Based On Bordignon et al (2016)

Summary

Main Questions:

  1. How does the runoff system differ from the single round system?

  2. Do the number of candidates differ across election types? How?

  3. What kinds of effects do different election types have on policy volatility?

Main Findings:

Ultimately find that runoff elections have more candidates and that policy volatility is lower under runoff elections. This is likely due to the fact that runoffs allow extremist parties a chance to stay true to their platform without having to compromise to conform to a specific party and that all parties are visible in the first round of the election.

Spread of cities with more and less than 15,000 people used to determine election type

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.0000  0.0000  0.3098  1.0000  1.0000

Estimate number_candidates = b0 + b1T + b2pop_census + e

## 
## Call:
## lm(formula = number_candidates ~ T + pop_census, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.2943 -1.0496 -0.2291  0.4946  9.4764 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.899e+00  3.570e-01   8.120 8.02e-16 ***
## T           1.196e+00  1.703e-01   7.019 3.04e-12 ***
## pop_census  6.023e-05  2.929e-05   2.056   0.0399 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.856 on 2024 degrees of freedom
## Multiple R-squared:  0.1234, Adjusted R-squared:  0.1226 
## F-statistic: 142.5 on 2 and 2024 DF,  p-value: < 2.2e-16

Based on this output, there does appear to be a difference in the number of people who run for office in runoff elections, on average, relative to the number of people who run for office in single round elections. There tend to be more candidates in runoff elections versus in single round elections.

Scatterplot

The coefficient on T from above measures the gap between the two lines at the threshold and b1 measures the slope of the two lines (red and blue) in this scatterplot.

Histograms

Based on these histograms it appears that sorting may have been an issue in 1995, but not in 2004. In 1995, it seems that there is a significant drop in cities with a population between 14,000 to 15,000 and a large jump back to 15,000 to 16,000 and slowly decreases. There seems to be a sorting issue potentially in 1995. In 2004, there is no significant jump at the threshold and no weird patterns going on so sorting does not seem to be an issue in this year.

Testing an Omitted Variable

## 
## Call:
## lm(formula = number_parties ~ T + pop_census, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.0494 -1.7120 -0.5976  1.3538 10.2297 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.909e+00  4.756e-01   6.117 1.14e-09 ***
## T           2.829e+00  2.269e-01  12.465  < 2e-16 ***
## pop_census  6.581e-05  3.903e-05   1.686   0.0919 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.473 on 2024 degrees of freedom
## Multiple R-squared:  0.2592, Adjusted R-squared:  0.2585 
## F-statistic: 354.1 on 2 and 2024 DF,  p-value: < 2.2e-16

Based on this output, I am concerned about the RD model estimated above. Because the potentially omitted variable does have a significant p-value on the T variable, we know this potentially omitted variable does jump at the threshold and is a concern for discontinuous error.