Statistics Homework Question 1: A researcher is interested in whether politically-motivated hiring and firing of civil s

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Statistics Homework Question 1: A researcher is interested in whether politically-motivated hiring and firing of civil servants affects the quality of the educational system. Her argument is that in many settings, politicians have the discretionto hire and fire education personnel (e.g., teachers and headmasters). She is interested in whether, following an election, a change in the ruling political party affects whether teachers are replaced, withpotential subsequent effects on pupils' grades. She has data on a country with two dominant politicalparties (i.e., we can ignore all potential other political parties), and estimates the following specification: + Y = A1 + Aznewi + Azagei+Ei where Yi is the outcome of interest (see below) newi is equal to 1 if school i is located in a district where the ruling political party changes at the election and otherwise agei denotes the average age of students in school i Ei is the error term She estimates two regressions, each with a different outcome of interest: 1. The percentage of teachers that is replaced in school i immediately after an election: Yi 2. The natural log of the average exam result of pupils in school i: In (Y) The researcher starts by estimating this specification by OLS. The results are reported in column 1 (using the percentage of teachers that is replaced as the dependent variable) and column 2 (using thenatural log of schools' average exam results) of Table 1 below: Table 1: OLS estimates of a change in the ruling political party on the percentage of teachers that is replaced (column 1) and on the natural log of schools' average test scores (column 2) (2) Dependent variable: Percent of In(Average teachers replaced schools exam results) newi 8.41 -0.065 (2.37) (0.034) Number of schools 4,182 4,182 Note: Robust standard errors given in parentheses.

a) What is the interpretation of the coefficient of interest A2 in the OLS regression of column (1) and column (2)

b) Explain why we cannot interpret the estimate in column (2) as a causal effect, giving examplesto describe the problem and show your understanding. Based on one of) your example(s), whatdo you expect the direction of the bias to be?