The Bank of Canada's New Quarterly Projection Model, Part 2. A Robust Method for Simulating Forward-Looking Models

In this report, we describe methods for solving economic models when expectations are presumed to have at least some element of consistency with the predictions of the model itself. We present analytical results that establish the convergence properties of alternative solution procedures for linear models with unique solutions. Only one method is guaranteed to converge, whereas most widely used methods, including the popular Fair-Taylor approach, do not have this property. This method, which we have implemented for simulation of the Bank of Canada's models of the Canadian economy, involves solving simultaneously the full problem, "stacked" to represent each endogenous variable at each time point with a separate equation, using a Newton algorithm.

We discuss briefly the extension of our convergence results to applications with non-linear models, but the strong analytical conclusions for linear systems do not necessarily carry over to non-linear systems.

We illustrate the analytical discussion and provide some evidence on comparative solution times and on the robustness of the procedures, using simulations of a simple, linear model of a hypothetical economy and of two much larger, non-linear models of the Canadian economy developed at the Bank of Canada. The examples show that the robustness of our procedure does carry over to applications with working, non-linear economic models. They also suggest that the limitations of iterative methods are of practical importance to economic modellers.