Leverage Cycle over the Life Cycle: A Quantitative Analysis of Endogenous Leverage and Policy Implications

This dissertation studies endogenous leverage and policy interventions related to leverage. The key contribution of this work lies in developing of a quantitative model of endogenous leverage, serving as a workhorse for research in this area. In the first chapter, a positive analysis captures the housing leverage cycle and demonstrates the amplification effect of leverage on housing price volatility. The second chapter shifts to a normative analysis, exploring how various macro-prudential policies influence market equilibrium.

This first chapter develops the quantitative model to rationalize two well-established trends on the US housing market: leverage moves in tandem with housing prices, whereas mortgage spreads move in the opposite direction. In this model, a large number of overlapping generations accumulate housing assets using leverage. They select mortgage contracts from a menu that specifies interest rates for various levels of loan-to-value ratio (LTV), often called a Credit Surface. Within this framework, large negative endowment shocks not only reduce housing prices due to households' decreased purchasing power but also reinforce the decline by weakening the ability of houses to serve as collateral for borrowing. The Credit Surface rises and becomes steeper as interest rates and spreads increase in downturns. In an application calibrated to the Great Recession, the model matches the 10-percentage-point drop in the leverage of first-time homebuyers that was observed at that time.

The second chapter examines policies aimed at mitigating housing leverage cycles, focusing on the impacts of taxing versus subsidizing mortgage contracts. Comparing the market outcomes under policy interventions with the one introduced in the first chapter as a benchmark, we find that taxing mortgage contracts leads to higher housing prices and leverage, while reducing interest rates and spreads. Additionally, taxation enhances consumption smoothing across the life cycle and states, resulting in welfare gains for young households but losses for older ones. In contrast, subsidizing mortgage contracts produces minimal effects and fails to improve welfare for any age group.

The observed asymmetric effects between tax and subsidy policies are caused by the unbalanced response from the supply and demand sides of the credit market. While demand responds little to these policies, taxing incentivizes lending by raising returns, whereas subsidizing leads lenders to suppress credit supply, exacerbating the credit climate. This study underscores the importance of considering the supply side responses in the credit market when designing effective policies.