Homework Answers
If two variables are linearly related, then the estimators are still unbiased, but have very large variances & standard deviations.
In case the two estimators are perfectly linear then, estimators are indeterminate.
In second part , we have omitted variable bias, then the coefficients are both biased & inconsistent.
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Prowide complete explanations with reevant equations and derivations if poessible 1. Consider the equation a. If...
Provide comp te explanations with relevant equations and terivo . Questi! 1 (15p): Consider the population...
Provide comp te explanations with relevant equations and terivo . Questi! 1 (15p): Consider the population model );-po +ax, + β2W, + u, a. What does it imply about the population that u, has a zero conditional mean? b. Let u be correlated with W, but not with X,. What can we say about the estimate d, in the case where Wi is included and when it is not included? c. What are the assumptions made for OLS estimiation? What...
7. In order to estimate the wage equation, individual's observed characteristics including years of schooling. In t...
7. In order to estimate the wage equation, individual's observed characteristics including years of schooling. In this problem, however, the error term contains unobserved characteristics such is likely that the error is correlated with the years of schooling, i.e., a highly motivated person tends to study more and also make more money. Choose the wrong statement an econometrician regresses the log of wage on motivation, and it as (a) The years of schooling is endogenous (b) The OLS estimator is...
Please help with 4. a) b) c)
1. Use the LNU dataset that allows you to estimate a wage equation. Estimate a wage equation including a dummy variable for female (FEMALE). Interpret the estimated coefficient for the variable Female. 2. Estimate the same model adding a dummy variable for public sector (PUBLIC). Interpret the estimated coefficient for the variable PUBLIC. Compare the estimate for FEMALE in this model and the model above where the variable PUBLIC was not included.3. Estimate the wage equations above separately for Men and...
4. Consider the following model: Let X = (1,X1,X2, Xs)". Suppose and that X is not perfectly colinear. Suppose further that ElY]oo and Exoo for 1 j S 3. Using a large sample of i.i.d. observa...
4. Consider the following model: Let X = (1,X1,X2, Xs)". Suppose and that X is not perfectly colinear. Suppose further that ElY]oo and Exoo for 1 j S 3. Using a large sample of i.i.d. observations from (XX1.x2, Xs), you estimate this equation using Ols. Let β-(%, 33) de- note the resulting estimate of β = (Ah-…β3). (a) Let θ-2A-β3. Is θη-2A-A3 a consistent estimate of θ? Is it an unbiased estimate of 0? (b) Express Var(0,] in terms of...
Please complete using R. Show all code needed to complete exercise. Will Thumbs up if done...
Please complete using R. Show all code needed to
complete exercise. Will Thumbs up if done neatly and
correctly.
Exercise 5 (More Simulation) Let X follow an exponential distribution with rate parameter λx = 2. Let Y follow a Poisson distribution with rate parameter λ 3. We write sd(X) for the true standard deviation of X and m(Y) for the true median of Y Let s be the sample standard median which is an estimate of m(Y) Suppose we take...
Need help with stats true or false questions Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% con...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
(1 point) Frobenius' method: finding solutions as generalized power series Example: Consider the equation Tºg +...
(1 point) Frobenius' method: finding solutions as generalized power series Example: Consider the equation Tºg + Tự+(x - 3) = 0. Dividing by r, the equation becomes y' + (1/2y + (1/x - 3/x)y = 0. Sincer(1/) = 1 and .ca(1/x - 3/) = x - 3 are both analytic, x = 0 is a regular singular point, so we can solve the equation by generalized power series around x = 0. Let y(x) = Cox® + C1.+1 + c2r4+2...
As follow above the (1.12), what is the variance of the equation? I hope you solve...
As follow above the (1.12), what is the variance of the
equation? I hope you solve it in details.
Some Elementary Statistical Inferences nple itesa estimate of -hz+h). This suggests the following estimate of f(a) at'a given ar The ponparametrie estimate of the leftside is the proportion of the that fall in the i 1.11) To write this more formally, consider the indicator sta a)-o otherwise, Then a somparanmetric estimator of a) is Since the sample items are identically distributed,...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2 3 .14 .25 .01 2 33 .10 .07 3 .03 .05 .02 Find the marginal probability distribution of Y and graph it. Show your calculations. b. Find the conditional probability distribution of Y (given that X = 2) and graph it. Show your calculations. c. Do your results in (a) and (b) satisfy the probability distribution requirements? Explain clearly. d. Find the correlation coefficient...
Please show your work. God bless 1. (40 points) Consider the following five observations. (9 points)...
Please show your work. God bless
1. (40 points) Consider the following five observations. (9 points) (x-x) (x - x) (y- y) (x - x)(y-y) 2*- {x = 1012 (-:-)= {(x - 1)2 = 20;-)) = (x x)(y- » a) (6 points) What are the sample means of x and y? b) Complete the entries in the table above. Put the sums in the last row. (Show work below) c) Calculate Bo and write out the equation for the fitted...
Provide comp te explanations with relevant equations and terivo . Questi! 1 (15p): Consider the population model );-po +ax, + β2W, + u, a. What does it imply about the population that u, has a zero conditional mean? b. Let u be correlated with W, but not with X,. What can we say about the estimate d, in the case where Wi is included and when it is not included? c. What are the assumptions made for OLS estimiation? What...
7. In order to estimate the wage equation, individual's observed characteristics including years of schooling. In this problem, however, the error term contains unobserved characteristics such is likely that the error is correlated with the years of schooling, i.e., a highly motivated person tends to study more and also make more money. Choose the wrong statement an econometrician regresses the log of wage on motivation, and it as (a) The years of schooling is endogenous (b) The OLS estimator is...
4. Consider the following model: Let X = (1,X1,X2, Xs)". Suppose and that X is not perfectly colinear. Suppose further that ElY]oo and Exoo for 1 j S 3. Using a large sample of i.i.d. observations from (XX1.x2, Xs), you estimate this equation using Ols. Let β-(%, 33) de- note the resulting estimate of β = (Ah-…β3). (a) Let θ-2A-β3. Is θη-2A-A3 a consistent estimate of θ? Is it an unbiased estimate of 0? (b) Express Var(0,] in terms of...
Please complete using R. Show all code needed to
complete exercise. Will Thumbs up if done neatly and
correctly.
Exercise 5 (More Simulation) Let X follow an exponential distribution with rate parameter λx = 2. Let Y follow a Poisson distribution with rate parameter λ 3. We write sd(X) for the true standard deviation of X and m(Y) for the true median of Y Let s be the sample standard median which is an estimate of m(Y) Suppose we take...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
(1 point) Frobenius' method: finding solutions as generalized power series Example: Consider the equation Tºg + Tự+(x - 3) = 0. Dividing by r, the equation becomes y' + (1/2y + (1/x - 3/x)y = 0. Sincer(1/) = 1 and .ca(1/x - 3/) = x - 3 are both analytic, x = 0 is a regular singular point, so we can solve the equation by generalized power series around x = 0. Let y(x) = Cox® + C1.+1 + c2r4+2...
As follow above the (1.12), what is the variance of the
equation? I hope you solve it in details.
Some Elementary Statistical Inferences nple itesa estimate of -hz+h). This suggests the following estimate of f(a) at'a given ar The ponparametrie estimate of the leftside is the proportion of the that fall in the i 1.11) To write this more formally, consider the indicator sta a)-o otherwise, Then a somparanmetric estimator of a) is Since the sample items are identically distributed,...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2 3 .14 .25 .01 2 33 .10 .07 3 .03 .05 .02 Find the marginal probability distribution of Y and graph it. Show your calculations. b. Find the conditional probability distribution of Y (given that X = 2) and graph it. Show your calculations. c. Do your results in (a) and (b) satisfy the probability distribution requirements? Explain clearly. d. Find the correlation coefficient...
Please show your work. God bless
1. (40 points) Consider the following five observations. (9 points) (x-x) (x - x) (y- y) (x - x)(y-y) 2*- {x = 1012 (-:-)= {(x - 1)2 = 20;-)) = (x x)(y- » a) (6 points) What are the sample means of x and y? b) Complete the entries in the table above. Put the sums in the last row. (Show work below) c) Calculate Bo and write out the equation for the fitted...
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