Chapter 11. Models using time-series data

1. Static versus dynamic models

In a static model, each equation involves values of variables at one point in time. In a dynamic model, in the same equation there are values of variables measured at different points in time. Future values are impossible to measure, so an equation for the dependent variable at moment may include variables measured at this or earlier moments.

Main new requirement: regressors are uncorrelated with the contemporaneous error (at the same moment) but can be correlated with errors in other equations.

2. Adaptive expectations

Hypothesis: expected values for period are formed in period according to

(1)

Since expected values are not observable, in regression models they must be eliminated. Assuming some model, use backward substitution to eliminate expected values and define a Koyck distribution. OLS may yield bad results because of multicollinearity and because estimates of the coefficients lead to conflicting estimates of the original parameters. Nonlinear least squares may be better.

3. Short-run versus long-run effects

Short-run effects are given by coefficients. Long-run effects are obtained assuming equilibrium (a variable has the same value in all periods). Illustrate using an example.

4. The partial adjustment model

It is assumed that the behavioral equation determines the desired value , rather than the actual value :

It is then assumed that the actual value is a weighted average of the current desired value and the previous actual value:

.

Show that

Example. In Brown’s habit-persistent model desired consumption is related to wage income and nonwage income :

where is a dummy variable equal to 0 for the pre-war period and 1 for the post-war period. The marginal propensity to consume out of wage income is likely to be higher than out of nonwage income, for two reasons. First, nonwage income tends to be received by relatively rich households with higher savings rates than poorer ones. Second, much of nonwage income originates as company profits, and companies normally pay out only part of their profits as dividends, retaining the remainder for investment. The behavioral equation is . Derive an equation in observable variables.

5. Friedman’s permanent income hypothesis

Using the permanent income hypothesis and assuming adaptive expectations for permanent income, show the short-run and long-run propensities to consume.

6. Give an example of and discuss a simultaneous equations system with autoregressive terms

7. Give an example of VAR and discuss the arising problems

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