If we allow for the existence of specific training, dollar investment costs are positively correlated with job duration since higher levels of investment (due partly to the existence of specific training) imply lower turnover rates, ceteris paribus.

The correlation between investment and job duration clearly holds in terms of dollar investment costs. However, the equations derived are in terms of ”time-equivalent” investment costs. So that when using the log-linear equations, a strong assumption must be made: there is a positive correlation between dollar Investment costs and the time spent Investing. The reason for the assumption Is that even though dollar Investment costs and completed job duration are positively correlated, the same need not be true between time-equivalent costs and job duration. The assumption permits us to say that there Is a positive correlation between time Investment and completed experience, since those with longer job duration will have more Investment, but by assumption they spend more time at It. comments

These hypotheses can be easily Introduced Into the earnings function If we assume the relationships to be linear. In particular, the level of Investment In the 1C^ Job (kQ^) Is given by:
where t1 Is the expected completed duration of the I21 job, and ir^ Is labor force experience prior to starting job l. The parameter measures the Importance of specific training on Investment behavior, while measures the effect of aging on the distribution of lifetime Investments.