Диссертация (1137741), страница 15
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They also analyze the consequences ofreforms on the welfare of different generations. A decrease in pensions leads to the standardBeetsma et al. (2013) analyse socially optimal design of the two-stage pension system in general equilibriumOLG model with an endogenous labor supply (as opposed to Beetsma, Bovenberg (2009) who considered anexogenous labor supply).65Studies on population aging usually employ dynamic calibrated computable general equilibrium (CGE)models as Auerbach and Kotlikoff (1987).66Pension system is similar to Nielsen (1994).6467result of a fall in the welfare of the oldest persons living in the period of the shock.
67 Anincrease in the retirement age does not affect the welfare of retirees and increases the welfareof future generations. The burden of reforms in this case falls on the working generation.The framework of Heijdra and Bettendorf (2006) and Nielsen (1994) was extended byNickel et al. (2008), who consider an unbalanced pension system.
68 They analyse three fiscalscenarios in an economy with a decreasing population (Buiter, 1988): a suspension of thepublic pension system and a decrease in lump-sum labor tax; the suspension of the publicpension system and a decrease in distortionary corporate tax; and an increase in the retirementage. Their results suggest that the adverse consequences of pension reforms can be decreasedby appropriate taxation policies. If the tax reform is conducted promptly, the negative effectof reform on consumption could be offset, while the public debt would reach a lowerequilibrium level.
69While Nickel et al. (2008) consider the government as a non-maximizing entity andinvestigate how the predetermined changes in policy instruments would affect the transitionof the main macroeconomic variables to the new equilibrium in an open economy, we definea socially optimal fiscal policy (social contributions, government expenditure and income tax)and compare the set of policy instruments in equilibrium with both an increasing anddecreasing population in a closed economy with an endogenous interest rate and aheterogeneous population.The fact that the income tax rate and social contributions can act as substitutes isillustrated by the comparison of the optimal policy mixes under both balanced and unbalancedpension systems. Under a balanced pension system social contributions are strictly positiveand decrease with population growth, while income tax rate is constant and does not dependon it.
In the case of an unbalanced pension system, on the contrary, the corner solution isoptimal: social contributions are at zero while the income tax rate decreases with populationgrowth. This policy mix remains optimal in the steady state regardless of life expectancy andlabor productivity.
Under an unbalanced pension system the optimal income tax rate changeswith the structural characteristics of the economy while social contributions are at zero.67This result is similar to that from the standard two-generation Diamond (1965) model.They also extend the model by assuming that firms issue equities and face adjustment costs in investment.69It was shown that a decrease of pensions to zero, de-facto abolishment of the pension system, is accompaniedby the decrease of the distortionary tax on the firms’ output, the negative effect on the consumption per capitacan be lowered in the short-run, while in the long-run the output and consumption are higher with lower levels ofprivate and public debt.6868Within the model which incorporates Ricardian and non-Ricardian consumers we showthat there exists a threshold level of the share of non-Ricardian consumers after which highersocial contributions and lower income tax are optimal.
It is shown that the optimal share ofgovernment expenditure is increasing with the share of non-Ricardian consumerscompensating their welfare at retirement.The chapter is organized as follows. Sections 3.2-3.4 present an extended OLG modelof Heijdra and Bettendorf (2006) with an unbalanced pension system in a closed economywith an endogenous interest rate. Section 3.5 presents the comparison of the optimal policymix and social welfare under balanced and unbalanced pension systems in an economypopulated by Ricardian consumers. It is also shown how the optimal policy mix depends onretirement age, life expectancy and labor productivity.
Section 3.6 provides the results for theoptimal fiscal policy in the economy with Ricardian and non-Ricardian consumers, with andwithout a pension system. Section 3.6 also includes an analysis of the optimal fiscal policywhen discrimination among agents based on their type is possible (the case of type specificsocial contributions is considered). Section 3.7 concludes.3.2. The model with Ricardian and non-Ricardian consumersThe model of Heijdra and Bettendorf (2006) is extended by introducing an unbalancedpension system with the deficit covered by a benevolent government, which conducts fiscalpolicy to maximize social welfare.
We consider a closed economy with an endogenousinterest rate.The economy consists of two types of households, firms, the government and thepension fund. Infinitely-lived Ricardian households maximize the present value of utility fromconsumption taking into account life expectancy. Non-Ricardian consumers, whose share is , consume all their disposable income, do not save, and do not have the ability to smoothconsumption over time. Both types of consumers work and pay income tax throughout theirlives, pay social contributions until the retirement age and receive pensions at retirement.Pensions are paid by the pension fund, the deficit of which is covered by the government.Public debt is financed by bonds held by Ricardian households and income tax payments.69In the model upper case variables are aggregates, lower case variables with a bar denoteindividual variables, and lower case variables without any notation are aggregates perefficiency units of labor.
703.2.1. Ricardian and non-Ricardian householdsThe representative Ricardian type consumer born at time maximizes at eachmoment t the expected present value of instantaneous lifetime utility of consumption:U R ( , t ) = (1 − ) ln c R ( , ) + ln g e( + )(t − ) d ,(3.1)twhere c R is personal consumption of Ricardian consumers, g is public spending and 0is its share in the utility function, 0 is the rate of time preference and 0 is theprobability of death.Following Bettendorf and Heijdra (2006) we consider a pay-as-you-go (PAYG) pensionsystem introduced by Nielsen (1994).
The households pay income taxes throughout theirlives, pay social contributions tW until the retirement age of and receive pensions z atretirement. The threshold level can only loosely be considered as a retirement age becausethe households continue to work after it.Ricardian consumers can save part of their disposable income, which can be invested incapital goods, k , and government bonds, (a G ) . They pay income tax on their labor incomeand receive an interest rate r (t ) on their financial wealth, a ( , t ) . The payment a( , t ) is theactuarially fair annuity paid by the life insurance company.
71 Interest and non-interest netlabor income, WI ( , t ) , are spent on consumption and saving. Financial wealth of Ricardianhousehold, therefore, consists of capital goods, k , and government bonds, (a G ) , bothdenominated in terms of consumer goods.The budget constraint of a Ricardian type consumer in terms of the consumption goodis:72a ( , t ) = (r (t ) + )a ( , t ) + WI R ( , t ) − c R ( , t )(3.2)a ( , t ) = k ( , t ) + a G ( , t ),(3.3)70Main variables and their notations are provided in Appendix 2.See Yaari (1965), Blanchard (1985). Yaari (1965) has introduced a notion of actuarial note, defined as a notethat the consumer can buy or sell and which is valid until the consumer dies, at which time it is automaticallycancelled.72A dot above the variable signifies the variable's time derivative: a ( , t ) = da ( , t ) / dt .7170(1 − tL )W N ( , t ) − tWWI R ( , t ) = N(1 − tL )W ( , t ) + zfor t − ,for t − ,(3.4)where W N ( , t ) is the wage at time t of the worker born at time .Labor supply for both types of consumers is non-elastic: each household supplies oneunit of labor.73 Labor productivity decreases with the age of the worker.
The worker ofgeneration at time t supplies n( , t ) efficiency units of labor (Bettendorf and Heijdra,2006):n( , t ) = E (t − ) l ( , t ),(3.5)where l ( , t ) = 1 is the labor hours worked and E(t − ) is the so-called efficiency index(Bettendorf and Heijdra, 2006), which falls exponentially with the worker's age as inBlanchard (1985):E (t − ) = 0 e − ( t − ) ,(3.6)where 0 , is normalized to 1 and 0 specifies the speed at which productivity falls withage.At each moment t the household chooses the paths of consumption and financial assetsto maximize lifetime utility (3.1) subject to budget constraint (3.2) and a transversalitycondition.
The initial value of the financial assets a( , t ) and the government consumption perhousehold are taken as given.The optimal path of household consumption is defined by the Euler equation:c R ( , t )= r (t ) − .c R ( , t )(3.7)In each moment consumption is proportional to total wealth:74c R ( , t ) = ( + )( a ( , t ) + aHR ( , t )) .(3.8)Human wealth, aHR , is defined as the present value of after-tax labor income:aHR ( , t ) = WI R ( , )e R (t , )+ (t − ) d ,(3.9)twhere R(t , ) = r ( s)ds.t73Heijdra and Romp (2009) analyze the consequences of demographic shocks and changes in pension system onmain macroeconomic variables in the OLG model with endogenous labor supply and endogenous retirement age.74For more details see Appendix 2.71Non-Ricardian households whose share in the total population is , consume all theirdisposable income.
Their consumption, therefore, is defined by (3.10):c NR ( , t ) = WI NR ( , t ) .(3.10)They have the same utility function as Ricardian consumers, defined by equation (3.1).Their net labor income is identical to that of Ricardian agents.(1 − tL )W N ( , t ) − tWWI NR ( , t ) = N(1 − tL )W ( , t ) + zfor t − ,for t − .(3.11)Households of this type consume all their income, and are unable to save and smoothconsumption over their lifetime. Similar to the human wealth of Ricardian agents, we candefine the human wealth of non-Ricardian agents. In this case it is equal to the present valueof their lifetime consumption.aHNR ( , t ) = W I NR ( , )e R (t , ) + (t − ) d ,(3.12)t3.2.2.
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