2. Year and Seasonal Effects
The estimated coefficients of the seasonal and calendar year dummies appear at the end of Exhibit 5.1. Recall that the calendar year dummies can be interpreted as the annualized growth rate in the first (winter) quarter holding all other variables constant. To obtain the annualized growth rate for the full year holding all other variables constant it is necessary to add the average of the seasonal coefficients (including zero for the winter quarter) to the calendar year coefficient. For the basic caseload equation, the average of the seasonal coefficients is 1.0 percent, i.e., .010 = (0 - 0.004 - 0.010 + 0.053 )/4. In interpreting these coefficients, it should be kept in mind that they may be misleading with respect to the extent of national participation growth not accounted for by the state variables because the state observations were not weighted by relative size in estimating the model. The simulations reported later (Chapter 6) do so. Nonetheless, the patterns of the year coefficients are closely related to the patterns of national growth not accounted for that are found in the simulations.
All but three of the calendar year coefficients are positive in the caseload equation with vital statistics after the seasonal adjustment. The positive values for each year from 1985 to 1991 are significant and substantial. This indicates that substantial growth in the caseload during this period is not accounted for by the variables in the model. The largest calendar year coefficient is 4.8 in 1990; after adjusting for seasonal effects, the estimate implies that the caseload grew by 5.8 percent in that year for reasons not accounted for by other variables in the model. The smallest coefficient is for 1981, the year that OBRA81 was implemented: -3.0 percent after adjustment. This represents only a portion of the possible effect of OBRA81, as we discuss further below. In all other years (1979-80, 1982-84, and 1992-94) the calendar year dummies are under 1.0 percent in absolute value after adjustment, and not statistically significant. Results are similar in other equations.
In summary, the state-level factors in the model appear to account for most of the growth in the caseload in eight of the 16 years of the sample period. For the seven years from 1985 to 1991, substantial growth is not accounted for by these variables, and these variables do not account for some of the decline in participation in 1981. As will be demonstrated by the simulations (Chapter 6), the state-level factors do explain much of the large cyclical variation in the caseload, but leave much of the long-term trend in the caseload unaccounted for.