1. If we had included a dummy variable for each quarter of the entire period, we would have eliminated entirely the role of purely time-series covariation in determining the coefficients. Our quarterly and yearly dummies are more restrictive than such a specification, but we think the difference is inconsequential. We also include separate dummies for OBRA81 and DEFRA84 in the reported results, to capture any nationwide effects of the implementation of those laws that was missed by the year and quarterly dummies. We also tried dummies for implementation of other legislation, but the estimated coefficients were not at all significant.
2. Grossman (1985) provides an example of a State model in which the dependent variable, caseloads, is in the levels. One of the explanatory variables in the model is a dummy for OBRA-81 implementation. The coefficient of this dummy represents the estimated effect of implementation on the level of the caseload in each State under the implicit assumption that the effect on the level is the same in all States. It would be more reasonable to assume that the effect in each State would be proportional to the size of the caseload -- the assumption implicit if the dependent variable were in logarithms.
3. We initially specified vital statistic variables -- marriages, out-of-wedlock births, and divorces -- in levels but switched to a change specification after finding that the latter had substantially more predictive power.
4. The autocorrelation parameter for each state could be negative because the dependent variable is a first difference. A value of zero in the first-difference specification corresponds to a value of one in a levels specifications. We estimated the model using the SAS/ETS, Release 6.10,procedure TSCSREG. We adjusted the standard errors and t-statistics obtained from SAS because of an error in the program that was confirmed by the SAS Institute. The standard errors reported by SAS were multiplied by [T/(T-P)].5, where T is the number of quarters in the sample period and P is the number of explanatory variables in the equation, and the t-statistics were divided by the same factor.
5. This limitation can be solved by imposing more structure on the variance and covariance parameters in the model, but this could not be implemented with TSCSREG.
6. For the same reason, we did not test for fixed state effects as originally planned. This would have required specifying the model in levels rather than changes and including 51 state dummies for the fixed effects, which was not possible given the length of the time series. Based on our earlier work concerning participation in SSA's disability programs, however, we were confident that we would not have rejected the fixed effect model.
7. The estimation was performed using the SAS procedure MODEL.
8. We initially planned to use polynomial distributed lags to impose some structure on the coefficients of the lagged unemployment rate variables because we expected collinearity among the lagged values to result in erratic patterns of the estimated coefficients. Collinearity was not, however, a serious problem, even with as many as nine lags.
9. The cubic spline specification requires each adjacent pair of annual observations to fall on a cubic function of time. The cubic function can be different for each adjacent pair, but the first and second derivatives of the two functions passing through a specific year's value are constrained to be the same.
10. The linear spline specification fits a continuous curve to the data by connecting successive input values with straight line segments. This method was used to produce the following quarterly series: IMMGTOTL, IRCA, MEDGAIN, MEDFAM3, SSIKIDS, and ZEBLEY. These variables are defined in Chapter 4.
11. This method is implemented using the EXPAND procedure in the Economic Time Series (ETS) component of SAS (see SAS/ETS Users Guide, 1993).