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Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the modelik’s parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.

This chapter considers the lag structures of dynamic models in economics, arguing that the standard approach is too simple to capture the complexity of actual lag structures arising, for example, from production and investment decisions. It is argued that recent (1990s) developments in the the theory of functional differential equations provide a means to analyze models with generalized lag structures. The stability and asymptotic stability of two growth models with generalized lag structures are analyzed. The chapter's penultimate section includes a speculative discussion of time-varying parameters.

We estimate a dynamic programming model of schooling decisions in which the degree of risk aversion can be inferred from schooling decisions. In our model, individuals are heterogeneous with respect to school and market abilities but homogeneous with respect to the degree of risk aversion. We allow endogenous schooling attainments to affect the level of risk experienced in labor market earnings through wage dispersion and employment rate dispersion. We find a low degree of relative risk aversion (0.93) and the estimates indicate that both wage and employment rate dispersions decrease significantly with schooling attainments. We find that a counterfactual increase in risk aversion will increase schooling attainments. Finally, the low degree of risk aversion implies that an increase in earnings dispersion would have little effect on schooling attainments.

Mehra and Prescott (1985) point out that it is difficult to reconcile certain empirical facts about equity and debt returns and the process of consumption growth with reasonable assumptions about the relative rate of risk aversion and the pure rate of time preference, in a conventional infinite-horizon model with an additively separable, constant relative rate of risk aversion (CRRA) utility function. The present note adds the further puzzle that if the mean rate of growth of consumption is not known with perfect certainty in such a model, both stocks and real perpetuities have an infinite price in terms of consumption goods. When maturity-specific claims on real output are introduced, the equity premium is seen to increase without bound at the most distant horizons. These in turn dominate asset pricing, so that the equity premium on claims on all future output is indeed infinite.

Climate control needs have reached momentum. While scientists call for stabilizing climate and regulators structure climate change mitigation and adaptation efforts around the globe, economists are concerned with finding proper and fair financing mechanisms. In an overlapping-generations framework, Sachs (2014) solves the climate change predicament that seems to pit today’s against future generations. Sachs (2014) proposes that the current generation mitigates climate change financed through bonds to remain financially as well-off as without mitigation while improving environmental well-being of future generations through ensured climate stability. This intergenerational tax-and-transfer policy turns climate change mitigation into a Pareto improving strategy. Sachs’ (2014) discrete model is integrated in contemporary growth and resource theories. The following article analyzes how climate bonds can be phased-in, in a model for a socially optimal solution and a laissez-faire economy. Optimal trajectories are derived partially analytically (e.g., by using the Pontryagin maximum principle to define the optimal equilibrium), partially data driven (e.g., by the use of modern big market data), and partially by using novel cutting-edge methods – for example, nonlinear model predictive control (NMPC), which solves complex dynamic optimization problems with different nonlinearities for infinite and finite decision horizons. NMPC will be programed with terminal condition in order to determine appropriate numeric solutions converging to some optimal equilibria. The analysis tests if the climate change debt adjusted growth model stays within the bounds of a sustainable fiscal policy by employing NMPC, which solves complex dynamic systems with different nonlinearities.