Taxing Fossil Fuels under Speculative Storage

Transcription

1 Taxing Fossil Fuels under Speculative Storage Semih Tumen Central Bank of the Republic of Turkey Ibrahim Unalmis Central Bank of the Republic of Turkey Deren Unalmis Central Bank of the Republic of Turkey D. Filiz Unsal International Monetary Fund February 20, 2013 Abstract Long-term environmental consequences of taxing fossil fuel usage have been extensively studied in the literature. These taxes may also impose several short-run challenges on macroeconomic policy; however, the nature of these challenges remains unexplored. This paper investigates the mechanisms through which environmental taxes on fossil fuels can affect main macroeconomic variables in the short-run. We concentrate on a particular mechanism: speculative storage. Using a dynamic stochastic general equilibrium model with an explicit storage technology and nominal rigidities, we show that the existence of forwardlooking speculators in the model improves the effectiveness of environmental taxes; but, at the same time, it pushes core goods inflation and real interest rates up, while impeding economic growth. We conclude that, in designing environmental tax policies, the fact that fossil fuels are storable (i.e., they are subject to speculative profit making motives) has to be accounted for. JEL codes: E31; E52; H23; O44. Keywords: Fossil fuels; environmental taxes; speculative storage; DSGE. The views expressed here are of our own and do not necessarily reflect those of the Central Bank of the Republic of Turkey or the International Monetary Fund. All errors are ours. semih.tumen@tcmb.gov.tr. Research and Monetary Policy Department, Central Bank of the Republic of Turkey, Istiklal Cad. No:10, Ulus, Ankara, Turkey. deren.unalmis@tcmb.gov.tr. Research and Monetary Policy Department, Central Bank of the Republic of Turkey, Istiklal Cad. No:10, Ulus, Ankara, Turkey. ibrahim.unalmis@tcmb.gov.tr. Communications and Foreign Relations Department, Central Bank of the Republic of Turkey, Istiklal Cad. No:10, Ulus, Ankara, Turkey. dunsal@imf.org. Research Department, International Monetary Fund, th Stret, N.W. Washington, D.C , USA.

2 1 Introduction This paper formulates and solves a dynamic stochastic general equilibrium (DSGE) model with nominal rigidities, in which the market for fossil fuels is formally modeled and the government implements tax policies to discourage the use of fossil fuels while encouraging renewable energy through subsidies. One distinctive feature of our model, which should perhaps be emphasized in advance, is the existence of a storage technology for fossil fuels. This technology operates through forward-looking speculators who desire to make profits based on the expectations they form about the future movements in fossil fuel prices. Actions of the speculators amplify the fluctuations in the prices of fossil fuels. These amplifications have important reflections on main macroeconomic variables such as inflation and economic growth; thus, they may induce further policy responses by authorities. Based on this mechanism, the storage technology can be thought of as a catalyst that relates movements in fossil fuel prices to macroeconomic policies. Having an explicit storage technology is important, because it is well documented in the literature that speculative demand shocks, which are inherently driven by expectations, have been important in explaining fluctutations in global fossil fuel prices [see, e.g., Alquist and Kilian (2010) and Kilian and Murphy (2013)]. As a result, any policy measure targeted at reducing fossil fuel usage through the cost channel (such as environmental taxes) is expected to trigger a response by speculators and, thus, induce further movements in prices that may be critical for macro policy. Although the literature agrees on the fact that speculative demand is a key forward-looking determinant of fossil fuel prices 1, there is no work in the literature investigating the role of storage motives on the mechanism through which environmental tax policies diffuse into the economy. Our paper is the first attempt in this direction. Our purpose is twofold. First, we want to understand the role of speculative storage on the short-run responses of the main macroeconomic variables to environmental tax policies. To this end, we run our model with and without storage; then, we compare the effects of fossil (2013). 1 See Dvir and Rogoff (2009), Hamilton (2009), Unalmis, Unalmis, and Unsal (2012), and Fattouh, Kilian, and Mahadeva 2

3 fuel taxes on the macroeconomic variables of interest under these two scenarios. Second, we examine the positive versus negative consequences of speculative storage and, then, discuss policy alternatives that would maximize the effectiveness of environmental taxes and minimize the costs. Our research setup is important, because both the climate change problem and the policies suggested to resolve it are, in nature, dynamic and uncertain; therefore, a DGSE model that is consistent with the scientific foundations of the fossil fuel related environmental issues would be an ideal basis to assess the interaction between environmental taxes and the main macroeconomic policy questions of interest. Our main finding is that introducing taxes on fossil fuels would reduce the use of fossil fuels in production and consumption; but, the speculative demand for fossil fuels would surge due to increased real return to speculation. On the one hand, increased speculative demand enhances policy effectiveness, because it is accompanied by a decline in fossil fuel usage; as a consequence, carbon emissions would go down. On the other hand, it leads to distortions in several aggregate variables including inflation, investment, and growth, which are undesirable from the vantage point of macroeconomic policy. Therefore, the main take-away lesson in this paper is that speculation motives should be accounted for in evaluating the potential short-term effects of fossil fuel taxes on macroeconomic aggregates. That taxing fossil fuels under speculative storage may entail both costs and benefits naturally poses the question: how should the central banks re-design monetary policy in a way to minimize the costs while retaining the benefits? We perform several policy experiments to answer this positive question. We conclude that central banks should respond to the secondround effects of the environmental taxes rather than the immediate effects. To be concrete, our policy recommendation is that the monetary policy should respond to core (e.g., nonenergy) inflation rather than responding directly to the CPI inflation. CPI inflation includes the changes in the energy prices and, thus, it jumps siginificantly when environmental taxes are introduced. If the monetary policy responds directly to energy prices, then it may lead to extra volatility in consumption and investment; as a result, welfare may decline. We show that responding to core inflation reduces consumption volatility, limits the negative effects 3

4 taxes on economic growth, and leads to a more moderate cut in capital investment. This is the first paper in the literature arguing the role of speculative storage on the channels through which environmental taxes affect the main aggregate variables. Unalmis, Unalmis, and Unsal (2012) is the most closely related paper in the literature in terms of the modeling principles and the main mechanisms at work. Similar to Unalmis, Unalmis, and Unsal (2012), we introduce fossil fuel speculators into an otherwise standard DSGE model with nominal rigidities. Building on this benchmark framework, we analyze the effect of environmental taxes on the short-run responses of the main macroeconomic variables. There are two main differences between this paper and their work. First, we incorporate renewable energy into the model to capture substitutions away from fossil fuels toward other energy sources as a response to the introduction of taxes on fossil fuel usage. And, second, we endogenize the supply of fossil fuels to be able to capture more realistic responses to increased environmental taxes. This paper is also closely related to the emerging body of literature on the importance of storage in the analysis of the market for fossil fuels. The consensus in this literature is that the standard models cannot explain the surge in fossil fuel prices in , unless speculative motives are appropriately accounted for [see Fattouh, Kilian, and Mahadeva (2013) for a survey]. The main argument is that fossil fuel futures have been financialized after the late 1990s and speculation has become a major force determining the prices of fossil fuels. Accordingly, the fossil fuel speculator is defined in the literature as anyone buying crude oil not for current consumption, but for future use is a speculator from an economic point of view [Alquist and Kilian (2010)]. Based on this view, Unalmis, Unalmis, and Unsal (2012) study the role of storage in a DSGE framework to show that accounting for storage improves the fit of the model to the price data. Our paper is related to this basic view in that we highlight the role of storage in evaluating the effectiveness of environmental tax policy. 2 2 There is a vast literature investigating the effects of environmental taxes on the workings of the market for fossil fuels. In this broad area, there is a particular strand focusing on the short-run macroeconomic impacts of environmental taxes. For example, Ganelli and Tervala (2011) construct a two-country New Keynesian model to analyze the effects of country-specific environmental tax policies on the macroeconomic variables in both countries. Golosov, Hassler, Krusell, and Tsyvinski (2011) calculate the optimal taxes in the global economy to maximize welfare while minimizing carbon emissions in general equilibrium. 3 Sinn (2008) develops a simple dynamic model to assess the supply-side responses to fossil fuel taxes. de Miguel and Manzano (2011) assess the welfare effects of green tax reforms. That environmental taxes may distort macroeconomic aggregates in the short run is a 4

5 The plan of the paper is as follows. Section 2 introduces the model in detail. Section 3 presents the results along with a detailed discussion of the calibration, impulse responses, and policy implications. Section 4 concludes. 2 Model Our model is an extension on Unalmis, Unalmis, and Unsal (2012) (UUU hereafter). We enrich their model by incorporating renewable energy, which is endogenously produced. Besides, in contrast to UUU, where fossil fuel production is assumed to follow an exogenous process, fossil fuel production is partly endogenous in our model. We include a more detailed treatment of fiscal policy, where the government is assumed to promote the use of renewable energy instead of fossil fuels through its tax policy. The government is no longer assumed to have a balanced budget, since it is allowed for the goverment to sell bonds and borrow from the future. The model economy is populated by households, firms producing core goods, firms producing renewable energy, firms producing fossil fuel, a government, a monetary authority and fossil fuel storers. Households receive utility from consumption, provide labor to the firms producing core goods, hold the capital stock and rent it to all three types of firms in a perfectly competitive rental market. The households own all the firms in the economy, and therefore receive profits from these firms. Energy is consumed directly and also used as an input in production. The total energy used in production or consumption are aggregates of renewable energy and fossil fuel. As stated above, there are three types of production firms. The first type of firms produce a differentiated core consumption good using capital, labor, and energy as inputs. These firms set prices in a staggered fashion, and hence prices are sticky. The second and third types of firms produce renewable energy and fossil fuel, respectively, using only capital. Households consume the core consumption goods and energy. Following Backus and Crucini (2000), fossil fuel production is partially exogenous. 4 common conjecture in this literature. However, the role that speculative storage in amplifying and deepening these distrotions is unknown in this literature. Our paper contributes this literature by introducing speculative storage as a viable mechanism that amplifies the responses of the main macroeconomic aggregates to environmental taxes. 4 Backus and Crucini (2000) model fossil fuel supply partially endogenously, in a neoclassical setup, by assuming that OPEC supply is exogenous. See also Nakov and Pescatori (2010), who also distinguish between OPEC and non-opec supply, but supply is determined endogenously in both. 5

6 In the model, one major difference between renewable energy and fossil fuel is that fossil fuel is storable. The activity of the risk-neutral, profit-maximizing, competitive fossil fuel storer firms (speculators) is to carry forward fossil fuel as above-ground fossil fuel inventories from one period to the next. They buy fossil fuel from the producers and optimally decide how much to sell or store through an intertemporal arbitrage condition. Conditional on the current information, whenever expected appreciation (depreciation) in the price of fossil fuel exceeds the marginal cost of storage, speculators increase (decrease) their stockholding until the equilibrium in the fossil fuel market is restored. In what follows, small letters denote percentage deviations of the respective variables from their steady-state levels. We briefly sketch the model here, while the details of the model and all the log-linearized equations are provided in the Appendix. 2.1 Households The economy is populated by a continuum of households indexed by j [0, 1]. A representative household is infinitely-lived and seeks to maximize the expected present value of the period utility given by: E 0 t=0 β t ( (Ct (j) H t ) 1 σ 1 σ N ) t(j) 1+ϕ, (2.1) 1 + ϕ where H t = hc t 1 captures external habit formation for the optimizing household with h [0, 1], 0 < β < 1 is the subjective discount factor, σ > 0 is the inverse of the intertemporal elasticity of substitution of consumption, ϕ > 0 is the inverse of the intertemporal elasticity of hours, C t (j) denotes consumption and N t (j) denotes hours of work. Note that the habit stock refers to the aggregate habit consumption rather than the individual habit consumption. Aggregate consumption is: ( 1 C t = 0 ) ε C t (j) ε 1 ε 1 ε dj, (2.2) 6

7 where ε denotes the elasticity of substitution between varieties. C t (j) is a CES aggregate of energy consumption E C,t (j) and non-energy core consumption Z t (j): C t (j) = [ (1 ω ec ) 1 ρc Z t (j) ρc 1 ρc + ω 1 ρc ec E c,t (j) ρc 1 ρc ] ρc/(ρ c 1), (2.3) where ρ c is the intratemporal elasticity of substitution between energy and core consumption and 0 < ω ec < 1 indicates the expenditure share of the energy in the consumption basket of households. E c,t (j) is a CES aggregate of renewable-energy consumption RE c,t (j) and fossil fuel consumption O c,t (j): E c,t (j) = [ (1 ω oc ) 1 ρe RE c,t (j) ρe 1 ρe + ω 1 ρe oc O c,t (j) ρe 1 ρe ] ρe/(ρ e 1), (2.4) where ρ e is the intratemporal elasticity of substitution between renewable energy and fossil fuel consumption and 0 < ω oc < 1 indicates the expenditure share of the fossil fuel in the energy basket of households. Let P e,t and P z,t denote the prices of energy and non-energy consumption goods, respectively. The consumer price index (CPI) P t can be written as: P t = [ (1 ω ec )P 1 ρc z,t ] + ω ec P 1 ρc 1/(1 ρc) e,t. (2.5) Let P re,t and P o,t denote the prices of renewable energy and fossil fuel, s re,c,t and τ o,c,t denote the percentage subsidy on P re,t and percentage tax imposed on P o,t, respectively. Hence, the energy price index P e,t can be written as: P e,t = [ (1 ω oc ) { (1 + s re,c,t ) 1 P re,t } 1 ρe + ωoc {(1 + τ o,c,t )P o,t } 1 ρe ] 1/(1 ρe). (2.6) Demand functions for renewable energy consumption, fossil fuel consumption, and core consumption are given by: [ RE c,t (j) = (1 ω oc ) (1 + s re,c,t ) 1 P ] ρe re,t E c,t(j), (2.7) P e,t 7

8 [ O c,t (j) = ω oc (1 + τ o,c,t ) P ] ρe o,t E c,t(j), (2.8) P e,t and Z t (j) = (1 ω ec ) [ Pz,t P t ] ρc C t (j), (2.9) respectively. The household enters period t with portfolio D t (j) that pays out one unit of currency in a particular state, earns wage income by hiring labor, earns rental income from hiring capital, and receives profits (e.g., dividends) Π t (j) from monopolistic firms that produce core goods. K 1,t (j), K 2,t (j), and K 3,t (j) are the beginning of t capital stocks; and R K 1 t (j), R K 2 t (j), and R K 3 t (j) represent rate of return on capital used in core goods production, renewable energy production and fossil fuel production respectively. W t (j) is the nominal wage. In each period, the household purchases consumption goods C t (j) and investment goods I 1,t (j), I 2,t (j) and I 3,t (j). We assume that investment goods are composed of only non-fossil-fuel goods. D t+1 (j) is the expected nominal pay-off in period t + 1 of the portfolio held at the end of period t, including the shares in firms. Hence, the representative household s budget constraint in period t is: P t C t (j) + P z,t I 1,t (j) + P z,t I 2,t (j) + P z,t I 3,t (j) + Rt 1 D t+1 (j) D t (j) + W t N t (j) + R K 1 t K 1,t (j) + R K 2 t K 2,t (j) + R K 3 t K 3,t (j) + Π t (j) (2.10) and the capital accumulation equations are: ( ) Iι,t (j) K ι,t+1 (j) = (1 δ)k ι,t (j) + Φ K ι,t (j), (2.11) K ι,t (j) where ι = 1, 2, 3. ( ) In Equation (2.11), δ is the depreciation rate, and the term Φ It(j) K t(j) K t (j) captures capital adjustment costs where we assume that the steady state values of Φ, its first derivative and 8

9 its second derivative are Φ ss = δ, Φ ss = 1, Φ ss = ξ < 0, respectively, with δξ = 1. The representative household, therefore, maximizes the utility (2.1) subject to (2.10) and (2.11). Under the assumption of complete asset markets, households entertain perfect risk-sharing, and consumption is equal across households. Therefore, there is no need for index j. R t is the risk-free nominal interest rate. The equilibrium conditions for households are given by: [ (Ct+1 ) σ H t+1 P t βe t C t H t P t+1 ] = 1 R t, (2.12) and (C t H t ) σ N ϕ t = W t P t, (2.13) { (Ct+1 ) σ H t+1 P ( ) } t P z,t Λ t = βe t R Kι ι,t+1 + P z,t+1 Λ ι,t+1 Φι, (2.14) C t H t P t+1 where Φ ( ) ( ) ι = (1 δ) + Φ Iι,t+1 ι K ι,t+1 Φ Iι,t+1 Iι,t+1 ι K ι,t+1 K ι,t+1 prices of capitals. and Λ ι,t = 1/Φ ι ( ) Iι,t+1 K ι,t+1 is the shadow 2.2 Firms Producing Core Goods There is a continuum of monopolistically competitive firms which produce a differentiated core (non-energy) good indexed by i [0, 1] with identical production functions: [ ] Y z,t (i) = A 1t (1 ω ey ) 1 1 ρy/(ρy 1) ρy Vt (i) (ρy 1)/ρy ρy + ωey E y,t (i) (ρy 1)/ρy, (2.15) where O y,t (i) is the amount of fossil fuel used in production by firm i, ρ y is the elasticity of substitution between fossil fuel and value added inputs, 0 < ω ey < 1 indicates the share of energy in production and A 1t represents a stationary total factor productivity shock in the goods sector that is common to all firms. Each producer utilizes labor and capital to produce 9

10 a value added input V t (i) which is characterized in CES form: V t (i) = [(1 ω ny ) 1 ρv K 1,t (i) (ρv 1)/ρv + ω ny 1 ρv (N t (i)) (ρv 1)/ρv ] ρv/(ρ v 1), (2.16) where ρ v is the elasticity of substitution between capital and labor inputs, 0 < ω ny < 1 indicates the share of labor in production. The energy input E y,t (i) is produced by using renewable energy and fossil fuel, which is characterized in CES form: E y,t (i) = [ ] ρe/(ρe 1) (1 ω oy ) 1 ρe (A 2t RE y,t (i)) (ρe 1)/ρe + ω 1 ρe oy (A 3t O y,t (i)) (ρe 1)/ρe, (2.17) where ρ e is the elasticity of substitution between renewable energy and fossil fuel, 0 < ω oy < 1 indicates the share of fossil fuel in production. Assuming that firms take the price of each input as given, cost minimization of the firm implies: W t N t (i) 1/ρv ω 1/ρv ny = RK 1 t K 1,t (i) 1/ρv (1 ω ny ) 1/ρv and (1 + τ o,y,t )P o,t O y,t (i) 1/ρe ω oy 1/ρ ea (ρ e 1)/ρ e 2t = (1 + s re,y,t) 1 P re,t RE y,t (i) 1/ρe, (1 ω oy ) 1/ρe A (ρe 1)/ρe 3t which hold for each firm i. P re,t and P o,t the price of renewable energy and fossil fuel are in fact determined endogenously in our model, as will be explored later. The nominal marginal cost of production is constant and the same across all firms, given by: where MCt n = 1 [ (1 ω ey )C 1 ρy v,t A 1t ] 1/(1 ρy) + ω ey C 1 ρy e,t, (2.18) ( C v,t = (1 ω ny ) ( R K 1 t ) 1 ρv + ωny (W t ) 1 ρv ) 1 1 ρv (2.19) 10

11 and ( ( ) (1 + sre,y,t ) 1 1 ρe ( ) ) 1 1 ρe P re,t (1 + 1 ρe τo,y,t )P o,t C e,t = (1 ω oy ) + ω oy. (2.20) A 2t A 3t We assume that core goods producing firms set prices according to Calvo (1983) framework, in which only a randomly selected fraction (1 θ) of the firms can adjust their prices optimally in each period. We also assume a partial indexation scheme where ς captures the degree of inflation indexation in the economy. Hence, firm s optimal price setting strategy implies the following marginal cost-based (log-linearized) Phillips curve: π z,t = β 1 + βς E t {π z,t+1 } + ς 1 + βς π z,t 1 + (1 θ)(1 βθ) mc t, (2.21) θ(1 + βς) where π z,t = p z,t p z,t 1 is the non-fossil-fuel CPI inflation between t 1 and t. The CPI inflation (π t = p t p t 1 ) is given by: π t = (1 ω ec )π z,t + ω ec π e,t, (2.22) where π e,t = p e,t p e,t 1 is the energy price inflation. 2.3 Firms Producing Renewable Energy and Fossil Fuel There are two types of competitive firms in the energy market, which produce either renewable energy or fossil fuel, with identical production functions. Fossil fuel is partially endogenously produced and the endogenous fossil fuel production utilizes capital in a linear production function: O endo s,t = A 4t K 2,t, (2.23) 11

12 where A 4t represents a stationary capital efficiency shock. The renewable energy is produced using a similar production function: RE s,t = A 5t K 3,t (2.24) where A 5t represents a stationary capital efficiency shock in renewable energy production. The energy price inflation is given by: { π t = (1 ω oc ) π re,t s } { re,c s re,c,t + ω oc π o,t s re,c τ } o,c τ o,c,t, (2.25) 1 + τ o,c where π re,t = p re,t p re,t 1 is the renewable energy inflation and π o,t = p o,t p o,t 1 is the fossil fuel price inflation. 2.4 Monetary Policy The monetary policy reaction is assumed to follow a simple Taylor rule: r t = φ r r t 1 + (1 φ r )φ π π t + (1 φ r )φ y y z,t, (2.26) where φ r [0, 1] is the interest rate smoothing parameter, φ π and φ y denote the monetary policy responses to consumer price inflation and output. 2.5 Fiscal Policy The government has a balanced budget: τ o,y,t P o,t O y,t +τ o,c,t P o,t O c,t = G t + S RE,y,t P RE,t RE y,t + S RE,c,t P RE,t RE c,t, (2.27) where τ o,y,t is tax on fossil fuel consumption of producers, τ o,c,t is tax on fossil fuel consumption of consumers, S RE,y,t and S RE,c,t are subsidies for each unit of renewable energy consumption paid by the government to producers and consumers respectively. G t denotes government 12

13 spending. We assume that τ o,y,t, τ o,c,t, S RE,y,t and S RE,c,t follow AR(1) processes τ o,y,t = ρ o,y τ o,y,t 1 + ε o,y,t, (2.28) τ o,c,t = ρ o,c τ o,c,t 1 + ε o,c,t, (2.29) S RE,y,t = ρ RE,y S RE,y,t 1 + ε RE,y,t, (2.30) and S RE,c,t = ρ RE,c S RE,c,t 1 + ε RE,c,t, (2.31) where ε o,y,t, ε o,c,t, ε RE,y,t, ε RE,c,t are i.i.d. tax shocks with variances σ 2 ε o,y,t, σ 2 ε o,c,t, σ 2 ε RE,y,t, σ 2 ε RE,c,t, respectively. 2.6 Goods Market Equilibrium The equilibrium condition in the goods market requires that the production of core goods satisfies: Y z,t (i) = G t (i) + I 1,t (i) + I 2,t (i) + I 3,t (i) + Z t (i). (2.32) 2.7 Storage and Fossil Fuel Market Equilibrium Fossil Fuel Storage Fossil fuel storage takes the form of holding above-ground fossil fuel inventories. There is a continuum of competitive fossil fuel storers, competitive speculators, indexed by l [0, 1] who are able to buy and sell on the spot market and are able to store fossil fuel. In line with the literature, we assume that there are no barriers to enter to the storage sector and storers are risk neutral. They form rational expectations about the returns to their activities. The profits earned by a representative storer l from storing S t (l) is the difference between revenue in period t + 1 and the cost of purchasing S t (l) in the spot market in period t while 13

14 covering the storage costs. Fossil fuel storers seek to maximize their expected profit which is: ae t (P o,t+1 )S t (l) R t P o,t S t (l)(1 + Υ(S t (l))), (2.33) where Υ(S t (l)) = κ + Ψ 2 S t(l) is the (physical) cost of storing one unit of fossil fuel with κ < 0 (reflecting convenience yield) and Ψ > 0 (where the cost is increasing with the amount of fossil fuel). 5 We denote (1 a) as the waste, where a [0, 1]. As each storer shares the same rational expectations with other storers, there is no need for storer specific index l. In line with the existing literature on commodity storage, there is a non-negativity constraint on aggregate storage; S t 0 it is impossible to borrow stocks from the future. 6 For this price-taker storer, the F.O.C. with respect to S t, given the constraint, yields: ae t [P o,t+1 ] = R t P o,t (1 + κ + ΨS t ). (2.34) Equation (2.34) is the decision rule for competitive storers: profit maximizing competitive storage, if positive, will set the expected marginal revenue from storage equal to the marginal cost. The log-linearized version of the storage demand equation is s t = Θ(E t { p o,t+1 } p o,t (r t π t+1 )) + sd t, (2.35) where Θ = aβ ΨS > 0, and p o,t = p o,t p t is the real price of fossil fuel. On the right hand side of Equation (2.35), we add an exogenous storage demand (sd t ), in order to capture the exogenous disturbances to fossil fuel stocks. The storage demand shock is assumed to follow a stationary stochastic process. According to Equation (2.35), storage demand is driven by the expected real price of fossil fuel, the current real price of fossil fuel, the real interest rate and an exogenous storage demand. 5 The existence of convenience yield is a common assumption in commodity storage literature. The non-exhaustive list includes Brennan (1991), Fama and French (1988), and Gibson and Schwartz (1990). More recently, Alquist and Kilian (2010) also adopt this modeling device. 6 The level of storage is always positive in our framework as the steady state level is positive and sufficiently high and deviations of storage from its steady state are sufficiently small (within the neighborhood of the steady state). Incorporating non-linearities associated with storage technology is beyond the scope of this paper. Although conceptually appealing, this would make solution and estimation of the model considerably more complicated without providing any additional insight for the issues we focus here. 14

15 2.7.2 Energy Market Equilibria We assume that fossil fuel supply is partially exogenous (O exo s,t ), which is subject to shocks defined by a stationary AR(1) process. 7 Given storage, the total quantity demanded by households and firms is equal to the sum of exogenous and endogenous production, plus old inventories net of depreciation, minus new inventories: O c,t + O y,t = O exo s,t + O endo s,t + as t 1 S t. (2.36) For the renewable energy, the total quantity demanded by households and firms is equal to the production. RE c,t + RE y,t = RE s,t. (2.37) 3 Results and Discussion In this section, we perform a quantitative assessment of the model we outline in Section 2. We investigate the channels through which fossil fuel tax shocks are transmitted within the country and how the presence of fossil fuel storage affects the impulse responses. We seperately focus on a positive fossil fuel tax shock on consumers, on producers, and on both. We start with our calibration and, then, discuss the impulse responses followed by a subsection on policy implications. 3.1 Calibration We calibrate the model with reasonable values mostly as they are set in the literature [see Table (1)]. Time is measured in quarters. We set β = 0.99, implying a riskless annual return of approximately 4% at the steady state. This numbers are consistent with Nordhaus s critique [Nordhaus and Boyer (2000), Nordhaus (2007)] of the Stern (2007) report. The inverse of the elasticity of intertemporal substitution is taken as σ = 1, which corresponds to log utility. The habit persistency parameter is 0.2. The inverse of the elasticity of labor supply ϕ is set 7 For the sake of simplicity, we assume that the profits from selling and storing fossil fuel are distributed evenly among the consumers and are included in the lump-sum transfers in the budget constraints of households. 15

16 to 3 since it is assumed that 1/3 of the time is spent on working. The share of capital in production (η 1 ) is set to 0.32 and the share of labor in the production (η 2 ) is taken as 0.63 so that the share of fossil fuel in the production (1 η 1 η 2 ) is The depreciation rate (δ) is set to The Calvo probability (θ) is assumed to be 0.75, which implies an average period of one year between price adjustments. We use the original Taylor estimates and set φ π = 1.5 and φ y = 0.5. The persistency parameter of the interest rate in the monetary policy reaction function is set to φ r = 0.5. The persistency of the tax shocks are set to 0.9. Following Gali, Lopez-Salido, and Valles (2007), we set the share of government purchases in GDP as Following the Energy Information Agency s (EIA) 2009 Annual Energy Report EIA (2009), we set expenditure share of fossil fuel in the energy basket of firms and households as 0.85 and 0.75, respectively. Since we do not have adequate storage data for fossil fuel other than the oil, we use EIA s oil data to calculate the steady state fossil fuel storage over fossil fuel demand ratio. We set the convenience yield (k) as 0.03 which is in line with the literature. Substitution between consumption and energy is set to be 0.4 as in Harrison, Thomas, and de Weymarn (2011). van der Werf (2008) estimates the elasticity of substitution between fossil fuel and value added input, and the elasticity of substitution between capital and labor as and for the U.S. economy, respectively. Intertemporal elasticity of substitution between renewable energy and fossil fuel is set 0.5 following Gerlagh and van der Zwaan (2003). The expenditure share of energy in the production of firms and consumption basket of households are set to be 0.1 and 0.13, respectively, as in Huntington (1991). For steady state tax rate, we take the average U.S. tax rate on fossil fuel that is Impulse Responses Taxing households. Figure (1) documents the impulse responses of the model under the scenario that only the household-level consumption of fossil fuels is taxed. The solid lines show the case in which there is no speculative fossil fuel storers in the model. In such a scenario a 1 percent rise in the taxes on fussil fuel consumption of households reduces the real price and households consumption of fossil fuel. On the other hand, fossil fuel consumption in 16

17 β = 0.99 σ = 1 h = 0.7 ϕ = 3 δ = ς = 0.5 ω ny = 0.66 θ = 0.75 φ π = 1.5 φ y = 0.5 φ r = 0.5 ω oy = 0.4 ω oc = 0.2 G y = 0.18 ω ey = 0.1 ω ec = 0.13 ρ c = 0.4 ρ y = 0.54 ρ w = 0.32 ρ e = 0.51 S/O d = 0.1 k = 0.03 Subjective discount factor. Inverse of the intertemporal elasticity of substitution. Level of habit persistence Frisch elasticity of labor supply. Depreciation rate. Inflation indexation parameter. Share of labor in production. Calvo parameter. Coefficient of inflation in the policy rule. Coefficient of output gap in the policy rule. Coefficient of lagged interest rate in the policy rule. Expenditure share of fossil fuels in the energy basket of firms. Expenditure share of fossil fuels in the energy basket of households. Share of government spending. Expenditure share of energy in the production basket of firms. Expenditure share of energy in the consumption basket of households. Elasticity of substitution between consumption and energy. Elasticity of substitution between fossil fuel and value added input. Elasticity of substitution between capital and labor. Elasticity of substitution between renewable energy and fossil fuel. The steady state share of fossil fuel storage in total fossil fuel demand. Convenience yield in fossil fuel storage. Table 1: Parameter values and definitions. production increases due to cost advantage. Because of higher taxes on fossil fuel and higher subsidies on renewable energy, households substitute renewable energy with fossil fuel, hence, households consumption of renewable energy increases. Rising renewable energy demand stimulates the investment in this sector, while investment in fossil fuel sector declines. GDP falls initially due to lower capital investments and consumption, but then rebounds when capital investments increase. Marginal cost of firms declines as the real price of fossil fuel goes down. However, rising renewable energy prices increases the real cost of energy basket. Therefore, CPI increases, which causes a rise in interest rates. Responses of variables when there are fossil fuel storers in the model are shown in dashed lines. Fossil fuel storers response to a rise in taxes on household s fossil fuel consumption is to increase their fossil fuel holdings. This creates additional demand for fossil fuels, therefore, the fall in fossil fuel prices is relatively limited in this case. However, fossil fuel usage drops more, because income declines more with the storage facility. As a result, fossil fuel consumption decreases considerably more when there is storage facility. In other words, speculative fossil fuel storers improve the effectiveness of fossile fuel taxation policies on the fossil fuel demand. 17

18 It should also be highlighted that models with no storage facility are neglecting the general equilibrium effects of fossil fuel taxation policies. Taxing firms. Impulse responses are reported in Figure (2). When there are no speculative fossil fuel storers, a 1 percent increase in the fossil fuel taxes reduces the fossil fuel usage in production and increases the fossil fuel usage in consumption. The real price of fossil fuel declines almost in the same amount with the first case. However, contrary to the first case, the GDP increases initially and then declines sharply and stays below the steady-state level. As a result, total fossil fuel consumption decreases more than the first case. Including speculative storers to the model leads to a lower decline in real price of fossil fuel as in the first case. Fossil fuel consumption of consumers increases less but fossil fuel usage of producers declines more due to much higher contraction in GDP. All in all, the fall in total fossil fuel consumption almost doubles compared to the first case. To put it differently, taxing producers is more effective for reducing fossil fuel consumption. Taxing both households and firms. Impulse responses are reported in Figure (3). Without fossil fuel storage, a 1 percent increase in the fossil fuel taxes reduces the real price of fossil fuel by almost 1 percent. However, the increase in renewable energy prices balances this increase, hence, the real cost of energy basket declines mildly. Therefore, effects of the tax increase on the price level and on the interest rate are very limited. Fossil fuel usage in production increases initially, then declines below the steady-state level. Positive effects of spending on subsidies outweigh the negative effects of the drop in consumption and investment, hence, GDP increases. In consequence, the effect of the tax increase on total fossile fuel consumption is very small. Existence of speculative fossil fuel storers amplifies the effects of the tax increase on the real price of energy basket. Although the real price of fossile fuel declines less, real price of renewable energy rises so much that the cost of energy basket goes up. In this case, fossil fuel consumption of households and firms falls almost the same amount. Consequently, the decline in the fossil fuel consumption is the highest among the scenarios. Having speculative storers leads to higher marginal cost for firms hence the CPI. As a result, interest rate rises much more. Higher interest rates discourage consumption and investment, 18

19 Targeting Core Inflation Targeting CPI Storage No Storage Storage No Storage Consumption Output Investment Table 2: Policy experiments. This table reports the standard deviations calculated from the impulse response series of consumption, output, and investment. The main idea is to compare the standard deviations obtained with and without speculators in the model. In the first two columns, standard deviations are calculated under the assumption that the central bank targets core (i.e., non-energy) inflation. In the last two, they are calculated under the assumption that the CPI inflation is targeted. hence GDP declines contrary to the no storage case Policy Analysis One of the short-term challenges that policy makers face regarding the implementation of environmental policies is the risk, associated with this policies, to cause extra volatility in output, inflation, and investments. We perform an experiment assuming that the central bank uses core inflation instead of CPI in its policy rule, while taxes on fossil fuel consumption of consumers and producers are increased by 1 percent. The responses of variables are shown in Figure (4) and volatility measures (standard devations) are shown in Table (2). The results clearly show that targeting core inflation reduces the volatility of consumption and investment, but not the output when there is storage facility. If there are no speculative fossil fuel storers, the results would be opposite. In other words, targeting CPI minimizes the volatility of output. These results also show the importance of including storage facility in a model that seeks to evaluate the effects of tax policy on fossil fuels. 4 Concluding Remarks There is a burgeoning literature on the design and implementation of environmental tax policies. We contribute this literature by performing a quantitative assessment of the potential short-term effects of environmental taxes on main macroeconomic variables. In particular, we highlight the role that speculators would play in the diffusion of tax policy into macroeconomic aggregates. Accounting for speculative storage motives is important, because financialization of fossil fuel futures and the associated profit-making motives can have an enormous impact 19

20 on the process determining the fossil fuel prices. We show that incorporating speculative storage into a DSGE model produces results that feature amplified short-term macroeconomic responses to environmental tax policies. Specifically, we show that the existence of forward-looking speculators in the model improves the effectiveness of environmental taxes; but, at the same time, it pushes core goods inflation and real interest rates up, while impeding economic growth. We conclude that, in designing evironmental tax policies, the fact that fossil fuels are storable (i.e., they are subject to speculative profit making motives) has to be accounted for. It may be necessary to design supplementary policies that would reduce the welfare costs of environmental taxes, while retaining the benefits. 20

21 References Alquist, R. and L. Kilian (2010). What do we learn from the price of crude oil futures? Journal of Applied Econometrics 25, Backus, D. K. and M. J. Crucini (2000). Oil prices and the terms of trade. Journal of International Economics 50, Brennan, M. J. (1991). The price of convenience and the valuation of commodity contingent claims. In D. Land and B. Oksendal (Eds.), Stochastic Models and Options Values, pp New York, NY: Elsevier. Calvo, G. (1983). Staggered prices in a utility-maximizing framework. Journal of Monetary Economics 12, de Miguel, C. and B. Manzano (2011). Gradual green tax reforms. Energy Economics 33, S50 S58. Dvir, E. and K. S. Rogoff (2009). Three epochs of oil. NBER Working Paper # EIA (2009). Annual Energy Report. Washington, DC: Energy Information Administration. Fama, E. F. and K. R. French (1988). Business cycles and the behavior of metals prices. Journal of Political Economy 43, Fattouh, B., L. Kilian, and L. Mahadeva (2013). The role of speculation in oil markets: What have we learned so far? Forthcoming, Energy Journal. Gali, J., J. D. Lopez-Salido, and J. Valles (2007). Understanding the effects of government spending on consumption. Journal of the European Economic Assocation 5, Ganelli, G. and J. Tervala (2011). International transmission of environmental policy: A New Keynesian perspective. Ecological Economics 70, Gerlagh, R. and B. van der Zwaan (2003). Gross world product and consumption in a global warming model with endogenous technological change. Resource and Energy Economics 25,

22 Gibson, R. and E. S. Schwartz (1990). Stochastic convenience yield and the pricing of oil contingent claims. Journal of Finance 45, Golosov, M., J. Hassler, P. Krusell, and A. Tsyvinski (2011). Optimal taxes on fossil fuel in general equilibrium. Unpublished manuscript, Yale University. Hamilton, J. (2009). Causes and consequences of the oil shock of Brookings Papers on Economic Activity 40, Harrison, R., R. Thomas, and I. de Weymarn (2011). The impact of permanent energy price shocks on the UK economy. Bank of England Working Paper #433. Huntington, H. G. (1991). Substitution between activities with different energy intensities. Resources and Energy 13, Kilian, L. and D. Murphy (2013). The role of inventories and speculative trading in the global market for crude oil. Forthcoming, Journal of Applied Econometrics. Nakov, A. A. and A. Pescatori (2010). Oil and the great moderation. Economic Journal 120, Nordhaus, W. D. (2007). A review of the Stern Review on the Economics of Climate Change. Journal of Economic Literature 45, Nordhaus, W. D. and J. Boyer (2000). Warming the World: Economic Models of Global Warming. Cambridge, MA: MIT Press. Sinclair, P. J. (1990). On the optimal trend of fossil-fuel taxation. Oxford Economic Papers 46, Sinn, H.-W. (2008). Public policies against global warming: A supply side approach. International Tax and Public Finance 15, Stern, N. (2007). The Economics of Climate Change: The Stern Review. Cambridge, UK: Cambridge University Press. 22

23 Unalmis, D., I. Unalmis, and D. F. Unsal (2012). On oil price shocks: The role of storage. IMF Economic Review 60, van der Werf, E. (2008). Production functions for climate policy modelling: An emprical analysis. Energy Economics 30,

24 Figure 1: Impulse responses to tax shocks on consumption. 24

25 Figure 2: Impulse responses to tax shocks on production. 25

26 Figure 3: Impulse responses to tax shocks on both production and consumption. 26

27 Figure 4: Impulse responses to tax shocks on both production and consumption under core inflation targeting. 27