Econ 520 - Fall 2009

The model on the left has five equations based economic theory, accounting identities, and definitions. Thinking about the equilibrium and how it changes would be difficult given the algebraic complexities of these equations.

Therefore, we will work with linearized versions, where lower-case letter denote logarithms of upper-case variables. The linearized model is on the right.

The definition of the real exchange rate (1) has an exact equivalent in logs. Uncovered interest parity (2) in logs requires just the one approximation that log(1+x) is approximately x for small x. The definition of the real interest rate (3) uses the same approximation in the form that the rate of inflation is approximately the difference over time of the log of the price level. The LM equation (4) and the IS equation (5) both replace the unspecified functions on the right with linearized versions in logs. The net exports function, for example, does not appear in the linearized IS equation, but the logs of the real exchange rate and foreign income do. Changes in the latter variables affect y via an implicit path involving net exports.

The model on the right has the advantage that we will be able to figure out what happens when a variable changes.

We have six endogenous variables (not counting expectations!), but only five equations. We need an extra equations (and a theory of expectation formation). The extra equation could be we are already at full employment or that the price level is fixed. The former is a long run view while the latter is more short run.