Luca Taschini. King s College London London, November 23, 2010

Transcription

1 of Pollution King s College London London, November 23, / 27

2 Theory of externalities: Problems & solutions Problem: The problem of (air) pollution and the associated market failure had long been a part of the microeconomic theory. Economists saw pollution as the consequence of an absence of prices for certain scarce environmental resources (Baumol and Oates [1988]). : Economists prescribed the introduction of surrogate prices in the form of unit taxes or tradable permits in order to induce people to economize on the use of these resources. Motivation: The basic rationale behind market-based instruments is that a high price level for emission permits should attract those regulated companies with lower marginal costs for pollution abatement in order to exploit consequent price differences. Result: An effective implementation of market-based instruments should modify the operational decisions of regulated companies, ultimately generating investments in process improvements or adoption of low-emitting technologies. of Pollution 2 / 27

3 Tradable permits: The cap-&-trade scheme The Regulator: Allocates permits (for allocation criteria see Aihman and Zetterberg [2005]); Set the non-compliance penalty and enforce the verification and monitoring procedures (enforcement structure). Regulated firms: Attempt to achieve compliance by abating emission (adoption of low-emitting technology, modification of the production process, technology innovation); trading emission permits (spot and futures contracts). Examples: There are few examples in operation The Acid Rain Program in the U.S. (sets a national cap on SO 2); The European and UK Emission Trading Schemes (EU ETS and UK ETS set caps on CO 2); of Pollution 3 / 27

4 CO 2 permits and spatial flexibility Spatial trading: Each agent can reduce its emissions below the allocated number of allowances, transferring the unused permits to other agents. Or it can decide not to abate its emissions and purchase permits to cover the emissions above its allocation of allowances. Consequence: A high price level of emission permits brings affected companies with lower marginal abatement costs to exploit the consequent price difference. of Pollution 4 / 27

5 CO 2 permits and temporal flexibility Temporal trading: Relying on banking, units can save their unused allowances for using in the future. Conversely, the one-year borrowing gives the opportunity to cover temporarily a permit shortage. Consequence: This translates into a larger flexibility in the control of investment timing. of Pollution 5 / 27

6 Deterministic price of allowances Since Montgomery [1972], research on the theoretical price dynamics of emission permits has developed substantially. Most of the research has been concentrating on the substitution principle between emission permits and abatement technology. In a deterministic setup, Tietenberg [1985], Cronshaw and Kruse [1993], and Rubin [1996] show that S t = MC t t [0, T ] where S t is the permit price at time t, MC t is the marginal cost to reduce one ton of CO 2 at time t, and T is the end of the regulated period. In the medium-run fuel-switching is reckoned to be the cheapest abatement alternative with the highest probability to be implemented under the European Union ETS. Fuel-switching indicates the possibility for CCGT (Combined Cycle Gas Turbine) plants to switch the input-factors, i.e. to switch from coal to gas, and vice-versa. of Pollution 6 / 27

7 McKinsey abatement cost curve of Pollution 7 / 27

8 : Abatement vs. permits In a pollution-constrained economy, each regulated firm faces a basic choice from three main abatement alternatives: 1. trade marketable permits (short-term abatement option); 2. modify the production process which generates the emissions as a by- product (medium-term abatement option); 3. change the production technology (long-term abatement option). Typically, medium and long term abatement measures are perceived as: expensive and irreversible commitments lasting decades; not viable investments because not sufficiently flexible. of Pollution SO 2 example: Purchase of allowances can be adapted to changing conditions whereas a scrubber might be under-utilized if demand falls. Also, the cost of a scrubber might be excessive after a fall in the permit price. 8 / 27

9 (Non) perfect substitute Intuitively, trading permits and abatement investments are equivalent measures exclusively when both lead to equal emissions reduction for the same total costs at the same time. Chao and Wilson [1993] and Zhao [2003] framed their studies of tradable permits calling into question the principle of perfect substitution between permits and (long-term and irreversible) abatement measures. They argue that the price of tradable permits must include a premium that recognizes the value of the permit flexibility when compared to (irreversible and instantaneous) abatement alternative. Contribution 1. We should account for those situations where a firm can reverse the investment decision (McDonald and Siegel [1986] and Brekke and Øksendal [1994]). 2. We should account for those realistic situations where a firm faces physical or technical constraints that allow the implementation of economic decisions only after a given time-interval. of Pollution 9 / 27

10 Taschini (2009) in a nutshell We propose an infinite-time horizon model where a risk-neutral firm is subject to environmental regulations from time zero up to T. The firm maximizes its expected discounted pay-off flow and constantly emits α units of pollution at each instant. At each time (t, 0 t T ), the firm can either undertake a modification of the production process or purchase allowances at time T for a price P t. This model can support regulated companies and policy makers in identifying at which permit price level it would be optimal to undertake a (ir)reversible (instantaneous or delayed) abatement investment. Accounting for reversible and delayed abatement measures, the (firm-specific) value of flexibility implicitly embedded in the price of tradable permits is quantified, extending the results of Chao and Wilson [1993]. of Pollution 10 / 27

11 Allowance price The allowance price P t is the value which makes the firm indifferent between the two choices: V t e ρ(t t) [α(t t)] P t {z } Unmodified profits - permit purchase = V m t {z} Modified profits If the firm undertakes a costly modification of the production process at time t (Vt m ), then an equivalent (substitute) reduction of emission by trading permits must corresponds to a purchase at time T of α (T t) permits for a unit-price P t. of Pollution Lemma.(Taschini [2009]) Purchasing permits at time T is equivalent to undertaking a reversible and costly modification of the production process at time t if, and only if, the price of the permits is where V t and V m t P t = e ρ(t t) V t V m t α (T t), are defined in equation (1), V t > V m t. 11 / 27

12 Allowance price decomposition In light of our discussion about the substitution principle, the allowance price P t can be decomposed into two parts: P t = e ρ(t t) V t V m t α (T t) = e ρ(t t) m,nd Vt Vt α (T t) + e ρ(t t) V m,nd t V m,d t α (T t) {z } Flexibility Premium The emission permit price is equal to the (per unit) difference between the unmodified net operating profits and the (instantaneous) modified net operating profits. The flexibility premium is the value lost under the delayed abatement alternative due to delays in the implementation process. of Pollution 12 / 27

13 Optimal reversible and delayed abatement policy We model optimal investment and disinvestment decisions as the valuation of a perpetual American option contract. At any time t a risk-neutral firm can undertake an abatement project resulting in new operating profits that depend on the new instantaneous cash flow {S m t, t 0}: ds m t = µs m t dt + σs m t Z t, S m 0 = x, where µ and σ are constants and (Z t, t 0) is a Brownian motion defined on a filtered probability space (Ω, F, (F t) t 0, P). We denote by Vt m the expected sum of the discounted perpetual cash flows starting from t, V m t = E t h Z t i e ρ(u t) Su m du. (1) where the discount rate ρ is constant and E t[ ] stands for the conditional expectation E[ F t]. of Pollution 13 / 27

14 Optimal reversible and delayed abatement policy Let h I and h D be, respectively, the entry and exit levels; Let τ I and τ D be stopping times which correspond to the delayed criterion with time-windows d I, d D : g V 0,h t (V m ) = sup{s : s t, V m t = h V m 0 = x}, τ I (V 0,h I ),d(v m ) = inf{t 0 : t g V m 0,h I t τ D (V 0,h D ),d(v m ) = inf{t 0 : t g V m 0,h D t d I, V m t h I V m 0 = x}, d D, V m t h D V m 0 = x}; So, τ I (τ D ) represents the first instant when the process Vt m has consecutively spent d I (d D ) units of time above (below) a specific threshold. Let C I > 0 and C D R represent the investment and disinvestment costs. Because we are in the perpetual case, the investment and the disinvestment decisions will occur at the first instant when Vt m hits some constant optimal threshold hi or respectively hd. of Pollution 14 / 27

15 Graphical interpretation of the problem I The firm maximizes the present value of its opportunities, namely it solves the following problem: h i maxm E0 e ρτi (VτmI CI ) 1{τI < } + e ρτd (CD VτmD ) 1{τD < } hd hi, V0 hi of Pollution 15 / 27

16 of the Problem To solve the problem, we rely on the general results obtained in Chesney et al. [1997] and Costeniuc et al. [2008] In particular, we use the Laplace transform of the delayed investment (disinvestment) time; the moment generating function for the process Vt m at the delayed investment (disinvestment) time t; stopped the independence between the invest./disinvest. times and the position of the underlying value process at that time; and we adopt the following notation: b = µ σ2 2 σ, of Pollution θ 1 = b + 2ρ + b 2 σ and θ 2 = b 2ρ + b 2. σ Also, we define φ(z) as the moment generating function: φ(z) = 0 x exp(zx 1 2 x 2 )dx. 16 / 27

17 of the Problem Combining such results we can re-write the maximization problem VS(Vt m ) as: φ(b di ) ( V0 ) θ1 max h D h I h I φ( (2ρ + b 2 )d I ) ( hi ) θ2 φ( + h D φ( (2ρ + b 2 )d D ) where (2ρ + b2 )d I ) { φ( d I (σ + b)) h I φ(b C I + d I ) φ( b d D ) ( φ(b φ( (b + σ) d D ) C D h D d I ) φ( b d D ) VS(Vt m,nd ) represents the (instantaneous) maximization problem, i.e. when d I = d D = 0, whereas VS(Vt m,d ) represents the maximization problem under the delayed criterion, i.e. when d D > 0 and d I > 0. )} of Pollution 17 / 27

18 Premium for the flexibility Theorem.(Taschini [2009]) Consider a company which has two pollution abatement measures at its disposal: trading permits or modifying the production process. The premium θ t for the flexibility embedded in the price for marketable permits at time zero is: θ t = e ρ (T t) VS (V m,nd t ) VS (V m,d α (T t) t ) When the modification of the production process can be implemented instantaneously, trading permits and abatement investments are equivalent measures. The presence of implementation delays makes production modification an attractive alternative if, and only if, a company is sufficiently compensated (or faces high compliance costs). Implementation delays significantly increase the emission permit price. Irreversibility significantly increases the emission permit price.. of Pollution 18 / 27

19 Model We now present a brief discussion of the optimal investment and disinvestment thresholds hi and hd in terms of the time windows d i and d d. (a) If d I = d D = 0 we recover the well-known case of the instantaneous investment and disinvestment problem. (b) If d D = 0 and d I 0, then hd equals the instantaneous disinvestment level. (c) If d D, then hi converges to hoi (the optimal investment threshold for time-window d i while disinvestment is not possible, Gauthier and Morellec [2000]). (d) If d D 0 and d I 0, then h D h ND. of Pollution 19 / 27

20 Model implications We now investigate the sensitivity of the premium for flexibility θ and assess its likely magnitude. d Table: Premium benchmark case. The parameters we used are ρ = 0.13; µ = 0.05; σ = 0.40; C D = 50; C I = 170; V 0 = 100; α = 1. of Pollution When d I = d D = 0 trading permits and production modification are perfect substitutes. This implies, first, that the company is indifferent in undertaking an instantaneous modification of the production process or purchasing the needed amount of permits and, second, that the firm is not requiring a premium, i.e. θ = 0 (upper-left corner of the tables). 20 / 27

21 Model implications Optimal instantaneous irreversible investment value hii, and delayed optimal investment hi and disinvestment hd values. d I = d D = 3 d I = d D = 5 σ hii hi hd hi hd An increase in uncertainty delays instantaneous irreversible investments, increasing the instantaneous investment threshold. of Pollution 2. In the presence of implementation delays, conventional findings on the effect of the uncertainty of the underlying process on investment and disinvestment are reversed. A higher volatility of the underlying process hastens both investment and disinvestment. 3. The model of Bar-Ilan and Strange [1996], who study the effect of delays on reversible investment, is then nested into this model. 21 / 27

22 Model implications When d D, the level h I converges to hoi = θ1c I φ(b d I ) θ 1 1 φ((b + σ) d I ), where h OI represents the optimal investment threshold for time-window d I while disinvestment is not possible. 1. The required premium for irreversible investments (θ OI ) is larger than the premium for reversible investments (θ D ). of Pollution θ OI θ D d I σ Figure: Plot of the difference between θ D and θ OI. These values are respectively the premia for reversible and irreversible investments. 22 / 27

23 A graphical interpretation of the premium of Pollution Figure: Plot of the different levels of premium lined-up per type of industry (left diagram). Plot of the permit price over the premium grid (right diagram). 23 / 27

24 When the modification of the production process can be implemented instantaneously, trading permits and abatement investments are equivalent measures (for equal total abatement and investment costs). Conversely, companies should be sufficiently compensated. Such a compensation is reflected in the premium companies ask when offering unused permits. Extending the results of Chao and Wilson [1993], we derive an analytic solution of the premium for the flexibility embedded in tradable permits when abatement investment are reversible and delayed. Regulated companies face different abatement alternatives and different abatement costs. This implies that the value of flexibility is company-specific. Policy makers should be concerned about this differences when attempting to implement effective environmental regulations. of Pollution 24 / 27

25 I M. Aihman and L. Zetterberg. Options for emission allowance allocation under the eu emissions trading directive. Mitigation and Adaptation Strategies for Global Change, 10: , A. Bar-Ilan and C. Strange. Investment lags. The American Economic Review, 86: , W. J. Baumol and W. E. Oates. The Theory of Environmental Policy. Cambridge University Press, Cambridge, K. A. Brekke and B. Øksendal. Optimal switching in an economic activity under uncertainty. SIAM Journal on Control and Optimization, 32, H. Chao and R. Wilson. Option value of emission allowances. Journal of Regulatory, 5: , M. Chesney, M. Jeanblanc, and M. Yor. Parisian options and excursion theory. Advances in Applied Probability, 29: , of Pollution 25 / 27

26 II M. Costeniuc, M. Schnetzer, and L. Taschini. Entry and exit decision problem with implementation delay. Journal of Applied Probability, 45(4):1 2, M. B. Cronshaw and J. B. Kruse. Permit markets with banking. Working paper, Dep. of, University of Colorado, L. Gauthier and E. Morellec. Investment under uncertainty with implementation delay. In New Developments and Applications in Real Options. Oxford University Press, Oxford, R. McDonald and D. Siegel. The value of waiting to invest. International Economic Review, 26, W. Montgomery. Markets in licenses and efficient pollution control programs. Journal of Economic Theory, 5, B. Øksendal. Optimal stopping with delay information. Working paper series, Department of Mathematics, University of Oslo, of Pollution 26 / 27

27 III of Pollution J. D. Rubin. A model of intertemporal emission trading, banking, and borrowing. Journal of Environmental and Management, 31: , L. Taschini. Environmental and Modeling Marketable Permits. Asian Pacific Financial Markets, 17(4): , T. Tietenberg. Emission trading: An exercise in reforming pollution policy. Working paper, Resources for the Future, Washington D.C., J. Zhao. Irreversible abatement investment under cost uncertainties: Tradable emission permits and emissions charges. Journal of Public, 87: , / 27