### Endogeneity and Bias Questionnaire

Problem 1 Endogeneity & Bias The ACT (an abbreviation of American College Testing) is a standardized test used for college admissions in the United States. Suppose you are interested in whether ACT preparation courses improve ACT scores. Consider the following model: ???? = ?? + ?? ???????????? + ?? , where ??????????? measures the number of hours of ACT preparation courses and ??? is ACT scores. Each student is denoted by the subscript ?. ̂ ? = ?? and ? ̂ ? = ?. ?. Suppose you estimate ? a. b. c. d. What is the dependent variable? What is the independent variable? (4 points) ̂ ? = ?? mean? (4 points) What does ? ̂ ? = ?. ? mean? (4 points) What does ? Describe a scenario where the independent variable is endogenous. (4 points) Problem 2 Hypothesis Testing Suppose you are interested in the effect of neighborhood crime incidents on high school graduation rates. You run the following regression model: ??????????? = ?? + ?? ?????? + ?? You would like to test whether the neighborhood crime incidents have a statistically significant effect on high school graduation rate at the 5% level of significance (α = 0.05). ̂? = −?. ?? and ??(? ̂? ) = ?. ???.

You estimate the model and find that ? a. b. c. d. e. f. Write down the null hypothesis and alternative hypothesis. (4 points) ̂? . (5 points) Calculate the ? ????????? of ? What is the critical value of the ? ????????? for the 5% level of significance? (2 points) Calculate the 95% confidence interval for the coefficient on ?????? (6 points) Based on your answers to the questions b, c, and d, do you reject or fail to reject the null hypothesis you defined in question a? Justify your answer. (5 points) ̂? statistically significant at the 5% level? (3 points) Is ? Problem 3 Stata Output Analysis Suppose a study investigates the causal effect of education on wages. Table 1 reports the results of an OLS regression of wages (wage per hour in dollars) on education (years in education). Table 1 Source SS df MS Model Residual 18904467 191011981 1 3,015 18904467 63353.8909 Total 209916448 3,016 69600.9444 wage Coef. education _cons 29.56644 183.9342 a. b. c. d. e. f. g. Std. Err. 1.711605 23.15976 t 17.27 7.94 Number of obs F(1, 3015) Prob > F R-squared Adj R-squared Root MSE = = = = = = 3,017 298.39 0.0000 0.0901 0.0898 251.7 P>|t| [95% Conf. Interval] 0.000 0.000 26.21041 138.5237 32.92247 229.3447 How would you write this relationship using the Core Model? (4 points) ̂? ? {2 points) What is the value for ? ̂? ? (2 points)

What is the standard error of ? What is the R squared for the model? (2 points) ̂? at the 5% level of significance? (2 points) What is the ? ????????? for ? What is the 95% confidence interval? (2 points) Explain what the regression output tells you about the effect of education on wages. In ̂? . (5 points) other words, interpret the meaning of the slope coefficient estimate ? h. Is this effect of education on wages statistically significant at the 5% level of significance? Justify your answer. (4 points) i. Use the ? ????? approach to determine whether the effect of education on wages is statistically significant at the 5% level of significance. (3 points)

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