代写MPA 2040 Problem Set #1 Summer 2024代做迭代

MPA 2040

Problem Set #1

Summer 2024

QUESTION 1 - INCUMBENCY ADVANTAGE

One of the most remarkable features of electoral politics in the United States is the high degree of electoral success of incumbent candidates. For example, for the last five decades, conditional on running for re-election, incumbent candidates have won elections to the House of Representatives about 90 percent of the time. This phenomenon has prompted much empirical research aimed to estimate the “incumbency advantage,” that is, the causal effect of incumbency on the vote share obtained by a candidate.

Suppose that you have data on every two-candidate race (with both a Democrat and Republican running) to the House of Representatives for some period of time. You want to estimate the “incumbency advantage” for Democratic candidates.

For each of the following estimators, describe possible sources of selection biases. Explain which direction you would expect the results to be biased and why.

(a) “Vote Share Difference”—the difference in average vote shares between Democratic incumbents and Democratic non-incumbents.

(b) “Sophomore Surge”—among those Democratic candidates who were elected to office and who run for a second term immediately after the first term, the difference in average vote shares between the two elections. (That is, the average vote share gains for freshmen winners who run again in the following election.)

(c) “Retirement Slump”—in districts where the Democratic candidates retire, the difference in average vote shares obtained by the retiring Democratic incumbents and the incoming Democratic candidates (who clearly are not incumbents) in the current election.

QUESTION 2 - EFFECT OF TVs ON LIFE EXPECTANCY

(a) Below are the results of a regression of life expectancy in years (lifeex) on number of televisions per hundred people (tv). Interpret the coefficient on tv.

. reg lifeex tv, robust

Linear regression                               Number of obs     =        119

                                                F(  1, 117)       =      82.40

                                                Prob > F          =     0.0000

                                                R-squared         =     0.5370

                                                Root MSE          =     7.1945

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             |               Robust

      lifeex |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

          tv |   .4155946   .0457829     9.08   0.000      .324924    .5062652

       _cons |   57.31097   1.074192    53.35   0.000     55.18359    59.43836

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(b) Below are the results of a regression of life expectancy (lifeex) on number of televisions per hundred people (tv) and income per capita (gdp). Interpret the coefficient on tv.

. reg lifeex tv gdp, robust

Linear regression                               Number of obs     =        119

                                                F(  1, 117)       =     100.03

                                                Prob > F          =     0.0000

                                                R-squared         =     0.6027

                                                Root MSE          =     6.6931

------------------------------------------------------------------------------

             |               Robust

      lifeex |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

          tv |   .1734937   .0592164     2.93   0.004     .0562081    .2907793

         gdp |   .0008514   .0001448     5.88   0.000     .0005648    .0011381

       _cons |   56.08268   1.015129    55.25   0.000     54.07208    58.09327

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(c) How and why does your interpretation of the coefficient on tv change? Make sure you explain why the coefficient on tv changes in the direction it does both (i) in a technical language, and (ii) in a way that a policymaker not well versed in statistics can understand.

QUESTION 3 - PREDICTIVE POWER OF THE ACT EXAM

In a paper titled “Improving College Performance and Retention the Easy Way: Unpacking the ACT Exam,” Bettinger et al. find that the English and Math sections of the ACT are more strongly associated with first-year college GPAs compared to the Reading and Science sections. Their results suggest that colleges’ emphasis on the ACT Composite score (which averages the scores for the four sections together) is inefficient.

In this question, we will analyze the results in Column (2) of Table 2 in their paper, which contains estimates of , , , and  from Equation (1) in the paper. Note that an estimate of  is not provided in the table. We will also analyze the results in Table 2 Column (1). 

(a) Write a regression corresponding to Column (1) in the table above. Denote the constant term by  and the coefficient on the independent variable by .

(b) Assume . According to Column (2), what is the predicted first-year college GPA for a student with a Math score of 35, English score of 34, Reading score of 31, and Science score of 28?

(c) Assume . According to Column (1), what is the predicted first-year college GPA for a student with a Math score of 35, English score of 34, Reading score of 31, and Science score of 28?

(d) Assume . According to Column (2), what is the predicted first-year college GPA for a student with a Math score of 28, English score of 28, Reading score of 36, and Science score of 36?

(e) Assume . According to Column (1), what is the predicted first-year college GPA for a student with a Math score of 28, English score of 28, Reading score of 36, and Science score of 36?

(f) Compare your answer to (c) with your answer to (e). Compare your answer to (b) with your answer to (d).

QUESTION 4 - CLASSROOM SEATING

In this question, we will consider the relationship between where students choose to sit and their test scores.

Define “front” as a binary variable that is equal to 1 if a student sits in the front of the classroom, and equal to 0 if a student does not sit in the front of the classroom.

Define “male” as a binary variable that is equal to 1 if a student identifies as male, and equal to 0 if a student does not identify as male.

Define “front X male” as the product of the two binary variables defined above. Note that this is also a binary variable.

Here is the result of a regression, where the dependent variable is test score.