A Macroeconomic Model with a Financial Sector

This paper builds and fully solves (rather than merely linearizes around a steady state) a continuous-time macroeconomic model in which financially constrained “experts” are more productive at managing capital than “households” but must finance their holdings partly with debt and limited outside equity, subject to a solvency constraint. The economy’s entire equilibrium is pinned down by a single state variable – experts’ aggregate net worth as a share of the capital stock – and behaves very differently depending on where that variable sits: near its stochastic steady state, experts are relatively unconstrained, absorb ordinary shocks through reduced payouts, and asset prices barely react to changes in net worth, so the system is calm and mean-reverting; but once a run of losses pushes net worth far enough below that point, an adverse feedback loop kicks in in which falling net worth forces experts to shed capital, which depresses the price of capital, which depresses net worth further, generating “endogenous risk” and volatility that is large relative to underlying fundamental shocks. The resulting long-run stationary distribution of net worth is bimodal – the system spends most of its time either near normal or in a deep crisis state, and moves quickly through the highly volatile region in between – a pattern the paper calls “ergodic instability” and shows is invisible to standard models that linearize around a single steady state. Two results are explicitly counterintuitive: lower fundamental (exogenous) risk encourages experts to hold thinner capital buffers and take on more leverage, so it can make the system more prone to systemic crises (the “volatility paradox”); and allowing experts to hedge idiosyncratic risk among themselves, as with securitization, likewise lowers their effective cost of capital and encourages more leverage, again amplifying systemic risk even though it improves risk-sharing for any given leverage choice. Because individual experts do not internalize how their own leverage and asset sales depress prices for everyone else during a crisis (a fire-sale pecuniary externality), the market outcome is not even constrained efficient, though the paper shows a planner facing the same financing frictions could in principle attain the first-best outcome using transfers or price-stabilization policy.

Yuliy Sannikov | Macro Paper Warehouse

A Macroeconomic Model with a Financial Sector