We construct a vintage capital model in which worker skills lie along a continuum and workers can be paired with different vintages (as technology evolves) under a matching rule of "best worker with the best machine." Labor reallocation in response to technology shocks has two key implications for the wage premium. First, it limits both the magnitude and duration of change in the wage premium following a (permanent) embodied technology shock, so empirically plausible shocks do not lead to the kind of increases in the wage premium observed in the U.S. during the 1980s and early 1990s (though an increase in labor force heterogeneity does). Second, positive disembodied technology shocks tend to push up the wage premium as well, and while this effect is small, it does mean that a higher premium does not provide unambiguous information about the underlying shock. Labor reallocation also means that if embodied technology comes to play a larger role in long-run growth, investment and savings tend to fall in steady state, with little effect on output and employment, enabling the household to increase consumption without sacrificing leisure. The short run effects are more conventional: permanent shocks to disembodied technology induce a strong wealth effect that reduces savings and induces a consumption boom while permanent shocks to embodied technology induce dominant substitution effects and an expansion characterized by an investment boom.
Trehan, Bharat, and Milton H. Marquis. 2007. “Productivity Shocks in a Model with Vintage Capital and Heterogeneous Labor,” Federal Reserve Bank of San Francisco Working Paper 2007-06. Available at https://doi.org/10.24148/wp2007-06