As mentioned above, the specification search led us to a specification that is very similar to the final specification for the Basic equations. The final distributed lag specification for the unemployment rate is identical, but the estimated coefficients are much larger. We estimate that a permanent increase in the unemployment rate of one percent (e.g., 5 percent to 5.05 percent) increases the UP caseload by 1.28 percent (.0128 = 1.283 * .01), compared to just 0.16 percent for the Basic caseload. We also estimate that after just six quarters a one percent increase in trade employment per capita reduces the UP caseload by 2.07 percent, compared to 1.00 percent for the Basic caseload. When we omit the trade variable from the specification (a specification not included in the exhibit), the long-run elasticity for the unemployment rate increases from 1.28 to 1.42. Findings for the other participation measures are very similar. We discuss these findings further in Section E, below.
Many have speculated that the effects of the business cycle on AFDC participation are asymmetric, with recessions having a large effect on participation but recoveries having a smaller, or perhaps more delayed, effect in the opposite direction. We tested for asymmetry by estimating a model in which we interacted the three distributed lag variables for the unemployment rate with a dummy variable for the direction of change of the unemployment rate in the current period, yielding separate distributed lags for increases and decreases in unemployment (a "switching" model). The two estimated distributed lags were very similar, and not statistically different. As discussed in the introduction, Steve Thompson has recently been able to find statistical evidence of asymmetry in a monthly time-series model for a Maryland by lagging the switch point. We did not have the resources to experiment with alternative switching specifications. It could be that the estimates we report are a weighted average of stronger business cycle effects in recessions and weaker effects in recoveries.