Policy Reforms and Ageing in the Small Open Economy

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Policy Reforms and Ageing

in the

Small Open Economy

An applied general equilibrium analysis

Master Thesis Economics

Department of General Economics University of Groningen

August 2008

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1. Introduction

The goal of this master thesis is to study the consequences of ageing and policy reforms in a computable general equilibrium model with overlapping generations for a small open economy. The focus will be on pensions and pension reforms.

It is well known that many of the western European countries face an ageing society. People tend to live longer and fewer young people are born.1 For the Netherlands, life-expectancy at birth has increased from approximately 71 in 1950 to approximately 80 in 2006. The average birth-rate in 1950 was 3 children per women. Nowadays it is only 1.7 children per women. The so-called ‘Grey Pressure’2 in the Netherlands has increased from 14 in 1950 to 24 in 2008. Besides that, the baby-boom generation slowly reaches the age at which they are eligible for state pensions, although the demographic effect of the post-war birth wave is limited. These demographic trends have negative effects on governments’ budgetary positions.

In a recent study into the Dutch situation, the CPB Netherlands Bureau of Economic Policy Analyses, forecasts that the dependency ratio will increase from 23.4% in 2006 to 43.4% in 2040. Without proper measures the government expenditures will increase by 7% from 48% to 55% of GDP in 2040. Although revenues will also increase (about 4%) this will not be enough to prevent tax increases in the future. The gap between government income and expenses is expected to increase about 3% between 2006 and 2040.3

The master thesis presented here is closely related to the article of Bouzahzah et al. (2002), who develop a computable general equilibrium model for a closed economy. Their research is extended in two ways. First of all, because we focus on the situation for the Netherlands, we adopt an open economy setting instead of a closed economy

1_{Whiteford, P. and Whitehouse, E. (2006). ‘Pension challenges and pension reforms in OECD countries’,}

Oxford Review of Economic Policy, 22(1):78-94, 2006.

2_{The grey pressure (in dutch: grijze druk) is measured as the ratio of the population of 65 years and older}

to the population between 20-64 years old.

3_{Van Ewijk et al. (2006). ‘Ageing and the Sustainability of Dutch Public Finances’, CPB Netherlands}

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setting. Second, we replace the exogenous retirement decision used by Bouzahzah et al. (2002) by a more realistic retirement decision. Following Sheshinski (1978), agents equate the marginal utility of additional income to the marginal utility of leisure (disutility of working). Labour is indivisible, households work either full time or not at all. This results in a six-period model in which households optimally choose the length of education in the first period, the retirement age in the fifth period and consumption/saving in each period.

Chapter 2 provides some background information on pensions. Pension design in general, its objectives and the situation in the OECD countries is covered first. After that the pension system in the Netherlands is discussed in detail. This is done to provide the reader some basic insights regarding pensions and help them understand the choices made in subsequent sections.

Chapter 3 sets out the model in detail. Each sector of the economy is dealt with, starting with the maximization problem of the households. Households maximize an intertemporal utility function subject to an intertemporal budget constraint. After that the productive sector is described. Profit maximizing firms produce a commodity which is traded in perfectly competitive international markets, using physical and human capital as inputs. The government adjusts the income tax rate to satisfy the government budget constraint.

Chapter 4 deals with household behaviour in each generation. Since we adopt an overlapping generations setting, behaviour of older generations depends on decisions made in previous periods. Different generations will therefore react differently to shocks in the economy. Younger generations are less constrained than older generations.

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Section 7 goes deeper into the effects of ageing. It establishes a baseline scenario by imposing a drop in the birth rate by 10%. Future generations will therefore be smaller than existing generations. After the baseline scenario is established, the four different policy alternatives are imposed on the ageing economy. In this way the effects of the policy reforms can be studied in the context in which they are meant to be implemented.

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2. Background

This chapter discusses some background issues related to this paper. First, it covers the topic of pensions and deals with the objectives of pension systems and pension design. Second, the main features and characteristics of the Dutch pension system are described. Third, since the retirement decision is an important part of our model, we deal with the issue of early retirement in the Netherlands.

2.1 Pension Design

There are different types of pension schemes adopted in different countries.4 There is no such thing as an ‘optimal pension scheme’ that can be applied to every country. Since pension schemes have evolved over the years they have to be evaluated in light of their history and the political situation in their respective country. The optimal policy for each country is path-dependent; it depends on decisions regarding the pension system made in history.

Objectives of pensions systems

The design of a pension system depends on the weight the government attaches to different objectives. The European Union has set out two main objectives for pension systems in its member states.5

• Ensure that older people are not at risk of poverty and can enjoy a decent standard of living; that they share in the economic well-being of their country and can accordingly participate in public, social and cultural life.

• Provide access for all individuals to appropriate pension arrangements, public and/or private, which allow them to maintain, to a reasonable degree, their living standard after retirement.

In a recent paper Barr and Diamond6 set out some of the objectives of pension schemes. The primary objectives are consumption smoothing, insurance, poverty relief and redistribution of income. These objectives will be described below.

4_{See Whiteford and Whitehouse (2006) for a comprehensive survey on pension systems and reforms in}

OECD countries

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Pension schemes provide people an instrument to save for retirement. People maximize utility not just today but over a period of time. They will not consume all their wealth today when they know they will not have any income tomorrow. People tend to smooth their consumption plans over time. Pension schemes allow (perhaps ‘force’ more appropriate in most OECD countries) people to save during their working years, in which they receive wages, for the period that they are retired and thus depend on their pension income for consumption. Unfortunately, people tend to under-save for retirement. The design of the pension scheme can stimulate these savings. This can be done, for example, by favourable tax-treatment of pension savings or by making participation in a pension scheme mandatory. The second objective of the European Union is clearly motivated by the consumption smoothing argument.

A pension system can therefore provide insurance against longevity risk. There are a number of uncertainties regarding pensions that people face. One of the largest uncertainties is that people do not know how long they are going to live. The agent faces the risk that he or she runs out of savings before she dies. A pension system can pool the risks faced by individual agents because the average life-expectancy is known, and guarantees pension payments for each agent for the rest of their life.

Another objective of pension systems could be poverty relief. By providing a base pension to all citizens that does not depend on whether they actually had a job during their life, the government can guarantee a minimum income to pensioners. This prevents the weak in a society, which are unable to save enough to sustain themselves after retirement, from falling below the minimum level of income necessary to fulfil their basic needs. All OECD countries have some sort of safety net to guarantee some minimum standard of living.7 The first objective of the European Union clearly coincides with the poverty relief argument.

6_{Barr, N. and Diamond, P. (2006). ‘The economics of pensions’, Oxford Review of Economic Policy,}

22(1):15-39.

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Pension systems provide the government with an instrument to redistribute income. This could be across generations, by increasing the contribution rate of current generations the future generations’ contribution rate could be lowered (or its pension benefits increased). This way the government redistributes income away from the currently working generations towards the retired generations. It can also be on a lifetime basis, by increasing the pension payments to low earners the government subsidises their consumption smoothing. This way it provides a kind of insurance against low earnings.

Besides these primary objectives Barr and Diamond8 state a few secondary objectives. Pension design could for example influence the participation rate of older workers. The participation rate in turn has an influence on output per capita and on the tax rate. A lower participation rate decreases the tax base and therefore increases the need for higher tax rates. A very generous public pension system can have adverse consequences on the tax rate, which in turn can have a negative influence on economic growth.

Funding

Pension systems can be categorized according to the way in which they are funded and according to the way the benefits are linked to contributions. Pension systems can be fully funded, in which case they are based on savings which are invested in assets. Assets are accumulated during the working years and are used to pay out the agent’s pensions during retirement. Another way of funding is the so-called ‘pay-as-you-go’ (PAYG) pension system. In a PAYG system the pensions of the current generation are paid out of taxes paid by the current working population.

There are also differences in the way pension benefits are determined. Three alternatives can be distinguished here: Defined Contribution, Defined Benefit and Notional Defined Contribution.

8_{Barr, N. and Diamond, P. (2006). ‘The economics of pensions’, Oxford Review of Economic Policy,}

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The first is the Defined Contribution (DC) scheme. Under a DC scheme the worker pays a fixed fraction of wage income into an account. These contributions are invested in assets. The return on those assets is added to the account. When retirement starts the worker receives a pension based on the amount of wealth accumulated in the account, his or her remaining life-expectancy and the rate of interest.

The second is a Defined Benefit (DB) scheme. In a DB scheme the worker’s pension benefit depend on their wage history. It could be indexed to for example the average wage the worker has earned during his or her life or to the last wage the worker earns before retiring. In the Netherlands the large majority (77% in 2004) of pension schemes are based on the average wage.

Third are the Notional Defined Contribution (NDC) schemes in which workers pay a fixed fraction of income into a notional individual account. The state pretends that there is an accumulation of financial assets and credits the account with a notional interest rate. In contrast to the DC scheme the government does not really match the value of the individual account with assets held in financial markets. NDC schemes are in place in Italy, Poland and Sweden.

What most pension systems have in common is that they consist of (at least) two tiers. Of all OECD countries only Ireland and New Zealand does not have a mandatory second-tier.

The first tier consists of a redistributive element, to ensure a minimum standard of living. There are different ways to achieve this, for example by social assistance or basic (flat rate) pensions. Some countries adopt targeted plans which pay higher benefits to the poor and lower to those who are better-off. There are also ‘minimum’ pension schemes, which are similar to targeted plans but form part of the rules of the second-tier programmes. The average safety net in OECD countries ensures a minimum income of about 29% of average national earnings.

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who earns half of national average income is about 72.5%. Somebody who earns the average national wage faces a replacement rate of 56.9% and someone with double the national average wage faces an average replacement of 47.6%. There are large differences between the OECD countries however. Luxembourg for example has replacement rates of 115.5%, 101.9% and 95.2% for someone with half, average or double the national average income. The United States has replacement rates of 49.6%, 38.6% and 28.1% respectively.9

2.2 The Dutch Pension System

The Netherlands have a long history regarding pension systems. The first pension arrangement dates back from September 14, 1579. The private synod of ‘Zuid-Holland’ decided that from that day the government would provide preachers in that region with a form of retirement income. It did not provide an income for the widows and orphans of a deceased preacher, however. Therefore so-called ‘weduwen- en wezenbussen’ were founded. A fixed annual contribution was paid to pay the pensions of the widows and provide income for the orphans of deceased preachers. If the contributions were insufficient, the pension pay-out was lowered to meet the budget constraint.10

At the end of the 19th century the first real company pension fund was founded by Stork. The first pension fund for an entire industry was founded 1917. The ‘Coöperatieve Verzekeringsfonds’, based in Leeuwarden, provided pensions for workers in the dairy industry. In 1957 the basic state pension, the AOW (described below), went into effect.11

The Dutch pension system consists of two major parts. The first is the basic state pension (the first tier) called the AOW. The second tier consists of occupational schemes. Besides the first two tiers there is also a third tier, consisting of individual pension arrangements, which include annuity insurance and endowment insurance.

Oxford Review of Economic Policy, 22(1):78-94.

10_{Speech of DNB president Dr. A.H.E.M Wellink for the PCOB, March 6, 2006.}

(http://www.dnb.nl/dnb/home/nieuws_en_publicaties/nieuwsoverzicht_en_archief/speeches_2006/nl/46-151487-64.html).

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From 1957, every citizen is eligible for the AOW, provided that they lived in the Netherlands between the age of 15 and 65, so for at least 50 years. AOW rights are built up per year. If someone lived outside the Netherlands for 10 years, the AOW pension decreases proportionally. In 2005 the AOW pension was about €869.52 for a single retired person, while married couples (or those officially living together) both received €610.51. Those who do not receive a full AOW pension and whose total income (so including the supplementary pension provided by the occupational pension scheme) is less than 70% of the minimum wage are eligible for social assistance.

The AOW pensions are paid out of taxation on income, with a maximum of 18.35%. It is therefore financed on a PAYG basis. The AOW provides a replacement rate of about 1/3 of the average wage earned by the average worker during his or her lifetime. The AOW is indexed to the minimum wage. When the AOW went into effect in 1957, the average life expectancy was 61. In 2007 it was 77.1 for men and 81.3 for women.12

The AOW ensures that the percentage of retired people that find themselves below the poverty line is one of the lowest in Europe, about 7%. It is also lower than the percentage of 0-64 years old with an income below the poverty line, which is 13%. The risk of having an income below the poverty line is approximately the same for both women (7%) and men (6%). Poverty relief seems to be one of the main goals of this system of basic state pensions.13

The second tier consists of the occupational schemes, which are part of the collective bargaining process and mandatory for about 90% of all employees. Normally the average pension fund aims at a replacement rate of about 70% of either the last wage or the average wage. In 2000 about 60% of the pension funds were based on the last wage and 32% on the average wage. In 2004 this was 13% and 77% respectively. The basic state pension is included in the calculation of the 70% replacement ratio. Unlike the AOW the company pension schemes are not indexed to the minimum wage but to either prices or wages in the respective sector. Indexation is often not guaranteed and if

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the financial position of the pension fund requires it the pension payments can lag behind the increase in prices or wages. Pension payments are tax deductible up to a certain maximum. The pension benefits are subject to taxation once they are paid out.

2.3 Early Eligibility Age

In the Netherlands people can retire from the age of 55. From January 1, 2006 new legislation regarding early retirement came into effect. For those who were 55 years or older before January 1, 2005 the old legislation is still in effect. These people are eligible for certain tax benefits regarding early retirement. The early retirement schemes were funded on a PAYG basis. Though the VUT/Early retirement schemes are not discussed in detail here, the main effect was that people could retire at the age of 60 (provided they met certain requirements) without any detrimental effect on their pension-wealth, creating a very high wedge on working (sometimes even more than 100%). In the transition period the workers that postpone retirement can save the VUT payments and add them to their pension benefits in an actuarially fair way. This provides them with an incentive to work past the age of 60.

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3. The model

In this chapter an overlapping generations model for a small open economy is constructed. There are six periods of 10 years in the model. The household reaches the age of 18 at the start of period 1 and dies at the end of the last period at the age of 78. There is no life-time uncertainty in this model. Each period the household has a time endowment of 1 which has to be divided between work and schooling in period 1 and between working and retirement in period 5. In period 2, 3 and 4 the household is assumed to work full-time and in the last period the household is full-time retired. The model builds on the model presented in the article by Bouzahzah et al. (2002) and is adapted for a small open economy and endogenous retirement.

3.1 Household behaviour

In each period a new generation of households arrive. The size of each new generation of households is given by:

1

t t

2 =m2₋

The household faces a lifetime utility function of the following form: 1 1/ 6 1 1 4 1 1 1 1 / t j j t j c U M σ

ρ

σ

− + − − =  −  = _ _ − −    

∑

,

ρ

≤1,

σ

>0,c≥0

where c is consumption, ρ is the rate of time preference and σ is the (constant) elasticity of substitution. M is the disutility of labour the agent faces in period 5 (see below). We assume that households value consumption in the present more than consumption in the future, i.e. ρ≤ . The inter-temporal elasticity of substitution is a positive constant 1 (σ > ). Each period is denoted by j (in the first period j=1, in the second j=2 etc.). 0 They maximize the utility function subject to a lifetime income constraint:

E≤W,

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6 1 1 1 1 (1 c ) t j t j t j t j E c_{+ −} τ_{+ −} R+ − = =

∑

+ 6 1 1 1 1 1 ( (1 w) j j j ) t j t t j t j t j t j W w τ l_{+ −}h_{+ −} T_{+ −} R+ − = =

∑

− +

Due to the assumption of a perfect credit market future labour income and expenditure on consumption is discounted by:

1 1 1 1 − − + _      + = j w j t t r R , Where w

r is the (exogenous) constant world interest rate.

Labour Supply

The household makes labour supply decisions in period 1 and period 5. In the first period the household decides on the fraction of his time endowment to be spent on schooling. In the fifth period the household decides at which age he wants to retire. The labour supply sequence for a particular household is represented by:

1 2 3 4 5 6

1 2 3 4 5 4

( ,l lt t+,lt+ ,lt+ ,lt+ ,lt+ )= −(1 et,1,1,1,zt+ , 0)

where e is the fraction of time invested in schooling during the first period and t zt+4 is the fraction of time spent working during period 5. Logically, (1−z_t₊₄) is the amount of time spent in retirement during period 5. In the last period the household faces disutility of working of the following form:

2

t M =vz

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Figure 1: 0 10 20 30 40 50 60 70 80 90 100 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Time spent working in period 5 (%)

D is u ti li ty Disutility of labour

The form of our labour supply function is not without its disadvantages however. In all periods except for the first and fifth period the labour supply decision is exogenous. Apart from the changes in labour supply by the first and the fifth generation of households, the labour supply is constant. In the real world the labour supply decision does depend on the tax rate. The average tax-rate influences the labour supply decision at the extensive margin (whether people participate or not). The marginal tax-rate influences the labour supply decision at the intensive margin (how many hours a person decides to work). Especially the labour supply of partners (mostly married women) seems to be elastic to changes in the tax-rate; their labour supply elasticity is estimated to be around 0.4-0.5 for the Netherlands. The labour supply elasticity of sole wage-earners is estimated to be around 0.1, while the labour supply elasticity for singles is around 0.214. The excess burden (or deadweight loss) of taxation cannot be studied using our model.

14_{Evers, M., R. de Mooij, D. van Vuuren (2005), ‘What explains the variation in estimates of labour}

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Human Capital

Human capital formation plays an important role in the model. Households invest in human capital when they are young. The human capital production function given by:

1 ( )e_t h et _t

φ _ψ

ϕ =ξ − , 0<e_t < 1

The production function depends on the average level of human capital in the previous period and on a scale parameter ξ.15 The parameter φ measures the productivity of existing human capital in the formation of new human capital. It can be varied between zero and one. Setting φ to one will give rise to a situation of endogenous growth, which we will not study in this master thesis. If φ is smaller than one there will be diminishing returns to average per capita human capital in the human capital production function.

The production function of human capital gives rise to an intergenerational externality. The intergenerational effect arises because the human capital investment decision of one generation influences the average available human capital per capita. The average human capital per capita in turn influences the human capital production function for the next generations because of the fact that average human capital today influences the production of human capital tomorrow (the term enters with a lag in ( )e_t h et 1 _t

φ _ψ ϕ =ξ − ).

There is a large literature on the intergenerational effects of education suggesting there is a positive intergenerational effect of parents’ education on childrens’ education. Behrman and Rosenschweig (2002) find that one extra year of education of the father leads to 0.36 extra years extra education for the child. Antonovics and Goldberger (2006) find smaller, but still positive, intergenerational effects. For a survey of the intergenerational effects of education, we refer to Minne, van der Steeg and Webbink (2007).16

15_{The production function of human capital is inspired by the production function used in Heijdra and}

Romp (2006) who propose a function of the following form: ( )e_t h et 1 _t φ

ϕ =ξ − . In our opinion it is more plausible that there are diminishing returns to education, given in our model byψ .

16_{Minne, B., van der Steeg, M., Webbink, D. ‘De maatschappelijke opbrengsten van onderwijs’,}

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In contrast to Bouzahzah et al.17 there is no intratemporal externality. The reason for that is the small open economy setting adopted in this master thesis. In a closed economy the average human capital per capita influences the productivity of physical capital and labour, thereby influencing the interest rate and wage rate. In the small open economy setting the wage rate and the interest rate are constant.

Social Security

The social security system is modelled in a simple way. In the first period the household receives an education subsidy for the duration of their schooling period. The subsidy takes the form of a fraction of the opportunity cost of working for those who invest in schooling. First period income will be equal to:

(1−e_t(1−s_t))(1−τ_tw)wϕ( )e_t

In period 5 and 6 the household receives a pension from the government during retirement. The government is the sole provider of pension benefits and pays its pensions out of the general budget. A household that retires at age 65 gets a fixed government pension worth 30% of his wage for the rest of his life. The only way for a household to retire before the age of 65 and/or consume more than earned by the pension is to save part of the income earned during their working years. The age at which the household is forced to exit the labour market is set at 68, the end of the last period. The AOW pensions will be paid from the age of 65 even if the household continues to work beyond the age of 68.

Although this model does capture the mixed Dutch system of pay-as-you-go funded state pensions (the first tier, or AOW) in a very acceptable way, the second tier is modelled in a more abstract way. There are no pension funds in the model, and pension savings are not tax deductible. Savings are part of the after-tax income. On the other hand, the pension payments (people consume out of their savings during retirement) are also not subject to the income tax. We also abstract from any of the early retirement

17_{Bouzahzah, M., De La Croix, D., Docquier, F. (2002). ‘Policy reforms and growth in computable OLG}

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schemes in place today. The fact that people finance early retirement out of savings is in line with the life-course arrangement that took effect from January 1, 2006, although there is no maximum amount of savings imposed and savings are not tax-deductible.

The per period direct transfers are given by: 1 2 3 4 5 6 1 2 3 4 5 4 5 (T Tt , t+ ,Tt+ ,Tt+ ,Tt+ ,Tt+ )=(sw(1−τ ϕtw) ( ), 0, 0, 0,et ϖPt+ ,Pt+ ) Where: P_t1+₄ =ς ϕw ( )e_t 2 5 ( ) t t P+ =ς ϕw e

ςis the replacement rate provided by the government pension (30% in our model) and

ϖ is the fraction of period 5 in which the agent receives the state pension (0.3 in our model, which corresponds to a retirement age of 61).

Financial Wealth

In the model households can save and borrow at the given world rate of interest. They can invest in government bonds, shares in domestic capital and foreign government bonds. The return on each of the financial assets is the same and equal to the constant world interest rate. The end-of-period financial wealth of an individual household is given by: ) 1 ( ) 1 ( ) 1 ( 1 1 1 1 1 1 1 2 1 c j t j j t j j t j j t j j t w j t w j j t j j t a r w l h T c a₊ ₋ = ₊−₋ + + −τ ₊ ₋ ₊ ₋ ₊ ₋ + ₊ ₋ − ₊ ₋ +τ ₊ ₋ Where:

(

)

5 5 1 1 j j j j t t t t j j a v f b = = = + +

∑

, 5 1 j t t t j v V K = = =

∑

It is assumed that the household has no bequest motive and consumes all his financial wealth during the last period so that individual financial assets at the end of period 6,

6 t

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3.2 Firms

The productive side of the economy is largely based on Heijdra and Romp (2006)18 except for the fact that it is adjusted for a discrete time setting instead of a continuous time setting. Perfectly competitive firms operating in international markets face a production function of the Cobb-Douglas form, using capital and human capital as inputs: β β − = 1 ) ( Y t t t K A H Y

Yt is output, Kt is physical capital, Ht is human capital and Ay is a scale parameter. The

firms rent their inputs in perfectly competitive markets for physical and human capital. The profit function of the firm is given by:

1 (1 ) t t t t t t t t Y w H I I K δ K₋ Π = − − ≡ − −

Output is a homogeneous commodity which is traded on international markets. The first-order conditions for physical and human capital give rise to the rental rates of the two types of capital:

Rental Rate of Physical Capital: w ( Y t)1 t A h r k β δ β − + = (A)

Rental Rate of Human Capital: (1 ) ( Y t)

t Y t A h w A k β β − = − (B) Where 5 1 5 1 j j t t j t t j _t t j l h H h L l = = =

∑

=

∑

and t t t K k L =

The human capital / physical capital ratio is constant over time because the interest-rate is constant and equal to the world-interest-rate, fixing the left-hand side of equation A. (The only endogenous variables in equation A are human capital and physical capital.) Equation B shows that the wage rate is a function of the same ratio of human capital / physical capital and is therefore also constant over time.

18_{Heijdra, B.J. and Romp, W.E. (2006), ‘Ageing and growth in the small open economy’, CESifo}

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The per capita stock of physical capital is obtained by dividing equation A by total labour supply. After some manipulation it follows that per capita physical capital is given by: t w Y t h r A k ( )1/(1 β) δ β − + = (C) Where: 5 1 5 1 j j t t j t t j t t j l h H h L l = = =

∑

=

∑

t t t L K k =

Total output is equal to the rental rates of the two types of capital times the stock of both types of capital:

( ) t

t t

y = r+δ k +wh (D)

By substituting equation C into equation into equation D we obtain per capita output in terms of average human capital per capita:

1 1 1 ( ) ( ) t t y y r A w h β β β δ − β −   =_ + + _  

Output per worker and capital per worker are both indexed to the average stock of human capital per worker. This implies that the growth rates of investment, capital per worker, and output per worker are all proportional to h . t

3.3 The Government

Government expenditures and income are modelled in a simple way. The government levies taxes on both labour income ( w

t

τ ) and on consumption ( c t

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The government budget constraint is given by:

The left hand side of the government budget constraint represents government income. The first term on the left-hand side represents taxes collected on labour income. The second term is taxes levied on consumption and the third term is the government debt in the next period.

The first term on the right-hand side are the pensions paid to households which reach period six at time t, and are therefore born at time t-5. The second term is pensions paid to the retirees in period 5. The third term is the education subsidy paid to the young generation.

Besides these direct transfers there are age-independent and age-dependent government expenditures. Age-independent government expenditures consist of for example expenditures on police, national defence etc. Besides these age-independent expenditures there are age-dependent expenditures which are for example expenditures on health care, which are higher for the older generations than for the young generations. Age independent government expenditures are linked to the productivity index h and the population indext γ , age dependent government expenditures are linked to productivity only:

6 1 1 j t t t j t j G G 2_{− +}g = = +

∑

, G=g hγ _t, g_tj =g g hj a t a

g and g are scale parameters we need for calibrating the model (the initial government expenditures must comply with an income tax rate of 30% and a government debt of 0.045, see chapter 5 for more details regarding calibration). The parameterγ is a population parameter and measures the size of the population relative to the initial steady state population size. In the initial steady state the population size

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will be 6. As the birth rate drops by ten percent, the parameter γ will gradually fall from 1 to 0.9. This formulation of government expenditures allows us to capture the notion of increasing total government expenditures on for example health care for an ageing population.

For the Netherlands the amount of age-independent government expenditures is about 19% of GDP, while age-dependent government expenditures are about 25% of GDP. The age-dependent government spending is loosely divided over the different generations based on data provided by the CPB.19 Figure 2 gives a graphical representation of benefits received by agents of different ages. Our estimates are based on the total benefits curve minus the social security cost curve and corrected for the fact that education spending takes the form of direct transfers in our model rather than indirect transfers, because of the existence of the education subsidy. The age profile of benefits in our model is given by:

1 0.12

g = , g =2 0.13, g =3 0.14, g =4 0.15,g =5 0.18, g =6 0.25 Figure 2:

Age Profile of Benefits

(€1000)

Age

Source: van Ewijk et al. (2006). ‘Ageing and the Sustainability of Dutch Public Finances’, CPB Netherlands Bureau of Economic Policy Analyses.

19_{Van Ewijk et al. (2006). ‘Ageing and the Sustainability of Dutch Public Finances’, CPB Netherlands}

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4 Per period household behaviour

In this section the behaviour of each generation of households is described. The model assumes households are blessed with perfect foresight. In the absence of shocks the decision-making process is intertemporally consistent and any decision made in the first period regarding future consumption and retirement will be perfectly forecasted. Once a shock occurs the different generations might react in different ways. This makes perfect sense since the older generations are locked in regarding the decisions made in previous periods. Since the decision regarding the investment in schooling is irreversible and previous period consumption cannot be undone, older generations are more limited in the possibilities they have to deal with shocks than younger generations.

4.1 Period 1

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The first guessed solution assumes that only the income constraint is binding (so λt>0,

, 1, 2, 3, 4, 5 t t t t t t

c c₊ c₊ c₊ c₊ c₊ are all greater than zero, 0 ≤ zt+4 ≤ 1 and 0 < et < 1. The

household maximizes lifetime utility, taking into account the disutility of working during period 5 and the lifetime income constraint. They maximize Ω with respect to consumption in all six periods, as well as schooling and retirement. If there are no shocks hitting the economy during the lifetime of the household, all decisions made by the household in period 1 will be exactly the same as the decisions made in consecutive periods because the household is blessed with perfect foresight.

Consumption

The dynamic programming problem presented above gives us the following FOCs regarding consumption in period 1, 2, 3, 4, 5 and 6:

1 (1 ) t c t t c σ λ τ   =  ₊    , 1 1 (1 ) (1 ) w t c t t r c σ ρ λ τ + +  +  =  ₊    , 2 2 2 2 (1 ) (1 ) w t c t t r c σ ρ λ τ + +  +  =  ₊    , 3 3 3 3 (1 ) (1 ) w t c t t r c σ ρ λ τ + +  +  =  ₊    , 4 4 4 4 (1 ) (1 ) w t c t t r c σ ρ λ τ + +  +  =  ₊    , 5 5 5 5 (1 ) (1 ) w t c t t r c σ ρ λ τ + +  +  =  ₊   

Which gives us the consumption Euler equation: 1

1 (1 ) (1 ) (1 ) c t t c w t t c c r σ τ τ ρ − + +  +  =  ₊ ₊    . Schooling

Due to the production function, Yt =Ktβ(AYHt)1−β, and the fact that the household lives in a small open economy, the rental rate of human capital is constant:

β β − − =(1 ) ( ) t t Y Y t K H A A

w . This implies that w1 = w2 = w3 = w (see below).

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Dividing by wϕ( )et and rewriting to e (noting thatt ( )et h et 1 t φ _ψ

ϕ =ξ − ) gives us:

The education decision is influenced by the world interest rate, the current and future tax rates on income, the education subsidy and the retirement age. The nominator represents the marginal value of an additional investment in human capital, which depends on future tax rates, the retirement age and the world interest rate. The marginal value of an additional investment in human capital is discounted by the income that could be generated by working instead of learning, which is equal to the after-tax value of work, and by the education subsidy provided by the government. The higher the subsidy, the more an agent will invest in education. The same argument holds for tax on wages, the higher the current tax on wages compared to future taxes on wages, the higher will be the fraction of time invested in education.

Retirement

The household maximizes lifetime utility by taking into account the disutility of working in period 5. After some manipulation the first order condition of Ω with respect to zt+4 gives us:

4 4 4 4 (1 ) ( ) (1 ) 0 2 w t t w t t w e r z v τ ϕ λ ρ + +  −   ₊      = ≥        

The retirement age depends on the marginal utility of wealth (λt), the disutility of

working (2υρ4) and on the after-tax income earned by working. The numerator represents foregone income caused by retirement, which is equal to the (discounted) after tax income. The denominator represents the disutility of working. The higher the disutility of working, the lower the retirement age will be. The second part is the foregone utility of continued working, which is positively related to the retirement age. The retirement decision also depends on the marginal utility of wealth, which in turn

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depends on the level of consumption _1/ 1 (1 ) t c t t c σ λ τ    =     _ ₊ _

 . The higher the level of consumption, the lower the marginal increase in utility the household can buy from postponing retirement. Consumption depends on the amount of savings and on the amount of after-tax income earned.

4.2 Period 2

In the second period the household takes as given the amount of schooling and consumption in period 1 and decides on the path of consumption for periods 2,3,4,5 and 6 as well as the optimal retirement age in period 5.

The maximization problem will be:

This langrangian is maximized w.r.t ct,ct+1,ct+2,et and zt+2:

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(

)

1 3 3 3 3 3 3 1 0, 0 1 c t t t t w t c c c _r σ_ρ _λ τ − ₊ + + +  ₊  ∂Ω _ _ = − ≤ ≥   ∂ ₊   , ₃ 3 * 0 t t c c + + ∂Ω = ∂ ,

(

)

1 4 4 4 4 4 4 1 0, 0 1 c t t t t w t c c c _r σ_ρ _λ τ − ₊ + + +  ₊  ∂Ω _ _ = − ≤ ≥   ∂ ₊   , ₄ 4 * 0 t t c c + + ∂Ω = ∂ , 4 4 4 5 4 5 4 (1 2 )(1 ) (1 ) 2 ( ) 0 (1 ) (1 ) w w t t t t w w t t z w e z r r ϖ ς ϖ τ ϖ τ υρ λ + + + ϕ +  + − + − −   ∂Ω = − + __ + _ _≥ ∂ __ + + _ _

(

)

₍

₎

(

)

(

)

1 1 2 1 1 2 3 3 1 3 1 4 1 3 4 1 (1 ) ( ) (1 ) ( ) (1 ) ( ) ... 1 ₁ (1 ) ( ) ( ) (1 ) ( ) (1 ) ( ) ... ... 1 1 (1 (1 ) w w w t t t t t t _w w w w w t t t t t t t w w t c t t t t w e w e w e r _r z w e w e w e r r c c τ ϕ τ ϕ τ ϕ τ ϕ ςϖ τ ϕ ς τ ϕ λ τ τ + − + − − + + − + − + − +    ₋  ₋     − + +    +  ₊  _{ } _  ₋ ₊ ₋   ₋  ∂Ω _ _{ } _ = + +     ∂ ₊ ₊     + − + + 1 2 2 3 3 4 4 2 3 4 0 ) (1 ) (1 ) (1 ) 1 (1 ) (1 ) (1 ) c c c c t t t t t t w w w w c c c r r r r τ τ τ + + + + + + +             ≥          + + +  + + +    ₊ ₊ ₊ ₊        0 t λ ≥ , _t* 0 t λ λ ∂Ω = ∂ Consumption

The first order conditions for consumption have no changed in comparison with the first period, except for the lambda of course. This gives us the same consumption Euler equation as in the first period:

1 1 (1 ) (1 ) (1 ) c t t c w t t c c r σ τ τ ρ − + +  +  =  ₊ ₊    . Retirement

The optimal retirement decision is virtually unchanged compared to the first period:

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4.3 Period 3

The maximization problem will not be presented anymore, just the optimal decisions made by the household.

Consumption 1 1 (1 ) (1 ) (1 ) c t t c w t t c c r σ τ τ ρ − + +  +  =  ₊ ₊    . Retirement 2 2 2 2 2 (1 ) ( ) (1 ) 0 2 w t t w t t w e r z v τ ϕ λ ρ + − +  −   ₊      = ≥         4.4 Period 4 Consumption 1 1 (1 ) (1 ) (1 ) c t t c w t t c c r σ τ τ ρ − + +  +  =  ₊ ₊    Retirement 1 3 1 (1 ) ( ) (1 ) 0 2 w t t w t t w e r z v τ ϕ λ ρ + − +  −   ₊      = ≥         4.5 Period 5

In this period the household chooses ct, ct+1 and the age of retirement zt.

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Retirement

The optimal retirement decision is virtually unchanged compared to the first period: 4 (1 ) ( ) 0 2 w t t t t w e z v τ ϕ λ  − −  = _ _≥  

The retirement decision depends on three factors. It depends positively on the marginal utility of wealth. The second factor is the after-tax wage income; the higher it is the higher is the incentive to work longer. The third is the disutility of working, which obviously has a negative effect on the effective retirement age.

4.6 Period 6

Since it is assumed that the household has no bequest motive, the household simply consumes all financial wealth and pension income during the last period, which implies that 6

0 t

a = . Consumption will be equal to: 6 5

1(1 ) (1 ) ( 5)

w w

t t t t

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5. Steady state and calibration

In this chapter the model’s steady state and calibration are discussed. Finding a steady state for the model begins with setting values for all parameters except the education subsidy s and the disutility of labour t υ; we need those parameters to calibrate the initial steady state values of e and _t z . The size of each generation of households is _t normalized to one(2 =1). The value of β, the capital share of national income, is set at 0.3. We set the rate of depreciation δ at 50% for ten years, approximately 6.7% per year. The rate of interest rw is set at 70%, which is approximately 5.5% per year. The consumption tax rate is 12% and the intertemporal substitution elasticity is 0.5. The rate of time preference is 0.7374 which comes down to 0.03 per year.20

The value of A is chosen in such a way to make sure that w=1 (Remember _Y

that ₌ ₋β −β ) ( ) 1 ( t t Y Y t K H A A

w ). This is convenient since setting w=1 allows us to drop w

out of every first order condition. Given the values of δ, β and rw we calibrateA at Y approximately 2.5878.

Human Capital

The steady state of this model depends crucially on the value of average human capital per worker since the growth in h determines the growth in output per worker and t capital per worker. Therefore, first we choose a steady state value of h for the model. t The value of h is set to 4. This implies that output per worker is equal to 6.57663 and t capital per worker is equal to 1.42857.

We want the education parameter e to be 0.4.t

21

This means households will receive education up to the age of 22. The education decision depends on the interest rate (which is fixed), the retirement age and the education subsidy. In the steady state the tax rate and the retirement age are constant, so we assume for the moment that the

20_{These numbers are based on Heijdra and Romp (2006) except for the intertemporal substitution}

elasticity, which is set at a lower rate to obtain a more realistic life-time consumption pattern.

21_{A value of 0.4 corresponds to an average of 17 years of schooling for a person that reaches the age of 5.}

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steady state retirement age is exactly the age we want (z=0.4) and calibrate e with the _t help of the education subsidy. It turns out that a subsidy of 0.496001 is necessary to calibrate e at 0.4. Note that the education decision is independent of any of the t parameters of the human capital production function except the parameterψ , the return to education, which we set to 0.1 to obtain sensible results for the subsidy rate.

Retirement

The retirement age depends on the after tax wage income, disutility of working and on the marginal utility of wealth. The retirement age is set at 0.4, representing an effective retirement of 62. This value lies above the current average effective retirement age (61) in the Netherlands. However, the abolishment of the fiscally facilitated early retirement schemes will most likely increase the effective retirement age in the future.

4 (1 ) ( ) 0 2 w t t t t w e z v τ ϕ λ  − −  = _ _≥  

Since we need the value of λ to set the value of υ, we first run a simulation of the model in which we keep the value of z fixed at 0.4, our preferred value. With the steady state outcomes of the simulation we are able to calculate the value of λ. Once the value of λ is known, we can calculate the value of υ. Following this procedure gives us a value for υ of 0.3605185.

Table 1: Calibration

Variable Value Variable Value Variable Value

δ 0.5 β 0.3 Ay 2.5878

σ 0.5 rw 0.7 ψ 0.1

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Steady State

Table 2 shows the values of the endogenous variables in the steady state. These values are independent of which scenario is used; all three scenarios start from the same steady state. In the steady state the ratio of total consumption to GDP is approximately 65%. The ratio of government expenditures to GDP lies around 28%. For the Netherlands, this ratio is approximately 40%. Our ratio is lower because the government does not levy taxes on assets or profits, so all government expenditures have to be paid by taxes on income and consumption. The level of government expenditures is calibrated to obtain realistic levels of income and consumption taxes.

Table 2:

Steady State results

Variable Value Variable Value Variable Value

Y 26.30652 c1 1.87352 a1 0.137185 K 5.71428 c2 2.09756 a2 0.683846 h 4 c3 2.3486 a3 1.3321 h 4 c4 2.62957 a4 2.11946 e 0.4 c5 2.94416 a5 1.67762 z 0.4 c6 3.29638 F -0.9479 B 1.1837934

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Table 3:

Calibration of the three scenarios.

Parameters Scenario 1 Scenario 2 Scenario 3

Education Parameter φ 0.2 0.3 0.4

Education Parameter ξ 3.3223 2.8923 2.5179

The three values of φ (recall from chapter 3 that φ is the productivity of existing human capital in the production of new human capital) are chosen such that they lie around the 0.3 value as advocated by Heijdra and Romp (2006, p.20). Starting from the steady state specified in the previous section we use Dynare22 to study the effects of four types of shocks.

22_{Dynare is a preprocessor and a collection of matlab routines that implements the methodology}

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6. Simulation Results

This chapter presents the simulation results of four policy alternatives meant to deal with the problems of an ageing population. These four policy alternatives are:

1. Pension reforms (1): increasing the eligibility age for public pension to 68 instead of 65 years.

2. Pension reforms (2): the PAYG part of pensions is suppressed at date t=1 so that agents rely fully on private saving for their old age income.

3. A fiscal shock by increasing the education subsidy by 20%. 4. Debt-repayment: government debt is repaid in one period.

All shocks are permanent shocks in which the economy converges towards a new steady state because of the fact that the intergenerational externality is below the value of 1. Figures 4 to 7 present the transition paths after the four shocks. In these figures the shocks occur at t=5 so the first period after the shock is at time t=6. The shocks represent once-off changes in government policy. In real-life changes in government policy are often introduced gradually, because of political pressure of certain interest-groups (‘if you can’t work it out, smooth it out…’).

Sensitivity analysis has shown that the simulation results are robust to different calibrations of the model, regarding for example the intertemporal substitution elasticity or the rate of time preference. The transition paths are similar but the size of the effects of the policy shocks is different under different calibrations. The relative effects (comparing the policy reforms) are however robust to different calibrations. The size of the effects is presented here to be able to compare the different policy reforms. It is important to keep this in mind when interpreting the results.

6.1 Pension Reform (1)

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The immediate effect of this policy change is the increase of the retirement age from 0.4 to 0.4295. This (at least in the eyes of most policymakers) positive effect lasts however only two periods. The retirement age drops in the second period after the shock to 0.404. In the third period it drops to 0.3986 and settles in the long-run at a value of 0.3955. Note that this lower than the original value! This is an interesting result because the policy change is meant to increase the participation rate of older workers. It turns out that the lower income tax rate allows people to save more in anticipation of a decrease in income in period 5. The policy change has an adverse long-run effect on the participation rate of older generations.

The education decision is not really influenced by the policy change. The length of schooling drops from 0.4 tot 0.398 in the long-run. This is caused by the lower retirement age which decreases the time a person can benefit from schooling. The long-run value of average human capital per worker decreases only from 4 to 3.997. The increase in the pension age has no large influence on the education decision. This is consistent with the findings of Bouzahzah et al. They find that only policy that directly affects the education decision (like a subsidy for example) has a large influence on the length of schooling chosen.

Because there are less pensions to support, the income tax rate falls by approximately 1.62%-point in the short run and 1.57%-point in the long-run. This increases the after-tax income of households, allowing them to consume and save more. The ratio of assets to GDP increases from 22.6% tot 24.1%.

Consumption in levels rises very slowly in the first two periods after the policy change. After that it gradually increases and reaches its new and higher level 7 periods after the shock occurred. The ratio of consumption to GDP falls in the first period after which it gradually increases to its new and higher steady state level.

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are presently generation 5) decreases because they did suffer the consequences of the increase in pension age. The young generations have more possibilities to cope with the policy change. First period consumption reaches the new long-term consumption level the fastest, followed by second period consumption etc. The percentage change in consumption per generation is illustrated in figure 3.

Figure 3:

Percentage change in consumption

-0,04 -0,03 -0,02 -0,01 0 0,01 0,02 0,03 1 2 3 4 5 6 7 8 9 Time c1 c2 c3 c4 c5 c6 Conclusion

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Figure 4:

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Retirement Age 0,37 0,38 0,39 0,4 0,41 0,42 0,43 0,44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time

Average Human Capital

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Consumption 15,05 15,1 15,15 15,2 15,25 15,3 15,35 15,4 15,45 15,5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time C/GDP 0,63 0,635 0,64 0,645 0,65 0,655 0,66 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time

(The blue line corresponds to scenario 1, the pink line corresponds to scenario 2 and the yellow line corresponds to scenario 3)

6.2 Pension Reform (2)

This policy change can be seen as a very crude transition from a PAYG system to a fully funded system. Though interesting from a theoretical point of view it is not likely that such a transition is going to happen because of the detrimental effects on income for the people with the lowest incomes. The state pension in the Netherlands is designed in such a way that it minimizes the risk of poverty for the older generations with very low income.

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generation, which see their pension income disappear, can now only consume out of the savings they had built up. The positive effect of the decrease in the income tax of about 7.3%-point allows people to consume and save more in the future in anticipation of the decrease in pension income.

In the short run there is a very sharp increase in the retirement age, assets and nominal GDP. The increase in nominal GDP is purely caused by the increase in the participation rate. GDP per worker is virtually unchanged during the transition path. Short run consumption falls due to the fact that the negative effect of the fall in old age income outweighs the positive effect of the fall in the income tax rate.

Conclusion

The effects of the suppression of government pensions are similar to, but stronger than the effects of an increase in the pension age. In the first ten years the effective retirement age is increased by almost a year. GDP is increased by almost 2.6%-point. In the long run the effective retirement age falls by approximately 3 months compared to the initial steady state. In the long run, GDP falls by .75%-point. The income tax rate falls by 7.3%-point.

Figure 5:

Effects of abolishing the AOW.

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C/GDP 0,54 0,56 0,58 0,6 0,62 0,64 0,66 0,68 0,7 0,72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time

6.3 Fiscal Shock

The third policy alternative we study is that of a fiscal shock in the form of an increase in the education subsidy of 20%. This means that the value of s increases from 0.496 to 0.5952. The results are displayed in figure 3. The households that have already made their education decision (those reaching period 2 or higher when the shock occurs) are only affected through changes in the income tax rate. This explains the fact that we observe a ‘kink’ in many of the graphs presented below when the last generation of ‘locked-in’ households pass away.

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Consumption in levels falls because of the increase in the income tax rate by about 2.3%-point. Once the locked-in generations have passed away consumption rises again. After the initial shock nominal consumption rises faster when the intergenerational externality is higher. Consumption as a percentage of GDP shows a different transition path. It rises in the first period after the shock because the decrease in output outweighs the decrease in consumption. After that in all three scenarios the ratio of consumption to GDP falls in the second period after the shock. From that period on it gradually rises again and the scenario with the highest intergenerational externality experiences reaches the highest value of consumption relative to GDP. Total and foreign assets experience the same transition paths as the ratio of consumption to GDP.

The retirement age falls marginally in the first period after the shock because of the increase in the income tax rate. This is caused by the increased government expenditures on the education subsidy. After that the retirement age gradually rises due to the fall in consumption in these years (remember that the retirement age depends on disutility of labour, after tax wage income and the marginal utility of wealth). In the third period after the shock the retirement age reaches the highest value because at that time the last generation who did not receive the higher education subsidy reaches the fifth period of their lifetime. In the fourth period after the shock the first generation of households that received the higher education subsidy reaches period 5 of their lifetime and it can be observed that the retirement age falls in that period. The economy slowly converges to its new equilibrium in which the retirement age is slightly higher (scenario 1 and 2) or lower (scenario 3) than its initial value.

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Conclusion

A 20% increase in the subsidy rate raises e by approximately 25%. In the short run _t GDP in levels falls. GDP per worker increases both in the short run and in the long run. Both the ratio of consumption to GDP and total assets held falls, which is primarily caused by the increase in the income tax rate of about 2.3%-point. The effective retirement age falls marginally in the first ten years. In the next thirty years the effective retirement age increases until it is about 2 months higher compared to the initial steady state. In the long-run it settles marginally above the initial value.

Figure 6:

Effects of a fiscal shock

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Education 0,29 0,34 0,39 0,44 0,49 0,54 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time Retirement Age 0,385 0,39 0,395 0,4 0,405 0,41 0,415 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time

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Income Tax 0,285 0,29 0,295 0,3 0,305 0,31 0,315 0,32 0,325 0,33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time Consumption 14,7 14,8 14,9 15 15,1 15,2 15,3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time C/GDP 0,625 0,63 0,635 0,64 0,645 0,65 0,655 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time

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6.4 Debt Repayment

This policy alternative assumes that the total government debt is repaid in the first period to decrease the interest payments in the future. To finance this, the income tax rate has to be increased sharply in the first period to cover the extra expenses caused by paying of the government debt. The Dutch government has pursued this policy since the end of the 20th century and with success. They have brought down their debt-to-GDP ratio from over 60% in the late 1990’s to about 45% in 2007.

The effect of this policy change on the income tax is an immediate increase in the first period from 30% to about 37,5%. After that the income tax drops because of the fact that the government no longer needs to make interest payments. In the long run the income tax rate drops to around 24.9%, approximately 5% lower than in the initial steady state.

The effects on the income tax rate cause a sharp increase in the length of education chosen in the first period. The intuition behind this is simple. The education rate depends positively on the ratio of future after tax income to current (foregone) after tax income. Since first period income tax rises sharply and future tax rates fall sharply, the nominator increases and the denominator decreases. This causes the ratio of future earnings to current earnings to increase sharply. After the first period the income tax falls quickly to its new (lower) steady state value. The length of education falls back to its initial level of around 0.4. This is because in the long run current and future tax rates are approximately equal and the ratio of future to current earnings is back around its old level.

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The retirement age drops in the first period due to the increase in the income tax. The households experience less additional benefit from working due to the increase in the tax rate. As the tax rate drops in the second period after the shock the retirement age increases. This effect lasts until the last of the locked-in households have passed away, which is after 5 periods. Younger households have the opportunity to save more because of the lower tax rate and are therefore able to retire a little bit earlier. The long-run retirement age is therefore lower than the original retirement age (0.375 against 0.4 in the initial steady state).

Although average human capital (and therefore GDP per worker) increases in the short run, nominal GDP falls sharply in the first period due to the decrease in the participation rate of the young generation and the decrease in retirement age. Both nominal GDP and GDP per worker show a hump-shaped pattern which lasts six periods. After that they slowly converge toward their long-run steady state values. GDP per worker reaches the same value as in the initial steady state, nominal GDP falls due to the decrease in the retirement age.

Consumption, both in levels and as a percentage of GDP, falls in the first period after which it gradually increases to a higher level. This is a natural consequence of the transition path of the income tax rate. This is also the explanation for the transition path of total assets, which drops in the first period after which it gradually moves to a value which is higher than in the initial steady state.

Conclusion

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Figure 7:

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Retirement Age 0,32 0,34 0,36 0,38 0,4 0,42 0,44 0,46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time

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Consumption 14 14,5 15 15,5 16 16,5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time C/GDP 0,6 0,62 0,64 0,66 0,68 0,7 0,72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time

6.5 Discussion

An important insight gained from this section is that different generations will react differently to a change in policy. This is caused by two effects; the lock-in effect and the anticipation effect.

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The anticipation effect is caused by the fact that households respond to changes in (after-retirement) wealth. Abandoning the state pension scheme lowers after-retirement wealth for households. Households will react by saving more to smooth consumption over their lifetime. In other words, they anticipate on lower after-retirement wealth by saving more during their working years.

Policy makers have to take the lock-in effect and anticipation effect into account when implementing new policy. This is illustrated nicely by the two pension reform scenarios, which are meant to increase the participation rate of older workers. Although there is a sharp increase in the retirement age in the first periods due to the lock-in effect, the long-run retirement age is lower than the original retirement age, because people will save more in anticipation of lower after-retirement wealth (the anticipation effect). In this case the decrease in the retirement age is not purely caused by the anticipation effect but also by the decrease in the income tax rate, which increases the after-tax income and thereby the ability to save for retirement.

The lock-in effect and the anticipation effect are the main reasons why politically difficult decisions are often ‘smoothed out’ over several years or even decades. The reform of the VUT/Pre-pension schemes for example, as discussed in section 2, is subject to a long transition period. People that were past the age of 55 on January 1, 2005 are not subject to the new legislation, although the incentives to keep working were made more actuarially fair. In addition, those between 50 and 55 years old at the time the VUT/Pre-pension reforms went into effect, were given the option to save more than 12% per year. In this case the most constrained people were given more possibilities to adapt to the new situation.

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Policy Reforms and Ageing in the Small Open Economy