Distributed lags Distributed lags are dynamic relationships in which the effects of changes in some variable X on some other variable Y are spread through time. Distributed lags can arise for a variety of reasons including: 1.Costs of adjustment 2.The effects of expectations

Example: A dynamic consumption function This is a difference equation of the form:

Dynamic effects of an increase in disposable income

The Costs of Adjustment Model Quadratic adjustment costs penalise large deviations more strongly than small deviations.

Quadratic costs of adjustment give rise to the partial adjustment model. This provides a rationale for the introduction of lagged endogenous variables into regression models.

Backward substitution yields: The effects of a change in X on Y are spread out over time. The weights on past values of X decline for longer lags because:

The long run effect of a change in X on Y can be calculated using the following formula: For this limit to converge we need We also usually assume θ >0 for a sensible economic model.

Example:

Example: An accelerator model of investment In this case investment is determined by the following difference equation:

The long run effect of an increase in GDP on investment can be determined from the following expression: