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, with potential 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: where Yi new; age: Ei Y = A+ Amewi + Aaget + Ei is the outcome of interest (see below) is equal to 1 if school i is located in a district where the ruling political party changes at the election and 0 otherwise new denotes the average age of students in school i 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) Dependent variable: Percent of teachers replaced 8.41 (2.37) Number of schools 4,182 Note: Robust standard errors given in parentheses. (2) In(Average schools exam results) -0.065 (0.034) 4,182 c) To estimate the causal effect of a change in the political party on students' average test scores, the researcher exploits the fact that a change in the political party occurs when the vote share of the new party (denoted by VSNEW) exceeds that of the incumbent (VSINCUMBENT); i.e. when VSNEW > VSINCUMBENT. She uses a regression discontinuity design to estimate the following regression: Y = B + Bchange: + Bagei + f(Vote Margin) + Ui, where changet is a dummy equal to 1 if (VSNEW> VSINCUMBENT) in school i's district, and 0 otherwise (note that this is in fact the same as the variable new; above, but now described in terms of vote shares) Vote Margin is defined as (VSNEW - VSINCUMBENT U is the error term with Y; and age; defined above. Is this a sharp or fuzzy regression discontinuity design? Explain your answer. d) Explain the intuition behind this regression discontinuity design. Also discuss the assumptions necessary to estimate the causal effect of political party turnover on average students' exam results (i.e., using students' test scores as the outcome of interest). Are the assumptions likely to hold? e) Another researcher is interested in the effect of replacing teachers in schools on student achievement (i.e., not the effect of a change in the ruling political party). He argues that regressing student test scores on a dummy variable equal to 1 if the school changed at least one of their teachers and 0 otherwise would not allow them to estimate a causal effect, since the dummy is endogenous. Suggest an alternative way to estimate the effect of interest using a regression discontinuity design. Write out your equation(s) and mention briefly how this can be estimated. Finally, discuss the validity of this approach.