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The results are presented in Table 3.9.92Table 3.9. Optimal public spending, social contributions and income taxThe share of non-Ricardian consumers tL10%20%30%40%50%60%70%80%90%1%6.5%0.0%1%6.5%0.0%3%9.5%0.0%6%14.0%0.0%9%18.5%0.0%11%20.0%2.5%15%6.0%37.5%18%10.5%37.5%21%14.0%39.5%3.6.4.Optimal fiscal instruments if discrimination is possibleIn this subsection we focus on the case where a different level of social contributionscan be imposed on Ricardian and non-Ricardian agents.101 Similar to Subsection 3.7.2 let usconsider the case where income tax and both values of social contributions are chosenoptimally so to maximize the social welfare function. The parameter values are the same asthose used in the previous section.
The results are presented in Table 3.10.Table 3.10. Optimal choice of income tax rate and social contributionstL NRThe share of non-Ricardian consumers 30%40%50%60%70%80%90%10%20%20.0%20.0%19.5%16.5%4.5%1.0%0%0%0%0%0%2.5%15.0%54.0%54.5%50.0%43.5%39.0%The optimal level of social contributions of Ricardian agents is zero, which is consistentwith the results in Section 3.6. For the level of social contributions for non-Ricardian agentsthe situation is different. According to the estimates there still exists a threshold level for theshare of non-Ricardian consumers (for this calibration it is = 30% ) after which thefinancing of public spending and pensions is optimal via social contributions of non-Ricardianagents instead of via the income tax, which decreases with a higher level of .When different levels of social contributions can be imposed on the agents dependingon their type (Ricardian and non-Ricardian), the pension system with a fixed share ofpensions and financing via income tax and social contributions leads to a higher level ofsocial welfare.
Figure 3.8 shows that after the threshold level of , a higher level of capitalper capita is feasible (greater than in case of unified social contributions, Section 3.6.2), asmore is invested in capital by Ricardian consumers who do not pay social contributions.101Several adjustments to the baseline model were made to incorporate this assumption. Net income labor is nowdifferent among agents due to the different level of social contributions. The deficit of the pension fund is theweighted sum of social contributions by two types of agents and the pensions paid to them.9313kk (no pension system)k12111098λ700.10.20.30.40.50.60.70.80.91Figure 3.8. Per capita capital with and without pension systemSource: estimates based on the model.The higher level of capital per capita results in the higher level of per capitaconsumption Ricardian agents and the lower consumption of non-Ricardian consumers(Figure 3.9).
The inequality in consumption per capita is higher when agents pay differentsocial contributions. However, the discrimination of agents by their type allows higher socialwelfare to be achieved for higher than the threshold level.To illustrate the effect of a pension system on households’ behaviour let us considerindividual household consumption profiles. Individual consumption of Ricardian agents isdefined according to the equation (3.8), specifying the level of individual consumption of aRicardian type household as a share of the household’s assets. Individual consumption of nonRicardian consumers is defined by equation (3.10) and equals the disposable income of ahousehold of this type. The fact that the labor income of both types of households declineswith age (due to the decreasing labor productivity) is taken into account.
The value of socialcontributions and pensions is calculated on the basis of their current labor income.943Cc_Rc_R (no pension system)c_Kc_K(no pension system)2.521.51λ0.500.10.20.30.40.50.60.70.80.91Figure 3.9. Consumption of Ricardian and non-Ricardian agents with andwithout pension systemSource: estimates based on the model.Figure 3.10 illustrates how net labor income of both types of agents (WI) and theconsumption of Ricardian consumers change with the age of the worker. The figure is basedon the calibration of the previous section with a fixed level of pensions and the optimal choiceof income tax rate, social contributions and public expenditure.
WI NR (no pension system)shows the level of disposable income and, therefore, consumption of non-Ricardian agents inthe absence of a pension system. In the absence of a pension system disposable income ofRicardian and non-Ricardian agents would coincide: they have the same productivity, whichis gradually decreasing with age, and pay the same rate of income tax. Therefore, thedisposable income of Ricardian and non-Ricardian agents coincides prior to the retirementage with and without a pension system. In the model with a pension system the level ofdisposable income of non-Ricardian agents is lower than in the absence of a pension systembecause in the former case non-Ricardian agents pay social contributions. Figure 3.10 showsthat the introduction of the pension allows the consumption level of non-Ricardian agentsafter retirement to increase.952.11.9WI (v,t) (R)c (R)WI (v,t) (K)(nonp)pension system)WI (v,t) (K,1.71.51.31.10.90.70.502040age6080100Figure 3.10.
Net labor income and consumption profiles of consumersSource: estimates based on the model.3.7. ConclusionThe OLG model with infinitely living households developed by Bettendorf and Heijdra(2006) was extended by introducing an unbalanced pension system, where the deficit of thepension fund is covered by the transfer from the government budget in the model with anendogenous interest rate. The assumption that liabilities of the pension fund are financed bythe government makes the income tax and social contributions act as substitutes in thefinancing of pensions. During the next stage the model was extended to incorporate two typesof consumers: Ricardian consumers, and non-Ricardian consumers, who consume all theirdisposable income.First, the model with homogeneous agents was considered.
In the case of an unbalancedpension system when both social contributions and income tax are chosen optimally, theoptimal policy mix includes a positive income tax rate, which decreases with populationgrowth, and zero social contributions. In the case of a balanced pension system socialcontributions should be strictly positive to cover the spending of the pension fund. Thus,concerning the combinations of policy instruments, only an internal solution is considered.However, social welfare is lower under a balanced pension system, while the level of publicdebt is higher, compared to the case of an unbalanced pension system. Under a balancedpension system the optimal income tax is lower than under an unbalanced pension system anddoes not depend on population growth.
Social contributions, on the contrary, decrease with96population growth. The results also show that in equilibria with a higher retirement age,optimal social contributions (or income tax under an unbalanced pension system) are lower,as is the public debt. Therefore, pension reforms, namely increase in the retirement age, canbe introduced as an additional measure of fiscal consolidation.Second, on the basis of an extended framework, the way the optimal set of fiscalinstruments change with the share of non-Ricardian consumers was shown.
When income taxand social contributions are chosen optimally, the optimal rate of social contributions paid byall households becomes positive after a certain threshold level of the share of non-Ricardianconsumers, coupled with the lower rate of income tax. Higher taxes lead to a lower level ofper capita output. When discrimination among households is possible based on their type,after a certain proportion of non-Ricardian agents in the economy the optimal set of measuresincludes positive social contributions paid by non-Ricardian agents, decreasing with theirincome tax rate, and zero contributions paid by Ricardian agents.An analysis of the optimal choice of social contributions, income tax and publicspending shows that the optimal share of public spending increases with the share of nonRicardian agents to increase their welfare at retirement.
The optimal choice of fiscalinstruments taking into account the share of non-Ricardian consumers can lead to highersocial welfare.The developed framework can be applied to the analysis of the consequences ofdemographic changes to public finance and to the development of the optimal consolidationmeasures. The framework can be extended to analyse a wider set of optimal pension reformsand fiscal policy measures and can be calibrated for a specific country.97References1.Agénor, P.
R. (2012). Infrastructure, public education and growth with congestioncosts. Bulletin of Economic Research, 64(4), 449-469.2.Almeida, V., Castro, G. L., Félix, R. M., Júlio, P., Maria, J. R. (2013a), InsidePESSOA-A detailed description of the model, No. w201316.3.Almeida, V., Castro, G., Félix, R. (2009). The Portuguese economy in the Europeancontext: structure, shocks and policy. The Portuguese economy in the context ofeconomic, financial and monetary integration (Banco de Portugal).4.Almeida, V., Castro, G., Félix, R.
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