We propose a sectoral-shift theory of aggregate factor productivity for a class of simple 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 the Solow residual in these economies are driven by random and persistent endogenous fluctuations in the sectoral distribution of physical capital which, in turn, responds to persistent and reversible shifts in relative sector productivities. Surplus capital from less productive sectors is lent to more productive sectors in the form of secured collateral loans, as in Kiyotaki-Moore (1997), and also as unsecured reputational loans suggested in Bulow-Rogoff (1989). Debt limits slow down capital reallocation, preventing the equalization of risk-adjusted equity yields across sectors. Economy-wide factor productivity is highest when most capital has already shifted to the most productive sectors or, equivalently, when prolonged arbitrage has sufficiently reduced the sectoral dispersion of equity returns. If sector productivities follow a symmetric two-state Markov process, many of our economies converge to a periodic cycle alternating between mild expansions and abrupt contractions.