RDP 8706: Numerical Solution of Rational Expectations Models with and Without Strategic Behaviour 1. Introduction

The assumption of “model-consistent” or “rational” expectations, first implemented by John Muth (1961), has important implications for the solution of macroeconomic models. In models containing rational agents^[1], current variables depend on the expected path of future variables^[2]. Until recently, this assumption was only used in small analytical models because of the difficulty in solving models under rational expectations. Advances in computing power and technique have now allowed economy-wide and multi-country models to be solved^[3]. There still appears to be an aversion to applying the available numerical techniques perhaps due to the inaccessibility of the source literature to many economists. With the goal of making the literature more accessible, this paper surveys the major numerical techniques which have been developed to solve large models, where expectations of some agents in the model are assumed to be formed rationally.

Section 2 of this paper examines the key implications of assuming model consistent expectations using a very simple model of exchange rate dynamics. This simple model introduces the concepts used extensively in section 3 and provides a useful introduction to the problem to be solved numerically. In section 3, alternative numerical techniques are discussed, focussing on the intuition behind the formal derivations presented in the literature. These techniques are the general analytical solution of Blanchard and Kahn (1980), the Multiple Shooting algorithm of Lipton et al (1983), the Fair-Taylor algorithm (Fair and Taylor (1983)) and a fourth algorithm developed by the author in joint work with Jeffrey Sachs on the MSG model.

The goal of section 3 is to present the techniques in a way that makes the algorithms more transparent than the original articles. Section 4 introduces a technique developed with Jeffrey Sachs that extends the algorithm in Oudiz and Sachs (1985) and moves the discussion of solving rational expectations models to the case where agents interact in a strategic manner.

Footnotes

That is, agents who use all information available in deciding on actions and do not make any systematic errors. [1]

See Begg (1982), Sheffrin (1983) and Taylor (1985) for surveys of the use and relevance of the rational expectations assumptions. [2]

See for example the MSG model (McKibbin and Sachs (1986)), the Liverpool Model (Minford (1985)), the Taylor Model (Taylor (1986)) and Minimod (Haas and Masson (1986)). [3]