A Proofs and Supplementary Explanations
A.5 Numerical Results
Figure A.1 reports the numerical results for 25 sample countries, including Australia, Austria, Chile, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Italy, Japan, Lithuania, Luxemburg, the Netherlands, Norway, Poland, Portu-gal, Republic of Latvia, Slovenia, Spain, Sweden, Switzerland, and the United Kingdom.
The ratio of capital income tax revenue to GDP shows a U-shaped pattern for Australia, Chile, Estonia, Japan, Latvia, Lithuania, and Switzerland whereas it is monotonically increasing in ω for other countries.
[Figure A.1.]
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https://mpra.ub.uni-muenchen.de/99455/1/MPRA paper 99455.pdf
AUS
Labor income tax revenue (% of GDP, ave 95-16)
Popula!on ages 65 and above (% of total, ave 95-16)
(a)
AUSCAN AUT BEL
CZE
Capital income tax revenue (% of GDP, ave 95-16)
Popula!on ages 65 and above (% of total, ave 95-16)
(b)
Government deficit (% of GDP, ave 95-16)
Popula"on ages 65 and above (% of total, ave 95-16)
(c)
Figure 1: Each panel plots the data for OECD countries during 1995–2016. The vertical axis takes the average share of population aged 65 years and over. The horizontal axis takes the average ratio of labor income tax revenue to GDP (Panel (a)), the average ratio of capital income tax revenue to GDP (Panel (b)), and average ratio of deficit to GDP (Panel (c)). In Panel (c), the budget deficit is taken as an approximate variable for the public debt.
Source: OECD.Stat (https://stats.oecd.org/) (accessed on September 25, 2019).
0 10 20 30 40 50 60
Chile Korea Switzerland Australia Latvia Ireland Estonia Lithuania United States Japan United Kingdom Luxembourg Spain Czech Republic Slovak Republic Iceland Poland Netherlands Israel Norway Portugal Germany Slovenia Italy Greece Hungary Austria Finland Sweden Denmark France
Government expenditure (% of GDP, ave 95-16)
Figure 2: Average ratios of government expenditure to GDP for OECD countries during 1995–2016. Belgium, Canada, Mexico, Turkey, and New Zealand are not included in the figure because of missing data. The same applies to Table 1.
Source: OECD.Stat (https://stats.oecd.org/) (accessed on September 25, 2019).
AUS AUT CZE DNK FIN FRA DEU GRC HUN ISL IRL n 0.511 0.147 0.0326 0.139 0.11 0.181 0.0174 0.0251 -0.07 0.375 0.491
θ 1.78 18.8 3.64 61.5 26.7 77.1 5.5 8.36 8.84 3.89 2.28
ITA JPN KOR LUX NLD NOR POL PRT SVK ESP SWE
n 0.0957 0.0178 0.2 0.661 0.147 0.298 -0.0239 0.0428 0.0178 0.25 0.179
θ 8.1 2.38 1.14 3.33 4.68 5.01 4.24 5.22 3.67 3.37 32.8
CHE GBR USA CHL EST ISR SVN LVA LTU
n 0.281 0.193 0.318 0.38 -0.117 0.855 0.0543 -0.287 -0.284
θ 1.62 2.85 2.31 0.812 2.15 5.38 6.17 2.04 2.1
Table 1: The average population growth rate for OECD countries during 1995–2016 and the associated estimation of θ.
Source: OECD.Stat (https://stats.oecd.org/) (accessed on September 25, 2019).
Figure 3: Predicted ratios of government debt, capital income tax revenue, and labor income tax revenue to GDP for Iceland, Ireland, Israel, Korea, Slovakia, and the United States.
Figure 4: Numerical illustration of the effects of ωon ¯TK, ¯T, ¯G, ¯B, and ¯TK+ (1−α) ¯T−1 for the two cases of Korea: v = 0 and v = 1.5.
Figure 5: Numerical illustration of the effects ofω onbt/kt,τtK, andτtKRtst−1Nt−1/Yt for the cases of Korea (upper panels) and Iceland (lower panels). The results for the cases of v = 0 and 1.5 are plotted by dotted and solid curves, respectively.
Figure A.1: Predicted ratios of government debt, capital income tax revenue, and labor income tax revenue to GDP for 25 sample countries.