A continuous-time macro-finance model that solves the full equilibrium dynamics of an economy with financial frictions. A leveraged "expert" (intermediary) sector holds productive capital; experts' aggregate net worth is the key state variable. Near the steady state the system is stable, but adverse shocks can push it into occasional, violent crises marked by fire sales, spiking endogenous volatility, and high asset-price correlations. The central insight is the volatility paradox: in calm times (low exogenous risk) experts lever up, which makes the system more prone to systemic volatility spikes — so fragility is greatest exactly when measured risk is lowest.
What it models
How financial frictions turn modest fundamental shocks into large, highly nonlinear downturns through the net worth of constrained intermediaries — generating endogenous risk and amplification that log-linearized (local) models around the steady state miss entirely.
Specification
Two agent types: experts, who have superior ability/willingness to manage productive capital but limited net worth, and less-productive households who lend to them. Experts borrow and operate with leverage.
Continuous-time setting; aggregate capital and productivity follow diffusion processes driven by Brownian fundamental shocks.
The state of the economy is summarized by experts' share of aggregate net worth (η). Asset prices, leverage, and risk premia are all functions of this single state variable, solved over its full (global) range — not just near steady state.
Estimation
Not an empirical/estimated model: it is solved numerically for the full nonlinear equilibrium dynamics (the stationary distribution and laws of motion of the state variable), illustrated via calibration/simulation rather than structural estimation.
What it captures
Amplification spiral: a negative shock erodes expert net worth → experts delever and sell capital → asset prices fall → further net-worth losses, generating endogenous volatility far above the fundamental shock.
Persistence: depressed net worth keeps activity low for extended periods.
Fat-tailed crisis dynamics: the economy spends most time near steady state but occasionally enters volatile crisis regions with high asset-price correlations.
Externalities: securitization/derivatives improve sharing of exogenous risk but raise endogenous systemic risk; experts impose a negative externality by holding inadequate capital cushions.
Use & extensions
Foundational post-2008 model of systemic risk and crisis dynamics; underpins the intermediary-asset-pricing literature (He–Krishnamurthy) and macroprudential analysis of leverage, fire sales, and capital regulation. Methodologically influential for continuous-time solution of fully nonlinear macro models with financial constraints.
Limitations
Highly stylized (single expert sector, specific frictions); quantitative calibration is hard.
Solving the fully nonlinear global dynamics is analytically/numerically demanding and sensitive to functional-form assumptions.
Real-economy intermediation channel; abstracts from nominal rigidities, monetary policy, and heterogeneous-bank interbank networks.
Key references
Brunnermeier, M. & Sannikov, Y. (2014) — A Macroeconomic Model with a Financial Sector — American Economic Review
Brunnermeier, M. & Pedersen, L. (2009) — Market Liquidity and Funding Liquidity — Review of Financial Studies
He, Z. & Krishnamurthy, A. (2013) — Intermediary Asset Pricing — American Economic Review
Provenance: verified/generated from the paper's full text.
