Default Risk and Aggregate Fluctuations in an Economy with Production Heterogeneity Aubhik Khan The Ohio State University Tatsuro Senga The Ohio State University and Bank of Japan Julia K. Thomas The Ohio State University January 2013 Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 1 / 20
Introduction Were financial markets an important factor in the recent U.S. recession? A surge of corporate defaults Large reductions in lending volumes - Ivashina and Scharfstein (2009); Koepke and Thomson (2011) Evidence of an exogenous shock to credit availability - Almeida et al. (2009); Duchin et al. (2010) What are the real effects of a credit shock? How does the macroeconomic response compare to that following a real shock? Jermann and Quadrini (2012) Khan and Thomas (2011) - collateralized borrowing constraints (b 0 Θk) - persistent differences in firm-level productivities - specificity in capital (partial irreversibility) Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 2 / 20
The recent recession Peak-to-Trough Percent Changes: 2007 U.S. Recession -v- KT(2011) GDP I N debt TFP data 5.14 23.40 6.89 [19 48] 1.65 TFP shock 3.85 14.03 1.99 4.00 2.68 credit shock 4.20 22.98 3.62 22.80 0.97 Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 3 / 20
Overview Does default risk underlie the collateral constraint? Can it explain the slow recovery? We develop a DSGE model of endogenous firm defaults. external funding is limited to one-period, non-contingent debt firms face persistent shocks to their individual productivities firms may find it infeasible to roll over debt default forces exit, and implies a loss to the lender Non-contingent debt implies non-linear interest rate schedules we abstract from the capital specificity here Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 4 / 20
Overview of production competitive firms producing homogenous good: y = zεk α n ν z 2 fz 1,..., z Nz g with Pr (z 0 = z m j z = z l ) π z lm ε 2 fε 1,..., ε Nε g with : Pr ε 0 = ε j j ε = ε i πij labor from households (real wage ω) one-period debt with face value b 0 2 R (at relative prices q() 1 ) firm entering period identified by (k, b, ε) draw operating cost ξ H (ξ) operate -v- default operate: choose n, repay b, continue with probability 1 π d continue: choose k 0 2 R +, b 0 2 R, and D 2 R + Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 5 / 20
Net worth and default net worth describes a firm s state (k, b, ε) pre-operating cost net worth: x 0 π (k, ε; z, µ) b + (1 δ) k post-operating cost net worth: x x 0 k and b do not matter beyond the determination of x (no capital adjustment friction; firm default value unaffected by k) ξ financial friction influences choices of k 0, b 0, and D default returns θ(1 δ)k to competitive lender, where θ 2 (0, 1) loan discount factor: q (k 0, b 0, ε; z, µ) q 0 (z, µ) Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 6 / 20
Default probabilities and loan rates Consider firm next period with x 0 = x 0 jm, realizing ε = ε j and z = z m. firm will default if x 0 jm ξ is below x T solving V 1 x T, ε j ; z m, µ 0 = 0 which happens if ξ exceeds ξ T x 0 jm, ε j ; z m, µ 0 x 0 jm x T ε j ; z m, µ 0 We can recover loan rates from the financial intermediary s zero-profit condition, recalling that θ(1 q k 0, b 0, ε i ; z l, µ b 0 = N z m=1 δ)k 0 will be recovered under default. " H ξ T (xjm 0, ε j ; z m, µ 0 ) b 0 π z lm d m (z l, µ) N ε j=1 π ε ij h i + 1 H ξ T (xjm 0, ε j ; z m, µ 0 ) θ (1 δ) k 0 # Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 7 / 20
Firm problem: part 1 expected value of firm (k, b, ε) before operating cost draw Z ξu V 0 (x 0, ε; z, µ) = V (x 0 ξ, ε; z, µ) H(dξ) ξ L x 0 = π(k, ε; z, µ) b + (1 δ)k post-operating cost draw value, given x x 0 ξ n o V (x, ε; z, µ) = max V 1 (x, ε; z, µ), 0 post-production value V 1 (x, ε; z, µ) = π d x + (1 π d ) V 2 (x, ε; z, µ) Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 8 / 20
Firm problem: part 2 value of a continuing firm h V 2 (x, ε i ; z l, µ) = max (k 0 b 0 )2Φ(x,ε;z,µ) D subject to: + N z m=1 π z lm d m (z l, µ) N ε j=1 D = x k 0 + q k 0, b 0, ε; z, µ b 0 π ε ij V 0 x 0 jm, ε j; z m, µ 0i Φ (x, ε; z, µ) = k 0, b 0 2 R + Rj D 0 x 0 jm = π k 0, ε j ; z m, µ 0 b 0 + (1 δ) k 0 given µ 0 = Γ(z, µ) and loan discount rates q (k 0, b 0, ε i ; z l, µ) Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 9 / 20
Decision rules: rms in two categories To isolate (k 0, b 0, D) rules, group firms according to whether frictionlessly optimal investment plans will ever require q (k 0, b 0, ε; z, µ) < q 0 (z, µ). constrained firm: risk-premium in some possible state(s) shadow value of retained earnings exceeds that of dividends implication: D = 0; hence K c (x, ε; ) implies q(k c, B c, ε; )B c (x, ε; ) check if the firm can adopt k (ε; ) at q 0 (z, µ) 1 [type 1 constrained] :K c (x, ε; ) = k (ε; ) 2 [type 2 constrained] :K c (x, ε; ) 6= k (ε; ) unconstrained firm: permanent access to risk-free rate shadow value of dividends and retained earnings are equal k (ε; ) and any B w (ε; ) yields D w (x, ε; ) Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 10 / 20
Minimum savings policy for unconstrained rms B w (ε; z, µ) = min eb k (ε, z, µ), ε j ; z m, µ 0 fε j jπ ε ij >0 and z mjπ z lm >0g eb(k, ε; z, µ) π(k, ε; z, µ) + (1 δ) k ξ nh U i o + min k (ε; z, µ) + q 0 (z, µ)b w (ε; z, µ), x T (ε; z, µ) where x T (ε; z, µ) solves v 1 x T, ε; z, µ = 0 B w (ε i ; S) highest b 0 a current type ε i unconstrained firm can owe starting next period (with k 0 = k (ε i ; S)) and be unconstrained for sure eb(k, ε; S) highest b a type (k, ε i ) firm can owe this period and for sure implement k (ε i ; S) with b 0 B w (ε i ; S), while not defaulting on its debt Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 11 / 20
An example u(c, L) = log C + ϕl log z 0 = ρ z log z + η 0 z log ε 0 = ρ ε log ε + η 0 ε µ 0 potential entrants initial state x = x 0 ξ U(0, ξ U ) β : real rate = 0.04 ν : labor share = 0.60 δ : investment/capital = 0.07 annual model α : capital/output = 2.3 ϕ : hours worked = 0.33 µ 0 : producers = 0.80 Fixing θ = 1 (for now), we seek [π d x 0 ξ U ρ ε σ ε ] to match: moment aggregate debt/assets firm exit rate new/typical firm size mean (firm i/k) std. dev. (firm i/k) data model 0.37 0.43 0.07 0.08 0.10 0.33 0.12 0.14 0.34 0.33 Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 12 / 20
Steady state: equilibrium loan rates figure suggests very efficient financial markets. this model frictionless model cv ( k 0 (x, ε 4 ) jk 0 > 0 ) 0.13 0.00 total producers 0.80 2.15 Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 13 / 20
Stationary distribution overview financial frictions reduce steady-state output by 21 percent (TFP by 1/2 percent) Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 14 / 20
Aggregate productivity shock more on TFP onward! Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 15 / 20
Aggregate productivity shock 2 Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 16 / 20 back
Financial shock (50 ppt drop in default recovery rate) more on TFP onward! Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 17 / 20
Financial shock 2 Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 18 / 20 back
Progress report We have developed a DSGE model with one-period non-contingent debt to explore how endogenous collateral constraints affect aggregate responses to real and financial shocks. Results so far suggest that non-contingent debt arrangements: drive countercyclical default rates amplify responses to an aggregate productivity shock yield a large, protracted recession following a financial shock, and gradualize recoveries in employment, investment and GDP thereafter Calibration remains to be done. Misallocation effects may grow when we hit the relative size of entrants. Need targets for baseline default recovery rate and financial shock size Default rates [Covas and Den Haan (2011)] Credit spreads [Gomes and Schmid (2009); Gourio (2011)] Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 19 / 20
Nothing to see here. Khan, Senga and Thomas Default Risk and Aggregate () Fluctuations January 2013 20 / 1