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ALTERNATIVE MODEL DESIGNS: PROGRAM PARTICIPATION FUNCTIONS AND THE ALLOCATION OF ANNUAL TO 106 MONTHLY VALUES IN TRIM2, MATH, AND HITSM alternatives or the user ma y choose other participation rates. In any case those units simulated to participate in the baseline run that remain eligible under the program alternative are always simulated to participate under that alternative, with any additional units required to make up the target participation rates selected at random from newly eligible units. MATH SSI participation is determined in the PAPRAT module, which also simulates AFDC and GA participation. PAPRAT is a companion to the PBLAST module, which simulates eligibility for SSI, AFDC, and GA. The PAPRAT module first calculates participation rates to be used in selecting eligible units to participate. It counts the number of units simulated to be eligible and their simulated benefit amounts by filing unit type and, if desired, by region or state. Filing unit types are AFDC nonsingle parent, AFDC single parent, AFDC unemployed father, SSI aged, SSI disabled, and GA. The number of eligible units and benefit amounts are compared with control totals for participants in the same categories to derive coefficients for an equation of the form: where PROBPT is the probability of participation, a and B are coefficients, and SIMBEN is the simulated benefit amount. Hence, participation rates vary by benefit amount within each of the categories defined by filing unit type and, optionally, by region or state. Using these participation rates, the module first picks from among eligible people who reported receiving benefits from the particular program in the March CPS. If there is an insufficient number of these units, the module then selects from among the group of eligible nonreporters. The module also identifies ineligible units that can be selected to participate if the caseload and benefit controls within a cell defined by filing unit type and region cannot be met. (However, in the recent past, users of MATH have chosen to relax the regional controls rather than select ineligible units to participate, as this improves the simulation of public assistance cases with food stamps.) Finally, the module can invoke a microtracking procedure, which alters the probability of participation in one case if the actual cumulative selection rate among prior cases deviates significantly from the expected rate. (See the description of routine 506 in Doyle et al.  for a detailed discussion of the operation of PAPRAT.) HITSM Participation rates for the SSI program are estimated by using administrative data on the number of participants and the HITSM model's estimates of the