Stochastic growth models and their econometric implications

This article considers the consequences of explicitly allowing for stochastic technological progress and stochastic labor input in the discrete-time Solow-Swan and AK growth models. It shows that the capital-output ratio, but not output per capita, is ergodic irrespective of whether there is a unit root in technology, and thus is the more appropriate measure to use in the cross-sectional analysis of the growth process. Furthermore, the article derives the cross-sectional and time-series implications of the stochastic Solow-Swan model and contrasts these to those of its deterministic counterpart. Among these implications are that the mean of the capital-output ratio depends in a precise way not only on the saving rate and the growth rate of labor input, but also on the variance and higher-order cumulants of the capital-output ratio. Using the Summers-Heston data for seventy-two countries from 1960 to 1992, strong support is found for the predictions of the stochastic Solow-Swan model as compared to those of its deterministic counterpart (as well as those of the AK model), including a significant negative cross-sectional relationship between the mean and the variance of the capital-output ratio.