International capital allocations and the Lucas Paradox redux

This paper studies the marginal product of private capital (MPK) with new data and a new framework to obtain a better understanding of international capital allocations and the Lucas Paradox (LP). Our point of departure is three influential studies of MPK's and, based on the most recently available data, the LP is either sustained, inverted, or rejected. We then introduce three improvements in measuring spot MPK's, and the LP clearly reemerges. While these results are provocative, they may be misleading because they do not recognize the dynamics of the capital accumulation process toward steady-states. We develop and estimate a model that allows us to map spot MPK's into steady-state MPK's. The LP remains; the steady-state MPK's for poor countries is 48% to 77% higher than for rich countries. Four policy implications follow from these estimates. First, there is a great deal of misallocated capital globally: 14% to 21% of the global capital stock. Second, this misallocation is primary due to the difference between country-specific steady-state MPK's and the global MPK that would maximize world output. Third, the benefits of optimally reallocating capital and eliminating the LP are modest: 1.0% to 1.5% of global output or $873 to $1,309 billions of 2019 US dollars. Fourth, the estimates for both misallocation and reallocation depend crucially on the elasticity of substitution between capital and labor. Our empirical work uncovered three new puzzles that have emerged beginning in 1990, 1) the MPK's for both poor and rich countries have been rising sharply, 2) the gap has been widening, and 3) the steady-state MPK's exceed the average spot-MPK's. The later result is inconsistent with the Dynamic Inefficiency, Saving Glut, or Secular Stagnation hypotheses.