## Endogenous and exogenous variables

The IS-LM-FE model provides a good opportunity to illustrate and re-emphasize the distinction between endogenous and exogenous variables, and to show how institutional arrangements change the nature of a variable. A model always comprises

■ exogenous variables - their values are determined outside the model, and

■ endogenous variables - to describe their behaviour is the very purpose of the model.

A model may have an arbitrary number of exogenous variables. But it can only explain as many endogenous variables as it has (independent) equations.

The IS-LM-FE model has been reduced to three equations - which take the form of market

Box 4.5 continued Figure 1 Flexible exchange rates

Exogenous variables

Endogenous variables

Exogenous variables

Endogenous variables Figure 2 Fixed exchange rates

### Figure 1 Flexible exchange rates

Figure 2 Fixed exchange rates equilibrium conditions - to explain three endogenous variables. Figure 1 sketches how the exogenous variables have an impact on the three endogenous variables, and how the latter interact.

We must remember here, however, that our initial larger model, with equations explaining other endogenous variables such as consumption, investment, exports, imports and more, has been reduced to three equations by repeatedly substituting equations into each other and thus eliminating these variables. Thus, for example, consumption does not appear any more. But it can be considered a hidden endogenous variable whose equilibrium value is retrieved by substituting equilibrium income into the consumption function.

### Institutions and the endogeneity of variables

The above interpretation implicitly assumes that the exchange rate is flexible, determined by market forces. This makes the money supply M exoge nous, and puts it under the control of the policymaker.

The roles of the exchange rate and of the money supply are reversed if we move to a system of fixed exchange rates. Then the exchange rate becomes exogenous, is set by policy-makers, and the money supply adjusts endogenously. This modifies the model's structure to that shown in Figure 2.

In terms of the representations of market equilibria in the i-Y plane, the two institutional scenarios work as shown in panels (a) and (b) of Figure 3.

Under flexible exchange rates the positions of FE and LM are set exogenously. The exchange rate determines the position of IS, and endogenously adjusts so as to let IS pass through the given point of intersection between FE and LM (panel (a)).

Under fixed exchange rates the positions of FE and IS are set exogenously. The money supply, which determines the position of LM, endogenously adjusts so as to let LM pass through the given point of intersection between FE and IS (panel (b)). Income

(a) Flexible exchange rates Figure 3

Income LM moves up as central bank lowers money supply by buying home currency

(b) Fixed exchange rates

Income