Suppose that the true population regression is Y = Bo + BiXi +2X2+ € but you mistakenly estimate the equation Y= bo + b1X1 + u (a) Suppose that cov(X₁, X2) = 0 and suppose B2> 0. Is b1 a biased estimate of B₁? If so, is the bias positive or negative? How do you know? (b) Suppose that cov(X₁,X2) = 0.475 and suppose B2> 0. Is bia biased estimate of B₁? If so, is the bias positive or negative? How do you know?

Suppose that the true population regression is Y = Bo + BiXi +2X2+ € but you mistakenly estimate the equation Y= bo + b1X1 + u (a) Suppose that cov(X₁, X2) = 0 and suppose B2> 0. Is b1 a biased estimate of B₁? If so, is the bias positive or negative? How do you know? (b) Suppose that cov(X₁,X2) = 0.475 and suppose B2> 0. Is bia biased estimate of B₁? If so, is the bias positive or negative? How do you know?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

1. Consider the following regression model y = x3 + u. (1) Let 3 denote the Ordinary Least Squares (OLS) estimator of B. The so-called Gauss- Markov assumptions are: • MLR.1: The true model in the population is given by (1). • MLR.2: We have a random sample of n observations {(ri, Yi), i = 1, 2, .., n} following the population model in (1). .... • MLR.3: No one explanatory variable can be written as a linear combination of the remaining explanatory variables that is, there is no perfectcollinearity. • MLR.4: In the population, the error u has an expected value of zero given any values of the explanatory variables, that is Elu|x] = 0. • MLR.5: In the population, the error u has the same variance given any values of the explanatory variables, that is Var[u|x] = o? , an unknown finite, positive constant. In the following scenarios, state whether B is an unbiased and consistent estimator of 3, and provide a brief justification for your answer in each case - but no formal mathematical…
q4-
When Y is regressed on X, B, > 0, sx+ 0, sy # 0, and the fraction of the variation in Y explained by the least-squares regression of Y on X does not equal 1. In this example, the sum of the squares of the deviations of the actual Y-values from their mean would definitely be greater than the sum of the squares of the deviations of the predicted Y-values from their mean. 1 A) B) true false 4. When Y is regressed on X, the sample slope is negative, sx + 0, sy + 0, and Y; = Y; for every observation. In this example, the sum of the squares of the deviations of the predicted Y-values from their mean would definitely be less than the sum of the squares of the deviations of the actual Y-values from their mean. A) В) true false 3.
With Panel Data, if we assume that the individual effects vi are not correlated with the regressors Xit (i.e. E(vi|Xit) = 0), which one of the following statements is correct: The Fixed Effects estimator is not consistent. Both the OLS and the Random Effects estimators are not consistent. The OLS estimator is not consistent, but the Random Effects estimator is consistent. The OLS and the Random Effects estimator are consistent. All of the above. None of the above
A researcher investigating whether government expenditure crowds out investment estimates a regression on data for 30 countries. I-investment; G-government recurrent expenditure; Y=gross domestic product; all measured in $US billion. P= population measured in million. Standard errors are in parentheses. Î= 18.10 (7.79) R² = 0.99 1.07G + 36Y (0.14) (0.02) She suspects that countries with higher GDP may have more variability in their investment. She sorts the observations by increasing size of gdp per capita (Y)and estimates the regression again for the 11 countries with the lowest gdp(Y)and the 11 countries with the largest gdp(Y). The RSS1 from the first regression is 7186. The RSS2 from the second regresison is 28101. Perform a Goldfeld-Quandt Test at a 5% significance level. a. The test statistic for this test is 0.256 b. The critical value defining the rejection region for Ho is 3.18 c. Is there heterscedasticity? Yes=1 or No-0. The answer is 0
q4-
SSE SST X₂ The estimated regression equation for these data is ŷ = 7.6 +0.9x. Compute SSE, SST, and SSR (to 1 decimal). SSR 2 7 6 18 9 13 20 9 26 23 What percentage of the total sum of squares can be accounted for by the estimated regression equation (to 1 decimal)? % What is the value of the sample correlation coefficient (to 3 decimals)?
In regression model: Yi = B1+ B2Xi+ Ei, where Ei is a random variable independent of Xi, with mean and variance constant and different from zero. Ei ~(media, varianza) Obtain the OLS estimator of ẞ2. Show that the properties of finite samples hold.
Scenario 38-1. Consider the following OLS model applied to the data for workers wages and years of schooling, where e; stands for the residual: WAGE = -10.7+3.16 x SCHOOL + e. (20.7) (1.35) Refer to Scenario 38-1. Suppose that the residual term has a zero mean and is uncorrelated with the independent variable. According to the estimated model, each year of schooling decreases a worker's wage by $3.16. 000 decreases a worker's wage by $10.7. increases a worker's wage by $3.16. increases a worker's wage by $10.7.