Yongyang Cai

DSICE: A Dynamic Stochastic Integrated Model of Climate and Economy

This paper introduces a dynamic stochastic integrated model of climate and economy (DSICE), and a numerical dynamic programming algorithm for its solution. More specifically, we solve an example with annual time periods, a six hundred year horizon, and shocks to the economic and climate system. Our dynamic programming methods solve such models on a laptop in about an hour, and do so with good accuracy. This decisively refutes the pessimism one often hears about the possibility of solving such models.

Environmental tipping points significantly affect the cost−benefit assessment of climate policies

Significance Most current cost−benefit analyses of climate change suggest global climate policy should be relatively weak. However, relatively few studies account for the market or nonmarket impacts of passing environmental tipping points that cause abrupt and irreversible damages. We use a stochastic dynamic model of the climate and economy to quantify the effect of tipping points on climate change policy. We show that environmental tipping points can profoundly alter cost−benefit analysis, justifying a much more stringent climate policy, which takes the form of a higher immediate price on carbon. Most current cost−benefit analyses of climate change policies suggest an optimal global climate policy that is significantly less stringent than the level required to meet the internationally agreed 2 °C target. This is partly because the sum of estimated economic damage of climate change across various sectors, such as energy use and changes in agricultural production, results in only a small economic loss or even a small economic gain in the gross world product under predicted levels of climate change. However, those cost−benefit analyses rarely take account of environmental tipping points leading to abrupt and irreversible impacts on market and nonmarket goods and services, including those provided by the climate and by ecosystems. Here we show that including environmental tipping point impacts in a stochastic dynamic integrated assessment model profoundly alters cost−benefit assessment of global climate policy. The risk of a tipping point, even if it only has nonmarket impacts, could substantially increase the present optimal carbon tax. For example, a risk of only 5% loss in nonmarket goods that occurs with a 5% annual probability at 4 °C increase of the global surface temperature causes an immediate two-thirds increase in optimal carbon tax. If the tipping point also has a 5% impact on market goods, the optimal carbon tax increases by more than a factor of 3. Hence existing cost−benefit assessments of global climate policy may be significantly underestimating the needs for controlling climate change.

Shape-preserving dynamic programming

Dynamic programming is the essential tool in dynamic economic analysis. Problems such as portfolio allocation for individuals and optimal growth of national economies are typical examples. Numerical methods typically approximate the value function and use value function iteration to compute the value function for the optimal policy. Polynomial approximations are natural choices for approximating value functions when we know that the true value function is smooth. However, numerical value function iteration with polynomial approximations is unstable because standard methods such as interpolation and least squares fitting do not preserve shape. We introduce shape-preserving approximation methods that stabilize value function iteration, and are generally faster than previous stable methods such as piecewise linear interpolation.

Tipping Points in a Dynamic Stochastic IAM

We use a dynamic stochastic general equilibrium model of integrated climate and economy (DSICE) to account for abrupt and irreversible climate change. We model a climate shock in the form of a stochastic tipping point. We investigate the impact of the tipping point externality on optimal mitigation policy.We conclude that the optimal mitigation policy depends on the dynamic pattern of the impact. In the case of abrupt and irreversible climate change with a permanent impact, the optimal policy implies a constant anti-tipping effort to prevent the catastrophe, calling for immediate limitations on emissions.

Advances in Numerical Dynamic Programming and New Applications

Abstract Dynamic programming is the essential tool in dynamic economic analysis. Problems such as portfolio allocation for individuals and optimal economic growth are typical examples. Numerical methods typically approximate the value function. Recent work has focused on making numerical methods more stable, and more efficient in its use of information. This chapter presents two examples where numerical dynamic programming is applied to high-dimensional problems from finance and the integration of climate and economic systems.

The Effect of Climate and Technological Uncertainty in Crop Yields on the Optimal Path of Global Land Use

The pattern of global land use has important implications for the worlds food and timber supplies, bioenergy, biodiversity and other eco-system services. However, the productivity of this resource is critically dependent on the worlds climate, as well as investments in, and dissemination of improved technology. This creates massive uncertainty about future land use requirements which compound the challenge faced by individual investors and governments seeking to make long term, sometimes irreversible investments in land conversion and land use. This study assesses how uncertainties associated with underlying biophysical processes and technological change in agriculture affect the optimal profile of land use over the next century, taking into account the potential irreversibility in these decisions. A novel dynamic stochastic model of global land use is developed, in which the societal objective function being maximized places value on food production, liquid fuels (including bio-fuels), timber production, and biodiversity. While the uncertainty in food crop yields has anticipated impact, the resulting expansion of crop lands and decline in forest lands is relatively small.

Dynamic Programming with Hermite Interpolation

Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions. This paper uses Hermite data obtained from the optimization step and applies Hermite interpolation to construct approximate value functions. Several examples show that Hermite interpolation significantly improves the accuracy of value function iteration with very little extra cost.

Urbanization and property rights

Since the industrial revolution, the economic development of Western Europe and North America was characterized by continuous urbanization accompanied by a gradual phasing-in of urban land property rights over time. Today, however, the evidence in many fast urbanizing low-income countries points towards a different trend of “urbanization without formalization”, with potentially adverse effects on long-term economic growth. This paper aims to understand the causes and the consequences of this phenomenon, and whether informal city growth could be a transitory or a persistent feature of developing economies. A dynamic stochastic equilibrium model of a representative city is developed, which explicitly accounts for the joint dynamics of land property rights and urbanization. The calibrated baseline model describes a city that first grows informally, with the growth of individual incomes leading to a phased-in purchase of property rights in subsequent periods. The model demonstrates that land tenure informality does not necessarily vanish in the long term, and the social optimum does not necessarily imply a fully formal city, neither in the transition, nor in the long run. The welfare effects of policies, such as reducing the cost of land tenure formalization, or protecting informal dwellers against evictions are subsequently investigated, throughout the short-term transition and in the long-term stationary state.

Computing Equilibria of Dynamic Games

We develop a numerical method for computing all pure strategy subgame-perfect equilibrium values of dynamic strategic games with discrete states and actions. We define a monotone mapping that eliminates dominated strategies, and when applied iteratively, delivers an accurate approximation to the true equilibrium payoffs of the underlying game. Our algorithm has three parts. The first provides an outer approximation to equilibrium values, constructed so that any value outside of this approximation is not an equilibrium value. The second provides an inner approximation; any value contained within this approximation is an equilibrium value. Together, the two approximations deliver a practical check of approximation accuracy. The third part of our algorithm delivers sample equilibrium paths. To illustrate our method, we apply it to a dynamic oligopoly competition with endogenous production capacity.

A NONLINEAR PROGRAMMING METHOD FOR DYNAMIC PROGRAMMING

A nonlinear programming formulation is introduced to solve infinite horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to avoid inefficient discretization. Our numerical results show that this nonlinear programming method is efficient and accurate.