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1. There has always been much interest in the effect of school size on student performance. One claim is that, everything else being equal, students at smaller schools fare better than those at larger schools. This hypothesis is assumed to be true even after accounting for differences in class sizes across schools. The data set meap93 in the wooldridge package contains data on 408 high schools in Michigan for the year 1993. It contains the following variables. lnchprg percentage of students in school lunch program enroll school enrollment staff staff per 1000 students expend expenditure per student, $ salary average teacher salary, $ benef its average teacher benefits, $ droprate school dropout rate, percentage gradrate school graduation rate, percentage math10 percentage of students passing MEAP math sci11 percentage of students passing MEAP science totcomp salary + benefits ltotcomp log(totcomp) lexpend log(expend) lenroll log(enroll) lstaff log(staff) bensal benefits/salary lsalary log(salary) We can use these data to test the null hypothesis that school size has no effect on standardized test scores against the alternative that size has a negative effect. Performance is measured by the percentage of students receiving a passing score on the Michigan Educational Assessment Program (MEAP) standardized tenth-grade math test (math10). School size is measured by student enrollment (enroll). The following model controls for two other factors, average annual teacher compensation (totcomp) and the number of staff per one thousand students (staff). Teacher compensation is a measure of teacher quality, and staff size is a rough measure of how much attention students receive. math10 = ?0 + ?1 totcomp + ?2 staff + ?3 enroll + u. (a) [4 marks] Estimate the model above and write down the estimated equation. (b) [3 marks] Interpret all the slope parameters. (c) [3 marks] Test the null hypothesis that school size has no effect on performance against the alternative that size has a negative effect. 1 I suggest you use R Markdown as I explained in the lecture in Week 5. Another way of automatically saving the output of an R script (together with the commands) is to use the command txtStart("name.txt") at the beginning of your R code and the command txtStop() at the end of your R code. This creates a file called name.txt in your specified folder, which you can edit to enter your answers. You need to load the package TeachingDemos to use these commands. (d) [6 marks] Now estimate the model where all independent variables are in logarithmic form: math10 = ?0 + ?1 log(totcomp) + ?2 log(staff) + ?3 log(enroll) + u. Interpret all the slope parameters. (e) [2 marks] Test the same hypothesis in part (c) using the model estimated in part (d). What do you conclude? (f) [2 marks] Test for heteroskedasticity in the model in part (d). Obtain the robust standard errors. (g) [2 marks] How does using the robust standard errors change your conclusion in part (e)? (please use r studio program and code ) please use quickly

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Umar Sohail Qureshi

Numerade educator

This question makes use of the data set fringe in the wooldridge package. It contains 616 observations with information on individuals’ earnings, receipts of fringe benefits, personal characteristics and work place characteristics. The data were used to examine the trade off between fringe benefits and wages. The variables include: annearn: =annual earnings, $ hrearn: hourly earnings, $ exper: years work experience age :: age in years depends: number of dependents married: 1 if married tenure: years with current employer educ: years of schooling male: 1 if male white: 1 if white vacdays: $ value of vacation days sicklve: $ value of sick leave insur: $ value of employee insurance pension: $ value of employee pension annbens: vacdays+sicklve+insur+pension beratio: benefit ratio= annbens/annearn peratio: pension/annearn nrtheast : 1 if live in northeast nrthcen: 1 if live in north central south: 1 if live in south union: 1 if union member (a) [1 mark] For what percentage of the workers in the sample is pension equal to zero? (b) [6 marks] Define a binary variable, say pend, equal to unity if pension is greater than zero. Then estimate a linear probability model relating pend to exper, age, age2 , tenure, educ, depends, married, white, and male. Interpret the coefficients on tenure and educ. Which variables are statistically significant? In particular, does age have a statistically significant effect? (c) [2 marks] What is the observed average probability that an individual receives a pension? What is the predicted average probability that an individual receives a pension? (d) [2 marks] Obtain the predicted probability that an individual receives a pension for all the indi viduals in the sample and provide a histogram of the distribution of the predicted probabilities. Is there a problem with these predictions? (e) [2 marks] Does the probability of receiving a pension increase by age? Explain. (f) [6 marks] Now estimate the model by probit. Determine and interpret the average marginal effects of age and experience. Are they statistically significant? How do they compare to the marginal effects from the linear model? (g) [4 marks] Consider two individuals. Individual 1 is 35 years old male, unmarried white with no dependents and 10 years of education, and has 10 years of experience. Individual 2 is a 55-year old white male, has 30 years of experience, 15 years of education, and is married with no dependents. Both individuals have been with their current employer for 8 years. What are the predicted prob abilities of receiving pension for these two women if the probit model is used? What if the linear probability is used?

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