The Use of Multi-State Life Tables in Estimating Places for Biomedical and Behavioral Scientists: A Technical Paper (1997)

With the exception of death rates, the data used to estimate the transition rates were derived from the information collected by the SDR, a longitudinal sample survey undertaken biennially since 1973. From 1973 through 1989, the sample included (1) individuals who earned their doctorates in a science or engineering field from U.S. institutions, (2) U.S.-earned doctorates in education and professional fields, and (3) any doctorates employed in 1973 as scientists or engineers with foreign-earned Ph.D.s. These individuals were to be kept in the sampling frame for 42 years from the time they were first sampled.¹⁵

The sample used to generate the estimates included only those respondents who reported valid information in two adjacent surveys on employment status, occupation, birth year,¹⁶ and U.S. employment location in both the initial and the terminal year of the biennial period.¹⁷ The proportions were calculated by age of the survey respondent beginning with age category 28-29 and proceeding in two-year intervals through age category 68-69; the final category was age 70 and above.

To estimate transition rates for the biomedical and behavioral workforces, the data were aggregated into three distinct six-year periods: 1973-1979, 1979-1985, and 1985-1991. This provided a sample size that would be large enough to produce reasonably reliable estimates. It also provided some initial data that would allow

the panel to evaluate the assumption that transition rates were stable.¹⁸

Since during the course of a career an individual could have more than one transition to a retirement state, each transition was treated as a separate observation in the retirement rate calculations. To calculate the proportion of retiring biomedical or behavioral scientists, average age-specific retirement rates for combined six-year periods of time were used as model parameters. These rates were calculated by first summing the total number of persons retiring in three separate pairs of survey cycles. For example, survey years 1973 and 1975 represent one pair of survey cycles; persons employed in 1973 but retired in 1975 were counted as "retired" in this pair of survey cycles. Survey years 1973-1975, 1975-1977, and 1977-1979 represent three pairs of survey cycles. The total number of persons retiring in three pairs of survey cycles was then divided by the total number of persons in the workforce during the earlier year of each pair of survey cycles (e.g., 1973 in the 1973-1975 pair of survey cycles). In computing these retirement rates, the data were aggregated over both the biomedical and behavioral science workforces to enhance sample sizes. This aggregation assumes that age-specific retirement rates do not differ significantly between these two workforces.

Field mobility was defined as movement out of or into the field of biomedical or behavioral science. As with retirement rates, the mobility rates were based on the observed proportion of personnel moving out of or into a field over a two-year period. In the case of biomedical out-migration, for example, the rate was defined as the proportion of persons moving from the biomedical workforce state to a nonbiomedical workforce state between two survey cycles. The biomedical in-migration rate was defined as the proportion of persons moving from the nonbiomedical workforce to the biomedical workforce over a two-year period. As noted earlier, the base (or denominator) of these proportions was not the same for the two types of mobility. For outflows it was the field-specific workforce; for inflows it was the nonbiomedical or nonbehavioral workforce.

The methods used to calculate the mobility rates by age category for the two-year periods and for combined periods of time were the same as those described for retirement rates. Similarly, the methods used to calculate mobility rates for the behavioral workforce were the same as those described for the biomedical workforce.

The model includes four disjoint workforces: biomedical, nonbiomedical, behavioral, and nonbehavioral.¹⁹ The number flowing into the biomedical (or behavioral) workforce is constrained by the model to be equal to the number flowing out

of the nonbiomedical (or nonbehavioral) workforce.

The methodology used by the SDR to estimate the number of deaths was considered to be inaccurate as it was produced by a sample that was too small to be considered reliable. Therefore, death rates were estimated from data for TIAA policyholders used in a recent study of faculty labor markets.²⁰ The age-specific death rates were based on five-year rates from the mid-1980s.²¹

"New entrants" were defined in the model as individuals who either had entered the workforce for the first time or had reentered the workforce after a period of time in the nonworkforce state. The number was not estimated from existing data sources. Instead it was solved for by the model. The estimate represented the number needed to support a given projected rate of workforce growth.²² These new entrants were distributed by age based on SDR data from two pairs of adjacent surveys as shown in Appendix B.²³

The estimated transition rates generated from the SDR and the TIAA data are summarized by type of transition and period of analysis in Table 1.²⁴ When averaged over all age groups within a period, these estimated rates look reasonable and do not display large amounts of variation. Most of the observed variation reflects interperiod differences in the age distribution of the workforce. Age-specific mortality and retirement rates, as well as in-migration and out-migration rates, are shown in Appendix C. Overall rates are shown in Table 1 for the three cohorts.

The average mortality rate is about 1 percent in the biomedical workforce and

ranges between 1.2 and 1.5 percent in the behavioral workforce. Retirement rates show a clear upward trend and range from 1.4 to 2.7 percent. Mobility rates to other fields are in the 3 percent range in the biomedical workforce, and they are in the 2 percent range in the behavioral workforce. Mobility rates from other fields range from 0.6 to 0.9 percent in the nonbiomedical workforce and from 0.2 to 0.3 percent in the nonbehavioral workforce.²⁵ There was initial concern about the stability of these estimates over time since this is one of the critical assumptions underlying the model. Another concern was about the adequacy of the SDR sample for producing reliable estimates. The empirical analysis summarized below addresses these issues.

For each of the transitions, the data reveal a considerable amount of stability over time. It is reassuring to find the variability among time periods was only a fraction of the variability among age groups at a given period of time. This suggests that if we know the age distribution of the population, we can make projections with

some assurance that the process generating the transition rates is not changing, but only the size of the cohorts that are moving through those ages.²⁶ Table 2 summarizes the variability among age groups. The difference between high and low estimates (i.e., the range of estimates) is 9.9 percentage points for death rates (in contrast to the interperiod difference of 0.1 percentage points summarized in Table 1). The range exceeds 26 percentage points for retirement rates (in contrast to the interperiod difference of 1.4 percentage points summarized in Table 1). It exceeds 8 and 7 percentage points for mobility rates to other fields from the biomedical and behavioral workforces, respectively (in contrast to interperiod differences of 0.3 and 0.1 percentage points summarized in Table 1). And it exceeds 2 and 0.7 percentage points for mobility rates from other fields to the biomedical and behavioral workforce (in contrast to interperiod differences of 0.3 and 0.1 percentage points summarized in Table 1).

In addition to displaying a reasonable amount of stability over time, the rates seem to be reasonably precise. A commonly used statistical indicator of precision is the ''standard error'' of the estimate. This indicator is inversely related to precision (i.e., estimates with a small standard error are more precise than those with a larger Standard error). The "coefficient of variation"—the ratio of the standard error to the mean of the estimate—summarizes the relative variability of an estimate. This may be a more meaningful indicator of precision since it is adjusted for the size of the estimate. Again, an inverse relationship exists between the size of the coefficient and the precision of the estimate; an estimate with a small coefficient of variation is more precise than a large coefficient.

The coefficients of the estimated age-specific, period-specific transition rates derived from the SDR are summarized in Appendix D.²⁷ The distribution of these coefficients reveals that the estimates are reasonably precise and that the estimates for the biomedical workforce were more precise than those for the behavioral workforce. When aggregated over both workforces, over two-thirds were 0.3 or less. This means that these rates were more than three times the size of their standard errors, and that more than one-half of the coefficients for both workforces were less than 0.2, meaning that these rates were at least five times the size of their standard errors.