Choice of Environmental Policy Instruments and ...

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Choice of Environmental Policy Instruments and Welfare in middle-income developing countries. ASSA Boka Stéphane Kévin1. Abstract. The extent of ...
Choice of Environmental Policy Instruments and Welfare in middle-income developing countries

ASSA Boka Stéphane Kévin1

Abstract The extent of environmental consequences related to climate change in middle-income developing countries (MICs) creates a need for government intervention. The policy debate is what is the appropriate policy instrument to internalize the negative externalities of envrironmental degradation without deteriorating welfare in an uncertain world characterized by economic and environmental shocks. Hence, this paper aims to determine among pollution taxes, rules and combination of taxes-rules instrument, one that allows to increase welfare in MICs facing economic and environmental shocks. To do this, we used a dynamic stochastic general equilibrium (DSGE) model whose parameters are estimated to the Ivoirian economy by bayesian method. In this framework, we assumed that the government performs the cleanup activities through revenues from environmental taxes as well as other taxes and we modelize the environmental quality as a renewable resource to focus on the regeneration capacity of nature which both constitutes features of these countries. The three instruments are evaluated in the case where the government intervention through pollution abatement spending is not effective. Results of welfare comparison under three regimes show on the one hand that when public abatement spending are effective, welfare under pollution taxes are higher than pure rules if shocks are strong. But when rules are combined with output taxes for public clearance spending (mixed instrument), they become better than pollution taxes regardless of the type of shock. On the other hand, when the government intervention is inefficient, welfare under pollution taxes are almost equivalent to pure rules but remain lower than mixed instrument. Furthermore, the impulse response functions (IRF) analysis reveals that three instruments studies are pro cyclical under economic shocks while they are countercyclical when shocks come from the environment. Keywords: Middle-income countries, climate change, environmental policy instruments, general equilibrium, shock. JEL Classification Codes: C11; C68; D81; H23

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Department of Economics, University Felix [email protected]; Tel : +22549404482

1

Houphouet

Boigny

of

Cocody,

Email :

1. Introduction Middle-income developing countries (MICs) face issues related to the degradation of their environment. These issues are exacerbated by the effects of climate change, whose environmental and economic consequences are disastrous for these countries (Rockström et al. 2009 ; Nordhauss, 2011). A noteworthy example is Côte d’Ivoire, where environmental degradations concern forest cover degradation (from 16 million hectares in 1900, the Ivorian forest is currently 2 million hectares, representing a loss of about 85%), water and air pollutions and solid waste management. This situation is accompanied by the adverse effects of climate change which occur through flooding caused by heavy rains, coastal erosion, reduction of arable land and declining water resources (Goula et al. 2006; UNFCCC, 2000; Kouassi et al. 2013). Theses climate effects also have economic consequences including the decline in agricultural production. According to Hallegatte et al. (2016), land suitable for cocoa production could be negatively affected by climate change in Ghana and Cote d’Ivoire, which constitutes a major problem for theses two countries whose economies depend critically on employment and revenues from this export crop. All of these environmental issues result from the fact that economic agents do not internalize the effect of their actions on the environment, which leads to government intervention to choose appropriate policies that deal with these negative externalities. In the literature, the government intervention may be done through two types of instruments : price-based instruments and quantities-based instruments. Prices instruments or incentive instruments are essentially taxes, tradable emissions allowances (also known as cap-and-trade policy). As for instruments based on quantities or command-and-control instruments, they carry on a standard level of amount of pollution allowed by regulators to polluters. They include quota, performance standard which one can add to the Kyoto rules. These ones take the form of a numerical target to achieve long term pollution by reducing emissions by a certain percentage over a base year2. The appropriate choice of these instruments is facing two major problems. First, the size and source of uncertainties issues. These uncertainties may be related to both economic and environmental impacts (risks related to climate change). Second, the ability of countries especially developing countries to have the necessary resources to finance the activities of environmental protection and climate change adaptation (Angelopoulos et al. 2010). Theoretically, a certain or an uncertain situation is very determinative in the choice of instruments. Indeed, the optimality of the instruments in terms of price and quantity depends on the ability to assess the marginal cost of damage and the marginal benefit of abatement. In a certain environment, price and quantity are equivalent to achieve the first-best optimality (Weitzman,1974). Whereas, in a second-best setting where there are no environmental distortionary taxes, taxes are more advantageous than quota because they generate revenue to reduce the distorting effects of other taxes, what is called revenue-recycling effect (Bovenberg and Goulder, 2002). However, when the costs and benefits are imperfectly known and / or

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It is, for example, to reduce emissions by 25-40% from 1990 levels by 2020 these rules are from the Kyoto Protocol on climate change in 1997.

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unknown because of asymetric information, the two types of instruments are inefficient and neither dominates the other (Weitzman, 1974). Nevertheless, when the government can use a nonlinear tax on emissions, then this one dominates quota under uncertainty about damage costs and benefits of pollution abatement (Kaplow and Shawell, 1997). Also, in a dynamic setting, tax is still higher than quota due to its flexibility property to further reduce the adjustment costs (Briggs, 2011). However, quota produced similar results to taxes if there is a reserve system of pollution permits (Fell et al. 2012). A relative advantage of instruments based on prices compared to the quantity instruments is that price instruments generate tax revenues that would ensure the double dividend. In fact, the environmental taxes allow not only to internalize environmental costs but also to reduce the distorting effect of other taxes. Moreover, the regulatory authorities can use these revenues to ensure the environment protection where costs are extremely important especially in the context of the financing of adaptation policies and mitigation of the climate change effects. However, the use of two-part or mixed instruments allows to neutralize the efficiency disadvantage of the quantity-based instruments related to the price-based instruments (Bovenberg and Goulder, 2002). For instance, to get a meaningful comparison between quantity-based instruments (Kyoto rules) and price-based instruments (pollution taxes or permits), Angelopoulos et al. (2010) have combined Kyoto rules with output taxes (mixed rules). They found that pollution taxes and mixed rules (mixed instrument) are equivalent in a deterministic setup. But in a uncertain world, mixed rules are preferable to pollution taxes when environmental uncertainty is high. While, when environmental uncertainty is relatively low, pollution taxes are more better than mixed rules. Empirical studies are limited but the few papers that have attempted to evaluate environmental instruments under uncertainty yield mixed results. Some studies found that price instruments are superior to quantity instruments (Pizer, 1999; Newell and Pizer 2003; Dissou and Karnizova, 2012). In contrast, other studies have shown that the quantity-based instruments are preferable to price instruments because it is politically less constraining to implement them (Fischer and Springborn, 2011; Ohndorf and Rohling, 2012). Almost all of these studies have been carried out in developed countries. This lack of empirical work on the choice of environmental instruments in developing countries is one of the motivations of this paper. Hence, the aim is to determine which of the following instruments: pollution taxes, Kyoto rules policy and rule-taxes combination maximize welfare in MICs facing environmental and economic shocks. The choice of middle-income countries is justified on the one hand by the fact that these countries, unlike the low-income countries (LICs), are in a development stage where taking early environmental actions are less costly and may enhance benefits. Indeed, early environmental policies can positively influence output volatility by reducing potential risks to growth by increasing resilience to environmental shocks (such as natural disaster) or economic shocks (Hallegatte et al. 2012). On the other hand, these countries have taken enormous international commitments to reduce their

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Greenhouse gas (GHG) emissions3 by 2030, which can only be achieved through the implementation of appropriate environmental policy instruments. This paper contributes to the ongoing debate at three levels : first, the environmental instruments are assessed by taking into account the importance of the effectiveness of goverment pollution abatement spending. Specifically, unlike Angelopoulos et al. (2010), we also analyze situations where government intervention is inefficient, that is, when government expenditures are not effective. Then, we assumed that environmental quality is a renewable resource to focus on nature regeneration capacity (Brock and Taylor, 2004). Finally, the analysis of impulse response functions (IRF) allowed us to extend the findings of Angelopoulos et al. (2013) on pollution taxes responses to real business cycle to the other two instruments (rules and rules-taxes) under environmental shocks. After estimating the parameters of the model for Côte d’Ivoire’s economy by bayesian method, results of welfare comparison under the three instruments show on the one hand that when public abatement spendings are effective, pollution taxes are higher than pure rules when shocks are high. But when rules are combined with output taxes for public clearance spending (mixed instrument), they become better than pollution taxes regardless of the type of shock. These results differ from those obtained in Angelopoulos et al. (2010) according to which the best instrument depends on the type of shock. On the other hand, when government intervention is ineffecient because of the ineffectiveness of public abatement spendings, pollution taxes are almost equivalent to pure rules. But they remain inferior to mixed instrument, which suggests that rules combined with output taxes for public clearance spending is appropriate to deal with the economic and environmental shocks in MICs. In addition, the IRF analysis revealed that three instruments are pro-cyclical under productivity shock while they are counter-cyclical when the economy faces an environmental shock. The rest of the paper is organized as follows: the next section consists of a literature review. Sections 3 and 4 present model and estimating model parameters respectively. Section 5 compares welfare under the different instruments and Section 6 analyzes the IRF and the variation sources. Finally, section 7 closes the paper. 2. Comparison of environmental policy instruments Several environmental regulation instruments are proposed in the literature to internalize environmental externalities. In general, these instruments can be grouped in terms of prices and quantities. The aim of the regulation is to choose the instrument for achieving the social optimum at lower cost. The choice of environmental intruments has been the subject of more theoretical studies than empirical studies with mixed results. Theoretically, the choice of instruments (price and quantity) is still a debate because the optimality of price and quantity depends on the certain or uncertain environment. In the 3

In paris agreement, country’s Intended Nationally Determined Contribution (INDC) report show that MICs are committed to making enormous efforts to reduce their GHG emissions by 2030. For example, some MICs including Cote d’Ivoire, Ghana, Congo are committed to reduce their GHG emissions by 2030 of 28, 15 and 55 respectively. To more informations, please See http://unfccc.int/files/focus/indc_portal/application/pdf/albania_to_ghana.pdf

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literature, two approaches are generally used to evaluate the instruments effects on the welfare : firstly, the static approach based on the partial or general equilibrium analysis and secondly, the dynamic approach that takes into account the externality stock management. In a static model of comparative cost-benefit analysis, Weitzman (1974) shows that in a situation of complete knowledge and perfect certainty price and quantity are equivalent. While in an environment of uncertainty, price and quantity instruments give different results depending on the relative slope of the marginal benefits and costs of pollution abatement. For instance, a flat expected marginal benefit function (relative to marginal costs) favors prices, while a steep benefit function favors quantities. This result is valid only when taxes are fixed and linear. In contrast, if government uses nonlinear emissions taxes, taxes (price) exceed quotas (quantity) under uncertainty (Kaplow and Shawell, 1997). Similarly, Schöb (1996) reasoning within a second-best framework from a partial equilibrium model shows that the first best choice between price and quantity of Weitzman (1974) remains valid in second best under distortionary taxes. In other words, if the marginal cost function is uncertain, prices and quantity instruments (tradable quota) give the same result. This is because the expected tax revenue of the two instruments are to be equal. While in a dynamic environment with uncertainty, Pizer (1999) showed that when uncertainty increases the optimal level of pollution abatement, tax is preferred to the standard. Newell and Pizer (2003), in a model that incorporates benefits and stock adjusting costs, support the superiority of price to control externality stocks. When the regulator is facing price shocks as it is the case of extractive resources, Briggs (2011) proposes as optimal policy, a stationary tax rule that responds to a positive shock to the current price by reducing next period’s tax rate. However, under risk of tax depreciation, Ohndorf and Rohling (2012) find that quantities are preferred because they reduce price variance of marginal abatement costs4. Now, consider models based on an real business cycle (RBC) setup in which instruments are implemented in an economy facing total factor productivity (TFP) shocks. Fischer and Springborn (2011) compared three instruments: an emission tax, an emission cap and an intensity target (an emission target per unit of production). They find that the targeted intensity leads to low expected costs in terms of welfare or consumption; while taxes and an emission cap give equivalent results in relatively high costs on welfare. The superiority of the targeted intensity instrument (quantity) is due to the fact that it has the ability to adapt to changes in the economy, contrary to taxes that are considered fixed in the model. Unlike these two authors, Dissouu and Karnizova (2012) use a multisectoral framework that allows them to disaggregate the economy into six sectors grouped according to their energy intensities. By comparing two systems: an emission cap and an emission tax, they show that both instruments are equivalent in terms of costs of welfare when productivity shocks are from non-energy industries. However, an emission tax is less expensive than the emissions cap when shocks come from the energy sector. In the case where the economy faces both economic and environmental shocks, more realistic situations, Angelopoulos et al. (2010) using a DSGE model, find that pollution taxes 4

This risk is due to low implementation of price instruments (Rohling and Ohndorf, 2012).

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are more prefered than rules combined with output taxes under an economic shock. But they are less efficient when the shock is environmental (preference for the rules combined with output taxes). Furthermore, they show that the pollution permits are the least efficient instrument. Empirical studies are limited. However using a DSGE approach, Pizer (1999) showed that pollution taxes are preferable to the standard in a situation of high asymmetric information. Applying their model to the problem of greenhouse gas reduction in using data taken from the international climate policy context, Newell and Pizer (2003) find that prices increase 5 times the gain of welfare than quantities. While, Ohndorf and Rohling (2012), based on the same data showed that the quantities are preferred to prices through the effects of taxes depreciation. Similarly, using the parameters values from RBC literature5, Fischer and Springborn (2011) estimated a loss of 0.4% in terms of consumption expected in the targeted intensity against 1.6% in emission taxes. However, Dissouu and Karnizova (2012) by calibrating their multisectoral model on the US economy show that emissions taxes generate a welfare cost of 0.8448 against 0.8516 in emissions capped when shocks originate from intensive industries energy. Furthermore, Angelopoulos et al. (2010) using a DSGE model calibrated to the US economy in which uncertainty sources are both economic and environmental, showed that pollution permits are less efficient in all cases studied. But taxes are more efficient under the economic shock. Whereas if the shock is environmental, rules combined with output taxes are more effective than pollution taxes.

3. Model The setup is a real business cycle (RBC) model of dynamic stochastic general equilibrium (DSGE) developed in Angelopoulos et al. (2010). In this model, pollution is a by-product of output that creates damage to environmental quality. This one is considered as a public good insofar as private agents do not internalize the effect of their actions on the environment, which implies that competitive equilibrium is inefficient. Therefore, there is a need for government intervention. Since this intervention is also carried out in an uncertain environment, the result is second-best. In this paper, we assume that governments intervene through three environmental policy instruments: pollution taxes, rules and combining rules-taxes (mixed instrument). This framework is appropriate for a middle-income economy like the one of Côte d’Ivoire where cleanup activities are fully insured by government through public structures that are funded by public resources6.

The Standards RBC parameters values come from King, Plosser and Rebelo’s (1988) (hereafter KPR) and Prescott (1986) 6 In Côte d’Ivoire, the environmental policy is mainly implemented through three public structures namely: the National Environment Agency (NEA), the Ivorian Anti-Pollution Centre (IAPC) and the Ivorian Office of Parks and Reserves (IOPR). For details, see Environmental Profil for Côte d’Ivoire - Final Report, August 2006. 5

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As in the analysis of Angelopoulos et al. (2010), the private agent is not engaged in pollution abatement activities, the effectiveness of government intervention becomes very important. However, given the uncertain situation related to environmental problems including the effects of climate change, it led us to extend the analysis in case where the pollution abatement activities are not effective. In addition, we modelize the environmental quality as a renewable resource to focus on the regeneration capacity of the nature. Indeed, this assumption is consistent with the situation of some MICs and Côte d'Ivoire in particular, given this country is considered as a net sink of GHG. For example, the assessment of Greenhouse gas emissions shows that the total CO2 in Cote d’Ivoire amounts to –17 901,47 Gg (UNFCCC, 2000). We firstly present the decentralized competitive equilibrium model (DCE) with pollution taxes, secondly a DCE with pure rules, thirdly a DCE with mixed instrument (rules combined with output taxes) and at last, the social planner model that will be the benchmark case.

3.1.Model with pollution taxes We consider a stochastic endogenous growth model integrating environmental concerns and an environmental policy. We assume a representative private agent who consumes, saves and produces a single good. Production generates pollution which has a negative impact on environmental quality. This externality is not taken into account in his decisions leading to a suboptimal equilibrium, which leads the government intervention through pollution taxes. In MICs, pollution taxes are implemented but are less developed. For instance, in Cote d’Ivoire, the pollution taxes are ensured by IAPC but concerns only classified installations for environmental protection. Here, pollution taxes are allowed to deal with pollution generated by all production actitvies. Moreover, we assume that environmental quality improves agent’s utility. 3.1.1. Private agent’s behavior We consider a closed economy in discrete time infinite horizon inhabited by a continuum of households and government. We assume that the population size is constant and equal to 1. The household’s (or private agent) preferences are defined by an intertemporal utility function expected as follows: 

E0   t u  ct , Qt 

(1)

t 0

ct is stochastic consumption of the unique final good at time t , Qt denotes the quality of the environment t . 0    1 is a time preference rate and is an expectation operator based where

on the information available at time zero. We assume that Qt   0, Q  where

Q is the

environment quality without pollution. Following Acemoglu et al (2012), the instantaneous utility function u  ct , Qt  is increasing both in

ct and in Qt , twice differentiable and jointly concave in  ct , Qt  . It satisfies the

following conditions Inada : 7

u  c, Q  u  c, Q    , lim   et lim u  c, Q    c 0 Q 0 Q0 c Q

lim

(2)

The last two conditions imply that when the quality of the environment reaches its lowest level, it produces very significant adverse effect on agent’s utility. I assume finally that : u  c, Q  Q

0

(3)

which implies that when

Qt reaches Q , the value of the marginal increase in environmental

quality is small. We use a non-separable utility function of the form: 1

ct Qt1   u  ct , Qt   1

(4)

Where 0    1 are the weights given to consumption and environmental quality respectively and   1 is a measure of risk aversion. The private agent’s budget contraint:

kt 1  (1   k )kt  ct  1  tt  At kt

(5)

with yt  At kt function of current output. At is the total factor productivity. kt is the current capital per capita. t is the emission per unit of output, 0    1 the share of capital in production. . 0   k  1 is the capital depreciation rate and 0    1 is the rate of pollution taxes. The purpose of private agent is to choose ct , kt 1t 0 in order to maximize the intertemporal 

welfare expected (1) under the resources constraint (5) given the environmental policy (the pollution taxes) and the environment quality. This one is exogenous to the choice of agent because it is considered as a public good. Indeed, environmental quality is a good open access corresponding to the public goods features. 3.1.2. Dynamics of environmental quality The quality of the environment depends on the level of pollution stock. Following Jouvet et al. (2005), the pollution stock

St evolves according to:

St 1  1  h  St  Pt where

(6)

Pt is the pollution flow at time t and h is a nature regeneration rate with 0  h  1 .

Equation (5) means that the current pollution is the result of the variation between the beginning-of-period and end-of-period pollution stock. The quality of the environment

Qt can

be defined as the difference between the quality of the environment without pollution and pollution stock: 8

Qt 1  Q  St 1

(7)

Therefore, the motion of the environmental quality is given by (see Appendix 1 for details):

Qt 1  hQ  1  h  Qt  Pt

(8)

If I assume that the government carries out cleanup activities through revenues from pollution taxes, equation (7) becomes:

Qt 1  hQ  1  h  Qt  Pt  vGt where

(9)

Gt is public abattement spending and v  0 are parameters measuring how public

spending is translated into actual units of renewable natural resources. As pollution is a by-product of output, Pt becomes :

Pt  t yt  t At kt

(10)

At and t are assumed to be exogenous stochastic variables that follow a first order autoregressive, AR (1).

At 1  A

1 a 

t 1  

At a et1 a

(1  )



t  e

(11)

 t 1

(12)

a  with A et  are constants, 0  a ,   1 the coefficients of the AR (1) and  t t ,  t t are

2 2 Gaussian i.i.d. shocks with zero means and known variances,  a and   .

3.1.3. Government’s behavior The government intervenes through environmental policy. Specifically, the government collects revenue from environmental taxes and allocates them to the cleanup activities. Its budget constraint becomes:

Gt  t yt  t At kt

(13)

Assume now that the government uses a fraction of the non-environmental tax revenues to finance abattements activities as is the case in MICs in general. Following Economides and Philippopoulos (2008), the government budget constraint is:

Gt  gt  et   At kt

(14)

where gt  b At kt is the share of non-environmental tax revenue for other State spending with

0    1 the rate of non-environmental taxes.

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et  (1  b) At kt

is the amount spent on

abattement activities with 0  b  1 .

These taxes allocated for cleanup activities ( et ) is

combined with Pure rules to give mixed instrument (see section 3.3). The

Lagrangian

associated

with

the

problem

of

private

agent

is

given

by:



E0   t u  ct , Qt   t kt 1  (1   k )kt  ct  1  tt  At kt 

(15)

t 0

Where

t

is Lagrangian multiplier of the constraint (5)

First order conditions characterizing the decentralized competitive equilibrium (DCE) to t  0 are presented as follows (see Appendix 2 for details) : ut   Et ct

 ut 1  1   k  1  t 1t 1   At 1kt11     ct 1 

(16a)

kt 1  (1   k )kt  ct  1  tt  At kt

(16b)

Qt 1  hQ  1  h  Qt  t  vtt  At kt ,

(16c)

where

ut  1  1 1  1    ct  Qt    ct

Equation (15a) is the standard Euler condition of private agent while equations (15b) and (15c) describe the economy’s resource constraint and the motion of environmental quality respectively. This system of three equations provides private allocation policy level  t 0 with initial conditions 

ct , kt 1 , Qt 1t 0 for 

a given tax

k0 and Q0 ..

3.2. Model with rules. In this part, the government sets a target of a long-term pollution with a speed correction  t reflecting environmental policy (Angelopoulos et al. 2010). So, we have the following rule:

Pt 1  1   t  P   t Pt , where P is the long-term pollution and

(17)

0   t  1 is the speed correction.

This rule means that pollution of tomorrow will be a fraction of today pollution, which depends on the speed correction. This one is the lever of environmental regulation. As rule policy generates no tax revenue ( Gt

 0 ), this does not affect the private agent’s budget

which becomes:

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kt 1  (1   k )kt  ct  At kt

(18)

The DCE’s rule policy is defined as follows (see Appendix 3 for details) :  u  ut   Et  t 1 1   k   At 1kt11   ct  ct 1 

(19a)

kt 1  (1   k )kt  ct  At kt

(19b)

 1   t  P   tt At kt  kt 1    t 1 At 1  

1



(19c)

Qt 1  hQ  1  h  Qt  t At kt

(19d)

Equation (19c) describes the dynamics of capital stock consistent with rule policy. This system determines an allocation ct , kt 1 , Qt 1t 0 given the speed correction, the level of long-term 

pollution, and initial conditions k0 and

Q0 and stochastic processes At and t ..

3.3. Mixed instrument model (rules-output taxes) Assume now that the government chooses a mix regulatory policy which consists to combine rules with output taxes. The purpose of this policy is to address the lack of pure rules when compared to taxes in a stochastic situation (Angelopoulos et al. 2010). Unlike these authors, we combine pure rules with output taxes allocated for cleanup activities

(et ) to

approach more reality. The private agent’s budget constraint becomes:





kt 1  1   k kt  ct  1  (1  b) t  At kt

(20)

The first order conditions is given by (see Appendix 4 for details):  u  ut   Et  t 1 1   k  1  1  b  t 1   At 1kt11   ct  ct 1 





kt 1  1   k kt  ct  1  (1  b) t  At kt

 1  t  P  tt At kt  kt 1    t 1 At 1  

(21a) (21b)

1



(21c)

Qt 1  hQ  1  h  Qt  t  v 1  b  t  At kt

(21d)

A private allocation ct , kt 1 , Qt 1t 0 is chosen given the output taxes  t t 0 , the speed 



correction  t t 0 , the level of long-term pollution P , and the initial conditions k0 and 

stochastic processes:

At and t . 11

Q0 and

3.4.Social planner model In this section, we finally present social planner model which is considered as the benchmark case. The planner internalize environmental externalities so that the resulting allocation is a first-best. This latter aims to choose an allocation

ct , Gt , kt 1 , Qt 1t 0 that 

maximizes intertemporal expected utility (1) subject to economic and environmental resources. Social solution is given by (see Appendix 5): ut   Et ct

 ut 1   ct 1

1 ut   Et v ct

  t 1  k  1   1    1  v   At 1kt 1      

(22a)

 ut 1 1 u   1  h  t 1   Qt 1   Qt 1 v

(22b)

kt 1  (1   k )kt  ct  Gt  At kt

(22c)

Qt 1  hQ  1  h  Qt  t At kt  vGt

(22c)

The social allocation is characterized by ct , Gt , kt 1 , Qt 1t 0 being given the initial conditions 

k0 and Q0 and stochastic processes At and t . To evaluate the environmental policy instruments, we must have the economy parameters, wich lead to estimate the parameters of models.

4. Parameters estimation The model with pollution taxes introduced in Section 3 is estimated by bayesian method using two main economic and environmental variables, that is, the log difference of real GDP

(log yt ) and CO2 total emission (log Pt ) in the period 1960-2011. First, we estimate only this model to have the same settings for all other models in order to properly evaluate instruments associated with each model. Then, we used two variables for estimation to be compatible with the number of shocks. Finally, variables are in first differences to ensure they are stationary. Indeed, the stationarity tests indicate that

log yt and log Pt are I (1) which

follow a random walk process. The results of stationarity tests and variables sources are given in Table 10. The estimation procedure takes place in two steps : in the first step, we estimate the mode of the posterior distribution by maximising the log posterior function, which combines the prior information on the parameters with the likelihood of the data. In the second step, we used the Metropolis-Hastings algorithm based on the Markov chain Monte Carlo (MCMC) simulations to obtain the posterior distribution using the random walk law of motion and to generate an estimate of the marginal likelihood of the model.

12

Furthemore, since the bayesian method is based on the formulation of prior beliefs about the parameters values; and that this requires the data observation to update beliefs about these parameters by estimating the posterior density, the comparison of prior and posteriori variances allows to inform us about the additional information provided by the data related to that of prior beliefs. Thus, if the posterior variance is relatively lower than prior variance, then data give us more information about the parameters values relative to prior beliefs (Adjemian and Devulder, 2011). 4.1.Prior distribution of the parameters The choice of prior distributions is based on the work of Smets and Wouters (2003, 2005, 2007). This allows us to compare our results with those of the literature. Thus, the persistence of AR (1) process shock follows a beta distribution with mean 0.93 and standard deviation 0.02. The share of capital in production evolves according to a Gaussian distribution with mean 0.33 and standard deviation 0.05. Concerning the preference parameters namely the weight of the consumer and the coefficient of risk, they have Gaussian distributions with mean 0.6 and 2 and standard deviations 0.05 and 0.03 respectively. The discount factor follows beta process with mean 0.97 and standard deviation 0.002. The estimation procedure does not take into account certain parameters that are considered fixed (Smets and Wouters, 2007). The values of these parameters are selected according Angelopoulos et al. (2010). Thus, the capital depreciation rate is fixed at 0.1. The environmental quality without pollution and long-run total factor productivity are equal to 1. Regarding of pollution technology, it is set to 0.001 to be compatible with the environmental quality longterm. The nature regeneration rate is fixed at 0.1 consistent with a persistent environmental quality 0.9. Regarding of the share of the output taxes devoted to cleanup activities, I have chosen 1  b  0.008 which is consistent with the part of an annual environmental expenditure amounting to 29 million dollars compared to an annual tax revenue of 3.90124 billion dollars from Cote d’Ivoire in 20107. 4.2. Posterior estimates of the parameters Table 9 gives the mode, the standard deviation of the posterior distribution of the parameters obtained by the Metropolis-Hastings algorithm. Generally, the posterior variances are lower than those a priori belief, which means that data provided information on the parameters relative to the priori information. The mean weight of consumption in the utility function is estimated around 0.91, which is significantly higher than the value in Angelopoulos et al. (2010). This means that the Ivorian representative household gives more importance to the consumption that the environmental quality. This result is consistent with the fact that Côte d'Ivoire is a MIC. The mean discount factor is 0.97. This is in line with global real interest rates to 3% steady state. The mean of the share of capital in production is estimated around 0.62, which is relatively higher than those of 7

Data on environmental expenditures come from the IMF report (2012) on the implementation of the PRSP : https://www.imf.org/external/french/pubs/ft/scr/2012/cr12183f.pdf Tax revenues come from African economic outlok 2010. 13

Angelopoulos et al. (2010). Which means that in Côte d'Ivoire, capital represents 2/3 of output consistent with results obtained by Goedhuys and Sleuwaegen (2003) for the same country. Persistence of total factor productivity and persistence of pollution technology are estimated 0.95 and 0.97 respectively. These coefficients are relatively higher than those in Angelopoulos et al. (2010), which means that TFP and pollution technology are on average more persistent in Côte d'Ivoire. However, the persistence of pollution is relatively larger than those of TFP. 5. Welfare analysis The purpose in this part is to evaluate the impact of allocations obtained under the various schemes on welfare materialized by the intertemporal expected utility of the agent. We proceed as follows: First, welfare is evaluated in a certain situation based on its value in steady state. Second, we compute the value of welfare associated with each scheme under uncertainty related to environmental and economic shocks. To do this, the function of intertemporal expected utility is approximated to the second-order using the Schmitt-Grohé and Uribe (2004) method. We do this to compare welfare in this context. Indeed, the second-order approximation not only allows to take into account the second-order term of welfare function ignored in the first order approximation but also to take into account of volatility of exogenous variables of model representing shocks (Schmitt-Grohé and Uribe, 2004). The welfare comparison requires a measure of utility gains/losses associated with alternative regimes. Following Angelopoulos et al. (2010), we define  ij the compensation measure of welfare between regimes j and i . This measure is obtained by computing the percentage compensation in private consumption that the private agent would require in each time-period under regime j so as to be equally well off between regimes i and j  i . 5.1.Welfare evaluation in certainty situation  Table 1 summarizes the value of welfare defined by u  c, Q  and key variables such as

consumption c , environmental quality Q , production y and pollution P at steady state. The second column of Table 1 shows the results of long-term model with pollution taxes. The third column shows the results of pure rules. The results of mixed instrument (Rules combined with the output taxes devoted to government activities) are shown in the fourth column and finally the last column presents the results of social planner Table 1 shows firstly that welfare associated with pollution taxes and pure rule is valued at -6.051, which means that pollution taxes and pure rules are equivalent. This result is consistent with Weitzman (1974) analysis. Indeed, according to him, in certainty situation, price instruments (taxes) and quantity (rules) are equivalent. While, welfare is relatively higher in the mixed instrument (rules-taxes). The substantial improvement of welfare under rules combined with output taxes can be explained by the fact that government uses in addition to rules, revenue from taxes to make the cleanup activities. Second, the social planner model gives the best result in terms of welfare. This result was expected in the sense that social planner perfectly internalize environmental externalities, which makes welfare higher. 14

In addition, the long-term pollution level is the same for all models used, which made possible instruments comparison and strengthens the robustness of these models. Finally, the long-term rate of pollution taxes are around 0.02% for a long-term pollution level to 0.013.

Table 1: Expected lifetime utility under different regimes at deterministic steady state Variables

c

Taxes 6.843

Pure rules 6.843

Rule-taxes 6.839

Social planner 6.375

Q

0.869

0.868

1

7.832

y

13.112

13.112

13.107

13.097

P

0.013

0.013

0.013

0.013

u   c, Q 

-6.051

-6.051

-5.985

-5.398

Notes: Rules-taxes instrument or mixed instrument is pure rule combined with output taxes

1    u  c, Q  where devoted to public clearance activities. u  c, Q   t



1   

t  300 and   0 . t

5.2.Welfare evaluation in uncertainty situation We now analyze the case where the intertemporal expected utility of the private agent is affected by stochastic processes of production technologies and pollution. We assume that the economy is at steady state and it is undergoing productivity ( At ) and environmental ( t ) shocks. The analysis consists to compute the intertemporal expected utility under each regime for varying degrees of uncertainty ranging from the lowest (1%) at the height (5%) based on the standard deviation of production technologies and Pollution. Thus, five possible scenarios are studied : (i) the deterministic case ( a     0) ; (ii) when there is only one source of uncertainty (  a

 0.01 et    0 ;  a  0 et    0.01 ); (iii) a case of relatively low

uncertainty in both stochastic variables ( a     0,01) ; (iv) two scenarios representing high levels of uncertainty in one of the two stochastic variables (  a

 0.05 et    0.01 ;  a  0.01

and    0.05 ); (v) a scenario with relatively high uncertainty in both stochastic variables

( a     0.05)

15

Note that apart from the first scenario describing the deterministic case already analyzed, instruments comparison under other scenarios is based on the measurement of welfare gain/loss (  ij ) when the private agent chosen regime i instead of regime j with j  i . Thus, when the

 ij value is positive, it means that regime or instrument i is greater than regime j . Indeed if

 ij  x  0 , this implies that an agent who is in regime j will always need a subsidy in terms of consumption of x% for be indifferent between i and j . It is also interesting to consider the importance of the effectiveness of public abatement spending in the comparison of different regimes in this context of uncertainty. In fact, the effectiveness of government intervention depends on the ability of this latter to make optimal use of taxe revenues from the environmental policy or not in abatement activities. We first compare the different regimes in the case where government intervention is effective, that is ensuring the effectiveness of clearance activities. Then, we analyze the situation where environmental public expenditures are not effective. 5.2.1. Case 1: Effectiveness of public abatement spending We assume that revenues from the environmental policy allow to cover public abatement spending. To do this, we choose the parameter value v equal to 5 so that combined with tax, it bridges the intensity level of long-term pollution   0.1% (kt per unit dollars). Thus, at equilibrium we have v    0 . Table 2 summarizes the results of welfare under these different regimes. The welfare differences between pollution taxes and pure rules are given by  12 . This value is positive on almost all scenarios envisaged except where the economic and environmental shocks are relatively low. This means that taxes are relatively preferred to pure rules. For example, when

 a  0.01 and    0.05 ,

a welfare gain to 2.18% in terms of consumption

can be obtained if we use pollution taxes instead of pure rules. This is due to the fact that taxes play a role as an automatic stabilizer. Indeed, in our model, only economic shocks are internalized by private agents because environmental quality is considered as a public good. Since the government intervention is essentially to stabilize the economy overheated situation through fiscal policy, in this case the use of the environmental taxes allow the government to contain the relatively higher environmental shock. Another reason that may explain the superiority of taxes in relation to rules is that the environmental damage function is relatively flat and it is probably negatively correlated to the costs of private pollution due to high volatility. This result is consistent with that of Pizer (1999) which showed that taxes are more efficient than the control policy (rules) in uncertainty situation related to the environment. Nevertheless, pure rules give better result when both economic and environmental shocks are low

( a     0,01) . It prevents welfare loss much greater of 4.54% than taxe. The intuition is that in situation of low environmental volatility, the role of automatic stabilizer of the environmental taxes become excessive and it produces adverse effects on welfare.

16

 13 gives differences welfare between pollution taxes and mixed instrument. In all cases considered the value of

 13 is negative, which means that pollution taxes are less attractive than

rules combined with output taxes instrument. The mixed instrument helps therefore to avoid losses welfare. Results show that the losses are greater when the level of environmental uncertainty is relatively higher. For instance, in both scenarios (  a

 0.01 and    0.05 ) and

( a     0.05) where the environmental shock is relatively high magnitude, the losses are 297.08% and 294.12% respectively. In addition, it is also high when shock relate solely to the environment (    0.01 and

a  0

), either 50.23% instead of 1.17% in the case of an

economic shock. This result can be explained by the fact that the automatic stabilizer effect of pollution taxes is very low compared to that of output taxes. Another explanation is that pure rules, with its attenuation capacity of economic shocks, contribute to improving welfare when associating with output taxes for clearance activities, which is efficient under environmental shock. This result corroborates that of Angelopoulos et al. (2010) which showed that rule combined with output taxe is better than the pollution taxes under environmental shock. The negative value of

 23

indicates, as expected that the choice of pure rules instead of

the mixed instrument leads to a greater loss of welfare. This loss is all the greater than the environmental uncertainty is more important. For instance, in scenario where especially when (  a

 a   ,

 0.01 and    0.05 ) and ( a     0.05) ,the losses associated with

pure rules instrument are to 299.26 % and 296.29 %, or again when (    0.01 and

a  0

),

this loss amounts to 51.09%. These relatively poor results (with respect to taxe) are justified by the fact that pure rules are much less effecient under environmental shock because of its property of non stabilizer. Because, in pure rules, there is no automatic stabilizer to mitigate environmental volatility, which further degrades welfare. To better understand forces that might explain welfare differences in the three regimes discussed above, we analyze the first and second moments of the two arguments in the utility function, namely, private consumption,

ct , and the stock of environmental quality Qt . The

second order approximation of the utility function allows me to take into account the second moments and thus better understand the volatile variables effect on welfare. As the values of steady state solution (see Table 1) are the same for all three regimes, welfare differences under uncertainty are captured by differences in average, expected variances and covariance of the series for

ct and Qt (Appendix 6).

Tables 5-7 give the expected means, standard deviations and covariance of all three regimes under various levels of uncertainty. Welfare increases if means, small variances and low covariance.

17

ct and Qt for

ct and Qt have high

Tables 5 and 6 show that on average the quality of the environment is relatively higher under taxes (Table 5) than under pure rules (Table 6). In addition, environmental quality on average increases more when the environmental shock is relatively strong. For instance, the value of

E (Qt ) is equal to 9.83 under taxes against 6.92 under pure rules when the environmental

shock is higher than the productivity shock (  a

 0.01 and    0.05 ). It is to 10.44 against

7.54 in the case where the two shocks are still relatively high magnitude ( a     0.05) with standard deviations substantially the same. As for the values of

E (ct ) , they are substantially

identical as well under taxes than pure rules, as well as the covariance

 (ct , Qt ) . This result

consolidates the superiority of taxes compared to pure rules because it happens to improve on average the quality of the environment in the presence of uncertainty all things being equal. Now let's see the case of pollution taxes and mixed instrument. The values of the first and second moments are shown in Table 5 for taxes and Table 7 for mixed instrument. We note that under mixed instrument,

Qt variance is zero and that of ct is relatively small, which means

that rules combined with output taxes allows one hand to fully master the environmental volatile and mitigate the other risks on consumption. The covariance

 (ct , Qt )

between

ct and Qt is

negative, so low compared to that under taxes. These results clearly show why mixed instrument is better than pollution taxes. Finally, concerning pure rules and mixed instrument, previous results are also valid as shown in Tables 6 and 7. The preference of mixed instrument to pure rules is therefore justified.

18

Table 2: Expected lifetime utility under different regimes for various levels of uncertainty ( v  5 )

a



0

0 0.01

0

0

0.01

0.01

0.01

0.05

0.01 0.05

0.01

Taxes (1) -6.051

Pure rule Rule-taxe (2) (3) -5.986

-4.922

-9.578

-5.986

-4.923

-6.059

-5.993

-4.932

-9.585

-5.994

-4.933

-94.223

-6.004

-4.948

-9.764

-6.171

-5.180

-94.402

-6.182

-6.051 -9.503 -6.058 -9.994 -92.355 -9.689 -92.534

0.05 0.05 Source : Authors

Social planner

-5.194

 12

 13

 23

(%)

(%)

(%)

0.00

-1.18

-1.18

0.85

-50.23

-51.09

0.02

-1.17

-1.19

-4.54

-55.58

-51.03

2.18

-297.08

-299.26

0.84

-49.03

-49.87

2.17

-294.12

-296.29

Note : rule-taxe instrument or mixed instrument is pure rule combined with output taxe devoted

 Vt i  1 log  j  where Vt i to public clearance activities. The value of  ij is given by  ij   1     Vt  j

and Vt are respectively the discounted sums of second-order approximations to welfare averaged over 1000 simulations under regimes i and j over 300 years. Same for table 3 and 4.

5.2.2. Case 2: inefficiency of public abatement spending In this section we look at situation where spending abatement are not efficient in the sense that they are not effective,namely when v    0 . This would mean that the beneficial effects from more public abatement spending are outweighed by the detrimental effects from higher polluting output (Angelopoulos et al. 2013). We analyze two particular cases: in the first case, the ineffectiveness of expenditures is moderate with v  1.5 and in the second one has a greater ineffectiveness by choosing v  0.6 . Tables 3 and 4 present differences welfare under the three regimes in both situations of ineffectiveness. Let's start by comparing pollution taxes to pure rules. But before we notice that the values of welfare of pollution taxes in government inefficiency situation are relatively low compared to those where government intervention is effective. What constitutes a proof of the ineffectiveness of public abatement spending. The

 12 value is relatively positive in all

scenarios, but these values are very low. This means that taxe is almost equivalent to pure rule 19

when public abatement spending are not effective. One possible explanation is that the role of automatic tax stabilizer decreases strongly in a situation of ineffective government intervention Next, let's look now to welfare differences between taxes and mixed instrument. The value of

 13 is negative in all scenarios both in the first case ( v  1.5 ) in the second ( v  0.6 ). This

implies that the choice of taxes instead of mixed instrument allows to have losses welfare. These losses are relatively high when the environmental shock are more important. We can therefore deduce that rules combined with output taxes are better than pollution taxes even in a situation of ineffectiveness of pollution abatement costs. The justification of this result is similar to that given in the situation of effectiveness. Finally, concerning the comparison between pure rules and mixed instrument, the negative values of

 23

in the five scenarios, indicate that the choice of pure rules instead of mixed

instrument leads to a greater loss of welfare when ineffectiveness of abatement costs is moderate. This result shows unsurprisingly that pure rules are inferior to mixed instrument in a situation of governmental inefficiency. This is likely due to the stabilizing capacity of mixed instrument. In summary, the mixed instrument composed of pure rules and output taxes for abatement activities is preferable to pollution taxes, which itself is better than pure rules. The superiority of mixed instrument also remains valid if government abatement spending is not effective. However pollution taxes seem almost to be equivalent to pure rule in a situation of government inefficiency.

Table 3: Expected lifetime utility under different regimes for various levels of uncertainty ( v  1.5 ) Pure rules (2) -6,051

Rulestaxes (3) -6,032

Social planner -5,398

 12

 13

 23

(%) 0,00

(%) -0,34

(%) -0,34

a



0

0

Taxes (1) -6,051

0

0,01

-9,575

-9,578

-9,246

-5,406

0,03

-3,80

-3,83

0,01

0

-6,059

-6,059

-6,04

-5,409

0,00

-0,34

-0,34

0,01

0,01

-9,583

-9,585

-9,253

-5,417

0,02

-3,81

-3,83

0,01

0,05

-94,162

-94,223

-86,379

-5,591

0,07

-9,38

-9,45

0,05

0,01

-9,761

-9,764

-9,432

-5,683

0,03

-3,73

-3,76

0,05

0,05

-94,34

-94,402

-86,558

-5,857

0,07

-9,36

-9,43

Source : Authors

20

6. Impulse response functions (IRF) and determination of source fluctuations In this section, we examine the one hand, the responses of welfare and key economic variables under each environmental policy resulting of economic and environmental shocks through the IRF. On the other hand, we determine the sources of fluctuations via the variance decomposition. 6.1.IRF analysis Before analysing of the impulse responses, we will look if the simulated values over a period of 300 years of the variables of our economy namely consumption, capital stock, output and pollution are going in the same direction as those observed by data. To this end, we compare the second moments, specifically the correlation pairs of simulated variables to those observed. We find that the correlation pairs simulated and observed variables have the same sign, which means that model generally reproduces the stylized facts embodied by data (see Table 8). Let us now examine welfare, output, consumption, capital stock, the environmental quality responses under the three environmental policy instruments after a 5% increase of economic and environmental shocks. 6.1.1. Productivity shock effect Figures 2, 4 and 6 plot the deviation in % from the steady-state values of a productivity shock A of welfare function ( welfare ), economic variables (output y , consumption c and capital stock k ) and environmental variables (environmental quality Q and pollution P ) under pollution taxes, pure rules and mixed instrument (Rules-taxes) respectively. These figures also show how each instrument responds to the productivity shock. Generally, welfare and economic variables respond almost the same way under the three regimes to the productivity shock. While, environmental variables behave similarly under pollution taxes and pure rules, but less volatile under mixed instrument. Specifically, a positive shock of higher productivity leads to an increase welfare beginning of the period. The effect on welfare decreases in proportion as shock diminishes and disappears after 60 years under all regimes. Concerning economic variables, results show that these variables respond favorably to a positive productivity shock under all regimes. Furthermore, resulting of TFP shock under taxes, output increases and reaches a peak around 12 years, after it decreases. Similarly, capital stock increases and more than output to reach its highest level after 20 years. Consumption also follow the same rhythm but its peak is around 18 years. Regarding environmental variables, a productivity shock affects positivily pollution and negatively the quality of the environment. Indeed, the increase in pollution subsequent to the increase in output due to the positive productivity shock degrades the environment quality. The pollution response is the same under all regimes. For example under pure rules, pollution increases in the ten years after shock and diminishes thereafter to become blurred around 60 years. Environmental quality almost similarly responds under pollution taxes and pure rules 21

regimes but differently under mixed instrument. Under this one, the degradation of environmental quality is relatively lower and less volatile ( see Figure 6). Let's look at the policy instruments responses to the productivity shock. First, pollution taxes respond positively. It increases initially to a peak at around 18 years and falls thereafter. The increase of pollution taxes is due to the increase in pollution ( see Figure 2). Then, pure rules policy represented by the speed correction (  ) also responds positively (see Figure 4). Finally, concerning mixed instrument embodied both by the speed correction (  ) and output taxes for the cleanup ( e ), we note that the two elements of the policy respond favorably to positive TFP shock. For example, public abatement spending increase consecutively to the increase in output (see Figure 6) In summary, under TFP shock, environmental policies represented by three instruments are pro cyclical. This result is similar to those obtained by Heutel (2012) and Angelopoulos et al. (2013) who respectively examined solely on quota-taxes and output taxes. 6.1.2. Environmental shock Figures 3, 5 and 7 plot the responses of different variables to the environmental shock (assumed negative) of 5% under each regime. Welfare responds negatively in all three regimes under an environmental shock. The welfare response is relatively less important under mixed instrument. Indeed, an increase of 5% of the environmental volatility provokes at beginning of period, a deviation of -0.05% (compared to the value of steady-state) value of welfare under mixed instrument against -4% under pollution taxes and pure rules. Shock diminishes and disappears beyond 60 years (see Figures 2, 4 and 6). This justifies the relative efficiency of mixed instrument under environmental shock. Economic variables respond almost in the same way under pollution taxes and pure rules, but a little differently under mixed instrument. Under both taxes and pure rules regimes, output and capital stock respond positively early in the period until about the 20th year and they begin to be negative after that date. In contrast, consumption responds negatively at beginning of period until around the 10th year; it becomes positive from 10 to 30 years before becoming negative thereafter (see Figures 3 and 5). Under mixed instrument, three economic variables all respond negatively (see Figure 7). Regarding environmental variables (environmental quality and pollution), high environmental shock positively affects unsurprisingly pollution under all regimes. Which tend to degrade the quality of the environment under pollution taxes and pure rules ( see Figures 3 and 5). Nevertheless, we find that under mixed instrument, environmental quality positively responds to shock, which can justify the fact that mixed instrument mitigates the environmental shock (see Figure 7). Finally, regarding environmental policy instruments, one notice that taxes, the speed correction or speed correction combined with output taxes (  ), all these instruments respond positively to the environmental shock. However, unlike to productivity shock, the responses of these instruments are generally in opposition to those of real variables, which show that under 22

environmental shock, environmental policies are counter-cyclical. This result is consistent with Angelopoulos et al. (2013). 6.2. Variance decomposition This section discusses the contribution of both shocks (economic and environmental) to the volatility of welfare, economic and environmental variables in the three regimes studied. To this end, we use as a tool unconditional variance decomposition. It allows to focus on the persistence of environmental degradation and climate change effects. Table 10 shows results of the relative share of productivity (  a ) and environment (   ) shocks of a magnitude from 5% to the volatility of the different variables under pollution taxes, pure rules and rules combined with output taxes. These results first show that environmental shocks explain on average around 98% welfare fluctuations under the three regimes, which demonstrates the low resilience of MICs and especially the Ivorian economy to environmental degradation effects. The contribution of this shock is higher in pure-rule (98.25%) and lowest under mixed instrument (97.62%), which consolidates the superiority of rule combined with output taxes and the weakness of pure rules face to environmental shocks. Pollution taxes thus occupies second position in terms of efficiency for a relative share of 98.07%. Then, regarding economic variables, environmental shocks contribute to average around 44.26% (against 55.73% of productivity shocks) to output fluctuations, 43% those of consumption and 64.28% to those of capital stock under three regimes. Pure rules still holds the highest; pollution taxes contribution comes next and finally mixed instrument. At the level of capital stock for instance, the relative share of environmental shock is 67.25% under rule, 64.88% under pollution taxes and 60.70% under mixed instrument. The importance of environmental shock relative to productivity shock in capital stock fluctuations is explained by the fact that the pollution dynamic is determined by that of capital stock (see equation 9). Finally, as expected, I find that environmental shocks explain 100% the environmental variables volatilities: quality of the environment and pollution. 7. Conclusion In this paper, we compared welfare under three instruments: pollution taxes, pure rules and rules combined with output taxes in MICs using a DSGE model. We assumed the one hand that economy faces economic and environmental shocks and on the other hand that government intervenes through these instruments. Some instruments such as taxes and mixed instrument enable him to collect tax revenues that allocates to cleanup expenses, which is suitable for these countries. The parameters of model are estimated by bayesian method for the Côte d’Ivoire economy. Results show on the one hand that when public abatement spending are effective, pollution taxes are higher than pure rules if shocks are strong. But when rules are combined with output taxes for public clearance spending (mixed instrument), they become better than pollution taxes regardless of the type of shock. These results are consistent with those of Pizer (1999) but contrary to those of Angelopoulos et al. (2010). On the other hand, when government intervention in the field of pollution is inefficient, pollution taxes are almost equivalent to pure 23

rules but remain lower than mixed instrument. Morever, IRF analysis reveals that the three instruments studies are pro cyclical in the presence of TFP shock while they are countercyclical when shocks come from to environment. These results are consistent with those obtained in Heutel (2012) and Angelopoulos et al. (2013). These findings suggest that MICs’ governments in general and the Ivoirian government in particular, should improve their environmental tax system in oder to internalize the effects of environmental degradation. However, given the low development of environmental taxation in these countries, it is preferable to use the mixed instrument (rules combined with output taxes for public clearance spending) to face the economic and environmental impact of increasingly persistent. In this study, environmental issues were analyzed in a local context neglecting the transboundary pollution problems. In future research, it would be important to analyze the environmental policies in open economy framework in order to integrate these aspects.

24

Table 4 : Expected lifetime utility under different regimes for various levels of uncertainty ( v  0.6 )

Pure rules (2) -6,051

Rulestaxes (3) -6,046

Social Planner -5,398

 12

 13

 23

(%) 0,00

(%) -0,09

(%) -0,09

a



0

0

Taxes (1) -6,051

0

0,01

-9,577

-9,578

-9,441

-5,406

0,01

-1,55

-1,57

0,01

0

-6,059

-6,059

-6,053

-5,409

0,00

-0,11

-0,11

0,01

0,01

-9,584

-9,585

-9,448

-5,417

0,01

-1,55

-1,56

0,01

0,05

-94,199

-94,223

-90,943

-5,591

0,03

-3,82

-3,85

0,05

0,01

-9,763

-9,764

-9,627

-5,683

0,01

-1,52

-1,54

0,05

0,05

-94,378

-94,402

-91,122

-5,857

0,03

-3,82

-3,84

Source : Authors

25

Table 5: first and second moments of

ct and Qt under pollution taxes

a



E (ct )

E (Qt )

 (ct )

 (Qt )

 (ct , Qt )

0

0.01

7.0097

3.5677

1.3967

2.5828

0.6246

0.01

0

6.5965

0.87394

0.2250

0.0047

-0.9225

0.01

0.01

6.9236

2.2641

0.9920

3.0129

0.1690

0.01

0.05

12.9096

9.8283

24.5510

17.8755

0.1601

0.05

0.01

6.1231

2.4002

1.7071

2.6752

0.4171

0.05

0.05

11.9479

10.4446

24.8732

16.1900

0.2484

Source : Authors

Table 6: first and second moments of

ct and Qt under pure rules.

a



E (ct )

E (Qt )

 (ct )

 (Qt )

 (ct , Qt )

0

0.01

7.0162

3.4388

1.0351

2.4799

0.6242

0.01

0

6.5965

0.8738

0.2250

0.0047

-0.9225

0.01

0.01

6.9299

2.1498

1.0092

2.9513

0.1569

0.01

0.05

13.0667

6.9226

24.9947

16.2417

0.0950

0.05

0.01

6.1293

2.2862

1.7211

2.6070

0.4122

0.05

0.05

12.1045

7.5401

25.3177

14.4174

0.1865

Source : Authors

26

Table 7: first and second moments of

ct and Qt under rules-taxes.

a



E (ct )

E (Qt )

 (ct )

 (Qt )

 (ct , Qt )

0

0.01

6.9075

1.0000

0.2248

0.0000

-0.9187

0.01

0

6.5932

1.0000

0.2250

0.0000

0.9451

0.01

0.01

6.6517

1.0000

0.2837

0.0000

-0.6070

0.01

0.05

6.8183

1.0000

0.4843

0.0000

-0.9078

0.05

0.01

5.9077

1.0000

1.2709

0.0000

-0.4620

0.05

0.05

6.0785

1.0000

1.3892

0.0000

-0.6107

Source : Authors

Table 8: confrontations simulated correlations with those data (  a     0.01 )

 ( yt , ct )

 ( yt , kt )

 ( yt , pt )

 (kt , ct )

 (kt , pt )

 ( pt , ct )

Model (taxes)

0.5146

0.9761

0.4257

0.4525

0.4442

0.2239

Data

0.9698

0.9384

0.9551

0.9396

0.9533

0.9164

Source : Authors

27

Table 9: Prior and posterior distribution of structural parameters Parameters

 

Time discount factor

Prior distribution Distribution

Mode

Beta

posterior distribution St. Dev

Mode

St. Dev

0.970

0.0020

0.9708

0.0019

Normal

0.600

0.0500

0.9181

0.0096

0.0300

1.9924

0.0289

Consumption weight in utility function



risk d’aversion coefficients

Normal

2.000



Capital share in production

Normal

0.330

0.0500

0.6219

0.0052

Beta

0.930

0.0200

0.9494

0.0142

Beta

0.930

0.0200

0.9668

0.0090

a persistence of total factor productivity 

Persistence of pollution technology Source : Authors

28

Figure 1: Prior and Postérior mu

beta

sigma

200

50

10 100

0

0.6

0

0.8

5 0

0.965 0.97 0.975

alpha

1.9

2

rho_phi

2.1

rho_a

50 20

50

0

0.2

0.4

0.6

0

0.9

0.95

1

0

0.9

0.95

1

Source : Authors

Figure 2: Productivity shock effect (Taxes,  a Deviations (%)

A

 0.05 ) c

y

0.1

1

0.4

0.05

0.5

0.2

0

10

20

30 40 Years k

50

60

0

10

20

30

40

50

60

0

0.01

2

-0.02

0

20 -16

2

30

40

50

60

-0.01 10

20

30

40

50

60

40

50

60

Welfare

Theta

x 10

0.2 0.1

0 -2

-0.04

0 0

20

40

60

10

20

30

Source : Authors 29

30

40

50

60

40

50

60

P

0

10

20

Q

4

0

10

10

20

30

Deviations (%)

Figure 3: Pollution shock effect (Taxes,    0.05 ) Phi

y

c

0.1

5

5

0.05

0

0

0

20

40

-5

60

Years k

10 20 30 40 50 60

-5

10 20 30 40 50 60 P

Q

20

0

1

0

-2

0.5

-20

0

-4 10 20 30 40 50 60 Theta

10 20 30 40 50 60 Welfare

0.02

0

0.01

-2

0

-4 10 20 30 40 50 60

10 20 30 40 50 60

10 20 30 40 50 60

Source : Authors

Deviations (%)

Figure 4: Productivity shock effect (pure rules,  a  0.05 ) A

y

c

0.1

1

0.4

0.05

0.5

0.2

0

10 20 30 40 50 Years k

60

0

10

20 30

40 50

0

60

10

Q

4

0

2

-0.02

20 30

40 50

60

P 0.01 0

-0.04

0

10

20 30 -3

5

40 50

60

10

Gamma

x 10

-0.01

60

0.2

0 -5

20 30 40 50 Welfare

0.1

10

20

30 40

50

60

0

10

20 30

Source : Authors

30

40 50

60

10 20 30 40 50

60

Deviations (%)

Figure 5: Pollution shock effect (pure rules,    0.05 ) Phi

y

c

0.1

5

5

0.05

0

0

0

10

20

30 40 Years k

50

60

-5

10

20

30

40

50

-5

60

10

20

30

Q

60

1

-2

0

50

P

0

20

40

0.5

-4 -20

10

20

30 40 Gamma

50

10

60

2

20

30 40 Welfare

50

0

60

10

20

30

40

50

60

0 -2

1

-4 0

10

20

30

40

50

60

10

20

30

40

50

60

Source : Authors

Figure 6: Productivity shock effect (rules-taxes,    0.05 ) Deviations (%)

A

0.05 0

10

20

30 40 Years

50

60

1

0.4

0.5

0.2 0

0

10

k 1

2

0 10 -3

5

x 10

20

30

40

50

60

30

-1

40

50

Q

x 10

30

40

0

20

40

60

0.2

50

60

30

40

50

60

G

x 10

0

0 20

20

-3

2

0.1

10

10

60

Welfare

Gamma

0 -5

20 -15

4

0

c

y

0.1

10

Source : Authors

31

20

30

40

50

60

-2

0

20

40

60

Deviations (%)

Figure 7: Pollution shock effect (rules-taxes,    0.05 ) Phi

y

c

0.1

0.2

0

0.05

0

-0.05

0

20

40

60

Years k

-0.2 -15

0

2

-0.5

1

-1

0 10

20

20

30

40

50

60

40

60

-0.1

10

0

20

40

60

0

1

-0.05

50

60

60

20

0

-0.1 10

20

30

30

40

50

60

Welfare

1

40

10

Tau 0

30

50

0.1

2

20

40

0.2

Gamma

10

30 G

2

0

20

Q

x 10

40

50

60

10

20

30

40

50

60

Source : Authors

Table 10: stationarity tests Variables

DF-GLSa

ADFb

log( y )

-2.840

-2.981

log( p )

-2.840

-2.055

a . Elliott et al. (1996) statistic. The null hypothesis is that variables are random walk process. The critical values at 5 and 10 are 3.766 and 3.138 respectively. b. Dickey et Fuller (1979) statistic. The null hypothesis indicates that variables are random walks with or without drift. The critical values at 5 and 10 are also for 2 delay 3.508 and 3.185 respectively. Results show that we can not reject the null hypothesis at 5 and 10. log( y ) and log( p ) then are I(1). Data sources : pollution variable (CO2 total emission in kt) are taken from World Development Indicator (WDI 2013). real GDP come from Penn World Table (PWT 8)

32

Figure 8: stationary data

dlog(y) 0.2 0 -0.2

5

10

15

20

25 dlog(p)

30

35

40

45

50

5

10

15

20

25

30

35

40

45

50

0.5 0 -0.5 Source : Authors

Table 11: variance decomposition Taxes

Pure rules

Rules-Taxes

a



a



a



y

55.18

44.82

52.52

47.48

59.51

40.49

c

56.37

43.63

53.81

46.19

60.74

39.26

k

35.12

64.88

32.75

67.25

39.30

60.70

Q

0.00

100.00

0.00

100.00

0.00

100.00

P

0.00

100.00

0.00

100.00

0.00

100.00

A

100.00

0.00

100.00

0.00

100.00

0.00



0.00

100.00

0.00

100.00

0.00

100.00

welfare

1.93

98.07

1.75

98.25

2.38

97.62

Source : Authors

33

8. Références Adjemian. S & Devulder. A. (2011). Improving the forecasting performance of a bayesian dsge model for the euro area using missing observations series. Adjemian.S & Pelgrin. F (2008). Un regard bayésien sur les modèles dynamiques de la macroéconomie. Économie et Prévision, 183-184:127–152, 2008 An, S. & Schorfheide, F. Bayesian Analysis of DSGE Models. (2007). Econometric Reviews. , 26(2-4) , 113-172 Angelopoulos, K., Economides, G., & Philippopoulos, A. (2010). What is the best environmental policy? Taxes, permits and rules under economic and environmental uncertainty, Working paper 0–35. Angelopoulos, K., Economides, G., & Philippopoulos, A. (2013). First-and second-best allocations under economic and environmental uncertainty. International Tax and Public Finance, 20(3), 360– 380. Baldursson, F.M & von der Fehr, M. (2008). Prices vs. quantities: Public finance and the choice of regulatory instruments. European Economic Review 52 (2008) 1242–1255 Blanchard, O.& Kahn C. M. (1980): The Solution of Linear Difference Modelsunder Rational Expectations, Econometrica, 48, 1305–1313 Bovenberg, A., & Goulder, L. (2002). Environmental taxation and regulation. Handbook of Public Economics. Bovenberg, A.L., de Mooij, R.A., 1994. Environmental levies and distortionary taxation. American Economic Review 94 (4), 1085–1089. Briggs, R. J. (2011). Prices vs. quantities in a dynamic problem: Externalities from resource extraction. Resource and Energy Economics, 33(4), 843–854. Brock, W., & Taylor, M. (2005). Economic growth and the environment: a review of theory and empirics. Handbook of Economic Growth, (October). Working paper , nber, w4634 Conesa,J.C, Kitao,S., & Krueger, A. (2008). Taxing capital? Not a Bad idea after all! American Economic Review, 99, 25–48. Dissouu Y, Karnizova L. (2012). Emissions cap or emissions tax?A multi-sector business cycle analysis. Work. Paper, Univ. of Ottawa Economides, G., & Philippopoulos, A. (2008). Growth enhancing policy is the means to sustain the environment. Review of Economic Dynamics, 11(1), 207–219. Fell, H., MacKenzie, I. a., & Pizer, W. a. (2012). Prices versus quantities versus bankable quantities. Resource and Energy Economics, 34(4), 607–623. Fischer C, Springborn M. (2011). Emissions targets and the real business cycle: Intensity targets versus caps or taxes. Journal of Environmental Economics and Management.62: 352–366.. Goedhuys M. & Sleuwaegen. L. (2003). Technical efficiency, market share and profitability of manufacturing firms in Côte d'Ivoire: the technology trap. Cambridge Journal of Economics, Vol. 27, No. 6 pp. 851-866 Goula, B. T. A., Kouassi, V. J. & Savane, I. (2006). Impacts Du Changement Climatique Sur Les Ressources En Eau En Zone Tropicale Humide : Cas Du Bassin Versant Du Bandama En Côte D’ivoire. Agronomie Africaine 11(1) : 1-11 Goulder, L.H., Parry, I.W.H., Williams, R.C., Burtraw, D., (1999). The cost-effectiveness of alternatives for environmental instruments for environmental protection in a second-best setting. Journal of Public Economics 72 (3), 329–360.

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Hallegatte, S., M. Bangalore, L. Bonzanigo, M. Fay, T. Kane, U. Narloch, J.Rozenberg, D. Treguer, & A. Vogt-Schilb. (2016). Shock Waves: Managing the Impacts of Climate Change on Poverty. Climate Change and Development Series. Washington, DC: World Bank. Hallegate, S., G.Heal, M.Fay and D.Treguer, (2012). From Growth to Green Growth-A Framework, NBER Working Paper 17841. Heutel, G. (2012). How should environmental policy respond to business cycles? Optimal policy under persistent productivity shocks.Review of Economic Dynamics,15, 244–264. Hoel, M (1998). Emission Taxes versus Other Environmental Policies. The Scandinavian Journal of Economics, Vol. 100, No. 1 Kaplow, L., & Shavell, S. (2002). On the superiority of corrective taxes to quantity regulation. American Law and Economics Review. Klein, P., 2000. Using the Generalized Schur Form to Solve a Multivariate LinearRational Expectations Model. Journal ofEconomic Dynamics and Control 24(10), pp.1405-1423. Kouassi, K. A ; Yao, N.J.P ; Bie, G.R ; Digbehi, Z.B ; Bamba, M.K ; Goua, E.T ; Yao,K.C. (2013). Essai De Caractérisation Micropaléontologique Et Paléo-Environnementale Et Mise En Évidence De L’eao2 À L’interface Cénomanien/Turonien (C/T) Dans Le Bassin Sédimentaire De Côte D’ivoire, Afrique De L’ouest. Rev. Ivoir. Sci. Technol., 21-22 (2013) 95 - 118 Newell, R. G., Pizer, W. A. (2003). Regulating Stock Externalities Under Uncertainty Journal of Environmental Economics and Management 45, 416–432.. Nordhaus, W. (2011). Estimates of the social cost of carbon: background and results from the RICE2011 model, (1826). Pizer, W. a. (1999). The optimal choice of climate change policy in the presence of uncertainty. Resource and Energy Economics, 21(3-4), 255–287. Quirion, P., 2004. Prices versus quantities in a second-best setting. Environmental and Resource Economics 29, 337–359 Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin, F. S., Lambin, E. F., Lenton, T. M., Scheffer, M., and Folke, C. (2009). A Safe Operating Space For Humanity, Nature, 461(7263), 472–5. Rohling, M., & Ohndorf, M. (2012). Prices vs. Quantities with fiscal cushioning. Resource and Energy Economics, 34(2), Schmitt-Grohé, S., & Uribe, M. (2004). Solving dynamic general equilibrium models using a secondorder approximation to the policy function. Journal of Economic Dynamics and Control, 28(4), 755–775. Schöb, R. (1996). Choosing the right instrument: the role of public revenues for environmental policy, Environmental and Resource Economics, 8, 399-416 Sims, C. A., (2002). Solving Linear Rational Expectations Models. Computational Economics, 20(1), pp. 1-20. Smets.F et Wouters. R. (2003) .An estimated dynamics stochastic general equilibrium model of the euro area. Journal of the European Economic Association, 1:1123–1175, 2003. Smets.F et Wouters. R.. (2005). Comparing shocks and frictions in us and euro area business cycles : A bayesian approach. Journal of the European Economic Association, 20:161–183, 2005. Smets.F et Wouters. R.. (2007). Shocks and frictions in us business cycles : A bayesian dsge approach. American Economic Review, 97(3):586–606, June 2007. UEMOA (2007) programme régional de lutte contre l’érosion côtière de l’UEMOA, la commission l’UEMOA, 12 pages Uhlig, H., (1999). A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily. In R. Marimon and A. Scott, Editors, Computational Methods for the Study of Dynamic Economies, Oxford University Press, pp. 30-61 35

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9. Appendices Appendix 1 Accordind to equation (6), pollution stock

St  Q  Qt

St is defined by :

(6a).

By substituting equation (6a) into equation (5), we get: Q  Qt 1  1  h   Q  Qt   Pt (6b).

Rearranging of equation (7) :

equation (6b) give the motion of environmental quality represented by

Qt 1  hQ  1  h  Qt  Pt

(7).

Appendix 2 : pollution taxes model The first-order conditions of DCE, after substituting margin utility of consumption become :

 ct  

 1  1

 Qt 

1  1 

  Et  ct 1  

 1  1

Qt 1 

1  1 

1   k  1  t 1t 1   At 1kt11   

(15a)

kt 1  (1   k )kt  ct  1  tt  At kt

(15b)

Qt 1  hQ  1  h  Qt  t  vtt  At kt

(15c)

Appendix 3 : pure rules model We substitute margin utility of consumption into Euler equation (17a). Equation (19c) is obtained by substituting pollution flow equation (9) into rules equation (16). The rules DCE system then lead to:

 ct 

 1  1

 Qt 

1  1 

  Et  ct 1  

 1  1

 Qt 1 

1  1 

kt 1  (1   k )kt  ct  At kt

1   k   At 1kt11   

(17a) (18b)

36

 1   t  P   tt At kt  kt 1    t 1 At 1  

1



(19c)

Qt 1  hQ  1  h  Qt  t At kt

(20d)

Appendix 4 : rules-taxes model In rules-taxes model, we combined rules with output taxe devoted for public cleanup activities. As government uses only the share of tax revenues allocated to clearance activities (et ) , equation (25d) of the motion of environmental quality becomes:

Qt 1  hQ  1  h  Qt  t At kt  vet  Where et   (1  b) t  At kt . By substituting

(25d1)

(et ) into equation (25d1), we get equation (25d) :

Qt 1  hQ  1  h  Qt  t  v 1  b  t  At kt

The rest of equations of DCE system is similar to pure rule model.

Appendix 5 : social planner model By replacing the marginal utility of consumption and environmental quality, we get the social balance defined as follows:

   ct 1 1Qt1 1    Et ct11 1Qt11 1  1   k  1  t 1 v   

  A k  1   t 1 t 1   

(26a)

1  1 1 1 1  1   ct Qt   Et 1    ct11 Qt11 1 1  1  h  * ct 1 1Qt1 1   v v  

(27b)

kt 1  (1   k )kt  ct  G  At kt

(28c)

Qt 1  hQ  1  h  Qt  Pt  vGt

(29d)



ut  1  1  1 1  1    ct  Qt    Qt

37

Appendix 6 : first and second moments The review of means, variances and covariances of the variables defined as deviation from their steady state level allows me to understand welfare differences under uncertainty. Let x and y be random variables, their deviations from steady state are defined by: xˆ  x  x and yˆ  y  y where x et y are means of The mean of deviation of

x and y

respectively or their steady state values .

x become:

E ( xˆ )  E ( x)  x

(6.1)

Equation (6.1) implies that, when x is the same across regimes, any differences in the mean of x are due to differences in the mean of xˆ . Similarly, the variance of deviation xˆ is given by: var( xˆ )  E  xˆ  E  xˆ   E  xˆ    E  xˆ  2

2

2

(6.2)

Equation (6.2) gives the second order term xˆ 2 and the variance of xˆ . it implies that given the average of xˆ , any differences in the average value of xˆ 2 are captured by variance differences of xˆ . The variance of xˆ is identical to that of x . Indeed, var( xˆ )  E  xˆ  E  xˆ   E  x  x  E  x  x   E  x  x  E  x   x    x  E  x   var  x  2

2

2

2

Finally, the covariance that captures differences in the cross-products of xˆ and yˆ is defined as follows: ˆˆ   E  xˆ  E  yˆ  . with cov( xˆ, yˆ )  E  xy 2









cov( xˆ, yˆ )  E  xˆ  E  xˆ   yˆ  E  yˆ   E  x  E  x   y  E  y   cov  x, y 

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