Physical capital is often specific to a certain task and/or fixed to a particular location. These specificities imply that physical capital markets are subject to potentially important allocation frictions. Most of the modern macro literature has ignored these market imperfections and examined instead the effects of aggregate investment constraints such as time&to&build delays (e.g. Kydland and Prescott, 1982) or convex adjustment costs (e.g. Cogley and Nason, 1995).
The general conclusion from this literature is that in general equilibrium, such aggregate investment constraints have relatively small business cycle effects on their own. In this paper, we investigate whether the same holds true for market imperfections. In particular, we introduce search frictions for the allocation of physical capital into an otherwise standard real business cycle (RBC) model and ask whether these imperfections help generate more amplified and persistent responses to small exogenous shocks.
Our investigation is motivated by empirical evidence from industry& and firm&level data, discussed in detail in Section 2, that lead to three stylized observations. First, depending on the degree of specificity, a substantial amount of physical capital remains unmatched in any given period. Second, congestion in the physical capital market is countercyclical from the point of view of the supplier; i.e. the probability of (re&)allocating a given unit of capital to a firm increases in business cycle upturns and inversely decreases in downturns. Third, the distribution of investment rates across individual firms is wide, even in narrowly defined sectors and independent of aggregate conditions.
The three observations suggest that physical capital markets are characterized by similar frictions than labor markets and thus, our modelization draws on the now widely employed search approach for the labor market, pioneered by Blanchard and Diamond (1990) and Mortensen and Pissarides (1994), and introduced into the DGE context by Merz (1995), Andolfatto (1996) and Den Haan, Ramey and Watson (2000).
The model we develop in Section 3 is populated by representative households and firms. Firms must post projects at a cost to search for available physical capital that is supplied endogenously by households. The probability of a match varies with the state of the economy and depends on the ratio of available capital to the total number of posted projects. Once matched, households keep lending their capital to the same firm until separation, which is assumed to occur with exogenous probability in the baseline model. Once separated, the capital returns to the household for reallocation.
Under relatively weak conditions, the proposed search environment implies countercyclical congestion in physical capital markets, as in the data. This mechanism has potentially important aggregate consequences. In the wake of a positive technology shock, for example, the decrease in allocation frictions together with the presence of readily available unmatched capital means that the reaction of productive matched capital stocks and indirectly labor demand is more important than in the RBC benchmark. This effect continues over several periods after the shock and may lead to more amplified and persistent output dynamics.
To assess the quantitative importance of the search friction, Section 4 calibrates the model to fit long&run averages of firm&level capital flows using Compustat data and compares its business cycle characteristics with the ones of the RBC benchmark. The main result is that capital flows in and out of production are not important enough for search frictions to have a significant impact. Only when we increase separation and reallocation to counterfactually large flows does the model generate more amplified and persistent output dynamics.
Based on this result, Section 5 extends the baseline model with credit market frictions. Following Townsend (1979), firms are subject to idiosyncratic productivity shocks that occur after all optimal decisions are taken and that households (the lenders) can observe only after incurring a monitoring cost. This costly state verification problem implies an optimal debt contract that results in endogenous capital separation through default. In particular, households monitor all loss&making firms and sever the lending relationship with those whose productivity level is below some threshold that makes refinancing more expensive than reallocating the capital to another firm.
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