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We introduce a computational technique- precomputation of integrals - that makes it possible to construct conditional expectation functions in dynamic stochastic models in the initial stage of a solution procedure. This technique is very general: it works for a broad class of approximating functions, including piecewise polynomials; it can be applied to both Bellman and Euler equations; and it is compatible with both continuous-state and discrete-state shocks. In the case of normally distributed shocks, the integrals can be constructed in a closed form. After the integrals are precomputed, we can solve stochastic models as if they were deterministic. We illustrate this technique using one- and multi-agent growth models with continuous-state shocks (and up to 60 state variables), as well as Aiyagari's ( 1994) model with discrete-state shocks. Precomputation of integrals saves programming efforts, reduces computational burden, and increases the accuracy of solutions. It is of special value in computationally intense applications. MATLAB codes are provided.

Since the 1950s, increased agricultural productivity has allowed food supply growth to outpace demand on a global scale, resulting in a downward trend in world prices. Investments into agricultural research and development (R&D) have been the foundation for this achievement, but there is a long lag in agricultural productivity response to the investments. The optimal path of R&D spending depends on future population, income and climate change, all of which are highly uncertain. This study offers a dynamic framework for analyzing optimal agricultural R&D spending in the 21st century factoring in uncertainties in these drivers, as well as lagged pay offs on investments into improvements of agricultural productivity.

This paper introduces a nonlinear certainty-equivalent approximation method for dynamic stochastic problems. We first introduce a novel, stable, and efficient method for computing the decision rules in deterministic dynamic economic problems. We use the results as nonlinear and global certainty-equivalent approx- imations for solutions to stochastic problems, and compare their accuracy to the common linear and local certainty-equivalent methods. Our examples demon- strate that this method can be applied to solve high-dimensional problems with up to 400 state variables with acceptable accuracy. This method can also be applied to solve problems with inequality constraints. These features make the non- linear certainty-equivalent approximation method suitable for solving complex economic problems, where other algorithms, such as log-linearization, fail to produce a valid global approximation or are far less tractable.