Диссертация (1137741), страница 19

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This case can provideinsight into how key variables of the model depend on the share of non-Ricardian agents. Weuse this steady state as a benchmark to see the consequences of the introduction of a pensionsystem. The pension system is introduced in Subsection 3.6.2, which provides the results forthe optimal choice of income tax and social contributions. In Subsection 3.6.3 the set ofpolicy instruments is extended to include optimal government expenditure. The set of policyinstruments includes income tax, share of social contributions in the median wage and theshare of government expenditure in the total output.

In Subsections 3.6.2-3.6.3 Ricardian andnon-Ricardian consumers pay the same social contributions. Subsection 3.6.4 provides theresults for the case of possible discrimination of agents by their type, Ricardian and nonRicardian. This is modelled by setting different social contributions depending on the type ofthe agent.873.6.1.Optimal income taxFirst, let us consider the optimal choice of income tax and the corresponding steadystates under different rate of population growth. In the absence of a pension system, theoptimal tax rate, identical for both types of consumers, does not depend on the share of nonRicardian agents.

A tax rate of 15.5% is the lowest tax rate in found equilibria under differentparameter combinations (which satisfies the conditions). 96 Equilibria with a higher rate ofincome tax are characterized by lower investment in capital per capita, which leads to lowerwelfare. As a result, the lowest feasible equilibrium tax rate is optimal.The adjustment of the interest rate and public debt ensures the fulfilment of thegovernment budget constraint with the tax rate staying constant (the lowest feasible tax rate)which is paid by agents of both types.

In the absence of pension system there is no othergovernment spending except government expenditure. Tax revenues are changing along withthe capital per capita (with the wage in the economy). The higher is the share of nonRicardian agents, the lower is the level of capital per capita in the economy, as fewer agentscan hold savings. The lower level of savings is accompanied by a higher interest rate, whichexceeds the population growth. The results are provided in Table 3.6, where aGy is the share ofpublic debt in output.

The results are calculated with a fixed value of government expenditureat 10% of the output (close to the average optimal level of government expenditure for = 0.5 , see subsection 3.6.3). As a robustness check we compute the results for  = 0.25(see Appendix 2.4). The share of government expenditure in the utility  = 0.3. 97 Otherparameters are equal to the values in baseline calibration (  = 2.5% ,  = 1.25% ,  = 60 ).Table 3.6.

Steady states with the optimal choice of income tax rateThe share of non-Ricardian consumers 10%20%30%40%50%60%70%80%90%tL15.5%15.5%15.5%15.5%15.5%15.5%15.5%15.5%15.5%k12.512.111.711.210.710.19.48.77.9cTy60.0%60.6%61.3%62.1%62.9%64.0%65.1%66.4%68.0%aGy70.5%58.6%48.8%40.6%33.8%28.0%23.1%18.9%15.3%1.7%1.8%1.9%2.1%2.2%2.4%2.7%3.0%3.4%r96The choice of tax rate in equilibrium is limited by the equilibrium stability condition (forms lower constraint,see Section 3.3) and by the restriction that public debt should not exceed 1.5 times GDP, which provides theupper constraint.97When  = 0.25 the optimal level of income tax is higher due to higher public expenditure.88The share of total consumption in output, cTy , increases with the higher share of nonRicardian consumers, as fewer resources are directed to savings.

With the value of per capitaconsumption slowly decreasing with higher  , the share of consumption increases mainly dueto lower per capita output. For commonly used values of the share of non-Ricardianconsumers,  in the range of 40-50%, the model provides an estimate of consumption atabout 62%, which conforms to the OECD data. 98The allocation of total consumption between the two types of consumers is illustratedby Figure 3.5. While per capita consumption of non-Ricardian consumers is slowlydecreasing with  , the wage, which defines their consumption, is decreasing with a fall incapital. The interest rate on the savings of Ricardian agents almost doubles with  rising from10% to 90%, increasing the income of Ricardian agents. This leads to a significant inequalityin consumption of Ricardian and non-Ricardian agents with an increase in the share of nonRicardian agents.3c2.521.510.5λ000.10.20.30.40.50.60.70.80.91Figure 3.5.

Per capita consumption of Ricardian and non-Ricardian agentsas a function of the share of non-Ricardian agentsSource: estimates based on the model.98According to the OECD estimates an average share of final household consumption in GDP for 2010-2016 is61.02%. For 2016 its estimate is at 60.7%. For the USA the corresponding estimates are 68.36% in 2010-2016and 68.84% in 2016 (OECD, National Accounts at a Glance, National accounts database).893.6.2.Optimal tax instruments under an unbalanced pension systemIn subsection 3.6.1 we considered the choice of the optimal tax rate in the absence of apension system, now let us consider the choice of income and the share of social contributionswhich maximize social welfare in an economy with a pension system.

The value of pensionsfor both types of consumers is set at 30% of the median wage. The other parameter values arethe same as those used in the previous section. The results are presented in Table 3.7. 99Table 3.7. Optimal choice of income tax rate and social contributionsThe share of non-Ricardian consumers 10%20%30%40%50%60%70%80%90%tL20.0%20.0%20.0%20.0%20.0%18.5%0.5%0.5%0%0%0%0%0%0%2.5%34.0%34.0%35.0%The optimal level of social contributions is zero for a share of non-Ricardian agents lower than 50%. This result is similar to the results of Section 3.5, where zero socialcontributions and positive income tax were obtained in the absence of non-Ricardian agents.However, according to the estimates there exists a threshold level of the share of nonRicardian consumers (for this calibration it is  = 55% ) after which the financing of publicspending and pensions is optimal via social contributions instead of via income tax, whichdecreases with a higher level of  .100 For a low share of non-Ricardian agents income taxrevenue and public debt are sufficient to cover government expenditure and pensionpayments.

When the share on non-Ricardian agents is high enough public debt becomes loweras fewer agents (Ricardian type agents) are making savings.In the economy with a pension system and fixed share of pensions which are financedvia income tax and social contributions, the level of social welfare is lower than in theabsence of a pension system. Social welfare is lower as a result of a lower level of capital percapita. Higher income tax and positive social contributions imposed after a certain level of lead to lower investment in capital.

Figure 3.6 shows that the switch to the positive socialcontributions after the threshold level of  leads to a higher difference between levels ofcapital per capita in the steady state with a pension system and in its absence. In the formercase all agents, in addition to the income tax, pay social contributions.

As a result, Ricardianagents are able to invest even less in capital.The results for  = 0.25 are provided in Appendix 2.5. Both the optimal level of income tax and socialcontributions are higher. A threshold level for  continues to exist, after which the set of instruments consists ofa lower income tax and higher social contributions.100The threshold level for  is obtained from a maximization of social welfare with a 1% step for  .999013kk (no pension system)k12111098λ700.10.20.30.40.50.60.70.80.91Figure 3.6. Per capita capital with and without pension systemSource: estimates based on the model.The lower level of per capita capital (Table 3.8) results in a slightly lower level of totalper capita consumption, cT (Figure 3.7).Table 3.8.

Capital per capita and the share of consumption in output per capitaThe share of non-Ricardian consumers kk (no pension system)cTyTyc (no pension system)10%20%30%40%50%60%70%80%90%12.4012.5012.0412.1311.6311.7111.1711.2410.6510.7010.0310.118.939.448.388.707.727.8660.2%60.8%61.4%62.2%63.0%64.1%66.0%67.0%68.3%60.2%60.8%61.4%62.2%63.1%64.1%66.3%67.3%68.4%The level of social welfare in the economy with optimal fiscal policy and a pensionsystem is lower than in the case without a pension system.

In addition to the slightly lowerlevel of per capita consumption, social welfare is affected by a lower level of governmentexpenditure per capita: with the same fixed share of government expenditure of the output(10%), it is lower due to the lower level of per capita output in the economy with a pensionsystem.911.065C1.061.0551.051.0451.041.0351.03c_T (no pension system)c_Tλ1.02500.10.20.30.40.50.60.70.80.91Figure 3.7. Total per capita consumption with and without pension systemSource: estimates based on the model.3.6.3.Optimal public spending and the share of non-RicardianconsumersIn the absence of non-Ricardian agents the optimal choice of size of governmentexpenditure depends on the parameters of the pension system (the value of pensions, socialcontributions and retirement age) as well as on the income tax rate.

However, when the shareof government expenditure in the output is fixed it does not adjust to the population structure.On the contrary, in the economy with Ricardian and non-Ricardian agents the government cansmooth the utility of non-Ricardian agents, who do not have an opportunity to save for theirretirement.The optimal share of government expenditure grows with the share of non-Ricardianagents (Table 3.9). When the number of non-Ricardian agents is small (lower than 40%)government expenditure and pensions are financed by the income tax while socialcontributions for both types of agents are at zero.

With an increase in the share of nonRicardian agents and, therefore, the share of government expenditure, social contributions fornon-Ricardian agents become positive.The value of government spending is increasing, despite a decreasing with  capitaland, thus, output. The impact of the higher share of expenditure exceeds the effect of loweroutput.

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