Capital Misallocation and Aggregate Factor Productivity

We propose a sectoral-shift theory of aggregate factor productivity for a class of economies with AK technologies, limited loan enforcement, a constant production possibilities frontier, and finitely many sectors producing the same good. Both the growth rate and total factor productivity in these economies respond to random and persistent endogenous fluctuations in the sectoral distribution of physical capital which, in turn, responds to persistent and reversible exogenous shifts in relative sector productivities. Surplus capital from less productive sectors is lent to more productive ones in the form of secured collateral loans, as in Kiyotaki-Moore (1997), and also as unsecured reputational loans suggested in Bulow-Rogoff (1989). Endogenous debt limits slow down capital reallocation, preventing the equalization of risk-adjusted equity yields across sectors. Economy-wide factor productivity and the aggregate growth rate are both negatively correlated with the dispersion of sectoral rates of return, sectoral TFP and sectoral growth rates. If sector productivities follow a symmetric two-state Markov process, many of our economies converge to a limit cycle alternating between mild expansions and abrupt contractions. We also find highly periodic and volatile limit cycles in economies with small amounts of collateral.