Consumer Default and the Life Cycle Model

Article excerpt

Rates of consumer default have increased dramatically in the United States in the past decade. Between 1980 and 199 1, the total number of personal estates in bankruptcy increased from 315,000 to over a million. In 1980, 1.4 households out of every thousand declared bankruptcy. By 1991, this rate had increased to 4.6 per thousand households (Credit Research Center 1992). Although part of this increase reflects cyclical factors, much has been attributed to deregulation of interest rates in the 1980s that encouraged lenders to seek out more risky clients and to bankruptcy reform legislation in the late 1970s that reduced the costs of declaring bankruptcy. This legislation, for example, significantly increased the type and amount of assets exempt from collection.

In theory, default risk results either in higher rates and/or restrictions on loan size (Jaffee and Russell 1976; Stiglitz and Weiss 1981). Over the past decade, rates on twenty-four-month personal loans exceeded yields on twenty-four-month Treasury notes by about 70 percent (Federal Reserve Bulletin). In practice, of course, default risk cannot explain entirely such a large differential. Aggregate rates of consumer default remain quite small. In 1986, bank losses due to bankruptcy amounted to only 1 to 2 percent of the value of credit outstanding. Compared with earnings ratios of just 2 to 3 percent, however, these losses are certainly large enough to influence bank behavior (Luckett 1988). Furthermore, default risk has a large indirect effect on interest rate margins due to administrative costs associated with trying to reduce that risk.

Despite the potential importance of the default option to banks and consumers, most models of consumption ignore default. The consumption Euler equation typically is derived based on the explicit assumption that individuals borrow and lend freely at the same risk free rate. Consequently, empirical work generally focuses on the sensitivity of consumption to changes in the after-tax Treasury bill rate. This assumption constitutes a principal explanation for empirical rejections of these models (Hall and Mishkin 1982; Shapiro 1984; Zeldes 1989a). Although some life cycle models have incorporated borrowing restrictions, these generally have been imposed exogenously rather than explained as an endogenous response to default risk.(1)

An important question, therefore, is how a default option alters the standard implications of the life cycle model. To address this issue, I relax the assumption that consumers fully repay all loans and instead allow default to occur if an individual receives a bad draw of income in the second period. Using a simple, two-period model, I show how borrowing/lending rate differentials and, in some cases, quantity restrictions on debt arise endogenously. Hayashi (1987) uses a very similar model to point out how different assumptions about default risk influence the form of the consumption Euler equation and to show the circumstances under which Ricardian equivalence holds. My paper uses this model to explain more broadly how a default option influences the level of consumption, its sensitivity to income, and the type of borrowing constraints likely to emerge.

The theoretical starting point for this paper is the observation that a default option generates not only a budget set kink, but also an indifference curve kink. In the first part of the paper, I investigate the impact of default risk on consumption under the assumption that banks can observe individual probabilities of default. The second part of this paper focuses on the pattern of borrowing rates and quantity restrictions on debt that emerges in response to the adverse selection caused by imperfect information about individual default probabilities.

The paper has four parts. Part I sets up the consumer's choice problem and describes the behavior of the banking sector in a perfect information equilibrium. Part 2 discusses the implications of default risk for consumption behavior. …