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Consider the following one variable regression for the demand estimation: quantity demanded = Bo + Biprice...
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...
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual...
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual i's University GPA and xi is the individual's high school grades. a. What do you think is in ui? Do you think E[ulx) = 0? Suggest a variable that you think might affect University GPA that isn't included in the regression equation but should be. c. What sign of bias would you expect in an OLS regression of y on x? Briefly explain. d....
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...
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive...
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive the formula for the least squares estimator of p The least squares objective function is OA. n (v2-bo-bx?) i-1 Ов. O B. n (M-bo-bX) /# 1 n Click to select your answer and then click Check Answer. Exercise 4.11 OA n Σ (--B,χ?) O B. E (Y-bo-b,X)2 j= 1 n Σ (Υ-Βo-bΧ) 3. j= 1 D. n Σ (Υ-0-b,) i- 1 Click to select...
consider the following supply and demand schedules for steel Price ($/ton) Quantity demanded Quantity supplied Quantity...
consider the following supply and demand schedules for steel Price ($/ton) Quantity demanded Quantity supplied Quantity supplied (accounting for Social Cost) 0 160 0 ? 20 140 20 ? 40 120 40 ? 60 100 60 ? 80 80 80 ? 100 60 100 ? 120 40 120 ? 140 20 140 ? 160 0 160 ? 180 0 180 ? Pollution from steel production is estimated to create an external cost of $40 per ton. Based on this information...
3. a) Consider the following model for the demand function: Where Q Quantity demanded P price e e...
3. a) Consider the following model for the demand function: Where Q Quantity demanded P price e exponent, and U is the population error term i) Name at least one additional independent variable which may influence a. i) Linearize the above model by taking logs. b) Consider the following reciprocal regression model (sample): Y = b1 + b2(1/%) + ei 2 where bi and b2 are positive. i) What happens to Y as X increases? Show the relationship between Y...
Q1. For each part of this question, select one correct answer 3 points each). a. Statement:...
Q1. For each part of this question, select one correct answer 3 points each). a. Statement: When estimating a regression with a binary dependent variable, it is necessary to use heteroseedasticity-robust standard error estimates to test hypotheses about the regression coefficients A Agree B. Disagree b. Statement: If MLR.5 is violated, we can still use the salt and F statistics when the sample size is large enough. A. Agree B. Disagree c. Statement: Suppose that the dependent variable in your...
Consider the following demand and supply functions: where d is the quantity demanded, Q is the...
Consider the following demand and supply functions: where d is the quantity demanded, Q is the quantity supplied, P is the price, and all pa- rameters [ao, αι, βο'Al are positive constants unless otherwise stated. Denote θ as the partial derivative symbol, and Δ as the discretized units of change 1. (1 point) Derive the demand curve. What is the slope of the demand curve? A. 1 2. (1 point) What is the intercept of the demand curve (along the...
To test the effectiveness of a job training program on the subsequent wages of workers, We...
To test the effectiveness of a job training program on the subsequent wages of workers, We specify the model log(wage) = Bo + B,train + B2educ + Bzexper + u where train is a binary variable equal to one if a worker participated in the program. a. How do we interpret B, and B, in the model? b. Think of the error term u as containing unobserved worker ability. If less able workers have a greater chance of being selected...
2. Consider a simple linear regression i ion model for a response variable Y, a single...
2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x...
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...
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual i's University GPA and xi is the individual's high school grades. a. What do you think is in ui? Do you think E[ulx) = 0? Suggest a variable that you think might affect University GPA that isn't included in the regression equation but should be. c. What sign of bias would you expect in an OLS regression of y on x? Briefly explain. d....
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...
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive the formula for the least squares estimator of p The least squares objective function is OA. n (v2-bo-bx?) i-1 Ов. O B. n (M-bo-bX) /# 1 n Click to select your answer and then click Check Answer. Exercise 4.11 OA n Σ (--B,χ?) O B. E (Y-bo-b,X)2 j= 1 n Σ (Υ-Βo-bΧ) 3. j= 1 D. n Σ (Υ-0-b,) i- 1 Click to select...
3. a) Consider the following model for the demand function: Where Q Quantity demanded P price e exponent, and U is the population error term i) Name at least one additional independent variable which may influence a. i) Linearize the above model by taking logs. b) Consider the following reciprocal regression model (sample): Y = b1 + b2(1/%) + ei 2 where bi and b2 are positive. i) What happens to Y as X increases? Show the relationship between Y...
Q1. For each part of this question, select one correct answer 3 points each). a. Statement: When estimating a regression with a binary dependent variable, it is necessary to use heteroseedasticity-robust standard error estimates to test hypotheses about the regression coefficients A Agree B. Disagree b. Statement: If MLR.5 is violated, we can still use the salt and F statistics when the sample size is large enough. A. Agree B. Disagree c. Statement: Suppose that the dependent variable in your...
Consider the following demand and supply functions: where d is the quantity demanded, Q is the quantity supplied, P is the price, and all pa- rameters [ao, αι, βο'Al are positive constants unless otherwise stated. Denote θ as the partial derivative symbol, and Δ as the discretized units of change 1. (1 point) Derive the demand curve. What is the slope of the demand curve? A. 1 2. (1 point) What is the intercept of the demand curve (along the...
To test the effectiveness of a job training program on the subsequent wages of workers, We specify the model log(wage) = Bo + B,train + B2educ + Bzexper + u where train is a binary variable equal to one if a worker participated in the program. a. How do we interpret B, and B, in the model? b. Think of the error term u as containing unobserved worker ability. If less able workers have a greater chance of being selected...
2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x...
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