Two somewhat related papers this week.

**Overborrowing and systemic externalities in the business cycle**

*by Javier Bianchi*

http://d.repec.org/n?u=RePEc:fip:fedawp:2009-24&r=dge

Credit constraints that link a private agent’s debt to market-determined prices embody a credit externality that drives a wedge between competitive and constrained socially optimal equilibria, inducing private agents to overborrow. The externality arises because agents fail to internalize the debt-deflation effects of additional borrowing when negative income shocks trigger the credit constraint. We quantify the effects of this inefficiency in a two-sector dynamic stochastic general equilibrium model of a small open economy calibrated to emerging markets. The credit externality increases the probability of financial crises by a factor of seven and causes the maximum drop in consumption to increase by 10 percentage points.

**Rising indebtedness and hyperbolic discounting: a welfare analysis**

*by Makoto Nakajima*

http://d.repec.org/n?u=RePEc:fip:fedpwp:09-25&r=dge

Is the observed rapid increase in consumer debt over the last three decades good news for consumers? This paper quantitatively studies macroeconomic and welfare implications of relaxing borrowing constraints when consumers exhibit a hyperbolic discounting preference. In particular, the author constructs a calibrated general equilibrium life-cycle model with uninsured idiosyncratic earnings shocks and a quasi-hyperbolic discounting preference and examines the effect of relaxation of the borrowing constraint which generates increased indebtedness. The model can capture the two contrasting views associated with increased indebtedness: the positive view, which links increased indebtedness to financial sector development and better insurance, and the negative view, which associates increased indebtedness with consumers’ over-borrowing. He finds that while there is a welfare gain as large as 0.4 percent of flow consumption from a relaxed borrowing constraint, which is consistent with the observed increase in aggregate debt between 1980 and 2000 in the model with standard exponential discounting consumers, there is a welfare loss of 0.2 percent in the model with hyperbolic discounting consumers. This result holds in spite of the observational similarity of the two models; the macroeconomic implications of a relaxed borrowing constraint are similar between the two models. Cross-sectionally, although consumers of high and low productivity gain and medium productivity consumers suffer due to a relaxed borrowing constraint in both models, the welfare gain of low-productivity consumers is substantially reduced (and becomes negative in the case of strong hyperbolic discounting) in the hyperbolic discounting model due to the welfare loss from over-borrowing. Finally, the author finds that the optimal (social welfare maximizing) borrowing limit is 15 percent of average income, which is substantially lower than both the optimal level implied by the exponential discounting model (37 percent) and the level of the U.S. economy in 2000 implied by the model (29 percent).

The Bianchi paper shows that agents overborrow and this has negative consequences on the economy because of a larger risk of financial crises. The Nakajima paper argues that the observed increase in borrowing may be due to overborrowing due to hyperbolic discounting and financial innovation and the negative welfare effect of hyperbolic discounting dominates. Should one restrain consumer borrowing even if standard model indicate that completing markets should be welfare improving?