Environmental fiscal policy and its distributional and macroeconomic effects

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ENVIRONMENTAL FISCAL POLICY AND

ITS

DISTRIBUTIONAL

AND

MACROECONOMIC EFFECTS

Word count: 18.118

Student number : 01503549

Supervisor: Prof. Dr. Freddy Heylen

Master’s Dissertation submitted to obtain the degree of:

Master in Economics

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PERMISSION

I declare that the content of this Master’s Dissertation may be consulted and/or repro-duced, provided that the source is referenced.

Student’s name: Babette Jansen

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Preface

I am happy to present you my dissertation titled "Environmental fiscal policy and its distributional and macroeconomic effects". In this dissertation I looked at the possibility of achieving a double dividend where there is an improvement in environmental quality together with an improvement in macroeconomic factors, without harming living stan-dards for any household. During my studies in Economics I was always very interested in Macroeconomics and I am glad to end my studies with this challenging but fulfilling dissertation.

I would like to thank a few people for their help, guidance and encouragement. I especially would like to thank my promoter professor Heylen for introducing me to the topic and his feedback on all aspects. Writing this dissertation taught me a lot thanks to the interesting insights he gave me. I would also like to thank Pieter Van Rymenant and Lucas Rabaey for guiding me through Dynare. The technical part of my dissertation was often difficult and I am very grateful for the elaborate help I received. Finally, I would like to thank my friends and family for encouraging me while writing this dissertation and throughout my entire studies. Thank you for supporting me and brightening my day even when we were apart.

Babette Jansen Ghent, August 2020

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List of Abbreviations

CES Constant elasticity of substitution GDP Gross Domestic Product

IES Intertemporal elasticity of substitution LHS Left hand side

OECD Organization for Economic Co-operation and Development OLG Overlapping Generations

PAYG Pay as you go

PPP Purchasing power parity RHS Right hand side

UNFCCC United Nations Framework Convention on Climate Change

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List of Figures

3.1 Determination of the real wage. 22

3.2 Determination of the real interest rate. 22 5.1 Employment rate in hours, retirement age and unemployment rate among

low ability individuals, 1995-2007. 38 5.2 Participation in tertiary education (e, in %), 1995-2007. 40 5.3 Annual per capita growth rate of GDP (in %), 1995-2007. 41 5.4 CO2 emissions per 2011 PPP $ GDP (in %), 1995-2007. 42

7.1 Dynamic effects on employment, effective retirement age, and unemploy-ment of a permanent fiscal policy shock in period 1. 51 7.2 Dynamic effects on education rate, output, and annual growth of a

perma-nent fiscal policy shock in period 1. 52 7.3 Dynamic effects on environmental quality and harmful emissions of a

per-manent fiscal policy shock in period 1. 53 7.4 Welfare effects of fiscal policy shocks on current and future high and low

ability individuals. 55

C.1 Dynamic effects on output and environmental quality of a permanent fiscal

policy shock in period 1. XI

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List of Tables

3.1 Life cycle of an individual of generation t and ability a. 10 4.1 Key data on OECD countries (1995-2007) 28

4.2 Parameterization 30

4.3 Fiscal policy parameters (tax rates, in %) 34 4.4 Fiscal policy parameters (net replacement rates, in %) 35 4.5 Fiscal policy parameters (productive government expenditures and

govern-ment consumption, in %) 36

6.1 Steady state effects of fiscal policy shocks (equal to 0.5% of output, ex ante). 45 7.1 Net welfare effects after compensating welfare transfers (expressed as % of

initial GDP). 56

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1. Introduction

Human activities have increased the atmospheric levels of carbon dioxide by more than a third since the industrial revolution, leading up to the highest level in 650.000 years (Nunez, 2019). Climate change is becoming a more urgent topic every day. Under the UNFCCC, 197 members meet annually as the Conference of the Parties to fight climate change. In 2015 all parties helped outline the Paris Agreement, which imposed the mem-bers to take policy actions to prevent the global average temperature to rise 2°C above the pre-industrial level (UNFCCC, 2020). A few years later in that same country the yellow vests movement emerged. France, and other core EU countries, have among the highest taxes on fuel (European Commission, 2019). Households, who contribute two-thirds of the total transportation tax, are struggling every month to make ends meet (Eurostat, 2019).

To combine the environmental issue with the risk of higher inequality, this dissertation contributes to the literature the combination of heterogeneous abilities and environmen-tal fiscal policy in an overlapping generations framework based on Heylen and Van de Kerckhove (2019). Environmental fiscal policy can lead to distributional issues between generations, as the tax is levied on all current generations while the improved environ-mental quality can only be enjoyed by future and current young generations (Bovenberg & Heijdra, 1998). Inequality can also increase within generations due to differences in consumption and income. Low income households consume relatively more necessary and polluting goods, which results in higher tax payments (Chiroleu-Assouline & Fodha, 2011). The goal of this dissertation is to achieve the double dividend, without increas-ing inequality. The possibility of a double dividend means that there can be both an improvement in environmental quality without a decline in economic activity. To avoid negative economic effects and increased inequality, the tax revenues from the environmen-tal tax can be used to compensate the loss carried by low ability households (Aubert & Chiroleu-Assouline, 2019).

In this dissertation we set up six fiscal policy scenarios hoping to achieve our main ob-jective. An increase in the tax rate on the use of dirty intermediate goods in the final goods production process is used as a fiscal policy shock to improve environmental quality. As a compensating fiscal policy instruments we used the tax rate on labor income, the

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employer social contribution rate, the non-employment benefits and productive govern-ment expenditures. Out of the six fiscal policy scenarios we applied, only one was able to achieve the double dividend and significantly increase welfare among low ability individu-als over all generations. This was the scenario where the increase in the environmental tax was compensated by a reduction in the employer social contribution rate on low ability employment. Using the labor tax for low ability individuals as a compensating measure also induced an increase in environmental quality and economic activity, but no strong increase in welfare. Increasing the non-employment benefits was beneficial for environ-mental quality, but it lead to a decline in output. Compensating the environenviron-mental tax with an increase in productive government expenditures on the other hand led to a large increase in output while damaging environmental quality.

In the following chapter of this dissertation we will give a summary of the most important findings in today’s literature on the OLG framework, environmental fiscal policy and the double dividend. The third chapter will expand on the set-up of the model that will be used and it will exhaustively discuss all the aspects of the model. In the fourth chapter all the used parameters are further explained and given a value, either by calibration or based on published literature or fiscal policy parameters. The fifth chapter tests the empirical relevance by looking at how well the model can predict cross-country differences in key data in thirteen OECD countries. The sixth chapter discusses six fiscal policy scenarios and their numerical steady state effects. In the final chapter, we examine the transitional dynamic effects of the fiscal policy scenarios on key economic variables together with the welfare effects per generation.

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2. Overview existing literature

This chapter offers an outline of the main results in today’s literature relevant for this dissertation. First, there is a brief review of the OLG framework and the addition of heterogeneous abilities. Next is the discussion of imperfect labor markets. This chapter ends with an overview of environmental fiscal policy and the double dividend.

The OLG framework makes it possible to take into account decisions made by short-lived individuals with long-lasting effects. Specific to the OLG framework are the finitely-lived agents who are alive long enough to overlap with at least one other generation. The OLG model published by Diamond (1965), based on the previous work of Samuelson (1958), consists of only two overlapping generations. This dissertation adapts a more extended framework also used by Buyse, Heylen, and Van de Kerckhove (2017) and Heylen and Van de Kerckhove (2019). The OLG model constructed by the authors consists of four overlapping generations. These generations being the young, the middle-aged, the older and the retired individuals. The model describes the hours worked by the three active generations, the formation of human capital by the young, the retirement decision of the older workers and total welfare. This dissertation extends their framework with an environmental block and an imperfect labor market in a closed economy.

Taking into account overlapping generations allows discussing the distribution of welfare between generations. Once it is assumed that the lifespan of individuals may differ from the lifespan of the economy, it is possible to look at intergenerational problems (John & Pecchenino, 1994). The implementation of environmental policy can for example lead to such intergenerational conflicts. Older generations may suffer from welfare losses as a result from increased taxation, while the environmental improvements are only in favour of the younger generations and even for generations yet to be born (Bovenberg & Heijdra, 1998). At the same time, the polluting behavior of present generations harms environ-mental quality and consequently the welfare of future generations (Chiroleu-Assouline & Fodha, 2006).

To go deeper into the distributional effects within generations, Heylen and Van de Ker-ckhove (2019) also model heterogeneous agents. Within each generation there are three types of individuals who differ in their abilities, namely high ability, medium ability and

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low ability. Wages are earned according to one’s ability (Aubert & Chiroleu-Assouline, 2019). The distinction in abilities is based on differences in human capital, i.e. individ-uals with higher human capital have higher abilities. The growth in a person’s human capital can be approached in different ways. Glomm and Ravikumar (1992) explained differences in human capital between agents as a function of their parents’ human capital and quality of education. Jiang, Wang, and Wu (2010), Postel-Vinay and Robin (2002) and Sommacal (2006) on the other hand stated that people are born as either low or high skilled, independent of their parents’ skills. Another approach is that human capital is only determined by the ability of the young to transform its education into human capital (Docquier & Paddison, 2003). This dissertation explains the difference by combining the following two reasons (1) high ability individuals were born with more initial human cap-ital and (2) high ability individuals are more successful at improving their human capcap-ital through tertiary education (Buyse et al., 2017; Devriendt & Heylen, 2020; Heylen & Van de Kerckhove, 2019).

The first addition to the work of Heylen and Van de Kerckhove (2019) is the imperfect labor market for low ability individuals. For medium and high ability workers wage forma-tion is competitive: the total wage cost1 _{for the employer equals the marginal productivity}

of labor. In the labor market for low ability workers, there is union involvement. The union operates at firm level, hence represents all low ability workers of that firm. There-fore, the union has more power than an individual (low ability) worker and can exercise this power in the wage formation process. A single union is however not powerful enough to influence the fiscal policy parameters (Boone & Heylen, 2019). The union will set the wage above the competitive level and impose the minimum wage. The minimum wage equals a reference wage plus a mark-up. This reference wage depends on the competitive wage the low ability worker would normally earn, the average wage of the medium and high ability workers and the non-employment benefits (Boone & Heylen, 2019; Devriendt & Heylen, 2020). Employers will take the minimum wage into account when deciding how many low ability individuals to employ, and hence determining the unemployment rate. The higher the mark-up, the higher the unemployment rate (Fanti & Gori, 2011). As is clear from the competitive wages for medium and high ability workers, the risk of unemployment only exist for low ability individuals (Aubert & Chiroleu-Assouline, 2019). To internalize the environmental externalities, environmental fiscal policy is introduced (Chiroleu-Assouline & Fodha, 2006). Environmental fiscal policy can take different forms. Governments can introduce taxes, subsidies or emission allowances (Bachus, Defloor, & Van Ootegem, 2004). This dissertation will focus only on environmental taxes (also called green taxes). The advantage of using taxes as an instrument instead of policies that do

1_{The total wage cost includes the real gross wage per unit of effective labor and the employer social}

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CHAPTER 2. OVERVIEW EXISTING LITERATURE 5 not yield any revenues is that these revenues can be recycled, which will be useful later on when achieving the double dividend (Bovenberg, 1999). Environmental taxes differ from other taxes in such that they try to correct the behavior of economic agents. The tax tries to incorporate the externalities resulting from polluting behavior in the decision-making process. As a result they correct a distortion, in contrast to the usually distorting taxes (Pearce, 1991). Ideally a green tax would lead to a decrease in pollution, an increase in global welfare of current and future generations and simultaneously no decrease in welfare of each income class, thus being a Pareto improvement (Aubert & Chiroleu-Assouline, 2019).

Based on the polluter-pays principle, the optimal tax differs depending on the polluter (European Commission, 2012). Eurostat (2019) divides environmental taxes into three main pillars: (1) energy taxes, (2) transport taxes and (3) taxes on pollution and re-sources. These taxes can be levied on both consumption and production. According to Chiroleu-Assouline and Fodha (2006) a pollution tax should be levied on consumption as consumption leads to waste production. Waste production of both clean and dirty consumption is responsible for an increase in the long term pollution stock and a decline in the welfare of current and future generations, hence all consumption has to be taxed. Bovenberg (1999), Habla and Roeder (2013) and Aubert and Chiroleu-Assouline (2019) on the other hand charge pollution taxes only on the consumption of dirty goods, since the dirty or polluting good causes emissions that harm the environment. Taxing dirty consumption distorts the composition of the consumption basket: dirty consumption is (imperfectly) substituted by clean consumption. A third consumption tax is mentioned by Gonand (2016) who raises carbon taxes on consumers, depending on the share of en-ergy and transportation in their consumption. This share of enen-ergy and transportation in consumption increases with age, therefore older generations pay higher carbon taxes. Production, or more specifically production in capital intensive sectors, can be a source of pollution as well. The pollution resulting from the production process, in this case approached as the capital stock, lowers the environmental quality. Bovenberg and Hei-jdra (1998) levy a tax on capital, while Chiroleu-Assouline and Fodha (2011) tax the capital stock indirectly via a tax on savings. Recently, a lot of effort is put into replacing fossil-fueled resources by renewable resources. An example of a tax used to encourage this is the fossil-fueled energy tax, a tax levied on all natural resources except renewable resources, or dirty inputs in general (Chu, Cheng, & Lai, 2018; Fischer & Newell, 2008). Three arguments exist why some prefer taxes on capital over taxes on consumption. First, taxes on energy and transportation do not leave all income classes or generations better off. Indirect taxes affect the lower earning households and the older generations the most (Chiroleu-Assouline & Fodha, 2011; Gonand, 2016). The real after-tax labor income, labor income after labor and consumption taxes, decreases, while this source of income is relatively more important for low income households (Bovenberg, 1999). Second, focusing

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solely on the demand side of pollution will have no effect on the environment. Demand reductions of separate groups or countries for natural resources are useless as suppliers will shift their supply to other groups. Suppliers can lower their price and sell the reduction in demand to other consumers. In the end, total demand and supply of natural resources has remained constant. Demand policies are insufficient, hence the supply side of pollution should be taxed as well (Sinn, 2008). The third and final argument says that taxing the production process can lead to innovation in pollution control. It provides incentives through the price mechanism to reduce the production cost (Kemp & Pontoglio, 2011). Nevertheless taxation might be insufficient to boost innovation, extra incentives such as R&D subsidies are needed to improve technology (Fischer & Newell, 2008). Based on these three arguments this dissertation will use a tax on the use of dirty intermediate goods in the production process. The characteristics of this tax will be further elaborated in the next chapter.

To make the green tax more attractive, it is usually promoted as part of a package. In this way it can be introduced as fiscally neutral due to the double dividend (Pearce, 1991). The main idea is that the loss in consumers’ purchasing power due to an increase in an indirect tax, the environmental tax, can be compensated by the positive effects of a decrease in a distorting tax, for example the labor tax. This is called the double dividend due to the possibility of both an environmental dividend as an economic dividend (Aubert & Chiroleu-Assouline, 2019; Chiroleu-Assouline & Fodha, 2011). Achieving the double dividend is only possible if the increase in tax revenues is compensated by a decrease in distortionary taxes, and not by a lump sum transfer. In other words, the tax burden has to be transferred from the low income households to other households or fixed production factors (Aubert & Chiroleu-Assouline, 2019; Bovenberg & de Mooij, 1994). When compensating the environmental tax with a decrease in distortionary taxes reaps more benefits than compensating it with a lump sum transfer, it is called the weak double dividend. The strong double dividend on the other hand implies that recycling the green tax with a decline in a distortionary tax will not only have a bigger but also a non-positive effect on the tax burden, i.e. an increase in non-environmental welfare next to the increase in environmental welfare. Non-environmental welfare is described as the welfare resulting only from leisure and consumption. The strong version of the double dividend is however not realistic, as it demands the uncompensated wage elasticity of labor supply2 _{to be negative, while empirical results point to positive values (Goulder,}

1995).

How the environmental tax should be recycled depends on the redistribution that is opted. According to Gonand (2016) the share of carbon and transportation consumption increases with age, resulting in higher payments by older generations. To make up for

2_{The uncompensated wage elasticity of labor supply is defined as the percentage change in hours}

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CHAPTER 2. OVERVIEW EXISTING LITERATURE 7 the higher tax burden, the pension can be increased. This dissertation however will not focus on pension funding, so this option will not be discussed in more detail. Next to the older generation, also low-income households spend relatively more of their income on necessary goods, which are often dirty goods. Aubert and Chiroleu-Assouline (2019) even introduce a subsistence level of polluting goods, which hampers the substitutability between clean and dirty goods. The first argument why the compensation should focus on the low income households is that environmental taxes on consumption are considered as being regressive taxes, since they mostly harm the poorest households. A second reason why this is necessary is the increase in unemployment. When utility depends next to consumption also on leisure, the introduction of a green tax will affect hours worked. An environmental tax levied on consumption increases the price of consumption, lowering the gain of working and hence the opportunity cost of leisure, called the price effect. The price effect causes an increase in unemployment for both low and high skilled workers. Next to the price effect there is also the substitution effect. When the wage elasticity of labor supply is higher for low ability workers than for high ability workers, the former will demand a higher compensation in wages after the tax increase than the latter. The employer will substitute low ability workers for high ability workers (Aubert & Chiroleu-Assouline, 2019). The effect on hours worked for low ability individuals is unambiguous: both the price effect and the substitution effect lead to a decrease in employment3_{. To}

conclude, this dissertation will focus on the recycling of the green tax on production via changes in distortionary taxes that will decrease unemployment of low ability workers.

3_{For high ability workers the net effect is negative as well: the price effect overcomes the substitution}

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3. The model

This dissertation will employ a framework based on the previously mentioned set-up published by Heylen and Van de Kerckhove (2019). The authors use a framework that consists of four overlapping generations and three types of heterogeneous agents. This dissertation adds the existence of imperfect labor markets for low ability individuals and most importantly the implementation of environmental fiscal policy. This chapter will expand on the characteristics of its own framework, touching upon the households’ utility optimizing behavior, the final and intermediate goods producing firms, the environment and the government. The chapter ends with the general equilibrium derived from the model’s equations in a closed economy.

3.1 Basic set-up

The initial framework implemented by Heylen and Van de Kerckhove (2019) describes the behavior of individuals between the age of 20 and 80 years old. Hence, the four overlapping generations are periods of 15 years. Within each generation there are three individuals with different abilities. This means that the framework consists of a constant population of 12 individuals. The youngest group (between the age of 20 and 35) has the opportunity to participate in tertiary education, unless they have low abilities. The middle-aged and older workers can no longer spend their time on education, they can only choose between working or leisure. However, the older workers can decide to participate in early retirement. The oldest group (starting from age 65) are those who are officially retired. In figure 3.1 work is calculated as hours worked, education as time spent studying and leisure as the free time while employed. While the labor market for high and medium ability individuals is perfectly competitive, a wage floor (minimum wage) exists above the market-clearing level imposed by a union on the market for low ability individuals. This explains why some of the low ability individuals will be unemployed (Boone & Heylen, 2019).

The framework also describes the production of final and intermediate goods. Output is produced in a perfectly competitive market by firms who only manufacture final goods.

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These firms use as production factors clean and dirty intermediate goods produced in an imperfectly competitive market. These dirty goods are partly responsible for pollution which harms the environment and the individual’s welfare. The government’s role in this framework is to levy taxes and use the revenues for its expenditures, pension payments and unemployment benefits.

Table 3.1: Life cycle of an individual of generation t and ability a.

Note: et

1L= 0, 0 < Rta< 1 and for individuals of high and medium ability, ut+j−1= 0.

In the remainder of this dissertation the superscript t stands for the period in which the individual enters the model. The subscript j (= 1, 2, 3 or 4) stands for the current period of life and the subscript a (= L, M or H) indicates the ability of the individual. The time subscript t indicates historical time, this is used with variables such as unemployment, environmental quality and all variables used in the aggregate equilibrium.

3.2 Households

This section constructs all equations necessary for households to optimize their behavior. Households consist of individuals with the same ability and age. As a reference, this section will focus on the household that enters the model at time t, lives for j periods and has ability a.

3.2.1 Preferences and time allocation

Equations (1a) and (1b) demonstrate the intertemporal utility function maximized by a household who enters the model in period t and who has ability a (= L, M, H).

Lifetime utility is determined by consumption (ct

ja), enjoyed leisure (ltja) during

employ-ment (1 − ut+j−1) and environmental quality at the beginning of period t (Et−1). The

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CHAPTER 3. THE MODEL 11 preference for leisure and environmental quality. As unemployment is involuntary, time spent on voluntary leisure should lead to higher utility than being unemployed. In equa-tion (1b) this is approached by adding unemployment to the utility funcequa-tion (κ ut+j−1)1

(Dujardin & Heylen, 2018). θ stands for the inverse of the intertemporal elasticity of substitution in leisure. The IES in leisure is 1

θ, while for consumption this is 1, hence the

logarithmic specification. U_at= 4 X j=1 βj−1 ln ct_ja+ γj (l_jat )(1−θ) 1 − θ + ν ln Et−1 ! ∀a = H, M (1a) U_Lt = 4 X j=1 βj−1 ln ct_jL+ γj(1 − ut+j−1) (lt jL)(1−θ) 1 − θ + κ ut+j−1+ ν ln Et−1 ! (1b) with 0 < β < 1, γj > 0, ν > 0, κ < 0and θ > 0 (θ 6= 1).

Looking back at figure 3.1 it becomes clear that employed individuals need to allocate their time between work, education and leisure. Unemployed (low ability) individuals spend all their time on involuntary leisure. The variables lt

ja, ntja and etja have to be interpreted as

the share of employment time spent respectively on leisure, work and education, leading them to sum to one. Equations (2) - (5) describe the time allocation in terms of enjoyed leisure. lt_1a = 1 − nt_1a− et 1a, with et1L= 0. (2) lt_2a = 1 − nt_2a (3) lt_3a = Γυ(R_at(1 − ˜nt_3a))1−1ξ + (1 − υ)(1 − Rt a) 1−1_ξ ξ ξ−1 (4) lt_4a = 1 (5)

Equation (2) describes the enjoyed leisure of an individual with ability a when he is young and employed. Enjoyed leisure while young decreases with time spent working or studying (when medium or high ability). Equations (3) and (4) describe enjoyed leisure in the second and third period, where education is no longer possible. In the third period an individual chooses the optimal early retirement age, or the fraction of time between age 50 and 65 that the individual is still on the labor market (Rt

a). Early retirement is irreversible

and employment after retirement is not allowed. Thus, the time spent working during the third period is defined as nt

3a = Rtan˜t3a, with ˜nt3a the fraction time before early retirement

that the individual works. There is a divide between leisure while still on the labor market

1_{The parameter κ will be calibrated such that κ <} γj

1−θ(l t jL)

1−θ _{which makes that switching from}

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(Rt

a(1 − ˜nt3a)) and time spent in early retirement (1 − Rta). Equation (4) illustrates that

leisure before and after early retirement are imperfect substitutes as they can be used for different purposes. Leisure before early retirement can only be spent on activities of short duration while time in early retirement can be used for activities that demand a longer commitment. These two types of leisure are combined in a CES-function. The parameters ξ, υ and Γ represent respectively the constant elasticity of substitution, the share parameter and a normalization constant. The normalization constant is necessary to equal lt

3a to (1 − nt3a), such that lt3a and γ3 can be compared to the parameters of the

other periods in the utility function. Leisure in the final period, when retired, is equal to one as time can no longer be spent on work or education (Heylen & Van de Kerckhove, 2019).

3.2.2 Budget constraint

The budget constraints that individuals of the generation t with medium or high ability face during their life are described in equations (6) - (9). Equations (10) - (13) are the budget constraints for the low ability individuals of generation t. The RHS of each equation shows what sources of income make up the disposable income. The LHS then reveals on what disposable income is spent.

(1 + τc)ct1a+ ω t 1a = wa,tht1an t 1a(1 − τw) + dt+ zt ∀a = H, M (6) (1 + τc)ct2a+ ω t 2a = wa,t+1ht2an t 2a(1 − τw) + dt+1+ zt+1+ (1 + rt+1(1 − τk)) ωt1a Pt Pt+1 ∀a = H, M (7) (1 + τc)ct3a+ ω t 3a = wa,t+2ht3an˜ t 3a(1 − τw)Rta + berwa,t+2ht3an¯˜ t 3a(1 − τwb)(1 − Rta) + dt+2+zt+2+ (1 + rt+2(1 − τk)) ωt2a Pt+1 Pt+2 ∀a = H, M (8) (1 + τc)ct4a = pp t a+ dt+3+ zt+3+ (1 + rt+3(1 − τk)) ω3at Pt+2 Pt+3 ∀a = H, M (9) With nt 3a = Rtan˜t3a.

Low ability households are confronted with unemployment. When a member of a low ability household is unemployed the household receives unemployment benefits. In the

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CHAPTER 3. THE MODEL 13 following four equations these benefits are added to the budget constraints.

(1 + τc)ct1L+ ωt1L= wL,tht1Lnt1L(1 − τw)(1 − ut) + bwL,tht1Ln¯1Lt (1 − τwb)ut+ dt+ zt (10) (1 + τc)ct2L+ ωt2L= wL,t+1ht2Lnt2L(1 − τw)(1 − ut+1) + bwL,t+1ht2Ln¯t2L(1 − τwb)ut+1 + dt+1+ zt+1+ (1 + rt+1(1 − τk)) ω1Lt Pt Pt+1 (11) (1 + τc)ct3L+ ω t 3L= wL,t+2ht3Ln˜ t 3L(1 − τw)RtL(1 − ut+2) + berwL,t+2ht3Ln¯˜t3L(1 − τwb)(1 − RtL)(1 − ut+2) + bwL,t+2ht3Ln¯t3L(1 − τwb)ut+2 + dt+2+zt+2+ (1 + rt+2(1 − τk)) ω2Lt Pt+1 Pt+2 (12) (1 + τc)ct4L = pp t L+ dt+3+ zt+3+ (1 + rt+3(1 − τk)) ω3Lt Pt+2 Pt+3 (13) With nt 3L = RtLn˜t3L.

From the LHS of equations (6) and (10)2 _{it is clear that individuals spend their disposable}

income on consumption (ct

ja) and consumption taxes (τc) or on the accumulation of wealth.

The stock of wealth held by an individual with ability a at the end of his j-th period of life is shown by ωt

ja. Wealth is completely accumulated and spent during one’s lifetime,

no-one starts or finishes life with any wealth. During the first period of life, disposable income consists of real after-tax labor income, unemployment benefits (for individuals of low ability), dividends from ownership of the firms and a lump sum transfer. Real after-tax labor income is approached as the wage (wa,t) earned on effective labor (htjantja)

after paying labor taxes (τw). To calculate effective labor of the low ability individual it is

necessary to take into account the employment factor (1−ut+j−1). Unemployment benefits

depend on the replacement rate (b) and the labor income the low ability individual would normally earn when employed. The labor tax (τwb) and the hours worked (¯ntjL) that are

part of the unemployment benefits are exogenous to the household. When looking at alternative fiscal policy scenarios these variables will remain constant. The reason for this being that fiscal policy shocks implemented to increase the return of employment relative to unemployment (e.g. lower τw) must not increase unemployment benefits as

well. The profit making intermediate goods producing firms pay dividends (dt) to the

owners of the firm, which are the workers. The lump sum transfer (zt) is paid by the

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(1 + rt+1(1 − τk)) on the accumulation of wealth is added to disposable income (equation

(7) and (11)). In the third period workers can decide to leave the labor market before the statutory retirement age of 65, which explains the presence of early retirement benefits as a source of income (equation (8) and (12)). Early retirement benefits depend on the early retirement replacement rate (ber) and the income the individual would have earned

if he was still on the labor market. Equation (9) and (13) reveal that disposable income when retired no longer depends on labor income, unemployment compensation or early retirement benefits. Those income sources are replaced by the public pension (ppt

a). ppt_a = ρa 1 3 3 X j=1 wa,t+j−1ht−3ja n t−3 ja (1 − τw)(1 + x)4−j ∀ a = H, M (14a) ppt_L = ρL 1 3 3 X j=1 wL,t+j−1ht−3jL n t−3 jL (1 − τw)(1 − ut+j−1)(1 + x)4−j (14b) With nt 3a = Rtan˜t3a and nt3L = RtLn˜t3L.

The public pension is only received after the statutory retirement age of 65. This disser-tation uses a PAYG system where the pension of the current retired is financed by the current active generations. The pension a retired worker receives depends on his house-hold’s earnings in the past. This pension is a portion (based on the net replacement rate ρa) of the average after-tax labor income of the past three working periods. Past labor

income is revalued to the current standard of living ((1 + x)4−j_{). From equation (14b)}

it is clear that the households’ pension does not depend on the unemployment benefits received by unemployed individuals nor does the unemployed member of the household receive a pension.

3.2.3 Human capital formation

All individuals enter the model with a predetermined level of human capital. This pre-determined level is generation-invariant and only depends on the individual’s ability. It will be calibrated as a fraction (εa) of the normalized level of the human capital of a high

ability individual when he is young (h0). As a result, an individual with ability a will

enter the model with human capital:

ht_1a = εah0 ∀ a = H, M, L (15)

with 0 < εL< εM < εH = 1.

2_{For the remainder of this section a refers to L, M and H, unless explicitly stated otherwise for}

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CHAPTER 3. THE MODEL 15 During the first period of active life, high or medium ability individuals will engage in tertiary education. This results in additional growth in human capital in the first period and higher productivity in the second and third period. The rise in human capital depends on the amount of time spent on education (et

1a) and the initial level of human capital (ht1a).

The strength of the rise in human capital is enlarged with common elasticity of time input (σ) and a common efficiency parameter (φ), which is the same for both medium and high ability individuals. Low ability individuals on the other hand do not engage in tertiary education, their human capital and hence productivity remain constant. Human capital remains constant between the second and third period for all individuals. The previously mentioned evolution in human capital is summarized in equations (16a) - (17).

ht_2a = ht_1a(1 + φ(et_1a)σ) ∀ a = H, M (16a)

ht_2L = ht_1L (16b)

ht_3a = ht_2a ∀ a = H, M, L (17)

3.2.4 Optimization

Individuals optimize lifetime utility (1a) or (1b) by deciding on their consumption, labor supply, education and effective retirement age subject to equations (2) - (17). Optimal consumption is determined over all four periods, while labor supply only concerns the three periods of active life and when the person in on the labor market (not unemployed or in early retirement). Education is only possible while young and only for high or medium ability individuals. In the final period of active life, all employed individuals can decide on their optimal effective retirement age. To find the eight first-order conditions we substitute equations (2) - (5) for lt

ja and equations (10) - (13) for ctja into equations

(1a) and (1b), and maximize with respect to ωt

1a, ω2at , ωt3a, nt1a, nt2a, ˜nt3a, Rta and et1a.

The Euler equation (18) describes the optimal consumption path over time for all high, medium and low ability individuals. Individuals will postpone their consumption, or consume more in the future relative to their current consumption, when their time pref-erence is lower (i.e. higher β), when the after-tax return on capital is higher (i.e. higher (1 + rt+j(1 − τk))) or when the price of the final goods decrease over time (lower Pt+j).

ct j+1,a ct j,a Pt+j Pt+j−1 = β (1 + rt+j(1 − τk)) ∀ j = 1, 2, 3 (18)

Individuals pick the optimal labor-leisure combination for every period of active life. The optimal labor supply is where the marginal utility of leisure is equal to the marginal utility from work. Equations (19) - (21) indicate the optimal labor supply for all working

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individuals for all abilities. The LHS of each equation illustrates the utility gain of an extra hour of leisure, or the marginal disutility of work. For every equation, the RHS shows the utility gain of an extra hour of labor. Working an extra hour now can lead to higher utility via extra consumption in the same period and via extra consumption when retired due to a higher pension. More specifically, an extra hour of work will lead to extra after-tax income (wa,thtja(1 − τw)). With one extra unit of income, an individual

can buy 1

(1+τc) consumption units for which the marginal utility is

1 ct

ja. The extent to which the individual will be able to increase its consumption during retirement depends on the pension replacement rate (ρa) and the revaluation to the current state of living

((1 + x)4−j_{). Whether an individual is inclined to postpone his consumption depends}

on the time preference parameter (β4−j_{). Do notice that the unemployment benefits for}

unemployed low ability individuals do not rise when other individuals work more. γ1 (lt 1a)θ −∂lt 1a ∂nt 1a = wa,th t 1a(1 − τw) ct 1a(1 + τc) + β31 3 ρawa,tht1a(1 − τw)(1 + x)3 ct 4a(1 + τc) (19) γ2 (lt 2a)θ −∂lt 2a ∂nt 2a = wa,t+1h t 2a(1 − τw) ct 2a(1 + τc) + β21 3 ρawa,t+1ht2a(1 − τw)(1 + x)2 ct 4a(1 + τc) (20) γ3 (lt 3a)θ −∂lt 3a ∂ ˜nt 3a = wa,t+2h t 3aRta(1 − τw) ct 3a(1 + τc) + β1 3 ρawa,t+2ht3aRta(1 − τw)(1 + x) ct 4a(1 + τc) (21) The optimal effective retirement age in the third period of life for all abilities is described in equation (22). Working individuals pick their retirement age when the gain of par-ticipating in early retirement (LHS) is equal to the gain of working longer (RHS). The former indicates that when workers start their early retirement, this results in a rise in enjoyed leisure which increases utility. The latter indicates that postponing the effective retirement age leads to more labor income in the final period of active life and a higher pension when retired. The attractiveness of working decreases with the early retirement benefits the worker can receive during early retirement. The higher the replacement rate during early retirement, the lower the gain from working relative to the income during early retirement. The additional revenues in the third and fourth period can alter utility via higher consumption as already described above.

γ3 (lt 3a)θ −∂lt 3a ∂Rt a = wa,t+2h t 3a(1 − τw)(˜nt3a− bern¯˜t3a) ct 3a(1 + τc) + β1 3 ρawa,t+2ht3a˜nt3a(1 − τw)(1 + x) ct 4a(1 + τc) (22)

The final first-order condition (23) describes the optimal amount of time spent on ter-tiary education by high or medium ability individuals. To find optimal education, the gain in utility due to more leisure during the first period resulting from not participating

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CHAPTER 3. THE MODEL 17 in tertiary education (LHS) needs to be equal to the gain in utility due to an increase in revenues in all other periods (RHS). When participating in tertiary education, time spent on leisure will decrease and hence utility will be lower in the first period. However, after investing in education, human capital will be higher in the following periods lead-ing to higher income and as a result also a higher pension. The increased income and pension can be used for consumption and hence increase utility. The extent to which the revenues will increase depends on the individual’s after-tax wage, initial human capital, time spent working in the second and third period, the pension replacement rate (ρa)

and the revaluation parameter ((1 + x)4−j_{). The common elasticity of input (σ) and the}

common efficiency parameter (φ) will enhance the effect as well, and will be the same for all individuals. γ1 (lt 1a)θ −∂lt 1a ∂et 1a = β 1 ct 2a ∂ct 2a ∂et 1a + β2 1 ct 3a ∂ct 3a ∂et 1a + β3 1 ct 4a ∂ct 4a ∂et 1a ∀ a = H, M (23) with ∂c t 2a ∂et 1a = σφ(et_1a)(σ−1)wa,t+1h t 1ant2a(1 − τw) (1 + τc) ∂ct 3a ∂et 1a = σφ(et_1a)(σ−1)wa,t+2h t 1a(1 − τw) (Rta(˜nt3a− bern¯˜t3a) + bern¯˜t3a) (1 + τc) ∂ct 4a ∂et 1a = σφ(et_1a)(σ−1)ρa 1 3 P3 j=2(wa,t+j−1ht1antja(1 − τw)(1 + x)4−j) (1 + τc)

3.3 Firms, output and factor prices

The following section will first discuss production by both the final good producing firms and the two intermediate goods producing firms. The production by the intermediate goods producing firms motivates their demand for production factors (i.e. labor and capital). Thus, the market for production factors will be discussed subsequently. Finally there is a discussion of the prices of the final and intermediate goods.

3.3.1 Final good production

Output (Yt) is produced by final goods producing firms active in a perfectly competitive

market. These firms use only the dirty and clean intermediate goods in their production process. The dirty and clean goods are imperfect substitutes for the final goods producing firms. Equation (24) illustrates the CES production function of the final good, where ζ stands for the share parameter and λ resembles the elasticity of substitution between the

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clean and dirty goods. Yt= ζX λ−1 λ Ct + (1 − ζ)X λ−1 λ Dt λ−1λ (24) Given that the prices of the clean (PCt) and dirty (PDt) goods are set by the intermediate

goods producing firms, the final good producing firms will choose their demand for the intermediate goods to maximize their profits. This results in equations (25a) and (25b) who represent respectively the optimal demand for the clean intermediate goods and dirty intermediate goods. The final goods producers pay a tax (τD) for using the dirty

inter-mediate goods, as this is harmful for the environment (Chu et al., 2018). The derivation for both equations can be found in appendix A.

XCt = 1 ζ −λ_P Ct Pt −λ Yt (25a) XDt = 1 1 − ζ −λ_{(1 + τ} D)PDt Pt −λ Yt (25b)

3.3.2 Intermediate goods production

Given the demand for the clean and dirty goods, the respective intermediate goods pro-ducing firms will adjust their production to satisfy this demand. To produce intermediate goods, the firms use both capital and labor as production factors. These production factors are combined in the Cobb Douglas production functions in equation (26a) and (26b). YCt = XCt = BCtKCtα H 1−α Ct (26a) YDt = XDt = BDtKDtα H 1−α Dt (26b)

The production of clean intermediate goods (YCt) depends on the technology parameter

(BCt) and the usage of capital (KCt) and labor (HCt). The same goes for production

of the dirty intermediate goods. The technology parameters (BCt and BDt) represent

the technology stock in respectively the clean and dirty goods sector. The government invests in the technology stock of the clean sector (equation (27)). Productive govern-ment expenditures (gy) escalate the development of clean technology, conditional on the

effectiveness parameter (χ) of those investments. The development of clean technology enhances growth in this framework.

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CHAPTER 3. THE MODEL 19 In what follows we discuss the determination of employed effective labor by ability and the installed capital stock in each of the intermediate sectors. Important to know is that total labor demand for workers of each ability is equal to the sum of demand of both the clean and dirty goods producing firms. For workers of high and medium ability, demand equals supply, there is no unemployment. For low ability workers on the other hand there is union involvement which results in a discrepancy between demand and supply, leading to an unemployment rate of ut.

3.3.2.1 Labor and capital supply

Labor and capital supply results from the behavior of utility optimizing households. Equa-tion (28) presents total effective labor supply Ha,t by ability. Labor of the same ability

but different ages are perfect substitutes. Ha,t = nt1ah t 1a+ n t−1 2a h t−1 2a + n t−2 3a h t−2 3a ∀a = H, M, L (28)

Capital supply results from the accumulation of wealth at the end of every period by the households. Total capital supply at the beginning of period t will be equal to the sum of wealth accumulated by all individuals who were at working age in the previous period (equation (29)).

Ωt=

X

a=H,M,L

ω_1,at−1+ ω_2,at−2+ ω_3,at−3 (29)

3.3.2.2 Labor and capital demand

The aggregate CES function of employed effective labor (labor demand) of firm f is demonstrated in equation (30). In contrast with labor of the same ability but at different ages, labor of different abilities are imperfect substitutes. As a result s is the elasticity of substitution between the different ability types of labor. The input shares of the different ability types of labor are written as ηL, ηM and ηH. The input shares are equivalent

between the dirty and clean firms for each ability. Hf t = ηHH d,1−1_s H,f t + ηMH d,1−1_s M,f t + ηLH d,1−1_s L,f t s−1s ∀f = C, D (30) with ηH = 1 − ηM − ηL.

The clean goods producing firms determine optimal capital and labor demand to minimize costs. The costs of the clean goods producing firms consist of the labor costs and the

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capital cost. The former includes the wage (wa,t), the employer social contribution rate

(τp) and employed effective labor (Ha,Ctd ). The latter consists of the depreciation rate (δk)

and the interest rate (rt) paid on the capital stock (KCt). The following Lagrangian and

first-order conditions represent the cost minimizing behavior by the clean goods producing firm: L = wH,t(1 + τp)HH,Ctd + wM,t(1 + τp)HM,Ctd + wL,t(1 + τp)HL,Ctd + (rt+ δk)KCt + λt YCt− BCtKCtα HCt1−α (31) with HCt as defined in (30), ∂L ∂Hd H,Ct = wH,t(1 + τp) − λt(1 − α)Bt K_Ct HCt α ηH HC,t Hd H,Ct !1_s = 0, ∂L ∂Hd M,Ct = wM,t(1 + τp) − µt(1 − α)Bt KCt Hd Ct α ηM HC,t Hd M,Ct !1_s = 0, ∂L ∂Hd L,Ct = wL,t(1 + τp) − µt(1 − α)Bt KCt HCt α ηL Hd C,t Hd L,Ct !1_s = 0, ∂L ∂KCt = rt+ δk− λtαBCt HCt KCt 1−α = 0, ∂L ∂λt = YCt− BCtKCtα H 1−α Ct = 0.

Combining the first and the final two first-order conditions shown above gives the opti-mal demand by the clean intermediate goods producing firm for workers of ability H in equation (32). For simplicity we use Hd

H,Ct as an example, as the calculations for HM,Ctd

and Hd

L,Ct are analogous. For the full derivation of labor demand we refer to appendix A.

H_H,Ctd = rt+ δk wH,t(1 + τp) s_{1 − α} α s YCt BCtHCt _αs η_HsHCt (32)

Labor demand by the dirty good producing firms is equivalent, hence optimal labor de-mand or employed effective labor by firm f for workers with ability a can be written as: H_{a,f t}d = rt+ δk wa,t(1 + τp) s_{1 − α} α s Yf t Bf tHf t _αs ηs_aHf t ∀f = C, D. (33)

In the labor market for high and medium ability workers there is no union involvement. The labor market and wage formation are competitive, hence there is no unemployment.

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CHAPTER 3. THE MODEL 21 In the labor market for low ability workers the wage set by the union will be higher than the competitive wage at which there is market clearing. Equation (34) shows the union wage, which is a reference wage plus a mark-up (π). The reference wage is calculated as a weighted average of the competitive wage of a low ability worker (the wage without union involvement or unemployment), the average wage of the medium and high ability workers and the unemployment benefits. The weights used to calculate this average (q1, q2 and

q3) sum to one (Boone & Heylen, 2019).

wL,t = q1wL,tc + q2 wM,t+ wH,t 2 + q3bwL,t (1 + π) (34)

The optimizing behavior of the firms also applies to the demand for capital. To determine the optimal capital demand, the same Lagrangian (31) is taken into account. Equation (35) shows the capital demand by the intermediate goods producing firms when mini-mizing their costs. The wage and labor parameters of ability H are here shown as an example. The ratio of the ability specific values in equation (35) are constant and equal for all abilities. The full derivation of capital demand can also be found in appendix A.

Kf t= Yf t Bf t α 1 − α 1−α_w H,t(1 + τp) rt+ δk 1−α ηα−1_H Hf t Hd H,f t !α−1_s ∀ f = C, D (35)

3.3.2.3 Factor market equilibrium

Labor supply results from the individuals who want to work. Individuals are indifferent between working for the clean or dirty intermediate firm as wages are equal. Labor demand consists of the demand coming from the clean goods producing firms and the dirty goods producing firms. As there is no union involvement, supply and demand will be equal for high and medium ability workers (equation (36a)). However, for low ability individuals, the union sets a wage floor at which more low ability individuals will want to work than will be hired by the firms. This wage floor leads to an unemployment rate of ut. Only a fraction (1 − ut) of the labor supply will be employed (equation (36b)).

Ha,t = Ha,Ctd + Ha,Dtd ∀a = H, M (36a)

HL,t(1 − ut) = HL,Ctd + HL,Dtd (36b)

Labor demand and supply are illustrated in figure 3.1. Labor supply is an increasing function of the real wage, while labor demand decreases when the real wage rises. The competitive real wage for workers with high and medium abilities (wa,t) is established at

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wage for low ability workers (wc

L,t) is established in the same manner in the right panel

and is used by the union to set the minimum wage (wL,t). At the minimum wage labor

supply is larger than labor demand, resulting in unemployment (ut).

(a) Perfectly competitive labor market for high and medium ability workers.

(b) Wage setting by the union on the labor mar-ket for low ability workers.

Figure 3.1: Determination of the real wage.

The interest rate is the outcome of demand and supply of capital being equal. Demand of capital is determined by equation (35) resulting from the profit maximising behavior from the intermediate goods producing firms. Capital supply is the sum of the savings from all households, which is a consequence of the utility optimizing behavior (equation (29)). In equation (37) there is an interest rate that matches capital supply to capital demand.

Ωt= KCt + KDt. (37)

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CHAPTER 3. THE MODEL 23 Figure 3.2 demonstrates the determination of the real interest rate by comparing capital demand and capital supply graphically. Similar to labor demand and labor supply: capital supply is a positive function of the real interest rate while capital demand is a negative function of that same variable. The interest rate is determined at the intersection of both curves.

3.3.3 Product prices

The market for final goods is perfectly competitive, as a result there will be no profits for the final goods producing firms. Solving the zero-profit function of a final goods producing firm leads to an aggregate price level Pt which is a weighted average of the prices of the

intermediate goods. The full derivation can be found in appendix A. Pt= (ζ) λ 1−λ P_Ct1−λ+ ((1 + τD)PDt) 1−λ 1 1−λ (38) The market for intermediate goods on the other hand is imperfectly competitive. The intermediate goods producing firms are able to set their own prices and make profits. The prices of the intermediate goods are determined as a mark-up λ

λ−1

on the marginal cost. The marginal cost is calibrated by taking into account the production functions of the intermediate goods producing firms (equations (26a) and (26b)). The mark-up on the marginal cost is a negative function of the elasticity of substitution between the dirty and clean goods for the final goods producing firms (λ). The price of the clean intermediate goods is derived in appendix A.

Pf t = λ λ − 1 wH,t(1 + τp) 1 1 − α 1 Bf t Hf t Kf t α 1 ηH H_{H,f t}d Hf t !1_s ∀f = C, D (39)

The profits making intermediate goods producing firms will pay dividends to the owners of the firms, here the households. The profits an intermediate goods producing firm makes are calibrated as the difference between the revenues and the marginal cost of its production (equation (40)). Hence, the total amount of dividends or profits (Dt) is the

portion of the price that the firms receive on top of their marginal costs. This mark-up

1 λ−1

also depends on the elasticity of substitution between the clean and dirty good (λ). The higher the elasticity of substitution, the easier the final goods producing firms can alternate between the dirty and clean goods. This results in a lower profit margin for the intermediate goods producing firms and correspondingly also lower dividends. The dividends are equally divided among all households, independent of their ability and age

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(equation (41)). Dt = XCt 1 λ − 1 wH,t(1 + τp) 1 1 − α 1 BCt H_Ct KCt α 1 ηH Hd H,Ct HCt !1_s + XDt 1 λ − 1 wH,t(1 + τp) 1 1 − α 1 BDt HDt KDt α 1 ηH Hd H,Dt HDt !1_s (40) dt= Dt 12 (41)

3.4 Environment

The environmental stock Etrepresents environmental quality attained at the end of period

t. Equation (42) describes the environmental stock which is a function of last year’s environmental quality and current pollution (P olt) based on the function used in Chu

et al. (2018).

Et= Et−1− (1 − ψ)P olt (42)

The initial and exogenous environmental stock (E0) will later be defined as a positive

parameter which is necessary for the policy simulations in Dynare. Current harmful emis-sions will damage environmental quality when it exceeds the absorption level. The ab-sorption rate (ψ) illustrates the degree to which environmental quality can absorb harmful emissions (Naqvi, 2015). When pollution surpasses the absorption level, environmental quality will deteriorate. Pollution or harmful emissions is a function of the use of dirty intermediate goods in the final goods’ production process (YDt) and total consumption

(Ct) (Chiroleu-Assouline & Fodha, 2006; Chu et al., 2018). In equation (43), ι1 and ι2

stand for the rate at which respectively the use of dirty intermediate goods and total consumption contribute to harmful emissions.

P olt = ι1YDt+ ι2Ct (43)

3.5 Government

The government’s budget constraint consists of its expenditures and payments made to the households and firms on the LHS and its tax revenues paid by the households and firms on the RHS (equation (44)). The government invests in clean technology via its productive

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CHAPTER 3. THE MODEL 25 expenditures (Gyt). The nonproductive expenditures include consumption (Gt),

non-employment benefits and early retirement benefits (Bt), the pension benefits (P Pt), and

the lump sum transfers to all households (Zt). The government’s revenues include the

taxes on labor paid respectively by the employee and the employer (Tnt and Tpt), taxes

on interest income (Tkt), taxes on private consumption (Tct) and the environmental taxes

(TDt). There is no public debt, thus the government has a balanced budget.

Gyt+ Gt+ Bt+ P Pt+ Zt= Tnt+ Tpt+ Tkt+ Tct+ TDt (44) with Gyt = gyYt Gt= gcYt Bt = 3 X j=1 bwL,tht−j+1jL n¯ t−j+1 jL (1 − τwb)ut + berwL,tht−23L n¯˜ t−2 3L (1 − τwb)(1 − Rt−2L )(1 − ut) + X a=H,M berwa,tht−23a n¯˜ t−2 3a (1 − τwb)(1 − Rt−2a ) P Pt= X a=H,M ρa 1 3 3 X j=1 wa,t+j−1ht−3ja n t−3 ja (1 − τw)(1 + x)4−j ! + ρL 1 3 3 X j=1 wL,t+j−1ht−3jL n t−3 jL (1 − τw)(1 − ut+j−1)(1 + x)4−j Zt= 12zt Tnt = τw X a=H,M 3 X j=1 nt−j+1_ja wa,tht−j+1ja ! + τw 3 X j=1 nt−j+1_jL wL,tht−j+1_jL (1 − ut) Tpt = τp X a=H,M,L wa,t(Ha,Ctd + H d a,Dt) Tkt= τkrtΩt Tct = τc 4 X j=1 ct−j+1_jH + ct−j+1_jM + ct−j+1_jL TDt = τDYDt PDt Pt

The government will spend a fraction gy and gcof output, these fractions are fixed and will

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are adjusted to close the budget constraint and are equally divided among all individuals.

3.6 Aggregate equilibrium

Equation (45) describes the aggregate equilibrium comparing domestic supply to domestic demand in a closed economy. Domestic output (Yt) in the LHS will be equal to domestic

demand for consumption and investment as there can be no financing from abroad. The RHS consists of the consumption by the households (Ct), the investments by the

interme-diate goods producing firms (ICt and IDt) and the government’s productive expenditures

and consumption (Gyt and Gt).

Yt= Ct+ ICt+ IDt+ Gyt+ Gt (45)

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4. Economic context and parameterization

The set-up built in chapter 3 allows us to model an economy with households of different abilities and final and intermediate goods producing firms, and predict their response to environmental fiscal policy. Before we are able to do any predictions, the model needs to reflect reality perfectly. This chapter will elaborate on the construction of the main data and the parameters used to complete the model.

4.1 Data and context

Before describing and calibrating the parameters, it is important to give an overview of the economic reality concerning the most important indicators and countries. Table 4.1 illustrates essential data of a group of OECD countries. Key data consists of information on (un)employment, retirement, education, growth, and harmful emissions for thirteen OECD countries for the period of 1995-2007. This period allows us to observe economies in their steady state, assuming that there were no significant disruptions before the financial crisis of 2008.

Table 4.1 demonstrates data on the following variables: hours worked when young (n1),

middle-aged (n2) and old (n3), the effective retirement age, the education rate (e), annual

real per capita growth, CO2 emissions per unit of GDP and the unemployment rate among

low ability individuals (u). These statistics are shown for six core euro area countries, four Nordic countries, and three Anglo-Saxon countries. Employment is a measure of actual hours worked in the economy relative to potential hours worked. Employment in the third period is affected by the early retirement age. Employment in the third period rises when workers postpone their early retirement. The effective retirement age is the age at which workers decide to leave the labor market before the mandatory retirement age of 65 (60 in France). Heylen and Van de Kerckhove (2013) estimated this by the average of all individuals above the age of 40 who left the labor market permanently. The fifth column displays the education rate. The education rate measures the percentage of hours studied by a young individual to potential hours studied by a young individual. This is approximated by the ratio of full-time and part-time students to the total population of

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Table 4.1: Key data on OECD coun tries (1995-2007) Note: Data from OECD and Eur ostat. A ll data conc ern 1995-2007, exc ept for the effe ctive retir ement age (1995-2006). A mor e detaile d description of these variables and their sour ces can be found in app endix B.

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CHAPTER 4. ECONOMIC CONTEXT AND PARAMETERIZATION 29 young individuals (Heylen & Van de Kerckhove, 2019). Annual real per capita growth is calculated as the growth rate of real potential GDP per person of working age. Harmful emissions are approached by looking at CO2 emissions. The final variable is the

unem-ployment rate of low ability individuals. For all countries we use the unemunem-ployment rate for people without higher secondary education (Devriendt & Heylen, 2020). For a more detailed description of these variables we refer to appendix B.

Employment rates appear to be the highest among the middle aged workers for all coun-tries. In the European core countries, employment during the third period is extremely low. These observations are in line with the effective retirement age being lower in the core euro area than in the other countries. Due to the high education rate in the Nordic countries, employment among the young is rather low, but still higher than in the core Eu-ropean countries. The annual real per capita growth rate is remarkably high in the Nordic countries compared to the total average. Concerning the emission rate, the United States and Canada score much worse relative to the other countries. The unemployment rate for individuals without upper-secondary education appears to be the highest for France, Germany and Finland. However the results of Finland can be influenced by the very high unemployment rates during the 90’s resulting from the Finnish banking crisis.

In the policy simulations in chapter 6 we will use the policy variables of the six European core countries. The overall poor results on employment and above average levels of unem-ployment among low ability individuals in the core euro area give reason to focus on the redistribution of environmental tax revenues towards improving those (un)employment numbers.

4.2 Parameterization

To be able to simulate the wanted fiscal policy effects, we are required to first parameterize the model constructed in chapter 3. We will choose the optimal parameter values based on the values published in previous work, our own calibrations and fiscal policy parameters. Most of the parameters are based on those published in Heylen and Van de Kerckhove (2019) and for a more detailed description of the definition and source of the parameters we refer to appendix B.

Table 4.2 illustrates all the parameters that are used. The parameters are divided into technology and preference parameters and fiscal policy parameters. The remainder of this chapter will discuss the two categories of parameters respectively.

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Table 4.2: Parameterization

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CHAPTER 4. ECONOMIC CONTEXT AND PARAMETERIZATION 31

4.2.1 Technology and preference parameters

The technology and preference parameters are the ones concerning goods and human capital production, those used in the decision making process of the households and the parameters regarding the environment. The parameters are either taken from existing literature or calibrated to match our model. First the parameters from existing literature will be discussed.

4.2.1.1 Parameters from existing literature

As most of the parameters are based on the ones used in Heylen and Van de Kerck-hove (2019), we will only mention when another source is used. The parameters will be discussed in the same order as used in table 4.2.

The capital share in the Cobb Douglas production function of intermediate goods (α) is specified at 0.3. The elasticity of substitution between different ability types in effective labor (s) indicates how fast an intermediate goods producing firm can switch between workers of different ability types. The parameter is imposed at 1.5, proving the imperfect substitutability in the CES function. The share parameters of different ability types in effective labor (ηH, ηM and ηL) are respectively set equal to 0.48, 0.33 and 0.19, and

thus sum to 1. The elasticity of substitution between the two intermediate goods in the production of the final good (λ) shows how easy the dirty intermediate good can be replaced by the clean intermediate good (or the other way around) in the final good’s production process. The parameter λ is set equal to 2 (Malikov, Sun, & Kumbhakar, 2018; Papageorgiou, Saam, & Schulte, 2016). Also present in the CES production function of the final good is the share parameter of the two intermediate goods (ζ). Both types of intermediate goods are given equal weight, thus ζ is equal to 0.5. The technology parameter (BD) used in the Cobb Douglas production function of the dirty intermediate

good is normalized to 1. The parameters used in the reference wage set by the union (q1, q2 and q3) differ between country groups. The parameters shown in table 4.2 apply to

Belgium and all core euro area countries. Unions in the core euro area take into account the competitive wage, the average wage of the medium and high ability individuals and the non-employment benefits. The respective weights equal to 0.80, 0.05 and 0.15. Unions in Nordic countries tend to focus solely on the competitive wage and the non-employment benefits, as a result the parameters are respectively equal to 0.9, 0 and 0.1. The wage-setting in Anglo-Saxon countries on the other hand only depends on the reference wage and the average wage of medium and high ability individuals. The parameters are therefore equal to 0.9, 0.1 and 0 (Boone & Heylen, 2019).

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capital (εH, εM and εL). With εH equal to 1, the initial human capital of the high ability

individual is normalized to h0. The parameters εM and εL thus indicate initial human

capital relative to the high ability individual and are set equal to 0.84 and 0.67. Human capital production is also determined by the elasticity with respect to education time (σ) which takes the value 0.3 for all individuals.

Considering the same rate of time preference as Heylen and Van de Kerckhove (2019) equal to 1.5% per year, the discount factor (β) for a period of 15 years will be equal to 0.8. The inverse of the intertemporal elasticity of substitution in leisure (θ) is based on Rogerson (2007) and will be set equal to 1.25. In the composite leisure function of older workers, both leisure types are given equal weight (υ) and the normalization parameter (Γ) is equal to 2. Utility also depends on environmental quality, the weight at which environmental quality contributes to utility (ν) is set at 0.7 (Chu et al., 2018). Being unemployed leads to a constant decline in utility (κ). Dujardin and Heylen (2018) set this parameter equal to -1, as unemployment is involuntary and thus has to lead to lower utility for the same level of consumption. More exactly, this means that κ should be lower than γj

1−θ(l t

jL)1−θ, which is the case in this dissertation with κ equal to -1. Consequently,

lifetime utility for unemployed individuals is lower than utility for employed individuals, given the value of κ.

To determine the harmful emissions and environmental quality, there are a few parameters which still need to be determined. The rate at which the use of dirty intermediate goods and total consumption lead to harmful emissions (ι1 and ι2) are respectively equal to 0.4

and 0.1 (Bastin & Cassiers, 2013; Fullerton & Heutel, 2010). The absorption rate for harmful emissions (ψ) is set equal to 0.05 (Naqvi, 2015). The initial environmental stock (E0) is measured at 80, to make sure that the environmental stock starts at a positive

value during our simulation.

Finally, the capital depreciation rate (δk) is calculated as 0.714, given that the depreciation

rate per year is equal to 8%.

4.2.1.2 Calibrated parameters

Next to the parameters selected from the existing literature, we calibrate eight parameters to match the key data on Belgium. The target values that are used in the calibration process are the same as those mentioned in table 4.1.

Even though all parameters of the model simultaneously affect all target values, there is a strong link between certain parameters and the target values. To attain the correct employment rates for all age groups, we will focus on the taste for leisure for all three active periods (γ1, γ2 and γ3). The effective retirement age is closely linked with the elasticity of