Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 1 / of19

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1 Credit Crises, Precautionary Savings and the Liquidity Trap (R&R Quarterly Journal of nomics) October 31, 2016 Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 1 / of19

2 Overview Title: How credit crises cause liquidity trap by precautionary savings Key words credit crises: exogenous reduction in credit limit precautionary savings: saving in response to uncertainty regarding future income incomplete market (no insurance market) liquidity trap: nominal interest rate is essentially zero or very low Questions: (1) what are the effects of credit crises on aggregate variables/macro economic dynamics and (2) how are the responses distributed across workers (thus we have heterogeneous agent in the model) Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 2 / of19

3 Outline Model setup Calibration Steady states Transitional Dynamics Conclusion Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 3 / of19

4 Model setup basic model without flexible prices and durable goods heterogeneous agent; incomplete market; endogenous labor supply; no capital; one-period risk-free bond Households utility function (consumption, labor supply, bond demand) budget constraint E[Σ t=0β t U(c it, n it )] (1) q t b i,t+1 + c it + τ it b it + y it (2) where b it is bond holding, q t is bond price, τ it is tax, where all households pay a lump sum tax τ t and umemployed receive benefit υ t ; r t = 1/q t 1 is the implicit interest rate borrowing constraint b i,t+1 φ (3) Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 4 / of19

5 Model setup Optimal conditions for households U c (c it, n it ) β(1 + r t )E t [U c (c i,t+1, n i,t+1 )] (4) with equality if b i,t+1 φ is slack θ it U c (c it, n it ) + U n (c it, n it ) 0 (5) with equality if n it > 0 Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 5 / of19

6 Model setup Firms technology (labor demand) y it = θ it n it (6) where θ it is an idiosyncratic shock to the labor productivity of household i, which follows a Markov chain on the space {θ 1,..., θ S }. θ 1 = 0 is the unemployment state. Government (bond supply, unemployment benefit, lump sum tax) B t + υ t u = q t B t+1 + τ t (7) where u = Pr(θ it = 0) is the fraction of unemployed agents. Suppose B and υ are constant. Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 6 / of19

7 Model setup Equilibrium Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 7 / of19

8 Calibration Utility function U(c, n) = c1 γ (1 n)1 η + ψ 1 γ 1 η (8) Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 8 / of19

9 Steady state high level of b, permanent income hypothesis low level of b, concave, precautionary savings Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016Journal 9 / of19

10 Credit Crunch t = 0, initial steady state, φ = 1.04 unexpected shock starting at t = 1, lasting for 6 quarters, final φ = 0.58 φ t follows the linear adjustment path φ t = max{φ, φ t} Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 10 / of19

11 Credit Crunch Two effects that shift demand curve mechanical effect: exogenous reduction in borrowing limit precaitionary effect: households accumulate more wealth to stay away from the borrowing limit Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 11 / of19

12 Transitional dynamics: interest rate first main result: interest rate overshooting after a debt contraction Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 12 / of19

13 Transitional dynamics: interest rate Mechanism initial steady state: solid blue line bond accumulation: b i,t+1 b it (averaged over θ) Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 13 / of19

14 Transitional dynamics: interest rate Mechanism dashed line accumulation: agents near borrowing limits are more precautionary aggregate net bond accumulation is 0 since bond supply is fixed suppose interest rate jump to new steady state immediately integral of dashed green line in top panel using distribution of solid blue line in bottom panel is positive (since solid line distribution give more weight on positive values for dashed accumulation than dashed line distribution) excess demand of bonds need lower interest rate in initial periods Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 14 / of19

15 Transitional dynamics: output - consumption two effects exogenous reduction in credit limit(wealth reduction) consumption, larger reduction for consumers closer to the credit limit (precautionary savings) endogenous interest rate reduction consumption, larger increase for consumers farther away from the credit limit (PIH) Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 15 / of19

16 Transitional dynamics: output - consumption combine two effects lower wealth consumers reduce consumption, higher ones increase consumption Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 16 / of19

17 Transitional dynamics: output - Labor supply two effects credit crunch consume less and work more interest rate reduction work less combine two effects: work more in aggregate high wealth people (thus high productivity people) are more sensitive to interest rate average productivity decrease output reduction though working hours increase results rely on the parameters; reduce the upper bound on hours per week used to calibrate ψ thus labor supply policy is less convex, then the response of working hours changes Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 17 / of19

18 Transitional dynamics: output - Labor supply Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 18 / of19

19 Conclusion credit crises generate recession by depressing interest rate, especially in the short run two channels: exogenous repayment of debt by constrained consumers; increase in precautionary savings by unconstrained consumers Credit Crises, Precautionary Savings and the Liquidity Trap October (R&R Quarterly 31, 2016 Journal 19 / of19

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