ECON 5010 Class Notes Business Cycles and the Environment

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1 ECON 5010 Class Notes Business Cycles and the Environment Here, I outline a forthcoming paper by Garth Heutel in the Review of Economic Dynamics. The title is "How Should Environmental Policy Respond to Business Cycles? Optimal Policy under Persistent Productivity Shocks." 1 Introduction Main questions. 1. Should climate change policy respond to the business cycle? 2. And if so, how? 3. What are the bene ts of allowing climate change policy to respond to business cycles? Political economy bene ts; eliminate ad hoc measures to react to business cycles. Welfare improvements from smoothing abatement costs; disproportionately bene t the poorest households and electric utility companies. Borrow from previous research on dynamic stochastic general equilibrium (DSGE) models of the business cycle and optimal environmental policy. Main results. 1. Carbon dioxide emissions are inelastic with respect to GDP (elasticity ranges between 0.5 and 0.9). 2. Productivity shocks provide a price and an income e ect. 3. Optimal policy should increase emissions during expansions and lower emissions during recessions. Pegging emissions to GDP is a good approximation to the optimal policy. 4. Optimal emission tax rates and quotas are procyclical in a decentralized economy. Thus optimal policy dampens the procyclicality of emissions. 2 Empirical Analysis This section estimates how CO 2 emissions respond to GDP without optimal policy. Between 1981 and 2003, GDP increased by 100% while CO 2 emissions increased by 25% (see Figure 1). 1

2 Figure 2 shows HP ltered GDP and CO 2 emissions. CO 2 emissions have a standard deviation of 2.04% while GDP has a standard deviation of 1.31%. CO 2 emissions and GDP are positively related with a correlation of ARIMA models and regression models on detrended data (see Table 1) show a CO 2 emissions elasticity with respect to GDP in the range [0.5,0.9]. 3 Dynamic Model Centralized Economy 3.1 The Problem Consider the social planner s problem in the presence of a pollution externality. The problem can be cast as a dynamic programming problem: V (k t 1 ; x t 1 ; a t ) = max z t;i t;c t [U(c t ) + E t V (k t ; x t ; a t+1 )] (Value Function) subject to c t + i t + z t y t (Resource Constraint) k t = (1 )k t 1 + i t (Capital Accumulation) x t = x t 1 + e t + e row t (Pollution Stock) e t = (1 t )h(y t ) (Emissions) z t = g( t )y t (Abatement) y t = (1 d(x t )) a t f(k t 1 ): (Output) The social planner chooses abatement (z t ), investment (i t ), and consumption (c t ) to maximize expected discounted lifetime utility for the representative agent. Through substitutions, the choice variables become k t and x t. Technology shocks (a t ) follow a Markov process. Output loss from pollution d(x t ) and the fraction of emissions abated t are restricted to be in the [0,1] interval. 3.2 First-Order Conditions The consumption (capital) rst-order condition is n o U 0 (c t ) = E t U 0 (c t+1 ) (1 d t+1 )a t+1 f 0 (k t ) (1) t+1 + (1 ) (1) 2

3 where (1) t+1 is the marginal environmental damage from a larger capital stock. The abatement (pollution) rst-order condition is h U 0 (c t ) i (2) t + (3) t = E t U 0 (c t+1 )gt+1 0 h(y t+1 ) where (2) t is the marginal reduction in output from an increase in pollution and (3) t represents the e ect that more pollution means less is spent on abatement. (2) 3.3 Calibration The model is calibrated rather than estimated, using macroeconomic and environmental sources. See Table Simulation Results The system is solved using a linearized version of the model around the steady state Impulse Response Functions (IRFs) Figure 3 shows the IRFs from a one-time productivity shock. The dynamic patterns for output (y), consumption (c) and capital (k) are well-established in the RBC literature. Figure 4 shows the IRFs for abatement (z), emissions (e) and pollution (x). The results are... More output also means more emissions. However, the optimal response to a productivity shock is to spend more on abatement. The net result is ambiguous. For this calibration, the productivity shock leads to more emissions so the price e ect dominates the income e ect (i.e., optimal emissions are procyclical). Pegging emissions to GDP is a good approximation to the optimal policy. The pollution stock is very persistent because the rate of decay is small, (1 ) = 0: Welfare Analysis How valuable is an optimal emissions policy? To answer this question, Heutel calculates the constant compensating variation cv so the representative agent is indi erent between (a) the optimal policy and (b) a static policy of emissions xed at the steady-state level with an additional cv units of consumption. Over 250 simulations, the median compensating variation is approximately $1 billion, similar to the estimated value of other environmental policies. This is a small fraction of U.S. GDP (~$14 trillion) but disproportionately distributed across the economy. 3

4 4 Dynamic Model Decentralized Economy This section discusses how the rst-best environmental policy can be implemented in a decentralized economy. Through a series of time-varying emission taxes, the government can encourage household and rms to internalize the emissions externality. 4.1 Firms The representative rm maximizes pro ts: t = y t t e t r t k t 1 z t (3) subject to the emissions function e t = (1 t )h(y t ) (4) and the abatement cost function z t = y t g( t ); (5) where t is the emissions tax and r t is the rental rate for capital. The rst-order conditions set the marginal product of capital to equal the r t, and the marginal value of abatement equal to its price. 4.2 Households The consumer s problem is to choose consumption (c t ) and capital (k t ) to maximize E t P 1 s=t s U(c s ) (6) subject to the budget constraint c t r t k t 1 + t e t + t k t + (1 )k t 1 : (7) The rst-order condition takes the familiar form U 0 (c t ) = E t U 0 (c t+1 ) [r t+1 + (1 )] : (8) 4

5 4.3 Government The benevolent government choose the emissions tax rate t to maximize total expected discounted utility subject to all the constraints and the optimal choices of households and rms. Figure 12 shows one realization of the optimal decentralized policy. The main results are... Emissions rise during expansions because abatement is more costly when productivity is high. The emission tax rate rises during expansion, which moderates the rise in emissions. Without the emissions policy, rms would over-produce and over-emit CO 2. The rst-best outcome could also be reached through a cap-and-trade scheme. The optimal policy during a recession is to either lower the emissions tax or lower the emissions quota. It may be more politically feasible to weaken environmental policy during a recession, favoring taxes over quotas. There are no information asymmetries between regulators, consumers and rms. 5

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