More Complex Regression Models

When observations of the dependent variable form a series over time, special problems may be encountered. Perhaps the most significant difference from the models discussed thus far is the use as an explanatory variable of the value of the dependent variable itself for the preceding period. A rationale for lagged dependent variables is that they account for excluded explanatory factors. Lagged dependent and independent variables may also be used to correct for “stickiness” in the response of the dependent variable to changes in explanatory factors. For example, in a price equation based on monthly prices, changes in cost or demand factors might affect price only after several months, so that regression estimates reflecting changes immediately would be too high or too low for a few months; the error term would be autocorrelated. A lagged value of the dependent variable might be used to correct for this. Note, however, that inclusion of a lagged dependent variable makes the regression essentially predict change in the dependent variable because the preceding period value is regarded as fixed; this may affect interpretation of the equation’s coefficients. For previous examples, see Sections 13.6.2 and 13.6.3 .