Environmental Policy and Macroeconomic Dynamics in a New Keynesian Model

Transcription

1 Environmental Policy and Macroeconomic Dynamics in a New Keynesian Model Barbara Annicchiarico Fabio Di Dio October 213 Abstract This paper studies the dynamic behaviour of an economy under different environmental policy regimes in a New Keynesian model with nominal and real uncertainty. We find the following results: (i) an emissions cap policy is likely to dampen macroeconomic fluctuations; (ii) staggered price adjustment alters significantly the performance of the environmental policy regime put in place; (iii) welfare tends to be higher with a tax on emissions provided that the degree of price stickiness is not too high; (iv) the optimal policy response to inflation is found to be very strong as long as welfare is not affected by environmental quality and the environmental policy does not consist in an emissions cap. Keywords: New Keynesian Model, Environmental Policy, Macroeconomic Dynamics, Monetary Policy. JEL codes: E32, E5, Q58. Corresponding author: Università degli Studi di Roma Tor Vergata, Dipartimento di Economia, Diritto e Istituzioni - Via Columbia Roma - Italy. [email protected]. Sogei S.p.a. - IT Economia - Modelli di Previsione ed Analisi Statistiche [email protected]. 1

2 1 Introduction This paper seeks to understand the importance of different environmental policy regimes as a further conditioning factor for the dynamic response of the economy to nominal and real shocks. To this end, we formulate a dynamic stochastic general equilibrium (DSGE) model of New Keynesian (NK) type embodying pollutant emissions and environmental policy. The model that we construct has three key features. First, as in a standard NK model, the model embeds nominal price rigidities à la Calvo (1983) and monetary policy is described by a simple interest-rate rule. 1 Second, for what concerns the real side of the economy, we depart from the very basic model by introducing capital accumulation and capital adjustment costs, so that our setup generates more plausible response of the main macrovariables to shocks and is more general, embodying a Real Business Cycle (RBC) model as a special case. Third, the model includes pollutant emissions which are a byproduct of output. Emissions are assumed to be costly to firms which are so pushed to limit the environmental impact of their production activity by undertaking abatement measures. Emissions and firms abatement activities depend on the type of environmental regime adopted, namely: emissions cap (i.e. an exogenous limit on emissions), emission intensity target (i.e. an exogenous limit on emissions per unit of output) and tax policy (e.g. a carbon tax). With this characterization the paper asks the following questions: What is the impact of emissions regulations on the business cycle? To what extent do nominal rigidities influence the macroeconomic effects of the environmental policy regime put in place? What is the optimal policy response to inflation in this context? Our key findings are as follows. First, we find that an emissions cap is likely to dampen the response of the main macroeconomic variables to shocks, while emission permit price and firms abatement effort react more strongly to the changed economic conditions. Second, nominal rigidities are found to crucially alter the effects of the environmental policy regime adopted by introducing a certain degree of heterogeneity across firms. In this respect, we find that with nominal rigidities an intensity target environmental policy makes macroeconomic variables more volatile. Third, mean welfare tends to be higher with a tax, provided that the degree of price stickiness is not too high, while its volatility is always lower with a cap. On the other hand, if prices adjust very slowly, mean welfare will be higher under a cap policy. In terms of welfare, the performance of an emissions intensity target is found to be significantly altered by the degree of price stickiness. Finally, the optimal policy response to inflation is found to be very strong in all of the environmental regimes, with the exception of the cap policy which per se is able to act as a sort of automatic stabilizer for the economy. However, if we look at the optimal policy response to inflation under the assumption that the environmental quality enters the objective function of the policy maker, we find that the optimal response to inflation is milder as a result of the trade-off, faced by the policy maker, 1 See Woodford (23) and Galí (28). 2

3 between achieving a more efficient allocation of resources through prices stability and ensuring a better environmental quality. Preventing dangerous climate change is considered a priority of utmost importance by the international community. In this respect, a substantial cut of anthropogenic greenhouse gas emissions at worldwide level is advocated as a means to keep global warming under control. From this perspective it is clear why over the last decades the debate on the relationship between economic growth and environmental policy has attracted increasing attention in academic and policy circles. The debate mainly focuses on how protection of environment and economic activity could be seen as mutually consistent and not as competing aims. 2 However, at least in the short- to medium-term, environmental policy and economic activity are nevertheless portrayed as being in conflict with one another and, as a consequence, the policy actions undertaken play an important role in making the trade-off between environmental quality and economic efficiency more or less painful. In this respect, our paper aims at contributing to the theoretical debate on this trade-off by analyzing how alternative environmental policies are likely to condition the business cycle behavior of an economy whose equilibrium is distorted by the existence of imperfect competition and nominal rigidities. Our paper is related to the strand of literature that combines environmental economics and macroeconomics, aiming at a clear understanding of the interaction between environmental indicators and macroeconomic variables as well as of the potential effects of environmental regulations on the economy. 3 In particular, the closest predecessors of our paper are those studying environmental policy in a DSGE framework. Prominent examples include Fischer and Springborn (211), Heutel (212), Angelopoulos et al. (21) who study environmental policy in RBC models. 4 In detail, Fischer and Springborn (211) explore the macroeconomic performance of an emissions tax, an emissions cap and an intensity target in a RBC model in which production requires a polluting input, so that emissions abatement results from reductions in production in response to shocks and to the environmental policy regime put in place. 5 Heutel (212) develops a RBC model in which emissions are a byproduct of production and firms are able to reduce pollutant emissions thank to a costly abatement technology they have at their disposal. In this framework the author explores the optimal environmental policy over the business cycle in a centralized economy (first best) and in a decentralized economy (second best). Finally, Angelopoulos et al. (21) compare the performance of alternative environmental policy rules in a RBC model with uncertainty on total 2 On the importance of approaching the issue of climate change from an economic perspective, the R.T. Ely lecture given by David Stern at the AEA 28 Meeting represents a riveting introduction. See Stern (28). 3 See Fischer and Heutel (213) for an overview on the macroeconomic approach to the study of environmental related issues. 4 A number of previous studies deal with the relationship between economic fluctuations and environmental policy, but not in the context of a RBC model. See e.g. Kelly (25), Bouman et al. (2). 5 Starting with the seminal contribution of Weizman (1974), several other papers compare the performance of alternative environmental policies for regulating emissions, accounting or not for economic uncertainty, either in partial equilibrium settings (e.g. Hoel and Karp 25, Newell and Pizer 28, Quirion 25 among others) or in general equilibrium models (e.g. Goulder et al. 1999, Parry and Williams 1999 Dissou 25, Jotzo and Pezzey 27). 3

4 factor productivity, allowing also for exogenous shocks to the ratio of emissions to output, source of environmental uncertainty. In their model emissions are a byproduct of production, but only the government can engage in pollution abatement activity. Starting from these contributions we extend the analysis on the relationship between economic fluctuations and environmental policy by introducing nominal rigidities, 6 by exploring the role of monetary policy and by considering two additional sources of uncertainty besides the standard total factor productivity shocks, namely public consumption shocks and monetary policy shocks. To the best of our knowledge we are the first to explore the role of different environmental policy regimes as a further conditioning factor for the dynamic response of the economy to economic fluctuations in the presence of nominal rigidities and accounting for these additional sources of uncertainty. As a matter of fact, Fischer and Heutel (213) already recognize that the New Keynesian-DSGE modeling approach represents a promising alternative tool for environmental policy analysis. The structure of the paper is as follows. In Section 2 we outline the modified New Keynesian model extended to include pollutant emissions and abatement technology. Section 3 discusses the baseline calibration and the steady state properties of the model, considering alternative environmental policy regimes. In Section 4 we analyze the impulse response functions of the main macroeconomic variables to shocks and present the theoretical moments generated by the model, discriminating across different policy regimes. Section 5 shows results from the search of the optimal response to inflation according to a simple operational interest rate rule. Section 6 presents the main conclusions. 2 The Model The economy is described by a standard New Keynesian model with nominal prices rigidities à la Calvo (1983), extended to account for pollutant emissions and environmental policy. Time is discrete and indexed by t =, 1, 2,... There are five types of economic agents: (i) a continuum of monopolistically competitive polluting firms, each of which producing a single horizontally differentiated intermediate goods by using labor and physical capital as factor inputs; (ii) perfectly competitive firms combining domestically produced intermediate goods to produce a final consumption good; (iii) households who consume, offer labor services, and rent out capital to firms; (iv) a central bank making decisions on monetary policy; (v) a government deciding on fiscal and environmental policy. 6 Direct evidence on price rigidities for developed countries is provided by Àlvarez et al. (26), Bils and Klenow (24), Dhyne et al. (26), Klenow and Malin (211) among others. In general, a marked heterogeneity in the frequency of price adjustment is found across sectors. Further, prices seem to change less frequently in Europe than in the United States. 4

5 2.1 Final Good-Producing Firms We assume that firms producing final goods are symmetric and act under perfect competition. In each period the representative firm producing the final good Y t combines a bundle of differentiated intermediate goods Y j,t indexed by j [,1] according to a constant elasticity of substitution technology Y t =, where θ > 1 denotes the elasticity of ( ) θ 1 θ 1 θ substitution Y θ 1 j,t dj between differentiated intermediate goods. Taking prices as given, the typical final good firm chooses intermediate good quantities Y j,t to maximize profits, resulting in the usual demand schedule: Y j,t = (P j,t / ) θ Y t, with θ > 1 being interpreted as the price elasticity of demand for good j. Perfect competition and free entry drive the final good-producing firms profits to zero, so that from the zero-profit condition we obtain: ( 1 = which defines the aggregate price index of our economy. ) 1 P 1 θ 1 θ j,t dj. (1) 2.2 Intermediate Good-Producing Firms The intermediate goods sector is made by a continuum of monopolistically competitive polluting producers indexed by j [,1]. 7 The typical firm j hires L j,t labor inputs and capital K j,t in perfectly competitive factor markets to produce intermediate goods Y j,t, according to the constantreturn to scale technology: Y j,t = A t K α j,tl 1 α j,t, α (,1) (2) where α is the elasticity of output with respect to capital and the term A t represents the level of technology (total factor productivity), which evolves according to the following process loga t = (1 ρ A )loga+ρ A loga t 1 +ε A,t, (3) where < ρ A < 1 and the serially uncorrelated shock ε A,t is normally distributed with mean zero and standard deviation σ A. In modeling emissions and abatement we follow Heutel (212). 8 Emissions at firm level, Z j,t, are assumed to be proportional to output. However, this relationship is affected by the abatement effort U j,t. In particular, we assume Z j,t = (1 U j,t )ϕy j,t, (4) 7 Notably, the lack of competition is a source of inefficiency. Monopolistic competition, in fact, generates an average markup, which lowers the level of economic activity. 8 However, in this setup, pollution does not directly alter the production possibilities. 5

6 where ϕ > measures emissions per unit of output in the absence of abatement effort. The cost of abating a fraction of emissions C A is, in turn, a function of the firm s abatement effort and output: C A (U j,t,y j,t ) = φ 1 U φ 2 j,t Y j,t, φ 1 >, φ 2 > 1, (5) where φ 1 and φ 2 are technological parameters of abatement cost. Emissionsarecostlyto producersandthe unit costofemissionp Z depends on theenvironmental regime put into place. Clearly, in this context, the marginal cost of an additional unit of output has two components: the cost associated with the extra inputs needed to manufacture the additional unit, which depends on the production technology and inputs prices, and the costs associated with abatement and emissions, which depend on the available abatement technology and on the unit cost of emission. Prices are modeled à la Calvo (1983). In each period there is a fixed probability 1 ξ that a firm in the intermediate sector is allowed to set its price optimally, otherwise its price stays unchanged. The probability of changing price 1 ξ is assumed to be independent of the time elapsed since the last adjustment. This price setting mechanism implies that the average price duration is given by (1 ξ) 1. From the solution of firm j s static cost minimization problem, taking the nominal wage rate W t, the rental cost of capital R K t and unit cost of emission P Z as given, we have the following optimality conditions for the demand of labor, capital and the abatement effort, respectively: (1 α)a t K α j,tl α j,t Ψ j,t = W t, (6) αa t K α 1 j,t L 1 α j,t Ψ j,t = R K,t, (7) ϕ P Z,t = φ 1 φ 2 U φ 2 1 j,t, (8) where Ψ j,t is the marginal cost component associated to the manufacturing of a marginal unit of output and (8) equates the marginal value product of abatement (i.e. the cost saving related to lower emissions, ϕ PZ,t Y j,t ) to its marginal cost (i.e. φ 1 φ 2 U φ 2 1 j,t Y j,t ). Conditions (6) and (7) imply that all firms choose the same capital-labor ratio, so that the real marginal cost associated to the manufacturing of the good is common to all firms, namely 9 Ψ t = 1 α α (1 α) 1 α 1 A t ( Wt ) 1 α ( ) α RK,t. (9) 9 This can be seen by combining (6) with (7) to obtain K j,t = Wt α which implies that all firms employ the L j,t R K,t 1 α same capital-labor ratio. Using this result back into (6) or into (7) yields the expression for Ψ t. 6

7 From(8)itemergesthatalsotheabatementeffort, U j,t,iscommontoallfirms. Asaconsequence the marginal cost of producing an additional unit of output is equal across firms, i.e. MC t = Ψ t +φ 1 U φ 2 t + P Z,t (1 U t )ϕ. (1) Consider now the optimal price setting problem of the typical firm j which in period t is able to reoptimizeitsprice. Formally,thefirmsetsthepriceP j,t bymaximizingthepresentdiscountedvalue of profits earned until it will be able to reset its price optimally again, subject to demand constraints Y j,t+i = ( P j,t /+i) θyt+i for i =, 1, 2, 3,... and the available technology for production and abatement effort. At the optimum we have the following optimal pricing condition: p t = P t = θ X t +Ω t, (11) θ 1 Θ t with X t = λ t Ψ t Y t +ξβe t Π θ t+1x t+1, (12) Θ t = λ t Y t +ξβe t Π θ 1 t+1 Θ t+1, (13) Ω t = λ t [φ 1 U φ 2 t + P ] Z,t (1 U t )ϕ Y t +ξβe t Π θ t+1 P Ω t+1, (14) t wherewehavedroppedthej-indexsinceallfirmsabletosettheirpriceoptimallyattimetwillmake the same decisions. Q t,t+i denotes the stochastic discount factor used at time t by shareholders to value date t+i real profits and is related to the household s discount factor and the marginal utility of wealth λ t, i.e. Q t,t+i = β iλt+i λ t. 1 See the Appendix for details. It should be noted that in the limiting caseof fully flexible prices (i.e. ξ =, P t = ), condition (11), given (1), collapses to MC t = Ψ t +φ 1 U φ 2 t + P Z,t (1 U t )ϕ = θ 1, (15) θ accordingtowhichtherealmarginalcostofproductionmc t isconstant. Notethatthisisequivalent to saying that in the absence of constraints on the frequency of price adjustment price markups are at the desired level θ/(θ 1) The stochastic discount factor for nominal payoffs is, instead, defined as, Q N t,t+i = βi λ t+i λ t 11 In the standard New Keynesian model we would have that MC t = Ψ t = θ 1 θ. +i. 7

8 2.3 Households The representative infinitely-lived household maximizes the following lifetime utility: ( ) E t β t L 1+φ t+i logc t+i µ L, φ >, µ 1+φ L >, (16) i= where β (,1) is the constant discount factor, C t represents consumption of the final good, L t denotes hours of work and µ L weights the disutility of working and φ is the inverse of the Frisch elasticity. The period-by-period budget constraint of the typical household reads as C t + I t +Q N t B t = B t 1 +W t L t + D t +R k,t K t T t Γ K (I t,k t ), (17) where B t denotes the quantity of one-period nominal riskless bond purchased in period t and paying one unit of money at maturity, Q N t is the price of the bond, B t 1 denote bond holdings at the beginning of period t (carried from t 1), T t represents lump-sum taxes (or transfers from the government), D t are dividends from ownership of intermediate goods-producing firms, W t L t denotes labor income and R k,t K t is the rental (nominal) income from capital services. In each period t the representative household carries K t units of physical capital from the previous period and makes investment decisions I t, facing convex capital adjustment costs Γ K (I t,k t ), given by γ I 2 ( It K t δ K ) 2It with γ I >. 12 Investment increases the household s stock of capital according to K t+1 = (1 δ K )K t +I t, (18) where δ K (,1) is the depreciation rate of capital. At the optimum the following conditions must hold R 1 t = Q N t = βe t +1 C t C t+1, (19) µ L L t φ = 1 C t W t, (2) [ ( )( ) ] 2 1 R k,t+1 It+1 It+1 βe t +γ C t+1 P I δ k q t q t+1 +β(1 δ k )E t =, (21) t+1 K t+1 K t+1 C t C t+1 ( ) It It q t 1 γ I δ K γ ( ) 2 I It δ K =, (22) K t K t 2 K t 12 Convex adjustment costs imply that investments are less costly when spread out over a large time interval than when concentrated in a single period of time. 8

9 where we have used the fact that Q N t is the price of a risk-free bond paying one unit of the numéraire in period t + 1, so that Q N t = R 1 t, with R t being the risk free nominal interest rate, while q t measures the relative marginal value of installed capital with respect to consumption (i.e. the Tobin s q). The solution to the typical household s problem is described in the Appendix. 2.4 Public Sector and Environmental Policy Regimes The monetary authority manages the short-term nominal interest rate R t in accordance to the following interest-rate rule: R t = R ( ) ιπ Πt η Π t, (23) where Π denotes the deterministic steady-state inflation level, ι π is a policy parameter and η t is a monetary policy shock which, in turn, follows a stationary AR(1) process given by logη t = ρ η logη t 1 +ε η,t, (24) where < ρ η < 1 and the serially uncorrelated money supply shock ε η,t is normally distributed with mean zero and standard deviation σ η. The flow budget constraint of the public sector reads as T t +P Z,t Z t = G t, (25) where public consumption G t is financed by lump-sum taxes and revenues on emissions which depend on the environmental policy put into place. The term P Z,t Z t may, in fact, reflect the revenues from a tax policy or from the government sale of emissions permits. We assume that government consumption follows a stochastic process of the form: logg t = (1 ρ G )logg+ρ G logg t 1 +ε G,t, (26) where < ρ G < 1 and the serially uncorrelated money supply shock ε G,t is normally distributed with mean zero and standard deviation σ G. In what follows we will consider four different environmental policy regimes: No policy: emissions are costless to firms, (i.e. P Z,t = ) and there is no incentive to sustain the costs of emission abatement, i.e. U t = Emissions cap: Z t is fixed and the government sells emission permits to the producers at the market price P Z,t. Intensity target: there is a binding emission target of υ < ϕ per unit of output (Z t = υy t 9

10 for all t =, 1, 2, 3,...) and the government sells emission permits to the producers at the market price P Z,t. Tax policy: the government levies taxes on emissions at a constant (real) rate τ Z, implying that p Z,t = P Z,t / = τ Z, so that condition (8) now reads as ϕτ Z = φ 1 φ 2 U φ 2 1 t and the abatement effort of intermediate-good producers is constant Aggregation, Equilibrium and Emissions In equilibrium factors and goods markets clear, hence the following conditions are satisfied for all t: L t = 1 L j,tdj, K t = 1 K j,tdj which, in turn, imply that the aggregate production of intermediate goods can be expressed as 1 Y j,tdj = A t Kt αl1 α t. Using the fact that demand for each j variety of intermediate good is given by Y j,t = ( ) 1 θyt Pj,t dj, we have 1 Y j,tdj = Y t D p,t, where D p,t = 1 according to a non-linear first-order difference equation: ( Pj,t ) θdj is a measure of price (and so of output) dispersion which evolves D p,t = (1 ξ)p θ t +ξπ θ td p,t 1. (27) where p t = P t / and Π t = / 1. It follows that total production of the final good is equal to Y t = A t K α t L1 α t (D p,t ) 1. (28) It should be noted that the price dispersion term is generated by the Calvo s price staggering and, as shown by Schmitt-Grohé and Uribe (27), D p,t is bounded below at one. The higher the degree of price rigidities, the higher the price dispersion of the economy in response to shocks. It should be noted that this price dispersion term generates a wedge between aggregate output and production inputs, making aggregate production less efficient. The resource constraint of the economy reads as Y t = C t +I t +G t +C A,t + γ I 2 ( ) 2 It δ K I t, (29) K t where part of the output goes in the capital adjustment cost and in the abatement cost C A,t which depends on the environmental policy put in place. The aggregate abatement cost is obtained from (5) as follows: C A,t = φ 1 U φ 2 t 1 Y j,t dj = φ 1 U φ 2 t Y t D p,t. (3) 13 One could also consider a setting in which the tax on emissions is set in nominal terms, i.e. P Z,t = τ Z. We leave this hypothesis for future investigations. 1

11 Since in each period a fraction 1 ξ of firms choose their optimal money price Pt, the aggregate ( ) 1 1/(1 θ) price level = P1 θ j,t dj evolves according to Pt = [ ξpt 1 1 θ ] 1/(1 θ), +(1 ξ)p 1 θ t that is to say that the price level is just a weighted average of the last period s price level and the price set by firms adjusting in the current period. This equation can be rewritten as follows: 1 = ξπ θ 1 t +(1 ξ)(p t) 1 θ. (31) Finally, weassumethatemissionsaccumulateintheenvironment. LetM t+1 denotethepollution stock at the end of period t, then we have that the following accumulation equation holds M t+1 = (1 δ M )M t +Z t, (32) where δ M measures the fraction of pollution which naturally decays in each time period and aggregate emissions, Z t, are related to the final output according to the equation: Z t = 1 Z j,t dj = (1 U t )ϕ 1 Y j,t dj = (1 U t )ϕy t D p,t. (33) In the Appendix we summarize the equations of the model and formally define the competitive equilibrium of the economy under study. Before turning to the numerical solution of the model a couple of remarks are needed. It should be noticed that the economy described by this model features some sources of inefficiencies that make the competitive equilibrium distorted. The first source of inefficiency is to be attributed to the existence of monopolistically competitive intermediate-good producers which generates positive markups lowering the level of economic activity. The second source of inefficiency, instead, is due to price rigidities, here introduced according to the Calvo setting. As already pointed out, this pricing assumption gives rise to price dispersion which, in turn, creates an inefficiency loss, since the higher is price dispersion the more inputs are needed to produce a given level of output. Finally, the introduction of an environmental policy regime affects the allocation of resources across economic agents, so altering the competitive equilibrium, the response of the economy to uncertainty and hence the stabilizing role of monetary policy. 3 Calibration and Deterministic Steady State In this section we summarize the parametrization of the model which is in line with the existing literature. 14 Time is measured in quarters. The parametrization is summarized in Table 1. The discount factor β is equal to.99, so to imply an annual real (an nominal) interest rate of 4%. 14 See, for instance, Galí (28). 11

12 The capital return to scale α is set equal to 1/3. The capital depreciation rate δ K is set at.25, while the adjustment cost parameter on capital changes γ I is equal to 15. The inverse of the Frisch elasticity, φ, is set equal to 1. The price elasticity θ is set equal to 6 and the probability that firms do not revise prices ξ is set equal to 3/4. Total factor productivity A and the the parameter µ L on labor disutility are calibrated in order to get, in the no-policy scenario, a steady state value of labor hours equal to.2 and a level of output Y equal to unity. Public consumption G is set at.1, so that steady-state private consumption amounts to 7% of total output in the no-policy scenario. The coefficient of the interest rate rule measuring the responsiveness of the nominal interest rate to inflation, ι π, is set equal to 3, while steady-state inflation is equal to zero (Π = 1). 15 Turning to the calibration regarding emissions, we set the parameter δ M as in Heutel (212), so to haveapollution decay 1 δ M =.9979;the coefficient ϕ, measuring emissions per unit ofoutput, is set at.45, consistently with the carbon dioxide emissions, expressed as kilos per 25 PPP $ of GDP, and recorded by the US in 25 according to the World Bank Indicators. In the three policy scenarios, namely the tax policy, the emissions cap and the intensity target, the model is solved under the assumption that emissions are cut by 2%, consistently with the European Union reduction target of greenhouse gases emissions (from 199 levels) of the Europe 22 strategy. 16 The parameter φ 2 of the abatement cost function is set at 2.8, as in Nordhaus (28), while the scalecoefficient φ 1 is calibratedso to havean abatementcost to output ratioequal to.15%. 17 Note that in the case of intensity target the parameter measuring the binding emission target as a share of output, υ, is set at.3694 consistently with an emission reduction with respect to the benchmark no-policy scenario of 2%. As a consequence of this assumption, the three policy scenarios have the same deterministic steady state. This calibration strategy facilitates the comparison across environmental policy regimes. Given this parametrization, the deterministic steady state and the implied values for all relevant macrovariables in the no policy scenario and in the three policy scenarios are reported in Table 2, where we have defined p Z = P Z /P. As expected, the level of economic activity turns out to be lower under the three policy scenarios as a consequence of the additional costs of the environmental regulation borne by producers. In particular, in this economy, a 2% reduction of emissions is associated with a 2.54% reduction of output, while the welfare costs of achieving a lower level emissions amounts to %. As common practice in the DSGE literature this welfare cost is measured in consumption units, namely as the percentage reduction in consumption with respect to the no policy case that would be necessary to make a representative consumer indifferent between a no policy scenario and one characterized by emissions regulations. Finally, following Smets and Wouters (27), the persistence of the technology shock is ρ A = 15 For the sake of simplicity, we abstract from the presence of trend inflation. 16 For further details,.see en.htm 17 The amount of this cost will depend on the particular abatement technologies available to firms. On the measurement of the economic burden of environmental regulation, see Pizer and Kopp (25). 12

13 .95, while that of the government spending shock is ρ G =.97; the standard deviations of productivity and of the government purchases processes are set equal to σ A =.45 and σ G =.53, respectively; the quarterly standard deviation of the monetary shock σ η is set at.24, with a persistence of ρ η =.15. All the simulation results for the competitive economy have been obtained by using a pure perturbation method which amounts to a second-order Taylor approximation around a deterministic steady state Dynamics under Different Environmental Policy Regimes In this Section we analyze the dynamic properties of the model under alternative environmental policies (no policy, emission cap, intensity target and tax policy). To this end we first look at the equilibrium response of a number of macroeconomic variables of interest to three temporary shocks typically considered in the literature: a shock to technology, government consumption and the nominal interest rate. Finally, to further assess the implications of different environmental regimes, we compute the second moments of the key macroeconomic variables, given the same three sources of uncertainty under different degrees of price rigidities. 4.1 Technology Shock Figures 1 and 2 display the economy s response to a one percent increase in productivity A t under four different environmental policy scenarios: no policy (continuous lines), emission cap (dotted lines), intensity target (dashed lines), tax policy (dotted-dashed lines). All results are reported as percentage deviations from the initial steady state over a 2-quarter period. Figure 1 reports the impulse responses to the positive technology shock of the main macrovariables. Following a positive technology innovation, as expected, output, consumption, investment, hours and real wages all rise persistently. Clearly, the higher productivity brings about a fall of firms marginal costs. It should be noted that the reaction of hours is positive, despite the presence of price rigidities prevents intermediate-good producers from fully adjusting their prices downward to the new lower level of marginal costs. 19 Since the beneficial effects of a positive innovation on productivity are temporary, households will find it optimal to build up the capital stock and to work harder during the early phases of the adjustment process, when productivity is higher. This also explains why consumption follows a hump-shaped dynamics in response to the shock. Turning 18 See Schmitt-Grohé and Uribe (24a). The model has been solved in Dynare. For details see and Adjemian et al. (21). 19 The negative response of hours to a positive productivity shock emerges in basic NK models without capital accumulation, where price rigidities push producers to take advantage of the productivity increase by reducing labor demand (see e.g. Galí 28). Here the behavior of the economy is closer to that of a typical RBC model, because of the presence of capital. 13

14 now to the dynamic implications of the environmental policy regimes put in place, we observe that the emission cap policy slightly diminishes the response of output, consumption investment, hours and real wages. Intuitively, the emission cap, by pegging the aggregate level of pollutant emissions, forces firms increasing their production to sustain higher abatement costs. These higher costs, in turn, will diminish the level of output available for consumption and investment, so implying a milder expansion of these variables. On the other hand, with an intensity target environmental regime, emissions will expand with output, while with a tax policy firms will be able to increase pollutant emission at a constant marginal cost, so the dynamic behavior of the economy would mimic that observed under a no policy regime. Consider now the dynamics of the emissions related variables reported in Figure 2. Obviously, the increase in productivity induces a corresponding increase in emissions, since we assume a proportional relationship between output and emissions, as equation (33) reads, with no significantly differences among the tax policy, the intensity target regime and the no policy scenario. The only exception is given by the emission cap regime where, instead, the adjustment to the positive technology shock calls for a substantial reaction of the abatement effort in order to fully keep the target level of emissions. The abatement costs increase more than proportionally with respect to output as a consequence of the assumed convex abatement technology. As a result, the permit price goes up, reflecting the relative effort of the government in sustaining the emission cap. As already seen in Figure 1, the more resources devoted to the pollutant abatement will diminish the expansionary effect of the positive innovation to technology. Under a tax policy the permit price is constant, and so also the firms abatement effort. As already remarked, from a purely dynamic point of view the economy behaves like in the no policy scenario. Finally, looking at the response of these macrovariables under an intensity target rule, we notice that, at least initially, both the abatement effort and the permit price positively react in response to the shock, although the measure of this reaction is quite small in size. To understand why the abatement effort and the permit price initially increase also in the case of emission intensity, one should consider the behavior of the firms able to adjust their prices in response to the positive technology shock. Since marginal costs are lower, firms will find it optimal to cut prices to increase the demand. Given the existence of nominal rigidities only a fraction of firms will be able to cut prices, so expanding the demand of their production by more than under the flexible price case. As a result, these producers will expand their output by more than the other firms. This heterogeneity of firms behavior is summarized by the aggregate emission equation described by (33). Under an emission intensity policy (33) boils down to υ = (1 U t )D p,t, so implying that even for a given emission to output ratio, there is room for a varying abatement effort. Following the shock, in fact, the price dispersion D p,t will increase, and this will require a higher abatement effort to keep the ratio unchanged at aggregate level. At aggregate level, the higher abatement effort will translate into a slightly lower initial response of the emissions to the expansionary shock. 14

15 4.2 Public Consumption Shock We now consider the economy s response to a positive demand shock. In particular, we focus our attention on a positive innovation to public consumption G. Figure 3 illustrates the impulse responses of output, consumption, investment, hours and the real wage to this shock under the four different environmental policy regimes. Following the shock, output and hours worked increase, although the size of their response is negligible. As expected, this shock triggers a decrease of private consumption and investment which are crowded out by the higher government spending. Intuitively, in response to this shock, wealth effects are expected to drive the behavior of consumption and investment: following a public expenditure increase agents feel poorer because less resources are available for private use. As a result, they will tend to work harder decreasing consumption and investment. This increase in hours, in turn, gives a boost to output on impact. The overall expansionary effect on output will be higher, the higher the degree of price rigidities. As already observed in the case of technology shock, under an emission cap policy the expansionary effects are less pronounced, since respecting the cap absorbs more resources for emissions abatement. Turning to the response of the environment-related variables displayed in Figure 4, we observe emissions showing similar patterns across regimes, while abatement and permit price differ across regimes. In fact the increase in public spending induces a rise in output which translates into higher emissions in all regimes, with the exception of the emissions cap, where, as seen before, the expansionary policy entails a greater abatement effort and a boost in the permit price. Finally, as already emphasized, under a tax policy emissions behave exactly as in the no policy scenario, being constant the abatement effort. 4.3 Monetary Policy Shock Figures 5 and 6 display the impulse responses of the main macroeconomic variables to a monetary policy shock. More specifically, we consider an increase of.25% in the innovation η t which would imply and increase of 1% in the annualized nominal rate on impact. In this example, to abstract from the endogenous changes in the nominal interest rate induced by the response to inflation, we set ι π =. This policy shock generates an increase in the real interest rate, which in turn, depresses aggregate demand and so output. Output and hours, in fact, sharply decline in response to the tightening of monetary policy, following the contraction in consumption and investment resulting from the nominal interest rate hike. Not surprisingly, the real wage also declines as a result of downward pressure on nominal wage induced by the reduced labor demand. However, already in the second period, the economy recovers since the persistently higher real interest rate depresses 15

16 consumption and favors capital accumulation, so that output expands. From Figure 5 we note that in this case the environmental policy regimes do not affect the dynamic response to this contractionary policy shock, while some important differences across the environmental policy regimes are observed in Figure 6. In the case of emission cap, given the contraction of output, emissions should be lower and the cap should stop being binding. However, since emission abatement is a costly activity, firms will find it optimal to reduce their abatement effort in response to the contractionary shock, so that aggregate emissions stay at the cap level. Under an intensity target policy, emissions fall, while abatement and permit price hike on impact. Intuitively, since only a small fraction of firms are in the position of resetting their prices in response to the changed economic conditions, we observe that the abatement effort and the permit price initially increase. Firms resetting their prices, in fact, face a lower demand reduction than that faced by those firms whose prices are stuck at their previous period values. This implies that re-optimizing producers reduce less their output and the abatement effort raises, so that the intensity target constraint is fully met at aggregate level. Finally, in the tax policy scenario the abatement effort of producers is constant, implying a reduction in emissions that is proportional to output. 4.4 Theoretical Moments To better understand the dynamic behavior of the economy under different environmental policy regimes we compute the theoretical moments of the main macrovariables produced by the model. We consider three different degrees of nominal rigidities in order to further assess the implications of price rigidities: (i) ξ = 3/4 (benchmark level), (ii) ξ = (flexible prices), (iii) ξ = 4/5 (high degree of nominal rigidities). Table 3 gives the theoretical means of the main macrovariables. Table 4 reports the standard deviations of the main macrovariables(first column), also expressed in relative terms with respect to output (second column), while Table 5 presents the correlations with output. Finally, Table 6 reports mean and standard deviation of the welfare. The main findings of our analysis can be summarized as follows. From Table 3 we notice that as long as prices are fully flexible the intensity target and the tax policy regimes behave in the same way. The differences across environmental regimes arise when nominal rigidities come into play, although the differences are negligible for ξ = 3/4, while for higher degree of nominal rigidities (i.e. ξ = 4/5) the means of output and emissions are slightly higher with an intensity target than with a cap or a tax. Moreover, we notice that with a high degree of nominal rigidities marginal costs differ across regimes. As expected, the emission cap regime shows the highest marginal cost, reflecting the greater relative effort in abating emissions necessary to respect the cap. Now consider Table 4. First, as expected, the volatility of the economy tends to be higher, the higher the degree of nominal rigidities. Also the variables pertaining to the environment and the 16

17 emissions control are more volatile when the probability that prices will stay unchanged is high. Intuitively, when prices cannot adjust, or can only adjust slowly, output is demand determined and becomes more volatile, driving all the other real variables of the economy. Under flexible prices, instead, price changes mitigate the effects of real shocks and neutralize the effects of monetary policy shocks, and markups will be at the desired level (i.e. real marginal costs stay constant). Second, under the intensity-target emission-control policy, when prices are fully flexible, the economy behaves as under a tax policy regime, because of the lack of any source of heterogeneity across price-setting firms induced by nominal rigidities. On the other hand, for very rigid prices the differences between the two regimes are remarkably higher and the economy becomes more volatile under an intensity target regime. Third, under a cap policy regime and fully flexible prices, standard deviations of output, consumption, investment and hours are lower, while those of marginal cost, permit price and abatement effort are higher than under the other emission control policies. 2 As already remarked, the emissions cap imposes an immediate adjustment of the abatement effort when the economy faces a shock. This extra cost, in turn, limits the reactivity of output to shock, while making marginal costs more responsive and permit prices more volatile. It is worth noticing that when nominal rigidities are high (i.e. ξ = 4/5) also the volatilities of marginal costs, of abatement effort and of permit prices are lower with a cap than with an intensity target. Finally, with regards to the relative standard deviations, we notice that the relative variability of consumption with respect to output decreases when prices become stickier, while for hours and investments we observe the opposite. For a cap regime the relative variability of abatement effort and permit prices tends to increase when prices are more flexible. We now move to correlations with output displayed in Table 5. The main findings are the following. We observe that the correlation of hours, investments and marginal costs tends to be higher, the higher the degree of nominal rigidities. This is somehow connected with the idea that under high nominal rigidities most firms are in the impossibility of setting prices according to the current economic conditions and are forced to change their factor inputs to absorb the shocks. Also we notice the worked hours become slightly countercyclical when prices are flexible and the environmental policy is set according to an emission cap. Moreover, we observe that with fully flexible permit prices and abatement efforts are perfectly procyclical under a cap. Emissions move perfectly procyclically under tax policy and intensity target regimes. Under intensity targets permit prices and abatement effort are countercyclical. Obviously under this regime, when output is higher, emissions can increase proportionally requiring a lower abatement effort and inducing a drop of permit prices. Finally, Table 6 reports the mean and the standard deviation of the welfare. We observe that under fully flexible prices the higher level of welfare on average is achieved with an intensity target 2 This result is consistent with the findings of Fischer and Springborn (211). 17

18 and with a tax, but at a cost of higher volatility. As already emphasized, in fact, with a cap the economy is more stabilized. In the benchmark case, with an emission intensity target, mean welfare is slightlylowerthan with atax, but still slightly higherthat with acap, recordingahigherstandard deviation. On the contrary, when prices are very rigid, mean welfare is found to be higher under a cap. Overall, this analysis confirms that for a high degree of nominal rigidities the type of the environmental policy regime put in place is able to affect significantly the dynamics and the volatility of the economy. 5 Environmental Policy Regimes and the Optimal Policy Response to Inflation After having studied the dynamic properties of the economy, by jointly considering the implications of having different environmental regimes and different levels of price rigidities, we now search for the optimal response of the nominal interest rate to inflation according to rule (23). Such a rule is obtained by searching for the policy parameter ι π that maximizes households conditional welfare subject to the competitive equilibrium conditions that characterize the model economy, summarized in the Appendix. The optimal rule must have the following characteristics: (i) it must ensure equilibrium determinacy; (ii) it must maximize the expected life-time utility of the representative agent; (iii) it must respect the zero bound on the nominal interest rate. Following Schmitt-Grohé and Uribe (27) we focus on the conditional expected discounted utility of the representative household, that is 21 ( ) V = E β t 1+φ L t logc t µ L, (34) 1+φ t= To make our analysis more complete, we also consider the case in which agents have preferences over environmental quality, by looking at the optimal rule able to maximize the conditional expected discounted utility of the following form: ( ) = E β t 1+φ L t logc t µ L 1+φ M t+1, (35) V M t= 21 Specifically, the conditional measure of welfare assumes an initial state of the economy and allows to take into account the transitional effects from that initial condition to the stochastic steady state implied by the policy rule adopted by the monetary authorities. As commonly assumed, the initial state of the economy coincides with the deterministic steady state. 18

19 where the end-of-period stock of pollutant is assumed to be a source of disutility. 22. Notice that the time path of M is still governed by the accumulation equation (32) and so it solely depends on the environmental policy put in place. Numerically, we search for ι π restricted to lie in the interval [,1]. As in Schmitt-Grohé and Uribe (27), we approximate the non-negativity constraint on the nominal interest rate by requiring that a rule must induce a low volatility of the nominal interest rate around its target level, that is we impose the condition: 2σ R < R, where σ R denotes the standard deviation of the nominal interest rate. The results of our analysis are summarized in Table 7. When environmental quality does not enter the welfare function, optimality always calls for a strong reaction to inflation, with the exception of an economy governed by an emission cap policy. The intuition behind this result can be explained as follows. A strong inflation targeting policy is likely to prevail in many contexts, since this policy stabilizes expectations about future inflation and so price setters will not be tempted to react too strongly to uncertainty by setting higher markups. In addition, by stabilizing the price level, price dispersion and the related distortion are also reduced, with positive effects on the level of economic activity. This result is consistent with the literature on optimal monetary policy in which strong inflation targeting is likely to prevail. 23 Under a cap instead, the expansionary possibilities of an economy are limited by the cap itself which entails higher costs. Similarly, economic contractions are dampened by the reduced abatement costs. In other words, an emission cap policy per se is able to act as a sort of automatic stabilizer for the economy, while permit prices and abatement effort adjust accordingly. In this context the optimal policy still calls for an active rule (i.e. a more than proportional reaction to inflation), but the optimal reaction to inflation can be weaker. It should be remarked that when the environmental quality does not affect utility, the policy mix yielding the higher level of welfare is given by a cap, combined with a coefficient of response to inflation equal to 1.5. More interestingly when environmental quality is an argument of the welfare function, strong inflation targeting is no longer optimal also under the other regimes. The reason goes as follows. When the environmental quality enters the objective function, the optimizing policy maker also accounts for the negative externality on the environment deriving from production. In this context the monetary authorities face a trade-off between achieving a more efficient allocation of resources (by reducing the distortion derived by the price dispersion and the monopolistically competitive behavior of producers through a strong inflation targeting policy) and ensuring a better environmental quality, requiring either a higher abatement effort or a lower level of economic activity. It should be 22 In this way we account for the damages from pollution directly in the utility function. This is a common way to introduce the negative externality related to the deterioration of the environment into a macroeconomic model. See, for instance, Bartz and Kelly (28). 23 See, for example, Schmitt-Grohé and Uribe (27, 24b), who find that optimized policy rules feature muted response to output and no inertia. 19

20 noted that, in such circumstances, the policy mix displaying the higher level of conditional welfare consists in a tax policy and a reaction coefficient to inflation equal to 2. 6 Conclusion We present a New Keynesian dynamic general equilibrium model embodying pollutant emissions and environmental policy. We analyze the performance of alternative environmental policy rules under real and nominal uncertainty and find the optimal policy response to inflation. Our results are as follows. First, an emissions cap policy acts as an automatic stabilizer of the economy, since emission permit prices and firms abatement effort are procyclical, so dampening business cycle fluctuations. Second, stickiness in prices plays a major role in shaping the effects of emissions regulation. In particular, an emissions intensity target regime is likely to generate more macroeconomic volatility when the degree of price rigidities is high. Third, welfare is less volatile under a cap, as expected, while its mean value tends to be higher with a tax policy, provided that the degree of price rigidity is not too high, otherwise mean welfare tends to be higher under a cap policy. In the presence of nominal rigidities the adoption of an emissions intensity target policy is welfare detrimental. Finally, the optimal policy response to inflation is found to be very strong with an emissions intensity and with a tax. On the contrary, under a cap policy, which, as already pointed out, is able to moderate the response of the main macrovariables to shocks, optimality requires a weak response to inflation. A milder optimal reaction to inflation is also found in all environmental policy regimes when the negative externality of the environmental degradation enters the objective function of the policy maker. The present model is based deliberately on a number of simplifying assumptions in order to stress the intuition behind the influence of environmental policy on the transmission mechanism of some common shocks considered in the literature. We argue that the insights obtained here prepare the ground for more complex explorations on the relationship between business cycle and environmental policy. An important direction for future research might be to incorporate additional shocks into the analysis, since ideally these kinds of investigations should incorporate into the model all of the sources of uncertainty that are important drivers of economic fluctuations. Furthermore, the issue of the interaction between environmental and monetary policy has been touched upon in this paper but deserves much further research. The study of the optimal Ramsey monetary policy in this context represents a natural extension in this direction. Finally, accounting for the direct negative externalities that pollution may have either on agents welfare or on production possibilities would introduce an extra and non-trivial trade-off for the policy makers seeking to stabilize the economy and preserve environmental quality in the face of business cycle. 2

21 References Adjemian, S., Bastani, H., Juillard, M., Mihoubi, F.,Perendia, G., Ratto, M., Villemot, S., (211). Dynare: Reference Manual, Version 4, Dynare Working Papers no. 1, CREPEMAQ. Álvarez, L.J., Dhyne, E., Hoeberichts, M., Kwapil, C., Le Bihan, H., Lünnemann, P., Martins, F., Sabbatini, R., Stahl, H., Vermeulen, P., Vilmunen, J., (26). Sticky Prices in the Euro Area: A Summary of New Micro-Evidence, Journal of the European Economic Association, 4, Angelopoulos, K., Economides, G., & Philippopoulos, A., (21). What is the Best Environmental Policy? Taxes, Permits and Rules under Economic and Environmental Uncertainty, CESifo Working Paper Series 298, CESifo Group Munich. Bartz, S., Kelly, D. L., (28). Economic Growth and the Environment: Theory and Facts, Resource and Energy Economics, 3, Bils, M., Klenow, P.J., (24). Some Evidence on the Importance of Sticky Prices, Journal of Political Economy, 112, Bouman, M., Gautier, P.A., Hofkes, M.W., (2). Do Firms Time Their Pollution Abatement Investments Optimally? De Economist, 148, Calvo, G., (1983). Staggered Prices in a Utility-Maximizing Framework, Journal of Monetary Economics, 12, Dhyne, E., Alvarez, L.J., Le Bihan, H., Veronese, G., Dias, D., Hoffmann, J., Jonker, N., Lunnemann, P., Rumler, F., Vilmunen, J., (26). Price Changes in the Euro Area and the United States: Some Facts from Individual Consumer Price Data, Journal of Economic Perspectives, 2, Dissou, Y., (25). Cost-Effectiveness of the Performance Standard System to Reduce CO2 Emissions in Canada: A General Equilibrium Analysis, Resource and Energy Economics, 27, Fischer, C., Heutel, G., (213). Environmental Macroeconomics: Environmental Policy, Business Cycles, and Directed Technical Change, Working Papers, 13-2, University of North Carolina at Greensboro, Department of Economics. Fischer, C., Springborn, M., (211). Emissions Targets and the Real Business Cycle: Intensity Targets versus Caps or Taxes, Journal of Environmental Economics and Management, 62, Galí, J., (28). Monetary Policy, Inflation, and the Business Cycle, Princeton and Oxford: Princeton University Press. Goulder, L.H., Parry, I.W.H., Williams III, R.C., Burtraw, D., (1999). The Cost-Effectiveness of Alternative Instruments for Environmental Protection in a Second-Best Setting, Journal of Public Economy 72, Heutel, G., (212). How Should Environmental Policy Respond to Business Cycles? Optimal Policy under Persistent Productivity Shocks, Review of Economic Dynamics, 15,

22 Hoel, M., Karp, L., (22). Taxes versus Quotas for a Stock Pollutant, Resource and Energy Economics, 24, Kelly, D. L., (23). On Environmental Kuznets Curves Arising from Stock Externalities, Journal of Economic Dynamics and Control, 27, Kelly, D. L., (25). Price and Quantity Regulation in General Equilibrium, Journal of Economic Theory, 125, Klenow, P., Malin, B., (211). Microeconomic evidence on price-setting, in B. Friedman, M. Woodford (Eds.), Handbook of Monetary Economics, Elsevier, Amsterdam, Jotzo, F., Pezzey, J.C.V., (27). Optimal Intensity Targets for Greenhouse Gas Emissions Trading under Uncertainty, Environmental and Resource Economics, 83, Newell, R.G., Pizer, W.A. (28). Indexed Regulation, Working Paper 13991, National Bureau of Economic Research, Cambridge, MA. Nordhaus, W.D., (28). A Question of Balance: Weighing the Options on Global Warming Policies. New Haven and London: Yale University Press. Parry, I.W.H.,Williams III, R.C., (1999). Second-Best Evaluation of Eight Policy Instruments to Reduce Carbon Emissions, Resource and Energy Economics, 21, Pizer, W.A. (25). The Case for Intensity Targets, Climate Policy, 5, Pizer, W. A., Kopp, R., (25). Calculating the Costs of Environmental Regulation, in K. G. Mäler & J. R. Vincent (ed.), Handbook of Environmental Economics, edition 1, volume 3, chapter 25, Quirion, P., (25). Does Uncertainty Justify Intensity Emission Caps? Resource and Energy Economics, 27, Schmitt-Grohé, S., Uribe, M., (24a). Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function, Journal of Economic Dynamics and Control, 28, Schmitt-Grohé, S., Uribe, M., (24b). Optimal Operational Monetary Policy in the Christiano- Eichenbaum-Evans Model of the U.S. Business Cycle, NBER Working Paper no Schmitt-Grohé, S., Uribe, M., (27). Optimal, Simple, and Implementable Monetary and Fiscal Rules, Journal of Monetary Economics, 54, Smets, F., Wouters, R., (27). Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach, American Economic Review, 97, Stern, N., (28). The Economics of Climate Change, American Economic Review, 98, Weitzman, M.L. (1974). Prices vs. Quantities, Review of Economic Studies, 41, Woodford, M., (23). Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton and Oxford: Princeton University Press. 22

23 Appendix Optimization Problem of Intermediate-Good Producing Firms In each time period the typical intermediate goods-producing firm chooses L j,t, K j,t and U j,t in order to maximize its real profits D j,t = P j,t Y j,t W t L j,t R K,t K j,t φ 1 U φ 2 j,t Y j,t P Z,t Z j,t, (A1) given the current economic conditions and the technology constraints (2)-(4). The optimal static conditions (6)-(8) immediately follow, where Ψ j,t is the Lagrangian multiplier associated to the production technology (2). Consider now the price setting problem. The typical firm j able to set its price optimally at time t maximizes the present discounted value of expected real profits generated while the price remains unchanged. Formally, the Lagrangian function is E t ξ i Q R t,t+i i= [ P j,t +i Y j,t+i φ 1 U φ 2 j,t+i Y j,t+i Wt+i +i L j,t+i + RK,t +i K j,t+i PZ,t +i (1 U j,t+i )ϕy j,t+i ( +Ψ j,t+i At+i Kj,t+i α L1 α j,t+i Y ) j,t+i where Q R t,t+i is the real stochastic discount factor and Y j,t+i = first-order condition associated to the above problem gives P t = θ θ 1 ( E t i= ξi Q R Pt+i ) θyt+i t,t+i Ψt+i ( E i= t ξ i Q R Pt+i ) θ 1Yt+i + t,t+i [ ]( + Et i= ξi Q R t,t+i φ 1 U φ 2 t+i +P Z,t+i Pt+i ) θyt+i P (1 U t+i t+i)ϕ ( E t i= ξi Q R Pt+i ) θ 1Yt+i t,t+i ] + (A2) ( P j,t +i ) θyt+i for i =,1,2,3 The, (A3) which can be expressed as (11) by re-writing each of the expected values of the three infinite sums in this equation recursively, in terms of three artificial variables X t, Θ t and Ω t : ( ) θ X t = E t ξ i β i Pt+i λ t+i Ψ t+i Y t+i, (A4) Ω t = E t i= i= Θ t = E t i= ( ) θ 1 ξ i β i Pt+i λ t+i Y t+i, (A5) ξ i β i λ t+i [φ 1 U φ 2 t+i + P Z,t+i +i (1 U t+i )ϕ ]( Pt+i ) θ Y t+i. (A6) 23

24 Optimization Problem of Households The first-order conditions for the stochastic optimization problem of the typical household can be derived as follows. Let the Lagrangian function at time t be: 1+φ L logc t+i µ t+i L 1+φ + B t+i 1 L t = E t β i P +λ t+i t+i + Wt+i +i L t+i +D t+i + R k,t+i +i K t+i + ( ) 2It+i i= Tt+i +i I t+i C t+i Q N B t+i t+i +i γ I It+i +, 2 K t+i δ K +ζ t+i [(1 δ K )K t+i +I t+i K t+i+1 ] (A7) where λ t denotes the Lagrangian multiplier associated to the flow budget constraint expressed in real terms (17) and ζ t is the Lagrangian multiplier associated to the accumulation of physical capital. The first-order conditions for maximization of the lifetime utility function (16) with respect to C t, B t, L t, K t+1 and I t are, respectively, given by C 1 t = λ t, (A8) Q N t = βe t +1 λ t+1 λ t, (A9) µ L L t φ = λ t W t, (A1) [ ( )( ) ] 2 R k,t+1 It+1 It+1 βe t λ t+1 +γ P I δ k q t λ t +β(1 δ k )E t λ t+1 q t+1 =, t+1 K t+1 K t+1 (A11) ( ) It It q t 1 γ I δ K γ ( ) 2 I It δ K =, (A12) K t K t 2 K t where q t = ζ t λ t measures the relative marginal value of installed capital with respect to consumption (i.e. the Tobin s q) and Q N t = R 1 t, with R t being the risk free nominal interest rate. Conditions (19)-(22) in the main text immediately follow. 24

25 Competitive Equilibrium Let p Z,t = P Z,t /, r k,t = R K,t / and w t = W t /, then the economy is described by the following equations R 1 t = βe t +1 C t C t+1, (A13) µ L L t φ = 1 C t w t, (A14) [ ( )( ) ] 2 1 It+1 It+1 βe t r k,t+1 +γ C I δ k q t q t+1 +β(1 δ k )E t =, t+1 K t+1 K t+1 C t C t+1 (A15) ( ) It It q t 1 γ I δ K γ ( ) 2 I It δ K =, K t K t 2 K t (A16) Y t = C t +I t +G t +φ 1 U φ 2 t Y t D p,t + γ ( ) 2 I It δ K I t, 2 K t (A17) K t+1 = (1 δ K )K t +I t, (A18) Y t = A t K α t L 1 α t (D p,t ) 1, (A19) (1 α)a t K α t L α t Ψ t = w t, (A2) αa t Kt α 1 L 1 α t Ψ t = r K,t, (A21) ϕp Z,t = φ 1 φ 2 U φ 2 1 t, (A22) p t = θ X t +Ω t, (A23) θ 1 Θ t X t = λ t Ψ t Y t +ξβe t Π θ t+1x t+1, (A24) Θ t = λ t Y t +ξβe t Π θ 1 t+1 Θ t+1, (A25) ] Ω t = λ t [φ 1 U φ 2 t +p Z,t (1 U t )ϕ Y t +ξβe t Π θ t+1ω t+1, (A26) 1 = ξπ θ 1 t +(1 ξ)(p t )1 θ, (A27) D p,t = (1 ξ)p θ t +ξπ θ t D p,t 1, (A28) MC t = Ψ t +φ 1 U φ 2 t +p Z,t (1 U t )ϕ, Z t = (1 U t )ϕy t D p, t, M t+1 = Z t +(1 δ M )M t, C A,t = φ 1 U φ 2 t Y t D p,t, (A29) (A3) (A31) (A32) 25

26 T t +p Z,t Z t = G t, (A33) R t = R ( Πt Π ) ιπ η t, (A34) loga t = (1 ρ A )loga+ρ A loga t 1 +ε A,t, logg t = (1 ρ G )logg+ρ G logg t 1 +ε G,t, logη t = (1 ρ η )logη +ρ η logη t 1 +ε η,t. (A35) (A36) (A37) Definition 1: A stationary competitive equilibrium (i.e. decentralized equilibrium) is a sequence of allocations and prices {A t,c t, C A,t,D p,t,g t,i t,k t,l t,m t,mc t,p t,p Z,t,R t, r k,t,t t,u t, w t,x t, Y t, Z t, η t, Θ t, Π t, Ψ t, Ω t } t= that remain bounded in some neighborhood around the deterministic steady state and satisfy equations (A13)-(A37), given the environmental policy put in place (i.e. no policy, emission cap, intensity target, tax policy), the initial values for D p,t 1, M t, K t and a set of exogenous stochastic processes {ε A,t,ε G,t,ε η,t } t=. 26

27 Table 1: Parametrization Parameters Value Description α 1/3 Technology parameter β.99 Discount factor δ K.25 Depreciation rate of capital γ I 15 Capital adjustment cost φ 1 Inverse of the Frisch elasticity of labor supply θ 6 Price elasticity ξ 3/4 Calvo s price parameter for nominal rigidities A Total factor productivity µ L Disutility of labor ι π 3 Interest rate rule parameter 1 δ M.9979 Pollution decay ϕ.45 Emissions per unit of output φ Abatement cost function coefficient φ Abatement cost function parameter ρ η.8 Persistence of monetary shock σ A.45 Standard deviation of productivity shock σ G.53 Standard deviation of public consumption shock σ η.24 Standard deviation of monetary shock ρ A.95 Persistence of productivity shock ρ G.97 Persistence of public consumption shock ρ η.15 Persistence of monetary shock 27

28 Table 2: Deterministic Steady State of the Main Macrovariables No-Policy Environmental Policy Y C I L M C Z U.1791 p Z.521 C A.15 W elf are W elf are Cost % 28

29 Table 3: Means No policy Emission cap Intensity target Tax policy Y C I L ξ = 3/4 M C Z U p Z C A Y C I L ξ = M C Z U p Z C A Y C I L ξ = 4/5 M C Z U p Z C A

30 Table 4: Standard Deviations No policy Emission cap Intensity target Tax policy σ(x) σ(x)/σ(y) σ(x) σ(x)/σ(y) σ(x) σ(x)/σ(y) σ(x) σ(x)/σ(y) Y C I L ξ = 3/4 M C Z U p Z C A Y C I L ξ = MC Z U p Z C A Y C I L ξ = 4/5 M C Z U p Z C A

31 Table 5: Correlations with Output No policy Emission cap Intensity target Tax policy Y C I L ξ = 3/4 M C Z U p Z C A Y C I L ξ = MC Z U 1. p Z 1. C A Y C I L ξ = 4/5 M C Z U p Z C A

32 Table 6: Welfare No policy Emission cap Intensity target Tax policy mean sd mean sd mean sd mean sd ξ = 3/ ξ = ξ = 4/ Table 7: Optimal Response to Inflation No policy Emission cap Intensity target Tax policy V - steady state V - conditional mean ι π V M - steady state V M - conditional mean ι π

33 Figure 1: Impulse Responses to a Technology Shock Technology Shock no policy emission cap intensity target tax policy Output Consumption 6 Investment Hours.9 Wage

34 Figure 2: Impulse Responses to a Technology Shock.4 Pollution Stock 1.5 Emissions.3.2 no policy emission cap.1 intensity target tax policy Abatement Effort.1 Marginal Cost Permit Price 2 Abatement Cost

35 Figure 3: Impulse Responses to a Public Consumption Shock 1.5 Public Consumption Shock.4 Output 1.3 no policy.5 emission cap intensity target tax policy Consumption Investment Hours.15 Wage

36 Figure 4: Impulse Responses to a Public Consumption Shock 1.5 x 1 3 Pollution Stock.4 Emissions 1 no policy.5 emission cap intensity target tax policy Abatement Effort 5 5 x 1 3 Marginal Cost Permit Price.8 Abatement Cost

37 Figure 5: Impulse Responses to a Monetary Policy Shock 4 x 1 4 Monetary Policy Shock no policy emission cap intensity target tax policy 1 1 Output 2.1 Consumption 5 Investment Hours 2 Wage

38 Figure 6: Impulse Responses to a Monetary Policy Shock 2 x 1 3 Pollution Stock 1 Emissions no policy 2 emission cap intensity target tax policy Abatement Effort 2 Marginal Cost Permit Price 1 Abatement Cost