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FUKUYAMA THREE-PILLARS TEST: does the rule of law need the ballot?
DV = WGI Rule of Law (perception index, ~ -2.5..2.5). N=2304, 166 countries, 1996-2012
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[M1] RoL ~ electoral democracy (polyarchy) alone, year FE
   polyarchy b=2.485 (se 0.068, p=1.8e-289)  R2=0.422

[M2] RoL ~ polyarchy + log GDP pc, year FE  (HC1)
   polyarchy  b=1.590 (se 0.047, p=4.9e-250)
   log_gdppc  b=0.476 (se 0.010, p=0.0e+00)
   R2=0.691

[M2-standardized] beta polyarchy=0.416  beta log_gdppc=0.579  -> income carries 1.4x the ballot

[M3] + fiscal capacity (tax %GDP), N=1398
   polyarchy  b=1.493 (se 0.072, p=2.5e-96)
   log_gdppc  b=0.532 (se 0.017, p=6.5e-213)
   tax        b=0.001 (se 0.002, p=6.2e-01)

[M4] TWO-WAY FE (country+year), cluster by country  -- WITHIN-country
   polyarchy  b=0.581 (se 0.228, p=0.011)
   log_gdppc  b=0.327 (se 0.089, p=0.000)
   within R2=-0.105

[M5 robustness] DV=Gov Effectiveness: polyarchy b=1.535 (p=6.8e-203), log_gdppc b=0.502 (p=0.0e+00)

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HIGH rule of law (top quartile, RoL>=0.52) BUT LOW electoral democracy (<= median polyarchy 0.52), 2010-12 avg:
   SGP   RoL=+1.73  polyarchy=0.40
   HKG   RoL=+1.55  polyarchy=0.37
   QAT   RoL=+0.94  polyarchy=0.04
   OMN   RoL=+0.59  polyarchy=0.16
   MYS   RoL=+0.52  polyarchy=0.33
   COUNT of such 'liberal-institutions-without-the-ballot' cases: 5

Income+year alone R2=0.548 ; adding the ballot raises it to R2=0.691 (gain 0.144)
Ballot+year alone R2=0.422 ; adding income raises it to R2=0.691 (gain 0.269)