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MPs For Sale? Estimating Returns to Office in Post-War British Politics
Unformatted Document Text:  without our full set of covariates (including schooling, university education, occupation, gender, year of birth, and year of death). Just as in a randomized experiment, we expect the inclusion of covariates to have only a small effect on the estimate of τ because, in the close neighborhood of the threshold, all observed and unobserved covariates should be independent of W . Covariates may help to eliminate some residual bias that is the result of the inclusion of observations further away from the threshold, and they may improve precision to the extent that they are predictive of the outcome. Our RD estimates, presented in Table 4, mirror the graphical and matching results presented above: we find that Conservatives roughly doubled their wealth by winning a seat in Parliament, while Labourites did not financially gain from office. We again reject the null at conventional levels but the standard errors, as expected, are slightly larger than in the matching analysis because the RD approach focuses on the neighborhood of the threshold, where there are fewer observations. Also as might be expected, the inclusion of covariates does not change the substantive conclusions. C. Robustness Tests for RD Estimation C.1. Test for Wealth Jumps at Non-discontinuity Points Following the proposal by Imbens and Lemieux (2007), we test for jumps in wealth at points other than the threshold at which office was assigned. We produce RD estimates at several points along the range of the vote share variable, in each case limiting analysis to either the winning or losing candidates. 23 Figure 7 compares these placebo effect estimates with our estimate of the effect of winning office on wealth. (We focus on Conservative candidates, since we did not find an effect for Labour.) The upper panel presents the point estimates for each of the placebo runs contrasted with the estimate at the true threshold; the lower panel presents the corresponding t-values. The true effect estimate clearly stands of bandwidth, although obviously the standard errors tend to increase as the bandwidth is decreased dueto the smaller number of observations. For example, for the Conservatives the estimated treatment effect(including all covariates) is .98 (.64) when we use half the optimal threshold (i.e. 7.5 percentage points)and .54 (.28) when double the optimal bandwidth (i.e. 30 percentage points) is used. 23 By focusing on each subsample separately, we follow Imbens & Lemieux (2007, pg. 27), who note that otherwise our regression function would assume continuity at a point where we know there is a break. 17

Authors: Eggers, Andy. and Hainmueller, Jens.
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without our full set of covariates (including schooling, university education, occupation,
gender, year of birth, and year of death). Just as in a randomized experiment, we expect
the inclusion of covariates to have only a small effect on the estimate of τ because, in
the close neighborhood of the threshold, all observed and unobserved covariates should be
independent of W . Covariates may help to eliminate some residual bias that is the result
of the inclusion of observations further away from the threshold, and they may improve
precision to the extent that they are predictive of the outcome.
Our RD estimates, presented in Table 4, mirror the graphical and matching results
presented above: we find that Conservatives roughly doubled their wealth by winning a
seat in Parliament, while Labourites did not financially gain from office. We again reject
the null at conventional levels but the standard errors, as expected, are slightly larger than
in the matching analysis because the RD approach focuses on the neighborhood of the
threshold, where there are fewer observations. Also as might be expected, the inclusion of
covariates does not change the substantive conclusions.
C. Robustness Tests for RD Estimation
C.1.
Test for Wealth Jumps at Non-discontinuity Points
Following the proposal by Imbens and Lemieux (2007), we test for jumps in wealth at
points other than the threshold at which office was assigned. We produce RD estimates at
several points along the range of the vote share variable, in each case limiting analysis to
either the winning or losing candidates.
23
Figure 7 compares these placebo effect estimates
with our estimate of the effect of winning office on wealth. (We focus on Conservative
candidates, since we did not find an effect for Labour.) The upper panel presents the point
estimates for each of the placebo runs contrasted with the estimate at the true threshold;
the lower panel presents the corresponding t-values. The true effect estimate clearly stands
of bandwidth, although obviously the standard errors tend to increase as the bandwidth is decreased due
to the smaller number of observations. For example, for the Conservatives the estimated treatment effect
(including all covariates) is .98 (.64) when we use half the optimal threshold (i.e. 7.5 percentage points)
and .54 (.28) when double the optimal bandwidth (i.e. 30 percentage points) is used.
23
By focusing on each subsample separately, we follow Imbens & Lemieux (2007, pg. 27), who note that
otherwise our regression function would assume continuity at a point where we know there is a break.
17


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