Using the first stage auxiliary regression in 2SLS, express the 2SLS estimator in matrix algebraonly in terms of endogenous regressors X, instruments Z, and the dependent variable y.

In this problem, we are dealing with instrumental variable (IV) estimation using the two-stage least…

Answered: Using the first stage auxiliary…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Heteroscedasticity Stigler and Friedland (1983) conducted a study to determine whether the separation of company control from company ownership affects company profits. Using data from 69 companies in the United States, the authors estimate the following model: profiti = α + β1asseti + β2management_controli + ei Where i is company and: profiti = annual profit (in million dollar) asseti = company asset (in million dollar) management_controli = dummy variable that is worth one if the control of the company is held by the manager The regression results are presented in the table in the picture a. Explain whether the statements below are TRUE, FALSE, or CANNOT BE DETERMINED. "If there is a heteroscedasticity problem, the confidence interval of the OLS estimator is not valid." b. Determine the 95% confidence interval for the parameter 2, what can you conclude?
The null hypothesis being tested in the least-squares regression output for B is B1 = B1,0=1. True False
The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.
Derive the least squares estimator of Bo for model Y₁ = P + Ei the re regression
A researcher has estimated the following multiple regression model to investigate the determinants of capital structure in an emerging market based on data from 2016. LEV = 1.32 – 0.10TANG - 0.28PROFIT + 0.19GROWTH + e (0.92) (0.03) (0.25) (0.04) Residual sum of squares = 200Total sum of squares = 620Number of Observations = 90Standard errors of the coefficients are given in parentheses. The variables are:LEV = Leverage (total debt to total assets).TANG = Tangibility (net fixed assets to total assets). PROFIT = Profitability (net income to total assets). GROWTH = Firm growth (Percent change in sales). e = residual For each independent variable slope coefficient, test the null hypothesis that it is equal to zero against the alternative hypothesis that it is not equal to 0. The critical t value is 1.96 at the 5% significance level for a two-tailed test.
The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 16 In a t-test, suppose a researcher sets the significance level at 0.5%. What does this mean? The probability that the null hypothesis is true is 0.5% The researcher would be rejecting the null hypothesis, only if the p-value is less than 0.5% The researcher would be rejecting the null hypothesis, if the t-statistic is higher than 0.5 It does not mean anything, because the significance level can only be set at 5% QUESTION 17 In an MLR…
Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
Let 0 = (B, o^2)^T denotes the unknown parameters for multiple linear regression. Find the Cramer-Rao lower bound matrix for the vector of the parameters.
2
)A county real estate appraiser wants to develop a statistical model to predict the appraised value of 3) houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(u) = Bo + Bix, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 73 houses in Fast Meadow, the following results were obtained: y = 73.80 + 19.72x What are the properties of the least squares line, y = 73.80 + 19.72x? A) Average error of prediction is 0, and SSE is minimum. B) It will always be a statistically useful predictor of y. C) It is normal, mean 0, constant variance, and independent. D) All 73 of the sample y-values fall on the line.
An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.
The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 7 In the MLR model, the assumption of ‘linearity in parameters’ is violated if: one of the slope coefficients appears as a power (e.g. Y = b0 + b1*(X1^b2) + b3*X2 + u) the model includes the reciprocal of a variable (e.g. 1/X1) the model includes a variable squared (e.g. X1^2) the model includes a variable in its logarithmic form (i.e. log(X1) ) QUESTION 8 In the MLR model, the assumption of 'no perfect collinearity'…

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Using the first stage auxiliary regression in 2SLS, express the 2SLS estimator in matrix algebra only in terms of endogenous regressors X, instruments Z, and the dependent variable y.