Credit Crises, Precautionary Savings, and the Liquidity Trap

The paper opens by asking “how does an economy adjust from a regime of easy credit to one of tight credit?” and frames this as central to understanding the 2007-2009 U.S. recession, citing Hall (2011a,b) and Mian and Sufi (2011a,b) as empirical motivation that household balance-sheet deleveraging, not just firm-side credit frictions, was central to that downturn. The paper situates itself in “the vast literature on consumption and saving in incomplete market economies with idiosyncratic income uncertainty, going back to Bewley (1977), Deaton (1991), Huggett (1993), Aiyagari (1994), Carroll (1997),” but departs methodologically from the Krusell-Smith approach of approximating equilibria with a finite set of distributional moments: the authors instead “prefer to keep the entire wealth distribution as a state variable at the cost of focusing on a one time shock,” since their credit shock “affects very differently agents in different regions of the distribution.” The paper also distinguishes its approach from contemporaneous work by Curdia and Woodford (2010) and Eggertsson and Krugman (2011), who study credit-driven liquidity traps using representative borrower/lender models that “mute wealth dynamics… This implies that there is no precautionary effect on the lenders’ side.”

The baseline model is “a standard incomplete markets model in the tradition of Bewley (1977), with endogenous labor supply and no capital,” in which a continuum of infinitely-lived households face idiosyncratic labor-productivity shocks (including unemployment spells), can borrow and lend a single risk-free bond up to an exogenous limit tighter than the natural borrowing limit, and choose consumption and labor subject to an Euler equation and a labor-supply optimality condition. A tightening of the borrowing limit activates two reinforcing channels: “a direct channel, by which constrained borrowers are forced to reduce their indebtedness,” and “a precautionary channel, by which unconstrained agents increase their savings as a buffer against future shocks” because tighter future constraints make future consumption more responsive to income shocks, which (given prudent preferences) raises expected marginal utility and so “is as if there was a negative preference shock reducing the marginal utility of consumption today.” Both channels increase desired net lending, so with a fixed bond supply, the equilibrium interest rate must fall.

The model is calibrated quarterly with a coefficient of relative risk aversion of γ = 4, a Frisch elasticity of labor supply of 1, average hours of 40% of the time endowment, and an income process matched to Floden and Lindé’s (2001) PSID-based estimates and Shimer’s (2005) employment transition rates; the bond supply and borrowing limit are set to match 2006 U.S. household balance sheets, with a liquid-assets-to-GDP ratio of 1.78 and a consumer-credit-to-GDP ratio of 18%. The paper’s central experiment is an unexpected, permanent, and gradually-phased-in (over six quarters) reduction in the borrowing limit from φ = 1.04 to φ’ = 0.58 of annual output, “chosen so that the debt-to-GDP ratio drops by 10 percentage points in the new steady state” – with the gradual phase-in specifically included so that “no household is forced into default” despite all debt having one-quarter maturity in the model.

The paper’s first main result is that “the interest rate drops sharply after the shock, going negative for 6 quarters” before gradually rising back toward a new, lower steady-state level – a pattern the authors call “the interest rate overshooting after a debt contraction” and describe as “a fairly general qualitative outcome of this class of models and not just the consequence of our choice of parameters.” The intuition rests on comparing the two steady-state wealth distributions: because low-wealth, precautionary-constrained households accumulate bonds faster under the new (tighter) regime while high-wealth households decumulate faster given the lower new-steady-state interest rate, “the new distribution is more concentrated” – formally, “the initial distribution is a mean-preserving spread of the new distribution.” A “disequilibrium” thought experiment – jumping the interest rate directly to its new steady-state value – then reveals excess bond demand under the old (more spread-out) distribution, because the bond-accumulation policy function is convex; equilibrating the bond market therefore requires a lower-than-new-steady-state interest rate in the early transition, which rises back up only as the wealth distribution itself converges.

With flexible prices, the same disequilibrium logic applied to the goods market shows that, at the conjectured new-steady-state interest rate, average consumption demand would be below and average labor supply above their new-steady-state levels (since the consumption policy is concave and the labor-supply policy is convex in bond holdings), creating excess goods supply that must be absorbed by a falling interest rate; in the paper’s baseline calibration “the fall in consumption demand is the dominating factor, and output falls below its new steady state value” – 1% on impact. Crucially, the output drop is not uniform across households: “labor supply increases for low-productivity workers at the bottom end of the bond distribution, who are closer to the borrowing limit and are least interest-sensitive,” while “labor supply drops for high-productivity workers with high bond holdings, who are farther from the limit and are more interest-sensitive” – so “behind the drop in output there is a misallocation effect and a drop in average labor productivity,” and the paper shows that with a less convex (more concave) labor-supply policy function, calibrated by reducing the maximum feasible hours, “aggregate employment drops by more than one percentage point and the output drop is larger than 2%.”

The paper extends the model with monopolistically competitive firms facing menu costs large enough that “firms leave prices at their initial level,” so that with the nominal interest rate equal to the real rate, the central bank can in principle replicate the flexible-price real-rate path – except for the zero lower bound. Because “a credit crisis which produces a large drop in real interest rates under flexible prices can drive the economy into a liquidity trap,” the paper compares three scenarios: the flexible-price baseline; a central bank that replicates the flexible-price path subject to the zero lower bound; and a central bank constrained to hold the real rate at a higher value (1%, representing either a less aggressive central bank or an imperfect pass-through from the policy rate to the rates relevant for household borrowing). The paper reports that “the output responses are larger when the interest rate fails to adjust downward” as needed.

The paper shows that, because taxation is lump sum, an increase in the government bond supply B_t is formally equivalent to a loosening of the borrowing limit φ (only the sum B_t + φ matters for equilibrium), so that “in principle the government could completely neutralize the effect of a credit shock” with a sufficiently large bond-supply increase – though the paper studies only partial offsets “for the sake of realism.” Simulating a policy that raises bond supply by 20% in the new steady state, financed either by a lump-sum tax cut or by a temporary 50%-larger unemployment benefit for two years, the paper finds both policies “dampen the responses of both interest rates and output,” with the unemployment-benefit policy having “larger effects than reducing the lump-sum tax, because it is a policy targeted towards households that are more likely to be credit constrained.”

In the extended model, households can save via either bonds or durables, which serve as collateral (the borrowing limit is proportional to durable holdings) but are costlier to liquidate: a household selling durables faces a proportional resale cost ζ = 15%, making durables “a less liquid form of savings than bonds.” The authors note two offsetting forces: a precautionary-saving force that could raise durable demand among unconstrained savers (since durables are “an alternative store of value”), and a forced-deleveraging force that lowers durable demand among constrained borrowers who “need to sell durables in order to reduce their debt” – with the paper noting the novel possibility that “a credit shock can lead, at the same time, to an increase in demand for the liquid asset and to a reduction in demand for the illiquid asset,” a form of “flight to liquidity” on the household side.

A shock to the loan-to-value-style borrowing limit φ_k (calibrated to the same 10-percentage-point debt-to-GDP decline as the baseline) produces a smaller interest-rate decline than the baseline and, strikingly, a 0.4% increase in output, because durable spending – “a much more interest elastic component of consumer spending” – actually rises about 4% once the (smaller) equilibrium interest-rate drop is accounted for, even though a disequilibrium calculation shows durable spending would fall about 18% at the unchanged new-steady-state interest rate. In contrast, a permanent increase in the intermediation spread χ (which “affects all borrowers and not just those near the borrowing limit”) produces a gradual output decline with roughly a 3% contraction in durable purchases and an “almost negligible” drop in non-durables, since the typical affected household “prefers to smooth nondurable consumption and adjust to the shock by selling durables” rather than cut current consumption sharply. A larger, temporary spread shock – calibrated, following Hall (2011a), to represent the credit shock of the 2008-2009 U.S. recession, and large enough that the rate on a one-year loan rises by about 3.9 percentage points in its first quarter – produces a 3.5% output drop and a 17.2% contraction in durable purchases under flexible prices; adding sticky prices and a binding zero lower bound to this same shock deepens the contraction sharply, to a 44.5% drop in durable purchases and a 9.7% output decline.

The authors flag that unemployment risk in their model is exogenous and unaffected by the credit crunch itself, suggesting “it would be interesting to develop a version of the model with an explicit treatment of labor market frictions” so that weaker consumer demand could endogenously raise unemployment; and that the model omits physical capital entirely, noting that incorporating it “requires a theory of why claims to physical capital cannot be costlessly transformed into perfectly liquid assets like the bonds of our model,” which would require combining their household-side analysis “with financial frictions on the firms’ side or a richer model of intermediation.” In the durable-goods extension specifically, the authors note their calibration implies a larger interest elasticity of durable spending than may be realistic, since bonds and durables “remain very good substitutes, despite the illiquidity cost,” and suggest that richer adjustment-cost specifications or explicit durable-price risk (especially for housing) could reduce this substitutability in future work.