field (biomed, behavioral, other), non-R&D employment within broad Ph.D. field, employment outside of broad Ph.D. field, out of labor force or unemployed (combined), leaving the country, retirement, and death. All of the biennial transition proportions were obtained by 2 year age group by broad Ph.D. field, and by sex. The survey observations (i.e., people) in one set of biennial transitions are often the same people in subsequent sets (though older). ^{4}
Another data ingredient for the life tables is the distribution of states (same as above) of “new entrants to the SDR” for SDR waves 1975-1991, again by age, sex, and Ph.D. field. These are used as estimates of numbers of new Ph.D.s in each survey year.
These transition data sets constructed by NRC staff were transformed into proportions to be used as input into a Multistate Life Table program (Tiemeyer and Ulmer, 1991). Initial work involved explorations of data quality, sample sizes, and the stability of rates over time. To have large enough sample sizes for (what we would hope to be) reliable estimates of sex differences in career patterns as well estimates of how the career patterns have changed over time, it was necessary to aggregate the data into three broad time periods (as opposed to looking at a larger number of time periods): 1985-1991, 1979-1985, 1973-1979.
Life table construction begins by calculating a matrix containing the proportion of individuals exiting an origin state for each possible destination state between ages x and x+2 (in our case). This matrix is called M_{x}.
Our projection models hold the population of those employed “in field” to some constant growth rate. The following algorithm is used:
Survive the current specified Ph.D. population forward 2 years.
Calculate the number of individuals employed “in field”.
Calculate the differences between the target “in field” population and the number “in field” in the survived current population. This yields the number of new entrants needed to increase the “in field” population to its target size.
Divide the result of (3) by the proportion of new entrants who enter an “in field” employment state on receiving their Ph.D..
Use the result of (4) as the number of new entrants who would have had to enter the population between year y and y+2 to attain the target “in field” population. Add these individuals into the life table, distributed approximately by age and destination state.
Let N_{x,y} represent the number of individuals in the specified Ph.D. population in each employment state at age X for a given year Y. N_{x,y} is a k by k matrix, where k equals the number of states in the model. The columns indicate origin states (in the base year) and the rows destination states. So N_{x,1995}[4,1] would equal the number of people who were in the 4th state (out of field employment) in 1995 who were in the 1st state (in field post-doc) in 1991. For the base year, the off-diagonal elements of N_{x,1991} are all 0 and the ondiagonal elements are equal the number of individuals age X in 1991 in the specified Ph.D. population in each employment state.
Let N^{-}_{x,y} represent the number of individuals in each state (by origin state in 1991) in year y, BEFORE new entrants between year y and y-2 are added into the life table. Then N^{-}_{x,y} is given by:
Let F_{1991} represent the total number of individuals in the specified Ph.D. population employed “in field” in year 1991. Then F_{1991} is given by:
where x represents age, o represents origin of state, d represents destination state, N_{x,1991}[o,d] represents the dth row and the oth column of N_{x,1991'} and where states 1 through 3 represent the employed “in field” states.
Let F^{-}_{y} represent the total number of individuals in the specified Ph.D. population employed “in field” in year Y who were in the specified Ph.D. population (although not necessarily employed “in field”) in year Y-2. Then F^{-}_{y} is given by:
Let G represent the assumed 2-year growth rate for F_{y}. Then the target employed “in field” population size for any given year is:
Target “In Field” Population Size (y) = F1991 · (1+G)^{y·1991}
Let D_{x} represent the proportionate distribution by age and state of new entrants to the specified Ph.D. population over the two year period between Y and Y+2. D_{x} is a 1 by k vector with each column representing the proportion of all new entrants who are age X who enter that state on receiving their Ph.D. Summing D_{x} across all ages and states should equal one.
Finally, let R represent the proportion of all new entrants who enter an “in field” state on receiving their Ph.D. Then R is given by: