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ECON 306 - Homework 4

A solved homework set for ECON 306 covering economic principles.

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    ECON 306 - Homework 4 The following two problems will require a lot of calculations in. It will generate many pages of output. Here is how your should organize it. The first pages should contain your answers to all the questions, along with showing any key algebraic equations or explanations you need to use along the way. After that, include a printout of the output from the regressions you executed in support of your answers. Highlight any numbers in this output that you used in the first section. (You are encouraged to save pape r here , you may print this section with a small font, double - sided and/or with 2 - up format.) Last, include a copy of the DO file that contains the commands you asked STATA to execute. Be sure you organize these in a way that will be clear to the reader.

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    1) In this exercise we will examine whether a teacher’s physical attractiveness has any impact on student course evaluations. The dataset to use is called teaching ratings, and a description of the variables is available as well. You can access these through the course website. Use an α =.05 for hypothesis testing. We’ll first examine whether our control variables se em to have any predictive power for ratings. a.) We’ll start with some basic dummy variable regressions to test for differences between groups: 1) Regress course_ eval on minority. Report the coefficients and p - values. Do minorit y instructors have significantly different course evaluations compared to non - minorities? 𝒄𝒐𝒖𝒓𝒔𝒆 − 𝒆𝒗𝒂𝒍 = 𝟒 . 𝟎𝟏 − 𝟎 . 𝟏𝟐𝟑𝟏 𝒎𝒊𝒏𝒐𝒓𝒊𝒕𝒚 , 𝒑 − 𝒗𝒂𝒍𝒖𝒆 = 𝟎 . 𝟎𝟗𝟗 So being minority is not significant in evaluation result at 5% significance level. (Although it is significant and negative at 10% level) 2) Regress course_eval on female. Report the coefficients and p - values. Do females have significantly different course evaluations from males? 𝒄𝒐𝒖𝒓𝒔𝒆 − 𝒆𝒗𝒂𝒍 = 𝟒 . 𝟎𝟔 − 𝟎 . 𝟏𝟔𝟖 𝒇𝒆𝒎𝒂𝒍𝒆 , 𝒑 − 𝒗𝒂𝒍𝒖𝒆 = 𝟎 . 𝟎𝟎𝟏 Yes, Being female will decrease the evaluation score by 0.168, it is significant at 1% level. 3) Run a final regression to test whether the effect of being a minority changes depending on whether the person is female. Report the coefficients and p - values. Can you reject the hypothesis of no effect? 𝒄𝒐𝒖𝒓𝒔𝒆 − 𝒆𝒗𝒂𝒍 = 𝟒 . 𝟎𝟕 − 𝟎 . 𝟏𝟔 𝒇𝒆𝒎𝒂𝒍𝒆 − 𝟎 . 𝟎𝟗𝟔𝟖 𝒎𝒊𝒏𝒐𝒓𝒊𝒕𝒚 , 𝒑 − 𝒗𝒂𝒍𝒖𝒆 : 𝒇𝒆𝒎𝒂𝒍𝒆 : 𝟎 . 𝟎𝟎𝟐 After controlling for being minority, being female still has a significant negative impact on evaluation. Yes, you can reject the hypothesis of no effect. b.) Now regress course_eval on beauty, age, age^2 [you’ll need to create this] , nnenglish, female, minority, onecredit. Are any variables not statistically significant? Which? This is Model 1. 𝑴𝒐𝒅𝒆𝒍 𝟏 : 𝒄𝒐𝒖𝒓𝒔𝒆 − 𝒆𝒗𝒂𝒍 = 𝜷 𝟎 + 𝜷 𝟏 𝒃𝒆𝒂𝒖𝒕𝒚 + 𝜷 𝟐 𝒂𝒈𝒆 + 𝜷 𝟑 𝒂𝒈𝒆𝒔𝒒 + 𝜷 𝟒 𝒏𝒏𝒆𝒏𝒈𝒍𝒊𝒔𝒉 + 𝜷 𝟓 𝒇𝒆𝒎𝒂𝒍𝒆 + 𝜷 𝟔 𝒎𝒊𝒏𝒐𝒓𝒊𝒕𝒚 + 𝜷 𝟕 𝒐𝒏𝒆𝒄𝒓𝒆𝒅𝒊𝒕 age and age^2 are not significant. nnenglish and minority are significant at 5% level but not at 1% level. Use Model 1 to answer the following: 1) C alculate an F - test for the hypothesis that age and age^2 jointly have no effect on course_eval . You can execute this test however you prefer . 𝑭 ( 𝟐 , 𝟒𝟓𝟓 ) = 𝟎 . 𝟕𝟑 The answer is not significant, so we can not reject that age and age^2 have no effect on course - eval.

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