In an attempt to capture the complexity of the economic system many economists were led to the formulation of complex nonlinear rational expectations models that in many cases can not be solved analytically. In such cases, numerical methods need to be employed.
In chapter one I review several numerical methods that have been used in the economic literature to solve non-linear rational expectations models. I provide a classification of these methodologies and point out their strengths and weaknesses. I conclude by discussing several approaches used to measure accuracy of numerical methods. In the presence of uncertainty, the multistage stochastic optimization literature has advanced the idea of decomposing a multiperiod optimization problem into many subproblems, each corresponding to a scenario. Finding a solution to the original problem involves aggregating in some form the solutions to each scenario and hence its name, scenario aggregation.
In chapter two, I study the viability of scenario aggregation methodology for solving rational expectation models. Specifically, I apply the scenario aggregation method to obtain a solution to a finite horizon life cycle model of consumption. I discuss the characteristics of the methodology and compare its solution to the analytical solution of the model. A growing literature in macroeconomics is tweaking the unbounded rationality assumption in an attempt to find alternative approaches to modeling the decision making process, that may explain observed facts better or easier. Following this line of research, in chapter three, I study the impact of bounded rationality on the level of precautionary savings in a finite horizon life-cycle model of consumption.
I introduce bounded rationality by assuming that the consumer does not have either the resources or the sophistication to consider all possible future events and to optimize accordingly over a long horizon. Consequently, he focuses on choosing a consumption plan over a short span by considering a limited number of possible scenarios. While under these assumptions the level of precautionary saving in many cases is below the level that a rational expectations model would predict, there are also parameterizations of the model for which the reverse is true.
Source: University of Maryland
Author: Mirestean, Alin Tavi