The relation between labor force growth and labor productivity? I don't know. So I went looking.
Crazy Explanations for the Productivity Slowdown (PDF, 40 pages) by Paul M. Romer
For the explanation of the productivity puzzle, the key implication of this revised interpretation of growth accounting is that an increase in the rate of growth of labor will be accompanied by a fall in the rate of growth of labor productivity. This may explain the productivity slowdown in the United States since the 1960s...
Determinants of Labor Productivity: An Empirical Investigation of Productivity Divergence, by Misbah Tanveer Choudhry, University of Groningen, The Netherlands
We analyzed the determinants of labor productivity for the group of 40 countries, representing four different income groups in the world. This study confirms the diminishing return to labor force participation rate both in short run as well as in the long run. We find that negative impact of increased labor force participation is high in lower and lower middle income economies compared to high income and upper middle income economies.
WHY HAS THE EMPLOYMENT-PRODUCTIVITY TRADEOFF AMONG INDUSTRIALIZED COUNTRIES BEEN SO STRONG? by Paul Beaudry & Fabrice Collard. Working Paper 8754
Neoclassical growth theory predicts that, along a transitional path, countries with higher rates of labor force growth should exhibit less labor productivity growth due to the need to use scarce capital to equip new workers.
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