The Substitution Elasticity, Factor Shares, Long-Run Growth, and the Low-Frequency Panel Model

The value of the elasticity of substitution between labor and capital (ó) is a “crucial” assumption in understanding the secular decline in the labor share of income and long-run growth. This paper develops and implements a new strategy for estimating this crucial parameter by combining a low-pass filter with panel data to identify the low-frequency/long-run relations appropriate to production function estimation. Using spectral analysis, we assess the extent to which our choices of the critical periodicity and window defining the low-pass filter are successful in emphasizing long-run variation. The empirical results are based on the comprehensive panel industry dataset constructed by Dale Jorgenson and his research associates. Our preferred estimate of ó is 0.40. We document that standard estimation methods, which do not filter-out transitory variation, generate downwardly biased estimates. As high frequency variation is introduced into the model variables, ó declines by 40% to 70% relative to the benchmark value. Despite correcting for this bias, our preferred estimate is substantially below the Cobb-Douglas assumption of ó = 1, and thus implies that the secular decline in the labor share of income cannot be explained by secular increases in the capital/income ratio or secular decreases in the relative price of investment or capital taxation.