Stan Olijslagers

The Social Cost of Carbon: Optimal Policy versus Business As Usual

Job Market Paper

Climate change is a global externality. This externality can be internalized by introducing a global carbon tax. The Pigouvian optimal carbon tax equals the social cost of carbon (SCC), which is the welfare loss of emitting one unit of carbon expressed in monetary units. Currently, global climate policy is however far from optimal and closer to the business as usual (or no policy) scenario. The SCC is dependent on the policy scenario. We develop a stochastic climate-economy model to investigate the difference between the SCC in the optimal and business as usual scenario. In a simplified setting, a closed form solution for the SCC is obtained. Then a more realistic model is solved to quantify the effects. Our results show that especially for convex specifications of the damage function, the social cost of carbon is considerably higher in the business as usual scenario. To solve our high-dimensional model, a novel least-squares solution method is introduced.

Discounting the Future: On Climate Change, Ambiguity Aversion and Epstein-Zin Preferences

Joint with Sweder van Wijnbergen

We show that empirically strongly supported deviations from standard expected time separable utility have a major impact on estimates of the willingness to pay to avoid future climate change risk. We propose a relatively standard integrated climate/economy model but add stochastic climate disasters. The model yields closed form solutions up to solving an integral, and therefore does not suffer from the curse of dimensionality of most numerical climate/economy models. We separately analyze the impact of risk aversion (known probabilities), ambiguity aversion (unknown probabilities) and substitution preferences on the social cost of carbon. Introducing Epstein-Zin preferences with an elasticity of substitution higher than one leads to much larger estimates of the social cost of carbon (SCC) than obtained under power utility. Ambiguity aversion has more complicated consequences but overall leads to substantially higher estimates of the SCC.

Commit to a Credible Path of Rising CO2 Prices

Joint with Rick van der Ploeg and Sweder van Wijnbergen

CO2 pricing is essential for an efficient transition to the green economy. Despite Daniel, Litterman and Wagner (2019)’ claim that CO2 prices should decline, CO2 prices should rise over time. First, damages from global warming are proportional to economic activity and this makes CO2 prices grow at the same rate as the economy. Second, even if uncertainty about the damage ratio is gradually resolved over time, this only slows down the price rise. Third, if CCS is allowed for, the optimal CO2 price will rise before it declines but this decline does not occur until more than two centuries ahead. Fourth, damages are likely to be a very convex function of temperature which with rising temperature implies that CO2 prices must grow faster than the economy. Fifth, internalizing the social benefits of learning by doing or a shift towards technical progress in renewable energy production requires a subsidy for renewable energy, not a temporary spike in CO2 prices. Having high CO2 prices upfront is an artefact of failing to separate out renewable energy subsidies from the carbon price. Finally, efficient intertemporal allocation of policy efforts implies that a temperature cap or cap on cumulative emissions requires that CO2 prices must rise at a rate equal to the risk-adjusted interest rate, typically higher than the economic growth rate. Summing up, CO2 prices must rise at a rate at least equal to the economic growth rate and at most to the risk-adjusted interest rate. They should not decline.

Solution methods for DSGE models in continuous time: Application to a climate-economy model

We consider two solution methods to solve dynamic stochastic general equilibrium models in continuous time with Epstein-Zin preferences. The specific setting that we analyze is a stochastic endowment economy with disaster risk. We allow for an optimal policy setting, where the agent optimizes the value function over a set of controls. The first method directly solves the Hamilton-Jacobi-Bellman equation using a finite difference scheme for PDEs. To reduce the curse of dimensionality, sparse grid methods are used. The second method is more common in finance applications and makes use of simulation and regression techniques (Least Squares Monte Carlo). This method uses the Bellman equation and the conditional expectations are approximated using a regression. It does not suffer from the curse of dimensionality and is therefore applicable to multi-dimensional problems. Least Squares Monte Carlo techniques are not a common solution method in macro-models, but we show that this method is very suitable to solve DSGE models.  As a numerical example, we solve a 7-dimensional model in which the economy is subject to climate disasters and the representative agent can decide on abatement spending. Outcome variables of interest are the social cost of carbon, optimal abatement policy, the risk-free rate and the risk premium. The simulation and regression method outperforms the finite difference method in this 7-dimensional setting.

Debt sustainability when r-g<0: no free lunch after all

Joint with Nander de Vette and Sweder van Wijnbergen

Interest rates on public debt have for several years now fallen short of GDP growth rates in much of the Western world. In his presidential address to the AEA Blanchard argued that this implies that there are no fiscal costs to high debt (Blanchard, 2019). In this paper we argue that the safe rate is not the right interest rate to use for that comparison. We develop a General Equilibrium Asset Pricing model and econometrically estimate the relevant characteristics of the stochastic processes driving the primary surplus in relation to the growth rate of aggregate consumption and derive the proper risk premium. The resulting interest rate exceeds the growth rate. We then calculate the discounted value of future primary surpluses using the same stochastic process for the primary surplus and compare that to the market value of the (Dutch) public sector debt. We test various explanations for the gap between these two and derive the fiscal adjustment necessary to eliminate it (the “fiscal sustainability gap”).

Stan Olijslagers

PhD student at the University of Amsterdam