DEPARTMENT OF ECONOMICS OxCarre Oxford Centre for the Analysis of Resource Rich Economies. OxCarre Research Paper 137

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1 DEPARTMENT OF ECONOMICS OxCarre Oxford Centre for the Analysis of Resource Rich Economies Manor Road Building, Manor Road, Oxford OX 3UQ Tel: +44() Fax: +44() OxCarre Research Paper 37 _ Optimal Environmental Policy, Public Goods and Labor Markets over the Business Cycle Anna Grodecka University of Bonn and Karlygash Kuralbayeva Grantham Institute, LSE Direct tel: +44() oxcarre@economics.ox.ac.uk

2 Optimal environmental policy, public goods and labor markets over the business cycle Anna Grodecka University of Bonn Karlygash Kuralbayeva Grantham Research Institute (LSE), OxCarre and CFM May 4, 4 Abstract This paper studies the design of optimal fiscal policy in a real business cycle model with distortionary taxes and a climate change externality. Governments face the dual task of internalizing environmental externalities and raising revenues to finance the provision of public goods, including public capital. At their disposal governments have access to two tax instruments: tax on emissions and labor tax. We find that a tax on labor is an efficient instrument to finance public spending and facilitate the adjustment of the economy to the temporary improvement in productivity. Therefore, labor tax is cut in the model. Tax on emissions follows a distinct pattern depending on whether the potential economic expansion in response to a positive productivity shock is strong or weak: it is procyclical in the model that features public capital and is countercyclical in the models with public consumption only. The model implies that by restraining or boosting expansion in the short-run, the optimal carbon tax policy can help policy makers reconcile short-term concerns over economic growth with longer-term risks from climate change. The welfare gains from such short-run policies are non-negligible and can amount to USD.9 bn or.7% of the US GDP. Keywords: public finance, public goods, business cycles, distortionary taxes, environmental policy JEL Classifications: E3, H3, Q54, Q58 We thank Garth Heutel, Robert Marschinski, Sjak Smulders, Luca Taschini, Rick van der Ploeg and Jürgen von Hagen and seminar participants at LSE, University of Oxford, University of Bonn for helpful comments and discussions. Anna Grodecka acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG) through the Bonn Graduate School of Economics (BGSE). Karlygash Kuralbayeva acknowledges financial support by Global Green Growth Institute (GGGI), the Grantham Foundation for the Protection of the Environment and the UK Economic and Social Research Council (ESRC) through the Centre for Climate Change Economics and Policy. All potential errors are our own. Contact: k.z.kuralbayeva@lse.ac.uk (corresponding author)

3 Introduction A fundamental question of macroeconomics is how to set fiscal policy over the business cycle that helps governments achieve their multiple objectives. In this paper we focus on two major objectives faced by governments, the provision of public goods (including infrastructure), and the correction of climate change externalities, in an attempt to answer the above question. Specifically, this paper will investigate rationale for carbon pricing in the short-run, analyzing merits of carbon taxes for short-term concerns over economic growth and long-term climate policies. Our framework is an extension of recent work by Heutel (), who develops a real business cycle model in which production causes greenhouse gas emissions that accumulate in the atmosphere and lead to a climate change externality that adversely affects the production process. Our model differs from his model in two respects. First, our model incorporates labor. Second, we introduce fiscal policy by assuming that the government provides two public goods, namely public consumption, which is included in household preferences, and public infrastructure, which is an input in the private sector production process. Goods are produced by using private and public capital, and labor inputs. The adverse productivity effect of climate change can be counteracted by raising spending on abatement at the firm level. The government has access to two tax instruments, tax on labor, and tax on emissions. In this paper we want to study the issue of how a tax on emissions is to be introduced alongside taxes on labor. To simplify the analysis we do not introduce taxes on capital. We also consider two other versions of this model, one, assuming that public spending comprises only public consumption, and the other, where public spending is fixed at the steady state level. The model is calibrated to the US economy and we investigate the optimal response to a temporary improvement in productivity. Simulations of the models produce several results. First, some levels of emissions are always optimal, and it is never optimal to curb emissions completely. The pollution stock does not vary by much over the shortterm, thus direct productivity gains from carbon pricing are relatively small. At the same time, the temporary nature of the productivity shock, that directly affects productivity of inputs in production as opposed to the indirect effect of emissions tax, dictates Ramsey planner to give priority growth consideration in the short-run, resulting in higher emissions. Increasing spending on abatement to significantly curb emissions is never optimal, as spending a larger fraction of output income on abatement crowds out consumption and investment. The procyclicality of emissions is a well-known fact (see for instance, Heutel ()), and our contribution is to provide a theoretical explanation, using the framework of optimal fiscal policy, for this stylized fact. Second, in all three models considered, tax on labor is cut. The optimal response of the government is to encourage higher labor supply during the period of higher labor productivity, consistent with growth prospect priorities over the short-term as discussed above. With higher labor supply and an increase in aftertax wage of consumers (tax base), the government generates more labor tax revenues. The revenues from labor taxes are directly linked to changes in productivity, whilst environmental policy (tax on emissions) affects labor productivity indirectly through its effect on abatement and level of emissions. The first effect quantitatively dominates the second, and labor taxes are a more important source of government revenues than an emissions tax. Third, tax on emissions is procyclical in the core model, and is countercyclical in the other two models Some important contributions to this subject include Chamley (986), Zhu (99), Chari et al. (994)

4 3 without public investment. In the model, when public consumption is fixed at the steady state level, higher labor tax revenues motivate a reduction in tax on emissions as government spending can now be met with a lower tax on emissions. Similar intuition holds in the model when public consumption changes endogenously. As revenues from taxing labor increase by a level that still allows reducing revenues from taxing emissions, so the emissions tax is cut. The tax on emissions behaviour changes drastically in the core model as it becomes procyclical. With public capital as a productivity enhancing input of production, a productivity shock makes investment into private capital and labor even more attractive. This increases the severity of the pollution externality therefore requiring an increase in spending on abatement motivated by a higher emissions tax. Such behavior of the emissions tax has the following policy rationale. When coming from the government s standpoint, prospects for growth are high, as in the model with public capital, a tax on emissions is increased. If in the contrary, the prospects of growth are relatively weak and some additional stimuli are warranted. As in the other two models, extra impetus to the economy is provided through cuts in tax on emissions as opposed to larger cuts in tax on labor. This is so because changes in labor tax have larger effects on labor supply and the productivity of private capital, and therefore on output and pollution stock. To illustrate this intuition, we perform a counterfactual experiment, in which we contrast a baseline policy with an alternative policy containing a fixed tax on emissions. We show that if tax on emissions is kept constant over the business cycle, as opposed to a reduction as seen in the models without public capital, then under alternative policy, tax on labor is cut by more than prescribed in the baseline policy. This results in higher emissions and a larger deterioration of environmental quality. This observation provides guidance to policymakers trying to reconcile the management of long-term climate risks with short-term concerns over economic growth. Our findings should be considered as providing supporting evidence for green stimuli (such as subsidies to green technologies especially if growth prospects are weak) in the short-run that will also yield potential long-run benefits from averting climate change. On the quantitative side, when we evaluate the outcomes of the baseline as compared to the alternative tax policies, using the social welfare function, we find that gains from carbon policies changing with economic circumstances can amount up to USD.6 bn, or.7% of 3 US GDP. This implies that the costs of climate policies can be higher if short-run costs associated with business cycles are taken into consideration. Finally, we illustrate the relevance of our findings for policy-makers, referring to certain policies recently put forward that aim to reform the EU s Emissions Trading Scheme (EU ETS). In particular, some of the proposed reforms suggest the introduction of elements into the scheme that will help the system respond automatically to changes in carbon prices perceived to be excessive and triggered by unusual economic circumstances. This is in line with our findings on the behavior of emissions taxes which have a distinct behavior depending on whether the growth prospect is perceived to be strong or weak by fiscal authorities, and thus is procyclical or countercyclical depending on economic circumstances. It is clear that our main results crucially hinge on the labor markets reaction to the labor tax. When performing a sensitivity analysis, we find that changes in values of the elasticity of labor supply and riskaversion, exhibited by the household utility function, affect the cyclical behavior of taxes on labor and emissions. Specifically, with a lower elasticity of labor supply, increase of labor is smallest, and both taxes are cut since boosting output becomes relatively more important than curbing emissions which are low anyway. When risk-aversion is lower, both tax rates increase (emissions tax in initial periods after the shock). With lower risk-aversion, consumers have a greater willingness to work and the government takes

5 4 advantage of it by raising tax on labor. But an increase in tax on labor is such that it still allows an increase in labor supply; in fact, an increase in labor supply, and consequently in output, are the strongest with lower risk-aversion, so that emissions tax is also increased to deal with an increased severity of a pollution externality. This paper is part of an emerging literature on the analysis of environmental policies over the business cycle 3. Within this literature Chang et al. (9), Heutel () and Lintunen and Vilmi (3) consist of the only papers, to the best of our knowledge, that derive optimal environmental (emissions tax) policy over the business cycle similarly to us. But none of these papers have analyzed the interaction between environmental policy and public finance within a second-best setting as we do in this paper. This paper is also related to recent literature that investigates the rationale for carbon pricing beyond that of Pigovian taxation, and in particular, examines the efficiency and distributional impacts of policies where carbon tax revenues are used as means of reducing long-term budget deficits, or are part of revenueneutral tax reforms (Carbone et al. (3), McKibbin et al. (), Rausch (3)). This literature focuses on how the revenues generated from the introduction of carbon taxes can be utilized as a means of addressing other policy options. We instead investigate what is the optimal design of labor and emissions taxes in the short-run, given the two dual objectives of the government outlined before. This paper is also connected to earlier literature on the relation between environmental tax policies and economic growth using growth model frameworks (e.g., Bovenberg and de Mooij (997), van Marrewijk et al. (993), Smulders and Gradus (996)). The central difference is that we look at shorter-term issues, as opposed to longer-term trade-offs analyzed in those papers. The rest of the paper is organized as follows. Section describes the core model. Section 3 discusses the issues of the models calibration. Section 4 presents the results derived from impulse responses and discusses the baseline results. The section goes on describing the behavior of the model under different environmental tax policies, and welfare loss under a counterfactual policy experiment. Section 5 examines the sensitivity of the baseline results to a variation in the degree of risk-aversion, labor supply elasticity, elasticity of emissions to output, and the parameter of the abatement cost. Section 6 discusses policy relevance of our findings. Section 7 concludes the paper. Model In this section we outline the setup of the core model. We consider several versions of the model in the simulation section of the paper by simplifying its main structure. The theoretical structure of the model can be briefly summarized as follows. The model extends the real business cycle model with climate externalities of Heutel () by taking labor and fiscal policy into consideration. In this model the economy consists of households, firms, and the government. Households obtain utility from consumption of both public and private goods, as well as from leisure. Goods are produced using private capital, public capital, and labor. As in Heutel (), production causes greenhouse gas emissions, which accumulate and lead to climate change that negatively affects output. As in Heutel (), we assume that firms can counteract the adverse productivity effect of climate change by raising spending on abatement. 3 Fischer and Heutel (3) provide an overview of studies that use the RBC framework to study environmental policies over the business cycle.

6 5 The government levies emissions and labor taxes on firms. The raised revenue from the taxes are used to finance the provision of public goods and investment into public capital.. Households A representative household maximizes: U = E t= β t u(c t, l t, g t ) () In this utility function c t and g t represent private and public consumption, l t is the number of hours worked by the household. The representative household faces the following budget constraint: c t + i t = w t l t + r t k t + π t () where i t is private investment, π t is firm profits; Households derive income by supplying labor and capital to firms at rental rates w t and r t. The private capital stock is accumulated according to: k t = ( δ)k t + i t (3) First-order conditions of the household maximization problem imply: w t = u L (t) u c(t) (4) u c(t) = βu c(t + )[ δ + r t+ ] (5) Equation (4) equates the marginal rate of substitution of leisure for consumption to real wages and defines household labor supply. Condition (5) is a standard stochastic Euler equation, which determines intertemporal allocation: it equates the intertemporal marginal rate of substitution in consumption to the real rate of return on private capital.. Final goods production Output y t is produced by identical firms, and then can be used for consumption, investment, abatement or government spending. y t = ( d(x t ))f(k t, l t, k Gt ) (6) We assume that public capital boosts the productivity of private capital and labor, but also the stock of pollution in the atmosphere, which denoted by x t, adversely affects output. Profits of firms are defined as: π t = y t w t ( + τ Lt )l t τ Et e t r t k t z t (7) where z t is spending on abatement by firms; private abatement spending is assumed to abate the µ t fraction of emissions via the following relation: z t y t = m(µ t ) (8)

7 6 so that firms face the emissions constraint given by: e t = ( µ t )h(y t ) (9) Following Heutel (), we assume that firms do not take into account their emissions impact on the pollution stock and thus on productivity, in other words, firms take x t as a given. Firms also take the level of public capital as a given. Optimality conditions of the firm imply: r t = ( d(x t ))f k[ τ Et ( µ t )h (y t ) m(µ t )] () w t ( + τ Lt ) = ( d(x t ))f L[ τ Et ( µ t )h (y t ) m(µ t )] () τ Et h(y t ) = y t m (µ t ) () Equation () is an optimal condition of demand for capital, which implies that the return associated with an increase in capital stock by one unit is equal to the marginal product of capital, net of additional tax payments on increased emissions associated with an increase in output and net of additional spending on abatement to clean a given fraction µ of extra emissions stemming from an increase in output. Equation () is the counterpart of equation () for labor demand. Finally, equation () summarizes costs and benefits from abating one additional fraction of emissions, for a given level of output: the benefit is lower emission tax payment payτ Et h(y t ), the costs are additional spending on abatement activities in the amount of y t m (µ t )..3 Government The government budget constraint is balanced according to: g t + i Gt = w t τ L l t + τ Et e t (3) and the government raises revenues by taxing labor income and emissions. The revenues are used to finance two types of government spending: public consumption (g) and public investment into public capital, which is accumulated according to: k Gt = ( δ G )k Gt + i Gt (4).4 Carbon cycle Pollution stock decays at a linear rate η: x t = ηx t + e t + e row t (5) where e t is current-period domestic emissions that are related to the output produced and fraction µ t that is abated, while e row t is current-period emissions from the rest of the world. Damages from climate change come not just from emissions in the current period but also from accumulation of greenhouse gases in the atmosphere, captured by term x t.

8 7.5 Characterizing equilibrium To construct the Ramsey problem, we reorganize some of the constraints in order to reduce the number of choice variables and to obtain a compact expression for the household budget constraint. In particular, combining (),(7) and (3) gives the following resource constraint for the economy: c t + k t ( δ)k t + z t + g t + k Gt ( δ G )k Gt = y t (6) Next, by adding and substituting for w t from (4), we rewrite the government s budget constraint as follows: Substituting (4) into () gives:.6 Ramsey problem g t + k Gt ( δ G )k Gt = u L (t) u c(t) τ Ltl t + τ Et ( µ t )h(y t ) (7) u L (t) u c(t) ( + τ Lt) = ( d(x t ))f L[ τ Et ( µ t )h (y t ) m(µ t )] (8) Ramsey planner maximizes utility of households: subject to (5), (), (6), (7), (8) and E t= β t u(c t, l t, g t ) (9) y t = ( d(x t ))f(k t, l t, k Gt ) () where we also use the function () for definition of r t. x t = ηx t + ( µ t )h(y t ) + e row t () The government chooses c t, µ t, k t, y t, x t, l t, τ Lt,τ Et, g t and k Gt to maximize (3) subject to the constraints specified above. The Lagrangian for this problem is given by: L = E β t {u(t) + λ t [ u c(t) + βu c(t + )( δ + r t+ )] t= Ω t [c t + k t ( δ)k t + m(µ t )y t + g t + k Gt ( δ G )k Gt y t ] + χ t [τ Et h(y t ) y t m (µ t )] + +Λ t [ g t k Gt + ( δ G )k Gt u L (t) u c(t) τ Ltl t + τ Et ( µ t )h(y t )] λ pt [y t ( d(x t ))f(k t, l t, k Gt )] + [ ς t u L (t) ] u c(t) ( + τ Lt) ( d(x t ))f L(t)( τ Et ( µ t )h (y t ) m(µ t )) +Φ t [x t ηx t e row t ( µ t )h(y t )] The first-order conditions of the Ramsey problem are given by: + u c(t) λ t u cc(t) + λ t u cc(t)( δ + r t ) Ω t (Λ t τ Lt l t ς t ( + τ Lt )) u Lc (t)u c(t) u L (t)u cc(t) (u c(t)) = ()

9 8 ( d(x t ))τ Et h (y t )(λ t u c(t)f k(t) + ς t f L(t)) + χ t y t m (µ t ) + Φ t h(y t ) = = ( d(x t ))m (µ t )(λ t u c(t)f k(t) + ς t f L(t)) + Ω t m (µ t )y t + Λ t τ Et h(y t ) (3) Ω t = βe t [Ω t+ ( δ) + λ pt+ ( d(x t+ ))f k (t + )] + +βe t ( d(x t+ ))[ τ Et+ ( µ t+ )h (y t+ ) m(µ t+ )][ς t+ f Lk + λ t u cf kk] (4) Ω t m(µ t ) + λ pt + χ t m (µ t ) + ( µ t )h (y t )Φ t = ( µ t )h (y t )Λ t τ Et ( d(x t ))τ Et ( µ t )h (y t )[ς t f L(t) + λ t u c(t)f k(t)] + χ t τ Et h (y t ) + Ω t (5) Φ t d (x t )[ τ Et ( µ t )h m(µ t )](λ t u c(t)f k (t) + ς t f L (t)) λ pt d (x t )f(t) = βe t Φ t+ η (6) u L(t) λ t u cl(t) + λ t u cl(t)( δ + r t ) + λ t u c(t)r L(t) Λ t τ Lt u L (t) u c(t) +λ pt ( d(x t ))f L(t) (Λ t τ Lt l t ς t ( + τ Lt )) u LL (t)u c(t) u L (t)u Lc (t) (u c(t)) +ς t ( d(x t ))f LL(t)( τ Et ( µ t )h (y t ) m(µ t )) = (7) Λ t l t ς t = (8) ( d(x t ))( µ t )h (y t )[ς t f L(t) + λ t u c(t)f k(t)] + χ t h(y t ) Λ t ( µ t )h(y t ) = (9) u g(t) λ t u cg(t) + λ t u cg(t)( δ + r t ) Ω t Λ t + ς t ( + τ Lt ) u Lg (t)u c(t) u L (t)u cg(t) (u c(t)) = (3) Ω t + Λ t = βe t [Ω t+ ( δ G ) + λ pt+ ( d(x t+ ))f kg (t + ) + Λ t+ ( δ G )] +βe t ( d(x t+ ))[ τ Et+ ( µ t+ )h (y t+ ) m(µ t+ )][ς t f Lk G + λ t u cf kk G ] (3) Equations () and (3) jointly determine the intratemporal efficiency condition for private and public consumption. Equation (4) is the pricing equation for private capital, which equates the cost of installing one unit of private capital to the discounted value of the return on capital, net of depreciation. Equation (3) is the counterpart of equation (4) for public capital.

10 9 Equation (3) summarizes costs and benefits associated with an increase by a unit in fraction of emissions abated. The benefits, on the left-hand side include (i) for every capital or labor employed, firms pay less of emissions tax (in terms of utility, as multiplied by shadow price); (ii) larger fraction of emissions abated makes it easier to clean the environment; (iii) lower level of emissions valued as Φ t h(y t ). The costs include (i) for every unit of capital or labor employed, firms need to spend more on abatement; (ii) extra unit of fraction of emissions abated requires extra spending on abatement at Ω t m (µ t )y t and (iii) cleaner environment reduces public revenues by Λ t τ Et h(y t ). Equation (5) presents costs and benefits of increasing output by a unit. The costs include (i) higher emissions associated with higher output require extra spending on abatement Ω t m(µ t ) and (iii) require more spending on abatement per every unit of µ fraction of emissions abated χ t m (µ t ); (iii) one extra output brings more emissions Φ t ( µ t )h (y t ); and (iv) the value of output as costs for the economy, λ pt. The benefits include (i) more emissions boost public revenues Λ t τ Et ( µ t )h (y t ); (ii) more emissions make the environment dirtier and thus increase benefits from abatement per every unit of µ of emissions abated χ t τ Et h (y t ); (iii) more emissions associated with higher output affect the returns on private capital and labor, depending on rate at which emissions increase when output increases: if emissions increase at decreasing rate then there are gains through returns on inputs in production (in calibration h < ); (iv) the value of the output is Ω t that can be used for different purposes, e.g., for consumption. Equation (6) is the pricing equation for the pollution stock: it equates the value of additional one unit of pollution stock, including the pollution externality costs associated with output loss (third term on the left-hand side) and lower returns on capital and labor due to the externality (second term on the left-hand side) to the discounted value of the pollution stock. Equation (7) is the optimal condition for labor supply, while equation (8) determines the optimal level of tax on labor. Finally, equation (9) summarizes the costs and benefits from a higher emissions tax: a unit increase in tax on emissions boost public revenues by Λ t ( µ t )h(y t ), but have adverse effects on productivity of both private capital and labor (first term) and increases benefit from abatement by χ t h(y t ). 3 Parametrization In calibrating the model we select parameter values that enable the theoretical model to generate features that are, as closely as possible, consistent with the main features of the US economy. We assign values to structural parameters using values that are common in business cycle studies of fiscal policy and macroeconomic models with a climate change externality. In calibrating the climate part of the model, we draw strongly on estimates and parameter values used in Heutel () who also estimates one of those parameters by using US data on CO emissions. Baseline parameter values of the model are summarized in Table, while Table reports macroeconomic ratios implied by the theoretical model as well as the corresponding values for the US data. Data sources employed in these calculations are summarized in Appendix 8. In calibrating the model, one period is meant to be one quarter. The production function is given by f(k t, l t, k g,t ) = a t k α t l α t k γ Gt (3) We set α at.36, which is a value commonly used in the standard RBC literature. The public capital share in the production function is set at γ =.5 as in Kuralbayeva (3). For the TFP process, we assume that a t is an autoregression process ln a t = ρ ln a t + ε t, with ρ =.95, where ε t (,.7), and where the

11 Parameter Value Definition α.36 private capital share in the production function γ.5 public capital share in the production function ρ.95 persistence of the TFP shock σ ε.7 standard deviation of the TFP shock δ.5 private capital depreciation rate δ g.3 public capital depreciation rate β.98 subjective discount factor κ. coefficient of relative risk aversion θ.6 weight of public consumption in utility /ψ 3 Frisch elasticity of labor supply η.9979 pollution decay d 5.96e- damage function parameter d -.583e-6 damage function parameter d.395e-3 damage function parameter θ.3 abatement cost equation parameter θ.6 abatement cost equation parameter ν.696 elasticity of emissions with respect to output Table : Baseline parameter values value of standard deviation is as in Heutel () and is similar to the value.56 as in Schmitt-Grohe and Uribe (7). The private and public capital depreciation rates, δ and δ g, are set at.5 (Heutel ()) and.3 (Kuralbayeva (3)) respectively. We set the discount factor β at.98. For the quantitative analysis, we consider the following form of the households utility function: u(c t, l t, g t ) = c κ t κ + θ g κ t κ l+ψ t + ψ (33) with the coefficient of relative risk aversion, κ, set to., which implies that the value of the intertemporal elasticity of substitution (EIS) is.9 in the model. The standard value of κ in the literature is (see, e.g., Golosov et al. (3)). We set ψ = /3 which gives us a Frisch elasticity of labor supply of 3, in line with macroeconomic estimates reported by Rogerson and Wallenius (9). The weight of public consumption in the utility function, θ =.6 is chosen to match data on the ratio of government spending to output in the US. Following Heutel (), the pollution stock in the atmosphere evolves according to the following equation: x t = ηx t + e t + e row t. We set the value of η at.9979 as in Heutel (), who calibrated this parameter assuming that 83 years represents the half-life of atmospheric carbon dioxide. The emissions produced by the rest of the world, e row t are set to 4 times the steady state of domestic emissions, which is guided by the following considerations. According to data by the U.S. Environmental Protection Agency, the USA accounted for 9% of global CO emissions from fossil fuel combustion in 8, which means that global emissions were four times higher than those in the US

12 The loss of potential output due to the pollution is governed by the function d(x) = d x + d x + d. We set the values of d, d, d respectively to 5.96e-, -.583e-6,.395e-3, following Heutel () who calibrates these values to match the damages from carbon dioxide in the atmosphere estimated by papers in environmental literature. The values are scaled to match the calibration in arbitrary units to data in gigatons of atmospheric carbon for the US. The abatement cost function is taken directly from Nordhaus (8) and has the form m(µ) = θ µ θ. We set θ =.3 and θ =.6. Our chosen values of θ and θ are different from the values in Nordhaus (8), in which θ is a function of time, and it falls from.567 to.39 over 5 years, while θ =.8 in both Nordhaus (8) and Nordhaus and Sztorc (3). The values of parameters θ and θ are chosen so that the model s steady state spending on abatement represents.% of GDP as in the data for the US in 5. Finally, output is mapped into emissions through h(y t ) = y ν, with e t = ( µ t )h(y t ), where ν represents elasticity of emissions with respect to output. We set the value of ν at.696, which is the estimate from ARIMA regression (seasonally adjusted) of the log of emissions of CO on the log of GDP for US data in years 98-3 in Heutel (). We also consider several versions of the model depending on whether public consumption is fixed or changes endogenously. In the model with fixed government consumption, we fix its value to % of steady state output. Symbol Variable Model Data c/y personal consumption/output g/y government consumption/output.8.5 i/y private domestic investment/output.8.6 i G/y public investment/output.5.4 e/y emissions/output.57.6 µ fraction of emissions abated, % z/y abatement spending/output, %.. τ E tax on emissions, %.4 - τ L labor tax, % Table : Structure of the theoretical economy and the data 4 Simulation results In this section we discuss the simulation results of the core model presented in Section and its two simplified versions. These two simplified versions are one, without public capital and the other version, with a fixed public consumption which equals % of the steady state output. Throughout the rest of the paper we refer to the first simplification as the first model,and to the second version as the second model. As well, we refer to the core model as a third model, or a model with public capital.

13 4. Baseline case Figure shows the impulse responses of the key variables to a % increase in productivity. All variables are expressed in terms of percentage deviations from the steady state, except for the tax rates, for which responses are expressed as absolute deviations from their steady-state values 5. The baseline results reported are for three different versions of the model as discussed above. The continuous line represents the first version of the model, with fixed public consumption, the dashed line represents the second version of the model, with endogenous public consumption, and finally, the dotted line represents the core model with public investment and endogenous public consumption. Impulse responses gained from various model simulations resulted in the following key qualitative results. First, optimal emissions are procyclical, that is, periods of higher productivity are accompanied with higher levels of emissions. Second, the emissions tax is procyclical in the core model and is countercyclical in the other two models 6. Third, labor taxes are reduced during expansion in all three models. Fourth and lastly, the level of emissions is more persistent and results in a higher level of pollution stock in the public capital model. Intuitively, the government has a dual task of raising revenues to finance public goods (including public infrastructure), and taking care of the environment. In the economy, production causes emissions which accumulate in the atmosphere and adversely affect productivity and output. Emissions can be reduced by spending a fraction of total output on private abatement activities, which are affected by the government through the tax on emissions; a higher tax on emissions prompts firms to invest more into abatement. This environmental policy (a higher tax on emissions) exerts two effects on productivity of inputs in production. The first is the direct effect of the stock of pollution x t on productivity of output: a higher tax reduces emissions, improves quality of the environment, and boosts productivity. The second consequence is the indirect effect of an emissions tax on returns of inputs in production. The returns depend on two offsetting effects. On the one hand, a higher tax on emissions depresses the productivities of private capital and labor. On the other hand, a higher tax on emissions prompts firms to invest into abatement activities that result in smaller emissions and potentially lower emissions tax payments. These benefits will depend in particular on the effectiveness of abatement activities and the responsiveness of emissions to changes in output. Sensitivity of the baseline results to these parameters will be studied below in Section 5. Counteracting the adverse effects of an emissions tax on returns through abatement however generates a trade-off: spending a larger fraction of output income on abatement crowds out consumption and investment. In our framework the pollution stock does not vary much over the cycle so that potential productivity gains from environmental policies are relatively small and thus emissions tax influences returns of factors of production indirectly. At the same time, a shock to a t directly affects the productivity of inputs on production and output, and spending on abatement represents a very small fraction of GDP in the steady state, only.%. Thus, the direct effect of a productivity shock will always be quantitatively more important than an indirect effect on productivity through changes in tax on emissions. This is why growth prospects are the primary objective of a government that wants to take advantage of this temporary improvement in 5 Please note that for each time period t, we plot the values of those stock variables which enter current production process, namely x t and k t. Since e taffects x t contemporaneously, x t jumps in response to the shock, while k t does not. 6 Throughout this paper, for comparison purposes, we follow the definition of Heutel () and define procyclical taxes as ones that correlate positively with output, meaning cutting emissions taxes during recessions. Such behavior of tax rates implies countercyclical fiscal policy.

14 3 productivity, and thus emissions increase with said economic expansion. Ordinarily, a positive productivity shock raises labor productivity. During such periods of higher labor productivity the government s optimal response is to lower taxes on labor which then increases after-tax wages of consumers. This has the usual substitution and income effects. As the opportunity cost of leisure goes up, workers substitute leisure for work and increase their labor supply. But the income effect of an increase in real wages leads to a lower labor supply. With higher risk-aversion (such as the benchmark case here), the substitution effect is relatively weaker so that consumers have lower incentives to work. The optimal response of the government is thus to reduce the tax on labor to encourage a higher labor supply during the period of higher labor productivity. With an increase in labor supply and household wages (tax base), a positive technology shock generates more labor tax revenues. The revenues from labor taxes are directly related to the productivity of labor (tax base) that is affected by a productivity shock to a t. In contrast, environmental policy affects labor productivity indirectly through its effect on level of emissions and abatement. Thus, in the face of a productivity shock, the labor market and taxes on labor play a more dominant role in raising government revenues and in facilitating adjustment to the shock in the economy. Consequently, an emissions tax plays a lesser role in raising public revenues 7. As a result, the dynamic behavior of government revenue components exhibit similar trends across all models (figure ): labor tax revenues share in total government revenues goes up, whilst the share of emissions tax revenues to total government revenues decreases in the periods immediately following the shock. Given the relative importance of labor taxes in generating public revenues, it is now clear why the tax on emissions is cut in the first two models. In the first model, for instance, the government has to provide the same level of public goods as in the steady state model. Higher labor tax revenues motivate a reduction in tax on emissions as government spending can now be met through a lower tax on emissions. Similar intuition holds in the second model. Even though the level of public consumption responds endogenously to a positive TFP shock, revenues from taxing labor increase by such a level that allow for reducing revenues from taxing emissions, and thus said tax on emissions is cut. This conclusion explains the emissions tax s direction of change in these two models, but does not explain why the tax on emissions is lowered by more in the first model when g is fixed. To explain this we need to first note that in the model with fixed g, there are larger cuts in labor taxes, firms spend less on abatement and more on investment, and households consume more. The explanation is as follows. Consumers derive utility from consumption of both private and public goods. Since g is fixed in the first model, to increase consumer welfare, it is optimal for the government to encourage households to consume more private goods as well as to invest, to produce more goods in subsequent periods. This is motivated by further cutting the tax on emissions and boosting labor demand through a larger cut in the labor tax. More stimuli to the economy leads to a higher output and pollution stock when g is fixed than in the case when public consumption adjusts to the shock. Our explanation above on emissions tax behavior in the models without public capital misses one crucial element. That being, why is it not optimal for the government to provide more stimuli by resorting to larger labor tax cuts, as opposed to cuts on emissions taxes? Such policy option would result in lower labor tax revenues and would induce the government to increase environmental taxes to raise emissions tax revenues to balance its budget. Would this policy be more beneficial from an environmental point of view, given the 7 The fact that labor taxes are a more efficient means of generating public revenues than carbon taxes is an issue well discussed in early literature on the double dividend.

15 4 role of emissions taxes as a corrector of pollution externalities? We argue that under this policy option an increase in abatement activities that would accompany a lower - than prescribed by the baseline case - tax on labor policy would not sufficiently clean up the environment to counteract the higher emissions associated with higher output, resulting in a lower environment quality than under the baseline policy. To confirm our intuition, we perform a counterfactual experiment (discussed in next section), where we contrast our baseline economy with an alternative economy containing a fixed emissions tax. In contrast to the first two models without public capital, the core model features a procyclical emissions tax. Intuitively, with public capital as a productivity enhancing input of production, a TFP shock makes investment into private capital and labor even more appealing, increasing the severity of pollution externalities and therefore requiring an increase in abatement activities. To encourage more abatement and less private investment, tax on emissions is raised, leading to a smaller immediate response in private investment and emissions than in other two models. But with the effect of higher public investment on output spread over multiple periods, the adjustment of output and by-product emissions will be more persistent and will eventually result in a higher pollution stock than in the two other models. This conclusion explains how an increase in public investment deteriorates environmental quality further than in other models without productive public spending. Additionally, we argue that the composition of public spending - public consumption versus public investment - also matters for the quality of environment in subsequent periods following the shock. Specifically, we notice that both components increase, but increases in public spending are predominantly in public investment rather than in public consumption. This feature is not the result of an environmental policy conducted over the business cycle, but a feature that is standard in the conventional real business cycle model 8 which reflects the role that public investment plays as a means of absorbing shocks to the government s budget constraint. This has direct implications for environmental quality - a higher fraction of income spent on public investment compared with the fraction of income consumed increases output and thus the severity of the pollution externality in subsequent periods It is clear that the models outcome critically depends on the labor markets reaction to an increase in the labor tax, and therefore on the parameters that govern the responsiveness of labor supply and its behavior over the cycle. In the robustness section we will investigate how baseline results are sensitive to changes in labor elasticity and the value of risk-aversion. We will also see that the procyclicality of an emissions tax is not robust to changes when using the values of those parameters. 4. Baseline versus alternative tax policy To further assess the role of the emissions tax within the model we assess a counterfactual model, as mentioned above, in which the tax on emissions is fixed. The figures 3 and 4 show results for some key variables of interest for the first model,with fixed public consumption, and core models respectively 9. The counterfactual economy experiences higher emissions levels and a higher pollution stock over the 8 Such behavior of public investment compared with that for public consumption implies a higher variability of public investment. Intuitively, a relatively stronger response of public investment than public consumption helps to smooth utility across periods, as increases in public consumption affect household utility directly and immediately, whereas increases in public investment affect utility indirectly, with their effects being spread over multiple periods. Please see Kuralbayeva (3) for more on this topic. 9 The results of the second model, when public consumption changes endogenously, are qualitatively similar to ones for the first model with fixed public consumption and are available upon request.

16 5 long-run. Specifically, the pollution stock is larger under this alternative policy than under the baseline by some 5% in the core, and.7% and.% in other two models with a 5 year time period where the effect of a productivity shock is ceased and all other variables converge to their steady state values. In the core model, the counterfactual economy experiences higher emissions and a higher stock of pollution from the first period onwards. Contrastingly in the other two models, the adjustment of pollution stock can be broken down into two distinct periods: during the first phase (approximately 5 and half years), the counterfactual economy has a better quality of environment than the baseline economy, but during the second period, the situation reverses. The results of a higher pollution stock under the counterfactual economy compared with the alternative one in the core model are intuitive, since the emissions tax is higher under the former than under the latter policy. In the other two models, without public capital, the results can be explained as follows. In the counterfactual economy the government does not reduce its tax on emissions, thus generating more emissions tax revenues (see figure 3). This lowers labor tax revenues relative to the baseline tax policy. Lower labor tax revenues in turn suggest lower taxes on labor, and a larger stimulus to labor demand and private investment. And even though a higher tax on emissions under the alternative tax system shifts more spending into abatement than investment, this effect is weaker than the stimulus effect through a reduction in taxes on labor as the counterfactual economy experiences a larger increase in investment and labor supply. Since the effect of investment on output is delayed, the gap between production under the counterfactual experiment and baseline policy becomes larger over time, so too do emissions and pollution stock. This explains why the counterfactual economy experiences a larger deterioration in environmental quality when compared to the first model without public capital This counterfactual experiment highlights two points. First, a reduction in economic activity is a more effective way of significantly curbing emissions and improving environmental quality than spending on abatement. Second, and related to the first, in some situations when extra stimulus to the growth in the economy is warranted, tax on emissions can be an efficient instrument in providing an impetus to the economy with least possible adverse effect on environmental quality, as opposed to a tax on labor. This is because changing the labor tax results in large effects on labor supply and the productivity of capital, and consequently on output and pollution stock. 4.3 The effectiveness of baseline tax policy As discussed above, an optimal policy implies emissions tax changes in response to economic fluctuations. In this section we evaluate the effectiveness of such policy relative to the alternative tax policy, in which tax on emissions is fixed over the business cycle. For that purpose, we use the simulation results and conduct a welfare analysis. Simulation results of the core model under baseline and alternative tax policies suggest that the pollution stock is larger under the alternative than under the baseline in the core model by about 5% in a 5 year period. We carry out a thought experiment and assume that the US had conducted environmental policies, but one that has not reformed with changes in economic circumstances from This is a naive policy experiment, since up to date, federal carbon taxation has not been established in the US, but it Only some municipalities have introduced a carbon tax. For instance, in 6, the town of Boulder, Colorado introduced the nation s first carbon tax imposed on electricity usage, see

17 6 serves to assess how important a5% reduction in pollution stock is from the environmental point of view. Now, we utilize carbon dioxide emissions data on the US over a 5 year period from 983-8, during which the total emissions of CO amounted to GtCO. If the US would have conducted optimal environmental carbon tax policy as prescribed by the model, cumulative emissions would have been lower by 5%, that is by 6.43 GtCO. With abatement costs around USD 5 per ton (e.g.,creyts et al. (7)), a reduction of this additional pollution stock of 6.43GtCO would have cost US firms USD 3.5 bn. These estimates of abatement spending, if taken at face value, suggest that if these costs are spread over 5 years, firms must spend an extra USD.86 bn annually to abate this extra pollution stock. A U.S.Census Bureau (8) report states that in 5 US firms spent USD 6.58 bn on abatement activities. This suggest that the additional abatement costs estimated above account for almost 5% of total abatement spending by firms in 5. To further understand the effectiveness of the baseline environmental policy relative to the counterfactual, we conduct a welfare analysis. Our measure of welfare is the amount of baseline steady-state policy consumption a household would be willing to give up to be as well off under the alternative specification as under the baseline policy, following the procedure of Schmitt-Grohe and Uribe (7). We also conduct several experiments by varying the elasticity of labor supply and the coefficient of risk-aversion; with these results discussed in next section. All results are shown in Table 3. For the consumption-equivalence, a number of, e.g.,. means that the alternative environmental tax policy reduces welfare by % of consumption on average. Consumption-equivalents κ =. κ = κ =.75 κ =. κ =. /ψ =3 /ψ =3 /ψ =3 /ψ =. /ψ =.5 baseline case τ e Table 3: Welfare effects of alternative environmental tax policies: the core model In the table we see that the costs of adopting the alternative tax policy for baseline parameterization are non-negligible, and can account to more than percent of steady-state consumption in the baseline economy. To express this in monetary value, we use annual personal consumption expenditure in 3, which stood at USD,496. bn. By using this data we find that welfare losses from alternative tax policies amount to around USD.9 bn annually, which represents.7% of the US GDP in 3. To conclude, we have assessed the effectiveness of the baseline tax policy, by contrasting it with the alternative tax policy, where the tax on emissions is fixed over the cycle. This comparison was done by using simulation results and conducting a welfare analysis. While the impulse response analysis based on simulation results is more suitable for the analysis of costs from the perspective of firms (that have to But the introduction of carbon taxes is an ongoing debate in the US. For example, Congressional Budget Office (3) examines how a carbon tax, combined with uses of carbon revenues for deficit reduction and cutting existing labor taxes, might affect the economy and the environment Data source is the EIA: regions&syid=983&eyid=8&unit=mmtcd Data source is the NIPA table, see Appendix 8 for more details