What is the sign and exact magnitude of the omitted variable bias associated with the coefficient on standardized_looks as a result of not controlling for experience? Does this make sense? Explain.
Added by Deborah M.
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In this scenario, we have two variables: standardized_looks and experience. The coefficient on standardized_looks represents the effect of looks on the outcome variable (e.g., income, job success, etc.), while experience is another variable that may also influence Show more…
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Suppose that the population regression equation for earnings is Earnings_i = β_0 + β_1Female_i + β_2Bachelors + u_i (1) where Bachelors is a dummy variable indicating whether person i has completed a bachelors degree. However, when doing our analysis we (incorrectly) assume that the population regression equation for earnings is simply Earnings_i = β_0 + β_1Female_i + u_i (2) That is, we incorrectly omit the dependence of Earnings on Bachelors. It can be shown that you can write the expected value of the OLS coefficient in the incorrect regression as (you don't need to be able to prove this) E[β̂_1] = cov(Earnings_i,Female_i) / var(Female_i) (3) (a) Insert the "true" population regression in equation (1) into the expression for the expected value of β̂_1 in equation (3) to derive an expression for the omitted variable bias of β̂_1 in terms of the true regression coefficients {β_0, β_1, β_2} and the variances and covariances of Female_i and Bachelors_i. (b) Do you think each of the terms in the expression are positive or negative? Explain why? Combining these, is the omitted variable bias overall positive or negative?
Ameer S.
Suppose you didn’t include one of the important independent variables (x2) on a regression model, and the coefficient of the omitted variable is negative and the covariance between included independent variables(x1) and the omitted variable (x2) is negative. Explain what would happen to the coefficient of x1 in the regression model if x2 is omitted.
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Question 3 If there is omitted variable bias in our model, then: We cannot say that X causes changes in Y. Our estimates are consistent. E[u|X1,X2,...,Xk]=0 There is at least one variable omitted from the model that is correlated with at least one of our Xs. We cannot assume the conditional mean assumption is true. Our estimates are biased. Question 4 For our estimates of the population parameters to be consistent in a multivariable regression model, we need which of the following assumptions to be true? The variance of the error, u, given every value of every X, is constant. There is no perfect multicollinearity. The errors, u, are normally distributed. There is no imperfect multicollinearity. E[u | X1,X2,...,Xk]=0 The sample is randomly selected from the population of interest. There are no large outliers in X1, X2, ..., Xk, or Y. Question 8 What do you conclude from questions 5-7? We cannot reject the null hypothesis at the 5% level because the 95% confidence interval does not contain zero. We do not have enough evidence to conclude that increasing the student-teacher ratio will cause test scores to decrease. We conclude that an increase in the student-teacher ratio has a statistically significant negative relationship with test scores. We conclude that there is no statistically significant relationship between the student-teacher ratio and test scores. We fail to reject the null hypothesis at the 5% level. We can reject the null hypothesis at the 5% level, but we fail to reject at the 1% level. We can reject the null hypothesis at the 5% level. We conclude that increasing the student-teacher ratio will cause test scores to decrease. We can reject the null hypothesis at the 5% level because the 95% confidence interval does not contain zero. Now we also control for expenditures per pupil (Expn) because we think our previous model might have suffered from omitted variable bias (OVB): TestScore=649.6-0.29*STR -0.656*PctEL+3.87*Expn The standard error for beta0hat is 15.5. The standard error for beta1hat is 0.48. The standard error for beta2hat is 0.32. The standard error for beta3hat is 1.59. What can you conclude about OVB? Beta1hat suffered from positive bias in model 1. STR and Expn are positively correlated. Beta1hat suffered from negative bias in model 1. STR and Expn are negatively correlated. STR and Expn are uncorrelated. Beta1hat did not suffer from any bias in model 1.
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