A search-based neoclassical model of capital reallocation

The purchase of used capital accounts for at least 25% of firms’ total investment and more importantly, cross-firm reallocation of used capital exhibits intriguing business-cycle properties, such as (i) the quantity of capital reallocated is procyclical; (ii) the prices of used capital are procyclical and more so than those of new capital; (iii) the benefits to capital reallocation—measured by the dispersion of firms’ TFP—is countercyclical; and (iv) the dispersion of firms’ gross investment rates is procyclical despite the fact that the dispersion of firms’ Tobin q is countercyclical. This set of stylized facts do not seem to be mutually consistent with each other; e.g., the third stylized fact appears contradicting the first stylized fact since the quantity of capital reallocation is expected to be larger when the benefits to capital reallocations are greater. We build a search-based neoclassical model with variable capacity utilization to explain these seemingly “contradictory” facts. We show that search frictions in the capital markets are essential for our empirical success but not sufficient—the right type of aggregate shocks (i.e., shocks to the matching efficiency instead of aggregate TFP) are also important for simultaneously accounting for all the stylized facts, especially regarding the dispersion of firm-level TFP and the dispersion of firms’ investment rate.