method of moments or minimize the SSR to show that the βί-1-- ie1 (2) Find E(%) in terms...
Which of the following statements are true or false ? Give reasons for your answer. 5x2-10 (a) There is no difference between qualitative and quantitative variables. (b) For a standard exponential distribution, mean is 0 and variance is 1. If T is an unbiased estimator for θ, then T"is (c) 2 an unbiased estimator for θ 6 (d) Geometric distribution is a particular distribution obtained from Binomial distribution. If the mg.f. of X is M,(t) = exp (32t2), then (e)...
Answer each question by writing TRUE or FALSE 1. For OLS estimators to be linear the explanatory variables must be variable, non- stochastic and fixed in repeated samples. Under the conditions of perfect multicollinearity, the OLS estimators are not unique. The presence of heteroskedasticity causes the OLS method to overestimate the variances 2. 3. of the parameters. The Breusch-Godfrey LM test is applicable when a lagged dependent variable is used. If we include a non-influential variable in an equation the...
Question 2 (10 points) You are given the following model y-put ei. Consider two alternative estimators of β, b2xvix? and b = Zy/X 1. Which estimator would you choose and why if the model satisfies all the assumptions of classical regression? Prove your results. (4 points) 2. Now suppose that var(y)-hxi, where h is a positive constant (a) Obtain the correct variance of the OLS estimator. (2 points) (b) Show that the BLU estimator is now 6. Derive its variance....
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