Captial Reallocation and Productivity

This paper studies the effects of cyclical capital reallocation on aggregate productivity. Frictions in the reallocation process are a source of factor misallocation and lead to variations in measured aggregate productivity over the business cycle. The effects are quantitatively important in the presence of fluctuations in the cross-sectional dispersion of plant-level productivity shocks. The cyclicality of the productivity losses depends on the joint distribution of capital and plant-level productivity. Even without aggregate productivity shocks, the model has quantitative properties that resemble those of a standard stochastic growth model: (i) persistent variation in the Solow residual, (ii) positive co-movement of output, investment and consumption and (iii) consumption smoothing. The estimated model with dispersion shocks alone accounts for nearly 85\% of the time series variation in the observed Solow residual. Contrary to a model with productivity shocks, the model driven by dispersion shocks can mimic the dynamics of reallocation and the cross sectional dispersion in average capital productivity. Instead of relying on approximative solution techniques we show analytically that a higher-order moment is needed to solve the model accurately.