Диссертация (1137741), страница 18
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In this case the corner solution takes place: the optimal income taxrate is positive, while the rate of social contributions equals zero. The corner solution takes81place because zero social contributions and an optimal income tax leads to higher level ofcapital per capita. Other steady states with zero social contributions and a higher income taxrate are characterized by lower social welfare: capital per capita is lower due to higher incometax. Household savings are invested in the public debt and not in capital, which leads toinefficiency. As a result, the optimal combination consists of zero social contributions and theminimum equilibrium level of the income tax rate.The results of welfare maximization for = 60 and = 65 are presented in Table 3.3below.93Table 3.3.
Optimal income tax under different population growth and retirement agenL-0.25%0%0.25%0.5%0.75%1.25%1.75% = 60Income tax ratetL50.3%48%46.5%45.3%44.2%42.4%41.1%Pension fund deficitto outputdy8.1%7%6%5.2%4.4%3.3%2.4%Income tax ratetL48.9%47.2%45.7%44.5%43.4%41.8%40.6%Pension fund deficitto outputdy7.5%6.4%5.4%4.6%3.9%2.8%2.1% = 65The pension system is run with a deficit ( d y - the share of the deficit in output). Itdecreases with population growth and the retirement age. Pensions are set at 30% of themedian wage, which changes with the longer working period, so pensions adjustautomatically to the changes in the retirement age.Figure 3.2 shows how an optimal income tax depends on the population growth.Optimal income tax exhibits the same inverse relationship as social contributions (Figure 3.1).In this case social contributions are zero, while the income tax rate is decreasing with higherpopulation growth: the deficit and pensions can be financed with lower income taxes whenthe share of the young population is high.Different levels of birth rates are considered with constant death rate, = 1.25% .
This leads to different levelsof population growth nL .9382tLπ = 55π = 60π = 6552%48%44%40%-0.5%0.0%0.5%1.0%1.5%2.0%nLFigure 3.2. Optimal income tax under different retirement ageSource: estimates based on the model.Higher income tax and zero social contributions, when they both are chosen optimally,illustrate that these instruments can be considered as substitutes in financing pensions.Additional calculations show that an increase in by 0.5% leads to the decrease in theoptimal income tax rate by 0.2%.
However, combinations of lower income tax and positivesocial contributions result in lower level of capital per capita. Per capita capital is moresensitive to the change in the rate of social contributions than to the change in the income taxrate. The higher sensitivity of capital per capita to the income tax rate is explained, first, bythe shorter payment period of social contributions (while income tax is paid throughout thelife, social contributions are paid only up to the retirement age) and, second, by the fact thatsocial contributions are defined by the median wage and paid until the retirement age.3.5.2. Optimal policy under balanced and unbalanced pension systemNext, we consider how the optimal policy mix changes depending on whether thepension system is balanced or not. First, under the balanced pension system the optimalincome tax rate is lower than in the case of the unbalanced pension system for all growth rates(Figure 3.3). In this case pensions are financed by social contributions and not out of thegovernment budget.
Second, under a balanced pension system the optimal level of income taxis constant, while the share of social contributions decreases with population growth. A higher83birth rate increases the value of the social contributions to the pension fund because in thiscase more members of the young generation make contributions. Thus, the lower socialcontribution rate is needed to keep the pension fund balanced.tLd ≠ 055%d=050%45%40%35%-0.5%0.0%0.5%1.0%1.5%2.0%nLFigure 3.3. Optimal income tax under balanced and unbalanced pensionsystemSource: estimates based on the model.Depending on whether the pension system is balanced or not, either the optimal incometax or social contributions change with the growth rate, while the other instrument remains atits optimal level.
Figure 3.4 illustrates the results for the optimal level of for a balancedand an unbalanced pension system.In the case of a balanced pension system, social welfare is lower than in the case of anunbalanced pension system. An unbalanced pension system is accompanied by a higher levelof per capita capital and therefore, higher social welfare. This finding corresponds to theresults of the OLG models with a dynamically efficient steady state where a PAYG pensionsystem leads to lower social welfare.An equilibrium with an unbalanced pension system leads to higher social welfare and toa lower level of public debt due to the lower surpluses. This result is explained by thecomparison of budget surpluses, which serve as a provision of public debt.
Under a balancedpension system tax revenues are lower. First, the optimal tax rate is lower as pensions arefinanced by social contributions. Second, the aggregate wage is lower due to the lower capital84per capita. Public spending is also lower in the case of a balanced system: due to both lowergovernment expenditure and zero deficit of the pension fund.Ψd ≠ 040%d=030%20%10%0%-0.5%0.0%0.5%1.0%1.5%2.0%nLFigure 3.4. Optimal social contributions under balanced and unbalancedpension systemSource: estimates based on the model.3.5.3. Robustness check: life expectancy and labor productivityThe robustness check includes an analysis of how the optimal policy mix of socialcontributions and income tax is affected by the changes in life expectancy and laborproductivity.
We compare steady states under life expectancy which is equal to 60 and 80years under the unbalanced pension system. These levels of life expectancy correspond to being equal to = 1.67% and = 1.25% . Income tax and social contribution rates are chosenoptimally to maximize the social welfare. 94 We have considered a fixed retirement age so thatequilibria under the same birth rates were comparable. The optimal policy mix remains thesame: positive rate of income tax and zero social contributions (Table 3.4).To check the robustness of results the change in was considered for different retirement ages, for from55 to 70. Since the results for different retirement ages are similar, we provide here only the results for = 60 .9485Table 3.4.
Optimal income tax under different birth rates and life expectancy1%1.25%1.5%1.75%2%2.5%3% = 1.25%Population growthnL-0.25%0%0.25%0.5%0.75%1.25%1.75%Income tax rateCapital per capitaRatio of householdconsumption to outputtL50.23%47.94%46.48%45.23%44.16%42.43%41.16%kcy9.6110.4011.1111.3911.5411.6511.5153.7%52.3%50.8%49.6%48.5%46.4%44.5%Population growthnL-0.67%-0.42%-0.17%0.08%0.33%0.83%1.33%Income tax rateCapital per capitaRatio of householdconsumption to outputtL49.65%47.95%46.50%45.25%44.20%42.45%40.95%kcy9.6410.3610.9211.1611.3211.4411.2556.9%55.5%54.1%52.9%51.8%49.5%47.6% = 1.67%Under an unbalanced pension system, the higher life expectancy leads to higher level ofper capita capital, lower share of per capita private consumption in the output due to thehigher output and higher government expenditure in the steady state (defined as a fixed sharein the output).
Public debt is higher under higher life expectancy due to the highergovernment expenditure and lower interest rate, while the optimal income tax rate is higher ingeneral in the steady states with higher .95 Overall, comparison of the steady states underthe same birth rate and different death rate it not generally correct due to the differentpopulation growth in the steady states.The pension system is run with a deficit. Its share of GDP is the same under different because a per capita deficit of the pension fund is defined by the ratio of pensions to GDPis constant (14.7%), while the optimal share of social contributions, , is zero.
Although theabsolute value of pensions increases with higher life expectancy due to a higher level ofcapital, its change is proportional to the change in the output (as both output and median wageare functions of capital). That is why a share per capita deficit of the pension fund in the percapita output remains unchanged.Next, we consider the case of higher labor productivity.
It is modelled as the lowerspeed, , with which the product of labor decreases with age. Table 3.5 shows the results for = 1.25% and = 1.1%95For this case a higher precision was applied for the choice of t L (the step equals 0.01%).86Table 3.5. Optimal income tax under different labor productivitynL-0.25%0%0.25%0.5%0.75%1.25%1.75% = 1.25%Income tax ratetL50.3%47.95%46.5%45.25%44.15%42.4%41.1%Ratio of pensionfund deficit to outputdy8.08%6.95%5.99%5.15%4.42%3.27%2.39%Income tax ratetL50.4%48.3%46.8%45.45%44.35%42.6%41.2%Ratio of pensionfund deficit to outputdy8.32%7.17%6.17%5.29%4.55%3.36%2.47% = 1.1%Optimal income tax decreases with population growth and increases with laborproductivity. Higher labor productivity results in a higher capital per capita in the steady state,leading to higher output per capita, government expenditure and private consumption.
Higherproductivity leads to a higher wage, increasing the level of pensions to be equal to 30% of themedian wage. It puts higher pressure on the pension system and, thus, the government budget.However, despite the fact that the deficit of the pension fund is higher under higher laborproductivity, public debt is lower at equilibrium with the higher productivity due to the higherincome tax payments (driven by the higher wage), which have increased more thangovernment expenditure.3.6. Optimal fiscal instruments: the role of non-Ricardian agentsIn this section we consider the optimal choice of fiscal instruments under differenteconomic conditions. First, we consider the optimal choice of income tax in an economywithout a pension system (zero social contributions and pensions).
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