There are strong reasons to believe that the impact of changes in many determinants of AFDC participation are delayed. The most prominent example is the unemployment rate; substantial evidence already exists that increases in the unemployment rate have their full impact on participation only after several quarters have passed (see Lewin-VHI, 1995a).
The simplest way to capture delayed impacts of a specific explanatory variable is to include "lagged" (i.e., previous period) values of the variable as separate explanatory variables. For instance, in all models we include the current quarter's unemployment rate, the previous quarter's rate ("first lag"), the rate from the second previous quarter ("second lag"), etc., for as many as nine quarters. If DlnUst-l is the change in the log of the age-adjusted unemployment rate lagged l periods, and bl is its coefficient, the unemployment rate specification can be represented as:
Equation 3.7: Dln(Yst) = ... + b0DlnUst + b1DlnUst-1 + ... bl DlnUst-l + ... bLDlnUst-L+ ....
where L is the longest lag length. The sum of the coefficients of the current and lagged coefficients is the total, or long-run, elasticity of a permanent increase in the age-adjusted unemployment rate.(8)