by Steven J. Davis, Felix Kubler, and Paul Willen
No. 3, January 2005 - June 2005

Motivation for the Research
Borrowing presents a problem for life-cycle models of consumption and portfolio choice. In the classic Merton-Samuelson model, modified to include a realistic process for labor income, unsecured borrowing leads to huge, highly leveraged equity positions.

Life-cycle models that preclude borrowing can generate realistic equity holdings, but they fly in the face of evidence that unsecured consumer credit is widely available and widely used. In fact, unsecured debt is much more prevalent than equity in the portfolios of younger households.

In this paper, the authors construct a life-cycle model that resolves the tension between borrowing and equity holding.

Research Approach
The authors use a life-cycle model in which households can borrow, but at rates that exceed the risk-free investment return. Except for its treatment of borrowing, the model is standard. Agents face realistic income processes and can invest in risky and risk-free assets. The key elements of the analysis are realistic borrowing costs and the life-cycle structure.

Key Findings

• A model with a wedge between borrowing costs and the risk-free investment return can simultaneously deliver sensible life-cycle profiles for debt and equity holdings and high rates of nonparticipation in equity markets.
  
  
• Realistic borrowing costs dramatically reduce equity holdings, and equity demand is at its minimum when the borrowing rate equals the expected return on equity.
  
  
• The model with realistic borrowing costs does a better job of fitting observed life-cycle patterns in borrowing, equity market participation, and equity accumulation than alternative models with no borrowing or limited borrowing at the risk-free rate.
  
  
• The analysis highlights the role of borrowing costs and leverage as key factors in the demand for risky assets.

Implications
The opportunity to borrow at realistic rates in a life-cycle setting has important consequences for wealth accumulation. Because households face an upward-sloping income profile, they borrow in the early part of the life cycle, which delays the age at which they participate in equity markets or accumulate significant holdings. This implication of the model helps explain the low equity holdings of most households in the face of an apparently high equity premium.

The model implies that most households accumulate little or no financial wealth until middle age, consistent with much empirical evidence. Given its simplicity and its assumption of time-consistent, rational consumers, the model and analysis challenge claims that households save too little, or that they should be prompted to save more.

Full text of Working Paper 05-7