1 Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is kids = Bo + Bjeduc + u, where u is the unobserved error. (i) What kinds of factors are contained in u? Are these likely to be correlated with level of education? (ii) Will a simple regression analysis uncover the ceteris paribus effect of education on fertility? Explain.
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- RQ7. A teacher is trying to predict student test grades (Q). She believes test grades are a function of incoming GPA, hours studying, and hours spent on social media (a distraction). She runs a regression and it produces these coefficients: Variable Coefficient Intercept GPA Hours Studying Social Media 70.0 3.5 2.4 -4.0 For a given student Julian, his GPA is 2.0, he studies 4 hours for the exam, and he spends 6 hours on Facebook. Predict his exam score (round to the nearest whole number).b. The following model is a simplified version of the multiple regression model used by BEST Econometrics Group to study the trade off between time spent sleeping and working to look at other factors affecting sleep: sleep Bo + B₁totwrk + B₂educ + Page + μ₁ where sleep and totwork (total work) are measure in minutes per week and educ and age are measured in years. (i) If adults trade sleep for work, what is the sign of B₁? (ii) What signs do you think ₂ and 3 will have? (iii) Using the data in SLEEP75.RAW, the estimated equation is sleep = 3,638.25-.148totwrk-11.13educ - 2.20age, n = 706, R² = .113 If someone works five hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (iv) Discuss the sign and magnitude of the estimated coefficient on educ (v) Would you say totwrk, educ, and age explain much of the variation in sleep? (vi) What other factors might affect the time spent sleeping? (vii) Are these likely to be correlated with totwrk?Consider the population regression of log earnings [Y;, where Y,= In(Earnings,;)] against two binary variables: whether a worker is married (D₁, where D₁;= 1 if the th person is married) and the worker's gender (D2;, where D₂;= 1 if the th person is female), and the product of the two binary variables Y₁ = Po+B₁D₁+P₂D2i + P3 (D₁¡ × D₂i) + Hi- The interaction term: O A. indicates the effect of being married on log earnings. B. does not make sense since it could be zero for married males. C. allows the population effect on log earnings of being married to depend on gender. D. cannot be estimated without the presence of a continuous variable.
- Suppose we are interested in evaluating the impact on wages of being a college graduate and of residing in California. To this end we define the following dummy variables if college graduate if not college graduate coll = ncoll = if not college graduate if college graduate 1 cali = if residing in California S 1 if not residing in California ncali = if not residing in California if residing in California and for wages denoting yearly wages, we estimate the following model of returns to education wages = B1 coll+ B2ncoll + B3 cali + B4(coll x cali) + e where E[e|coll, cali] = 0. Which parameter or combination of parameters measures the increase in expected wages from obtaining a college degree (comparing to not having a college degree) when residing California? O a. None of the other options is correct O b. Bi – B2 O c. B1 – B2 + ß4 O d. B4 O e. Bi + B3 – ßi – B4 O f. Bi + B4 – ß2 – B4 Clear my choiceEconometrics Thomas Eisensee and David Stromberg wanted to measure how much news coverage of a foreign disaster impacted the amount of disaster relief provided by the U.S. government. They argue that the simple relationship would be biased. Let X = Minutes of News Coverage and Y= Disaster Aid. Choose a variable X2 that could bias the simple relationship. This variable should impact the amount of coverage and impact the amount of aid for reasons other than purely news coverage. Eisensee and Stromberg introduce an instrument Z = During the Olympics. Explain how Z could satisfy the relevant and exogenous criteria. Explain how you could use Z to estimate the impact of X on Y free from X2 bias. Hint: you should mention two stages.Suppose the researcher considers the following model : Wage = Bo+B,Female + u, and runs OLS, using wage data on 250 randomly selected male workers and 280 female workers. The researcher has obtained the estimated equation as Wage = 15 (1.00) 3 Female, R = 0.05. (0.5) In the equation, Wage is measured in dollars per hour, Female is a binary variable that is equal to 1 if the person is a female and O if the person is a male. The numbers in the parentheses are the standard errors of the coefficients. Which Statement is NOT correct? The coefficient of Female, -3.00, is statistically significant at 5%. O The p-value for the test that Ho: B = 0, H : B 0 is less than 0.05. This regression may suffer omitted variable bias. R Since insignificant. is too low, the wage difference between men and women is The researcher can increase R- by including more regressors in the model.
- 46) The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the trade-off between time spent sleeping and working and to look at other factors affecting sleep: sleep = Bo + B₁totwrk + ß₂educ + ß3age +u, where sleep and totwrk (total work) are measured in minutes per week and educ and age are measured in years. (i) If adults trade off sleep for work, what is the sign of f₁? (ii) What signs do you think ₂ and 3 will have? (iii) Using the data in SLEEP75, the estimated equation is sleep = 6,241.15 + 0.211totwrk + 9.22educ + 1.67age n = 211, R² = 0.981 If someone works five more hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (iv) Discuss the sign and magnitude of the estimated coefficient on educ. (v) Would you say totwrk, educ, and age explain much of the variation in sleep? What other factors might affect the time spent sleeping? Are these likely to be correlated with totwrk?In multiple regressions, the correlation coefficient of each independent variable can be measured in addition to the multiple correlation coefficient. How do the values of individual correlation coefficients compare to the value of the multiple correlation coefficient?A. B. Consider data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 1,388 births: bwght = 119.772 (0.572) n = 1,388, 0.514 cigs (0.091) R² = 0.0227, where standard errors are shown in parenthesis. What percent of the variation in birth weight is explained by cigs? What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.
- 3. Boyoung is writing a paper about the effect of Sunday liquor sales on drunk driving. She has panel data on which states allow liquor to be sold on Sunday in which years and wishes to estimate a difference-in-differences model. She writes the following regression equation: Year DUIRate;; = atate +a? + BTreatmentt +yControl;t + Eit i Which of the following changes does Boyoung need to make? a) She should include a constant in the regression equation. b) She should not include controls because they're already accounted for by fixed effects. c) She should include a time trend instead of time-fixed effects. d) None of the above are changes she needs to make.13. Collinearity in a multiple regression analysis Suppose you want to examine the effects of a training program on future earnings using the following model: earn98= 4.64 +2.376train +0.371earn96 +0.366educ- 1.86 age +2.534 married (1.14) (0.43) (0.016) (0.062) (0.013) (0.4) where earn 98- 1998 earnings, in thousands of dollars train -1 if the individual participated in the training program, and =0 otherwise earn 96- 1996 earnings, in thousands of dollars educ years of education age = age, in years married-1 if the individual is married, and -0 otherwise Suppose that there is a high degree of correlation (but not perfect) between earnings in 1996, education, age, and marital status. True or False: We should be concerned about this high degree of correlation because it affects our ability to reliably estimate the impact of the training program on 1998 earnings, T. True FalseQuantile regression (QR) is different from OLS in that: a. QR estimates marginal effects at the mean values of the dependent variables. b. QR does not estimate marginal effects at the mean values of the dependent and independent variables. c. QR minimizes the sum of squared residuals to obtain the coefficient estimates. d. QR only uses the data below the quantile where the quantile regression is being estimated.