This dissertation examines economies that may occasionally enter periods of crisis. I first develop a model of asset pricing in the presence of frictions to financial intermediation. This model generates recurrent financial crises due to its strong non-linear dynamics. Next, I develop methodological tools for analyzing these types of highly non-linear dynamic equilibrium models. I then apply these tools to a theory of housing boom-bust cycles driven by endogenous shifts in lending standards.
Chapter 1 introduces a model of asset pricing in the presence of agency frictions between savers and financial intermediaries. This model can generate asymmetric price movements where asset values suddenly collapse during a financial crisis. During normal times, intermediaries arbitrage away excess returns on assets and traditional asset pricing conditions hold. During a financial crisis, the net worth of intermediaries limits their ability to borrow from savers and they are unable to arbitrage away excess returns. Since their net worth depends on realized asset values, collapsing prices further tighten borrowing constraints leading to a large and sudden collapse in asset values.
In chapter 2, I introduce a local approach to solving highly non-linear models, generalizing perturbation to handle the class of piecewise smooth rational expectations models. First, I formalize the notion of an endogenous regime by introducing a regime-switching equilibrium (RSE) concept. This framework uses non-linear model features to explain macroeconomic regime changes, and makes the distribution of the regime an equilibrium object instead of imposing an external regime-switching structure. Then, I demonstrate how to apply perturbation within a slackened model, approximate the policy functions associated with a given belief about the regime, and solve for the equilibrium regime distribution using backwards induction. This approach (1) accounts for expectational effects due to the probability of regime change; (2) provides a framework for modeling regime-switching from first principles; and (3) connects macroeconomic theory to reduced-form regime-switching econometric models.
Chapter 3 develops a theory of housing boom-bust cycles driven by endogenous shifts in lending standards. The key friction is asymmetric information about default risk, implying that the economy occasionally and endogenously switches between two credit regimes. These regimes differ by whether or not lenders use income verification to screen the marginal homebuyer. A switch from the ``screening'' regime to the ``pooling'' regime leads to rapid home price appreciation, a collapse in down-payment requirements, and a reduction in income documentation --- consistent with the shift in lending standards during the US housing boom. The episode ends in a foreclosure crisis once fundamentals revert and the screening regime returns. The theory predicts patterns for debt accumulation and mortgage spreads consistent with existing micro evidence.