Stan Olijslagers

On Current and Future Carbon Prices in a Risky World

Joint with Rick van der Ploeg and Sweder van Wijnbergen

R&R at Journal of Economic Dynamics and Control


We analyse the optimal paths of abatement and carbon prices under a variety of economic, temperature and damage risks. Carbon prices grow in line with economic growth, but with convex damages and temperature-dependent risks of climatic tipping points grow more quickly and with gradual resolution of uncertainty grow more slowly. With temperature-dependent economic damage tipping points carbon prices are higher, but when the tipping point occurs, the price jumps downward. With a temperature cap the efficient carbon price rises at the risk-adjusted interest rate. Allowing for damages as well as a cap leads to a higher carbon price which grows more slowly. But as temperature and cumulative emissions approach their caps, the carbon price is ramped up ever more. Policy makers should expect a rising path of carbon prices.

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 which depend critically on the structure of risk preferences but overall leads to substantially higher estimates of the SCC.

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

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.

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. 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.  This method does not directly suffer from the curse of dimensionality and is therefore applicable to high-dimensional problems. Simulation and regression methods are not often used to solve macro-models, but we show that this method is very suitable.  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. The simulation and regression method outperforms the finite difference method in this 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

Researcher at the CPB