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• #### APPENDIX D 33-33

To approximate likelihoods or rates, the model generally expresses these flows as fractions of some relevant stock variable (e.g., the workforce).11 For example, among the outflows the likelihood of a member of the workforce dying (or death rate (dt)) was defined as the ratio of Dt to WFt. Comparable definitions were used for retirement rates (rt) and rates of mobility to other fields (moboutt).12 Only one inflow variable—mobility from other fields (mobint)—was expressed as a likelihood or transition rate. The stock used to deflate this inflow was the workforce of scientists and engineers in other fields (NONt) (e.g., nonbiomedical or nonbehavioral). New entrants (NEt) was treated as an endogenous variable, determined by the model, and was not deflated by a stock variable.

Given the assumptions about immigration and emigration, and given the transformations of numbers to rates, the workforce model can be summarized by the following equation:

An important issue for determining training needs is the number of new entrants that will be needed to support the workforce (i.e., to replace those who leave and to provide for adequate workforce growth). Equation (4) can be transformed to solve for this number. Solving for NEt, the equation becomes

The model assumes that the rates summarized in equation (4) (i.e., dt, rt, mobint, and moboutt) remain constant.13

The model presented above shows the calculation of the number of new entrants under the assumption that there is only one cohort, or, equivalently, that the entire population is the same age. In actual application, in a population consisting of a number of cohorts, NEt is calculated for each cohort and summed to get new entrants for the entire system.14

 11 An implication of this assumption is that the transition rates are assumed to be independent of the size of the pool from which these transitions occur. 12 Transition rates are denoted by lower case and quantities by upper case. 13 In more technical terms, the model assumes that the transition rates are characterized by a zero-order Markov process. 14 It is also possible to make the model even more complex by adding an endogenous "fertility" component. In this sort of a model, some fraction of the biomedical workforce enters the professoriate. These professors reproduce themselves by training new Ph.D.s. Their fertility may depend on research funding and the need for graduate student teaching and research. Fertility may also depend on length of time in the professoriate. Regrettable few data are available to permit enrichment of the empirical model in this way.

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