Suppose that the true linear regression model in a given situation is Now, assume that the...
Suppose that the true linear regression model in a given situation is
Now, assume that the researcher mistakenly believes that the true model is
,
and that he estimates this model, accordingly. Prove that his
(OLS) estimator of 
will be biased.
Homework Answers
![LD LALA LULUS As trive Y . . ß + B x tu, is the mode & E (Y :) = 8 + Petri (E(ui) = 0] ELY) = pi + B, X. where 7 = IY & x = [](http://img.homeworklib.com/questions/73048390-6e77-11eb-8730-917c66d26a65.png?x-oss-process=image/resize,w_560)
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Suppose that the true linear regression model in a given
situation is
Now, assume that the...
Prove that the OLS estimator As for β in the linear regression model is consistent Let's first sh...
Taking the yellow parts below as a model to solve the
question above. Thank you!!!!!!!!
Prove that the OLS estimator As for β in the linear regression model is consistent Let's first show that the OLS estimator is consistent Recall the result for β LS-(Lil Xix;厂E-1 xīYi Using Yi = X(B* + ui By the WLLN Assuming that E(X,X is non-negative definite (so that its inverse exists) and using Slutsky's theorem It follows In words: ßOLs converges in probability to...
7. In a simple regression model, suppose all of the assumptions of the classical linear regression...
7. In a simple regression model, suppose all of the assumptions of the classical linear regression morel apply, except that rather than assume E (ui | Xi) = 0, you assume that E (Ui / X;) = ali and E (xi) = 0 where a > 0 is a constant. (a) What is the conditional expectation of the OLS slope coefficient, i.e. E (B1 | 21, ..., XN)? (b) In this case, is ß1 an unbiased estimator of B1 or...
Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui....
Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui. 1. [3 points] What are the assumptions of this model so that the OLS estimators are BLUE (best linear unbiased estimates)? 2. [4 points] Let βˆ and βˆ be the OLS estimators of β and β . Derive βˆ and βˆ. 12 1212 3. [2 points] Show that βˆ is an unbiased estimator of β .22
sve v anu i, respectively. 7. Regression without any regressor. Suppose you are given the model:...
sve v anu i, respectively. 7. Regression without any regressor. Suppose you are given the model: Y = pi + uj. Use OLS to find the estimator of Bi. What is its variance and the RSS? Does the estimated By make intuitive sense? Now consider the two-variable model Y = B1 + B2X; +ui. Is it worth adding X, to the model? If not, why bother with regression analysis?
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series dat...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
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....
TRUE or FALSE and Explain why: If the error term in a simple regression model is...
TRUE or FALSE and Explain why: If the error term in a simple regression model is heteroskedastic, the estimated OLS coefficients are biased.
Suppose you are interested in studying the relationship between education and wage. More specifically, suppose that...
Suppose you are interested in studying the relationship between education and wage. More specifically, suppose that you believe the relationship to be captured by the following linear regre Wago = A * Education+u Suppose further that you estimate the unknown population Inear regression model by OLS What is the difference between , and,? OA Both. A, and OB. Bon. A, and are true parameters of the population regression line are OLS estimators of true parameters of the population regression line...
1. For a simple linear regression BMI = a + BIncome+u. Suppose you have a random...
1. For a simple linear regression BMI = a + BIncome+u. Suppose you have a random sample. Which of the following statement is true? a) OLS estimators are unbiased but inefficient when BMI does not vary much in the sample. b) OLS estimators are biased when the error u captures perseverance and self- control, and you believe that people who are perseverant and have more self- control tend to have higher income. C) OLS estimators are biased when Income does...
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...
Taking the yellow parts below as a model to solve the
question above. Thank you!!!!!!!!
Prove that the OLS estimator As for β in the linear regression model is consistent Let's first show that the OLS estimator is consistent Recall the result for β LS-(Lil Xix;厂E-1 xīYi Using Yi = X(B* + ui By the WLLN Assuming that E(X,X is non-negative definite (so that its inverse exists) and using Slutsky's theorem It follows In words: ßOLs converges in probability to...
7. In a simple regression model, suppose all of the assumptions of the classical linear regression morel apply, except that rather than assume E (ui | Xi) = 0, you assume that E (Ui / X;) = ali and E (xi) = 0 where a > 0 is a constant. (a) What is the conditional expectation of the OLS slope coefficient, i.e. E (B1 | 21, ..., XN)? (b) In this case, is ß1 an unbiased estimator of B1 or...
sve v anu i, respectively. 7. Regression without any regressor. Suppose you are given the model: Y = pi + uj. Use OLS to find the estimator of Bi. What is its variance and the RSS? Does the estimated By make intuitive sense? Now consider the two-variable model Y = B1 + B2X; +ui. Is it worth adding X, to the model? If not, why bother with regression analysis?
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
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....
Suppose you are interested in studying the relationship between education and wage. More specifically, suppose that you believe the relationship to be captured by the following linear regre Wago = A * Education+u Suppose further that you estimate the unknown population Inear regression model by OLS What is the difference between , and,? OA Both. A, and OB. Bon. A, and are true parameters of the population regression line are OLS estimators of true parameters of the population regression line...
1. For a simple linear regression BMI = a + BIncome+u. Suppose you have a random sample. Which of the following statement is true? a) OLS estimators are unbiased but inefficient when BMI does not vary much in the sample. b) OLS estimators are biased when the error u captures perseverance and self- control, and you believe that people who are perseverant and have more self- control tend to have higher income. C) OLS estimators are biased when Income does...
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...
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