Precautionary Saving or Denied Dissaving? The Response of the Interest Rate to a Borrowing Constraint

Precautionary saving in response to uninsurable income risk can ex-plain the stylized fact that aggregate saving increases with the cross-sectional variation in income, but it is questionable how much of this variation can be ascribed to uninsurable risk and how much is, in fact, predictable. Borrowing constraints o¤er an alternative explanation for this observation that does not require consumers to be uncertain about their future income. This paper employs a three-cohort, overlapping generations model with quadratic utility and no capital to show that, if agents are patient enough, heterogeneity alone can account for more than half the decrease in the equilibrium interest rate caused by a borrowing constraint. The possibility of facing a binding borrowing constraint in the future induces saving, and this saving increases with the cross-sectional variation in income. However, another channel through which the interest rate decreases is the direct e¤ect that currently constrained agents borrow I would like to thank Jim Bullard, Dave DeJong, Douglas Gale, Mark Huggett, Matt Mitchell, Gene Savin, Pedro Silos, and Dan Thornton for o¤ering suggestions and advice, and I would especially like to thank B. Ravikumar, Chuck Whiteman, and Steve Williamson for their comments. Financial support was received from the Federal Reserve Bank of St. Louis, although the views expressed are my own and do not necessarily reect o ¢ cial positions of the bank, the Federal Reserve System, or the Board of Governors. All mistakes are my own. 1 less. For low discount factors, this direct e¤ect dominates. If agents are patient enough, the two channels have roughly the same impact on the interest rate. JEL Classi\u85cation: E2