Online Appendix
As discussed above, we might be concerned that the conclusions of the analysis are somehow
affected by choices about how to deal with sample coverage. Figures 2a and 2b illustrate the
distributions of the t-statistics under alternative strategies for restricting the estimates in the
sensitivity analysis, using the Polity scaled measure. The solid blue line (“N 80+”) is the
distribution from the basic analysis. The dotted red line shows the distribution if we include
models that have less than 80 observations (“All estimates”), the dotted green line shows only
models with more than 100 observations (“N 100+”), and the dotted yellow line shows only
models with more than 120 observations (“N 120+”). The distributions do not change appreciably
for most variables. The “All estimates” distributions are slightly different for the sec.pupils,
prim.pupils, physicians and beds variables, because these measures have poor coverage, but the
substantive conclusion does not change. When we further restrict the densities to models with a
high number of observations, more than 100 or 120, the relationship between democracy and
secondary enrollment rates (sec.enroll) appears more positive, but many of the other variables
fare worse— the primary completion rate (prim.comp), water access (water), sanitation access
(sanitation), physicians (physicians), the infant mortality rate (infmort), the death rate (death),
and life expectancy (lifeexpect). For these seven variables, the estimates prove less likely to be
significant in the expected direction. This gives further reason to doubt the presence of a
democratic advantage.
Figure 2a: Sensitivity to Sample Coverage Approaches – Education Outcomes (Polity)
−2
0
2
−2
0
2
Density
4
t statistic
t statistic
Pupil Teacher Ratio Secondary (−)
(sec.pupils)
Pupil Teacher Ratio Primary (−)
(prim.pupils)
Density
t=−1.64
−4
−2
0
t statistic
2
4
t=1.64
−4
−2
0
2
4
t statistic
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
All estimates
N 80+
N 100+
N 120+
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
t=1.64
−4
4
Completion Rate Primary (+)
(prim.comp)
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
t=1.64
−4
Density
Enrollment Rate Secondary (+)
(sec.enroll)
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
Enrollment Rate Primary (+)
(prim.enroll)
t=−1.64
−4
−2
0
2
4
t statistic
Note: Figure summarizes distribution of estimated t-statistics from cross-section global sensitivity analysis
for five education public good measures from 1975-2009, using the Polity measure of democracy. The
straight dotted line represents the threshold necessary to reject the null of no effect at the .05 level with a
one-sided test. The figure illustrates the robustness of the findings across different sample coverage
approaches. All models employ OLS with robust standard errors. The predicted sign of the democratic
advantage hypothesis is shown in parenthesis.
Figure 2b: Sensitivity to Sample Coverage Approaches – Health Outcomes (Polity)
0
2
2
Density
−4
4
−2
0
t statistic
DPT Immunization (+)
(dpt.im)
Physicians (+)
(physicians)
Beds (+)
(beds)
−2
0
2
−4
4
Density
t=1.64
−2
0
2
−2
0
2
t statistic
t statistic
t statistic
Infant Mortality Rate (−)
(infmort)
Death Rate (−)
(death)
Life Expectancy (+)
(lifeexpect)
−2
0
t statistic
2
4
Density
t=−1.64
−4
−2
0
t statistic
2
4
4
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
t=−1.64
All estimates
N 80+
N 100+
N 120+
4
t=1.64
−4
4
2
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
0.0 0.1 0.2 0.3 0.4 0.5 0.6
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
t=1.64
t statistic
All estimates
N 80+
N 100+
N 120+
−4
−2
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
−4
4
t=1.64
−4
t=1.64
All estimates
N 80+
N 100+
N 120+
t statistic
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
−2
Measles Immunization (+)
(measles.im)
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
t=1.64
−4
Density
Sanitation Access (+)
(sanitation)
All estimates
N 80+
N 100+
N 120+
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
Water Access (+)
(water)
t=1.64
−4
−2
0
2
4
t statistic
Note: Figure summarizes distribution of estimated t-statistics from cross-section global sensitivity analysis
for nine health public good measures from 1975-2009, using the Polity measure of democracy. The straight
dotted line represents the threshold necessary to reject the null of no effect at the .05 level with a one-sided
test. The figure illustrates the robustness of the findings across different sample coverage approaches. All
models employ OLS with robust standard errors. The predicted sign of the democratic advantage
hypothesis is shown in parenthesis.
Increasingly, analysts are employing imputation procedures to deal with the missing data
problem. Instead of restricting the pool of estimates based on sample coverage, an alternative
approach is to impute the missing data and rerun the analysis on the imputed dataset. In line with
the recommendations of Honaker, King, and Blackwell (2011), I run an imputation model using
the Amelia II R package that accounts for the time series properties of the data. All dependent and
independent variables included in the analysis were included in the imputation model. In addition,
the imputation model includes polynomials of time (k=2) that are allowed to interact with country
fixed effects, which allows the temporal patterns in the data to vary across the different crosssectional units.1
The results of this exercise are shown in Figures 3a and 3b, which compare the results
using the Polity variable (with no lags) with listwise deletion (the standard approach in this
literature) and imputation. We can see that using imputed data does not appreciably change the
results; the distributions tightly overlap across the two approaches. The evidence in favor of the
“democratic advantage” does improve slightly for some variables— notably prim.enroll,
sec.enroll, water, sanitation, and lifeexpectancy— but gets worse for others – like sec.pupils,
prim.pupils, death, and physicians. Overall, the distributions of the estimates do not seem
sensitive to the different missing data approaches.
Because of the time intensity of running the sensitivity analysis (the code takes more than one
week to run), the analysis here relies on a single imputation (m=1) rather than multiple
imputations (generally m=5). Note that this practice effectively overstates the certainty in the
estimates, which will make us more likely to find significant results.
1
Figure 3a: Sensitivity to Listwise Deletion or Imputation – Education Outcomes (Polity)
−2
0
2
−2
0
2
Density
4
t statistic
t statistic
Pupil Teacher Ratio Secondary (−)
(sec.pupils)
Pupil Teacher Ratio Primary (−)
(prim.pupils)
Density
t=−1.64
−4
−2
0
t statistic
2
4
t=1.64
−4
−2
0
2
4
t statistic
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Imputation
Listwise Deletion
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
t=1.64
−4
4
Completion Rate Primary (+)
(prim.comp)
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
t=1.64
−4
Density
Enrollment Rate Secondary (+)
(sec.enroll)
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
Enrollment Rate Primary (+)
(prim.enroll)
t=−1.64
−4
−2
0
2
4
t statistic
Note: Figure summarizes distribution of estimated t-statistics from cross-section global sensitivity analysis
for five education public good measures from 1975-2009, using the Polity measure of democracy. The
straight dotted line represents the threshold necessary to reject the null of no effect at the .05 level with a
one-sided test. All models employ OLS with robust standard errors. The predicted sign of the democratic
advantage hypothesis is shown in parenthesis.
Figure 3b: Sensitivity to Listwise Deletion or Imputation – Health Outcomes (Polity)
0
2
2
Density
−4
4
−2
0
2
t statistic
DPT Immunization (+)
(dpt.im)
Physicians (+)
(physicians)
Beds (+)
(beds)
−2
0
2
−4
4
Density
t=1.64
−2
0
2
t=1.64
−4
4
−2
0
2
t statistic
t statistic
Infant Mortality Rate (−)
(infmort)
Death Rate (−)
(death)
Life Expectancy (+)
(lifeexpect)
−2
2
4
Density
t=−1.64
−4
−2
0
t statistic
2
4
4
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
0
t statistic
0.0 0.1 0.2 0.3 0.4 0.5 0.6
t=−1.64
Imputation
Listwise Deletion
4
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Imputation
Listwise Deletion
t statistic
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
t=1.64
t statistic
t=1.64
−4
−2
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
−4
4
Imputation
Listwise Deletion
−4
t=1.64
Imputation
Listwise Deletion
t statistic
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
−2
Measles Immunization (+)
(measles.im)
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
t=1.64
−4
Density
Sanitation Access (+)
(sanitation)
Imputation
Listwise Deletion
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
Water Access (+)
(water)
t=1.64
−4
−2
0
2
4
t statistic
Note: Figure summarizes distribution of estimated t-statistics from cross-section global sensitivity analysis
for nine health public good measures from 1975-2009, using the Polity measure of democracy. The straight
dotted line represents the threshold necessary to reject the null of no effect at the .05 level with a one-sided
test. All models employ OLS with robust standard errors. The predicted sign of the democratic advantage
hypothesis is shown in parenthesis.
Figures 4a and 4b show the “sensitivity of the sensitivity analysis” to the use of different binary
democracy indicators, specifically the measures developed by Cheibub, Gandhi and Vreeland
(2011) and Geddes, Wright, and Franz (2012). Interested readers are encouraged to read the GWF
codebook
(http://sites.psu.edu/dictators/wp-content/uploads/sites/12570/2014/06/GWF-
Codebook.pdf) to understand the sources of various discrepancies between the two. In total, about
300 country-year observations are coded differently between the two datasets in the analysis
period for this paper.
It turns out that the non-relationship between regime type and public good provision does
not appear to be the result of reliance on the GWF data. Figures 4a and 4b show the distributions
of t-statistics (only the contemporaneous models) across the GWF and CGV measures. There are
very few noticeable differences. The CGV distributions appear slightly more favorable to the
“democratic advantage” hypothesis, but they still tend to be centered at zero (or on the wrong side
of zero).
Figure 4a: Comparison of CGV and GWF – Education Outcomes
−2
0
2
−2
0
2
Density
4
t statistic
t statistic
Pupil Teacher Ratio Secondary (−)
(sec.pupils)
Pupil Teacher Ratio Primary (−)
(prim.pupils)
Density
t=−1.64
−4
−2
0
t statistic
2
4
t=1.64
−4
−2
0
2
4
t statistic
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
CGV
GWF
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
t=1.64
−4
4
Completion Rate Primary (+)
(prim.comp)
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
t=1.64
−4
Density
Enrollment Rate Secondary (+)
(sec.enroll)
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
Enrollment Rate Primary (+)
(prim.enroll)
t=−1.64
−4
−2
0
2
4
t statistic
Note: Figure summarizes distribution of estimated t-statistics from cross-section global sensitivity analysis
for five education public good measures from 1975-2009, comparing the GWF and CGV measures of
democracy. Only estimates from the contemporaneous model are shown. The straight dotted line represents
the threshold necessary to reject the null of no effect at the .05 level with a one-sided test. All models
employ OLS with robust standard errors. The predicted sign of the democratic advantage hypothesis is
shown in parenthesis.
Figure 4b: Comparison of CGV and GWF – Health Outcomes
0
2
2
Density
−4
4
−2
0
t statistic
DPT Immunization (+)
(dpt.im)
Physicians (+)
(physicians)
Beds (+)
(beds)
−2
0
2
−4
4
Density
t=1.64
−2
0
2
t=1.64
−4
4
−2
0
2
t statistic
t statistic
Infant Mortality Rate (−)
(infmort)
Death Rate (−)
(death)
Life Expectancy (+)
(lifeexpect)
−2
2
4
Density
t=−1.64
−4
−2
0
t statistic
2
4
4
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
0
t statistic
0.0 0.1 0.2 0.3 0.4 0.5 0.6
t=−1.64
CGV
GWF
4
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
0.0 0.1 0.2 0.3 0.4 0.5 0.6
CGV
GWF
2
t statistic
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
t=1.64
t statistic
t=1.64
−4
−2
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
−4
4
CGV
GWF
−4
t=1.64
CGV
GWF
t statistic
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
−2
Measles Immunization (+)
(measles.im)
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
t=1.64
−4
Density
Sanitation Access (+)
(sanitation)
CGV
GWF
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Density
Water Access (+)
(water)
t=1.64
−4
−2
0
2
4
t statistic
Note: Figure summarizes distribution of estimated t-statistics from cross-section global sensitivity analysis
for nine health public good measures from 1975-2009, comparing the GWF and CGV measures of
democracy. Only estimates from the contemporaneous model are shown. The straight dotted line represents
the threshold necessary to reject the null of no effect at the .05 level with a one-sided test. All models
employ OLS with robust standard errors. The predicted sign of the democratic advantage hypothesis is
shown in parenthesis.