Consider the following Y_i=β_0+β_1 X_i+u_i where Xi is endogenous. Assume that Zi is an exogenous variable that can be used in 2SLS.
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Consider the following Y_i=β_0+β_1 X_i+u_i where Xi is
endogenous. Assume that Zi is an exogenous variable...
Consider the model, Y; = Bo + B1 Xi+Uj, where you suspect Xi is endogenous. You...
Consider the model, Y; = Bo + B1 Xi+Uj, where you suspect Xi is endogenous. You have an exogenous instrument and you estimate the first stage to recover the residuals, Vhatj. You want to test for endogeneity so you estimate the following model using OLS: Y= Bo + B1 Xi + B2 Vhat; + Uj. The estimation results from 100 observations are in the table: Coefficient Standard Errors Constant 2.63 0.98 X 0.97 0.57 Vhat 0.47 0.10 Please select your...
1. Consider the following regression model with a single endogenous variable, ya : and given the...
1. Consider the following regression model with a single endogenous variable, ya : and given the reduced from for x: where z and are exogenous variables in the sense that cov(u,21) = cov(11,2 ) = 0 and cov(v,21) = cov(ng) = 0 (i.e., both zi and z2 are uncorrelated with u and v, and u is uncorrelated with v) (a) By substituting x into the equation for y, we obtain the reduce formed equation for y: Find the a in...
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with me...
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with mean zero. (a) What is the expected value of y? (b) Suppose you draw a sample of yi yn. Derive the least squares estimator for θ. For full credit you must check the 2nd order condition c) Can this estimator (0) be described as a method of moments estimator? (d) Now suppose є is independent normally distributed with mean...
1. Consider a variable y = θ+e where θ is an unknown parameter and e is a random variable with me...
1. Consider a variable y = θ+e where θ is an unknown parameter and e is a random variable with mean zero (a) What is the expected value of y (b) Suppose you draw a sample of in y-Derive the least squares estimator for θ. For full credit you must check the 2nd order condition. (c) Can this estimator () be described as a method of moments estimator? (d) Now suppose e is independent normally distributed with mean 0 and...
3. [20 marks] Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and X3 have the joint probability function where x = (zi, 2 2:23), θ = (θί, θ2), n = x1 + 2 2...
3. [20 marks] Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and X3 have the joint probability function where x = (zi, 2 2:23), θ = (θί, θ2), n = x1 + 2 2 + x3, θι, θ2 > 0 and 1-0,-26, > 0. (a) [4 marks] Find the maximum likelihood estimator θ of θ. (b) [4 marks] Find that the Fisher information matrix I(0) (c) [4 marks] Show that θ is an MVUE. (d)...
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the nu...
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
Consider two separate linear regression models and For concreteness, assume that the vector yi co...
please help me to solve that question
Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed to affect individual wealth in Australia, and he matrix X2 contains n observations on k2 explanatory variables which are believed...
Question 1 (32 marks) Consider a firm which produces a good, y, using two inputs or factors of production, x1 and...
Question 1 (32 marks) Consider a firm which produces a good, y, using two inputs or factors of production, x1 and x2. The firm's production function describes the mathematical relationship between inputs and output, and is given by (a) Derive the degree of homogeneity of the firm's production function. 4 marks) (b) The set is the set of combinations of (xi,x2) which produce output level yo.S is a level curve of f and is referred to by economists as the...
Assume that we have three independent observations: where Xi ~ Binomial(n 7,p) for i E { 1.2.3). The value of p E (0, 1) is not known. When we have observations like this from different, independent...
Assume that we have three independent observations: where Xi ~ Binomial(n 7,p) for i E { 1.2.3). The value of p E (0, 1) is not known. When we have observations like this from different, independent ran- dom variables, we can find joint probabilities by multiplying together th ndividual probabilities. For example This should remind you the discussion on statistical independence of random variables that can be found in the course book (see page 22) Answer the following questions a...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ (1), where wage is hourly wage, measured in dollars, and educ years of formal education. According to (1), a person with no education has a predicted hourly wage of [wagehat] dollars. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing...
Consider the model, Y; = Bo + B1 Xi+Uj, where you suspect Xi is endogenous. You have an exogenous instrument and you estimate the first stage to recover the residuals, Vhatj. You want to test for endogeneity so you estimate the following model using OLS: Y= Bo + B1 Xi + B2 Vhat; + Uj. The estimation results from 100 observations are in the table: Coefficient Standard Errors Constant 2.63 0.98 X 0.97 0.57 Vhat 0.47 0.10 Please select your...
1. Consider the following regression model with a single endogenous variable, ya : and given the reduced from for x: where z and are exogenous variables in the sense that cov(u,21) = cov(11,2 ) = 0 and cov(v,21) = cov(ng) = 0 (i.e., both zi and z2 are uncorrelated with u and v, and u is uncorrelated with v) (a) By substituting x into the equation for y, we obtain the reduce formed equation for y: Find the a in...
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with mean zero. (a) What is the expected value of y? (b) Suppose you draw a sample of yi yn. Derive the least squares estimator for θ. For full credit you must check the 2nd order condition c) Can this estimator (0) be described as a method of moments estimator? (d) Now suppose є is independent normally distributed with mean...
1. Consider a variable y = θ+e where θ is an unknown parameter and e is a random variable with mean zero (a) What is the expected value of y (b) Suppose you draw a sample of in y-Derive the least squares estimator for θ. For full credit you must check the 2nd order condition. (c) Can this estimator () be described as a method of moments estimator? (d) Now suppose e is independent normally distributed with mean 0 and...
3. [20 marks] Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and X3 have the joint probability function where x = (zi, 2 2:23), θ = (θί, θ2), n = x1 + 2 2 + x3, θι, θ2 > 0 and 1-0,-26, > 0. (a) [4 marks] Find the maximum likelihood estimator θ of θ. (b) [4 marks] Find that the Fisher information matrix I(0) (c) [4 marks] Show that θ is an MVUE. (d)...
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
please help me to solve that question
Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed to affect individual wealth in Australia, and he matrix X2 contains n observations on k2 explanatory variables which are believed...
Question 1 (32 marks) Consider a firm which produces a good, y, using two inputs or factors of production, x1 and x2. The firm's production function describes the mathematical relationship between inputs and output, and is given by (a) Derive the degree of homogeneity of the firm's production function. 4 marks) (b) The set is the set of combinations of (xi,x2) which produce output level yo.S is a level curve of f and is referred to by economists as the...
Assume that we have three independent observations: where Xi ~ Binomial(n 7,p) for i E { 1.2.3). The value of p E (0, 1) is not known. When we have observations like this from different, independent ran- dom variables, we can find joint probabilities by multiplying together th ndividual probabilities. For example This should remind you the discussion on statistical independence of random variables that can be found in the course book (see page 22) Answer the following questions a...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ (1), where wage is hourly wage, measured in dollars, and educ years of formal education. According to (1), a person with no education has a predicted hourly wage of [wagehat] dollars. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing...
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