Maturity Rationing and Collective Short-Termism Konstantin Milbradt (Kellogg & NBER) Martin Oehmke (Columbia)
March 7, 2014
Motivation Firms’ asset and liability sides interact in important ways Liability side: Shortening of debt maturities in recessions I
Mian and Santos (2011)
I
Chen et al. (2012)
Asset side: Shrinking of duration of firms’ real investments I
Dew-Becker (2012)
Previous theoretical work on maturity: I Often takes asset side as given I
Focuses on rollover risk generated by short-term liabilities
This Paper Integrated model of asset and liability side: I
Build on credit rationing literature to incorporate maturity domain
I
Allow for endogenous asset side adjustment
Main results: 1. Maturity Rationing: I
Limited commitment frictions increase with maturity
I
No financing beyond some maturity (despite constant NPVs)
2. Collective Short-Termism: I
Firms respond by adopting second-best projects of shorter maturity
I
This dilutes funded maturities, leading to a cross-firm externality and more rationing
This Paper
Equilibrium is inefficiently short-term Privately optimal asset side adjustments (i) can amplify shocks and (ii) can be socially undesirable
This Paper
Equilibrium is inefficiently short-term Privately optimal asset side adjustments (i) can amplify shocks and (ii) can be socially undesirable
Related Literature Interaction of asset and liability sides: I
von Thadden (1995)
I
Dewatripont and Maskin (1995)
I
Cheng and Milbradt (2012)
Endogenous adverse selection: I
Suarez and Sussman (1997)
I
Eisfeldt (2004)
I
Kurlat (2012), Bigio (2012)
Credit rationing & Contracting frictions: I
Stiglitz and Weiss (1981)
I
Bolton and Scharfstein (1990)
I
Hart and Moore (1994)
Model Setup: Primitives Firms and projects: I
Mass-one continuum of firms
I
Each firm has project of observable maturity t drawn from U 0, T
I
Project requires $1 in financing from risk-neutral financiers
I
No time discounting (for simplicity)
Project payoffs: I
Fraction α of projects is safe, pay R at maturity
I
Fraction 1 − α risky, pay e λt R with prob e −λt
I
For both safe and risky projects: NPVoriginal = R − 1 > 0
Remarks: I
maturity and project risk are linked (key assumption)
I
no ex-ante info asymmetry: safe/risky not known at contracting
Model Setup: Density and Quality
Project Density 0.25 T =10 0.20 0.15 0.10 original
0.05 0.00
T 2
4
6
8
10
Model Setup: Asset Side Adjustment Firms have the option to adjust their asset-side maturity: I
Adopt project of adjusted maturity t 0 6= t
I
Adjusted maturity t 0 can be chosen freely
Maturity-adjusted projects are second-best: I
Interpretation: Distortion away from first-best investment
I
Lower NPV modeled as additional default probability 1 − ∆: NPVadjusted = ∆R − 1 < R − 1 = NPVoriginal
I
Fraction e → 0 of firms adjusting gets stuck at original maturity
Endogenous asymmetric information: I
Maturity adjustment unobservable to financiers
Model Setup: Contracting Friction Key contracting friction: I
Success of project observable, but cash-flow non-verifiable
I
Firms that receive e λt R can claim to have received R and pocket difference
Debt financing: I
Equilibrium contract is a debt contract
I
Competitive financiers provide debt funding, break even at every t
I
Focus mostly on matching-maturity contracts
Timing: 1. Financiers simultaneously offer take-it-or-leave-it funding schedules contingent on project maturity t ∈ [0, T ] 2. Firms make maturity adjustments and fund themselves at the best rate, if funding is available
Joint Asset and Liability Side Equilibrium
In equilibrium, two conditions have to be satisfied:
(IR) Investors break even at each funded maturity (IC) Firms that are offered funding at their original maturity have no incentive to adjust the maturity of their projects
Break-Even Debt Contract Contracting friction implies “maximum effective face value:” I
If D > R, then firms simply report R
I
Leads to financier IR constraint: D≤R
Break-Even Debt Contract Contracting friction implies “maximum effective face value:” I
If D > R, then firms simply report R
I
Leads to financier IR constraint: D≤R
Can financier break even? I
Suppose financier expects a proportion p of original projects
I
Define average quality as β ≡ p + (1 − p ) ∆
Break-even face value: I
Given project maturity t and average quality β t : Dc (t, β t ) =
1 β t α + (1 − α) e −λt
Benchmark: No Maturity Adjustment Given average quality β = 1 (all original projects):
Dc (t, 1) =
1 α + (1 − α) e −λt
Maturity rationing: Contracting friction implies a funding cutoff Tb Dc Ht,1L 1.30 1.25
R
1.20 1.15 1.10 1.05
Dc Ht,1L Tb
1.00
t 2
4
6
8
10
What about Rollover Financing? Rollover contracts do not expand the contracting space: I
I
Project can be financed iff it can be financed by a matching maturity debt contract Any sequence of rollover contracts is payoff equivalent
Intuition: I
Project maturity is observable
I
No interim information about project is learned, except project failure Financiers update probability of firm type as they roll over
I
With small rollover cost: Matching maturities is unique equilibrium I
Firms with adjusted projects gain more from deviation to rollover Apply D1 equilibrium refinement
I
Any deviating firm will be treated as having second-best project
I
Asset Side Adjustment: Endogenous Short-Termism Who will adjust their project maturity? Unfunded firms: I
Always adopt for second-best projects of shorter maturity
I
Intuition: free option to get funding
Funded firms: I
May look for second-best projects of shorter maturity, but don’t
I
Intuition: too costly to lose funding at current terms
What are consequences for other firms? I
maturity adjustment dilutes pool of funded projects
I
changes in funding terms for other firms (cross-firm externality)
Asset Side Adjustment: Expected Profit Notation: I
Let F be set of funded maturities
I
Denote a firm’s type (original/adjusted) by θ ∈ {1, ∆}
Expected profit: I
For firm with maturity t, quality θ, given funding terms Dc (t, β t ) 1 , t ∈ F. π (θ, t, Dc (t, β t )) = θ R − β t + (1 − β t ) ∆
I
Expected profit independent of maturity (given β t )
Asset Side Adjustment: Two Observations 1. Average quality β is constant on funded set F : I
Conditional on maturity adjustment, indifference on F : π ∆, t 0 , Dc t 0 , β t 0 = π (∆, t, Dc (t, β t )) , ∀t, t 0 ∈ F
I
This requires: βt 0 = βt = β
2. Can ignore IC constraint (and focus on IR): I
Firms that can fund original project don’t adjust maturity
I
Always more profitable to fund higher-NPV original project: min π (1, t, D (t, β)) ≥ max π (∆, t, D (t, β))
t ∈F
t ∈F
Asset Side Adjustment: Maturity and Quality Lemma 1: Equilibrium funding terms take the cutoff form [0, T ]
Given funding cutoff T : I
The proportion of first-best projects is given by p (T ) =
I
This implies an average quality: β (T ) =
I
T −T T +∆ T T
The average quality increases in the cutoff T : β 0 (T ) > 0
T T
Asset Side Adjustment: Maturity and Quality Example: T = 6, so firms with t ∈ (6, 10] adjust maturity Project Density 0.25 T =10 0.20 0.15 0.10 original
0.05 0.00
T 2
4
6
8
Trembling hand: Mass ε → 0 stuck at t after adjustment
10
Asset Side Adjustment: Maturity and Quality Example: T = 6, so firms with t ∈ (6, 10] adjust maturity Project Density 0.25 T=6
T =10
0.20 0.15 adjusted 0.10 original
0.05
Ε®0 adjusted
0.00 2
4
6
8
Trembling hand: Mass ε → 0 stuck at t after adjustment
T 10
Equilibrium: Individual Rationality
Financiers can break even for all t ≤ T iff Dc (T , β (T )) ≤ R I
IR constraint most binding at T = max F
Define set that satisfies financier IR constraint as: IRc = T ∈ [0, T ] : Dc (T , β(T )) ≤ R
Interpretation: T ∈ IRc implies that [0, T ] can be funded
Competitive Equilibrium Proposition (Main result) The competitive equilibrium is given by the funding cutoff Tc = sup IRc , unless IRc = ∅, in which case funding unravels at all maturities.
Competitive Equilibrium Proposition (Main result) The competitive equilibrium is given by the funding cutoff Tc = sup IRc , unless IRc = ∅, in which case funding unravels at all maturities. Sketch of proof : 1. T ∈ / IR cannot be an equilibrium by inspection. 2. T ∈ IR with T < Tc cannot be an equilibrium. Suppose it is. Profitable deviation: offer a cutoff T 0 > T with T 0 ∈ IR I I I
Will face a better pool of projects because fewer firms adjust c Better pool results in ability to offer better rates, as ∂D ∂β < 0, ∀t Deviating financier can undercut and capture the whole market [0, T 0 ] at strictly profitable terms
Only Tc does not allow for profitable deviations.
Asset Side Adjustment: Two Forces Funding terms at threshold T : I I
Average quality on [0, T ] given by β (T ) with β0 (T ) > 0 Boundary face-value Dc (T , β (T )) changes with threshold T :
dDc (T , β (T )) dT
i h ∝ λ (1 − α) e −λT β (T ) − α + (1 − α) e −λT β0 (T ) {z } | | {z } Maturity effect
Dilution effect
Asset Side Adjustment: Two Forces Funding terms at threshold T : I I
Average quality on [0, T ] given by β (T ) with β0 (T ) > 0 Boundary face-value Dc (T , β (T )) changes with threshold T :
dDc (T , β (T )) dT
i h ∝ λ (1 − α) e −λT β (T ) − α + (1 − α) e −λT β0 (T ) {z } | | {z } Maturity effect
Dilution effect
Maturity effect: Decreasing T lowers face value as limited commitment frictions are less severe at shorter maturities. Dilution effect: Decreasing T leads to more adjustment, resulting in quality dilution and thus an increase in face value.
Illustration of Equilibrium
D 1.5 1.4
Dc Ht,DL
1.3 1.2 R 1.1 Dc Ht,ΒHTc LL Tc
1.0
t 2
4
6
8
10
Competitive Equilibrium is Constrained Inefficient Competitive equilibrium vs. constrained planner: I
competitive financiers have to break even separately for each t
I
constrained planner can cross-subsidize across maturities
In competitive equilibrium: I
IR binds at Tc and is slack otherwise
I
IC slack everywhere
Consider raising face values by factor 1 + η, with maximum R: Dη (t, β) = min {(1 + η ) Dc (t, β) , R }
Competitive Equilibrium is Constrained Inefficient Given Dη (t, β) = min {(1 + η ) Dc (t, β) , R }
I
strictly positive profits on [0, Tc ] without violating IR or IC use profits to offer funding at face value R on (Tc , Tc + δ]
I
choose η and δ such that IC satisfied on (Tc , Tc + δ]
I
Welfare improvement: Mass δ/T more first-best projects funded
Competitive Equilibrium is Constrained Inefficient Given Dη (t, β) = min {(1 + η ) Dc (t, β) , R }
I
strictly positive profits on [0, Tc ] without violating IR or IC use profits to offer funding at face value R on (Tc , Tc + δ]
I
choose η and δ such that IC satisfied on (Tc , Tc + δ]
I
Welfare improvement: Mass δ/T more first-best projects funded
Proposition (Constrained Inefficiency) Assume Tc ∈ 0, T . A constrained central planner funds more maturities than the competitive market, Tcp > Tc .
Optimal Funding Schedules Derive optimal funding schedules in presence of cross-subsidization I
use to characterize funding by constrained planner and monopolist
Pick funding schedule DT (t ) subject to: I IC and IR constraints I
Endogenous density of adjusted projects dT (t ) : T −T , tmax ≡ sup arg max π (∆, t, DT (t )) dT (t ) = δtmax (t ) t ∈[0,T ] T
Profit Π (T ): h Z T i 1 1 + dT (t ) ∆ α + (1 − α) e −λt DT (t ) − 1 + dT (t ) dt T T 0
Optimal Funding Schedules Optimal funding take the form: DT (t ) = min {C (T ) Dc (t, 1) , R }
Planner and monopolist charge DT (t ) but pick different T : I Planner picks maximum T such that Π (T ) ≥ 0 I
Monopolist picks T = arg max Π(T ) ≥ 0
Ranking planner, monopolist and competitive financiers: I
Planner always funds (weakly) more maturities than competitive financiers or monopolist
I
Monopolist may or may not fund more maturities than competitive financiers, depending on parameters I
Trade-off: appropriation of surplus vs. amount of surplus
Importance of Asset Side Adjustments Often rollover risk highlighted as a cost of short-term debt: I
Inefficiency arises because of early liquidation
I
Diamond and Dybvig (1983), Diamond (1991), etc.
We highlight a complementary channel: I
Contracting frictions can lead to rationing of long-term projects
I
Leads to endogenous short-termism on asset side
I
Endogenous adverse selection implies cross-firm externalities
Relates to classic (and current) debate on short-termism I
U.S. vs. Japan in the 1980s and 1990s
I
Here short-termism generic competitive outcome in rational model
Amplification through Collective Short-Termism Consider increase in dispersion parameter λ:
T
HWc -Wb LWb
10
0.2
D=.85
8
Λ 0.02
6 Tc
Tcp
0.04
0.06
0.08
-0.2
Tb
4
-0.4
2
-0.6 D=.81
Λ 0.02
0.04
0.06
0.08
0.10
-0.8
Privately optimal asset side adjustments: I
Reduce set of funded maturities (left)
I
Can lead to significant loss in surplus (right)
0.10
Are Firms’ Maturity Adjustments Efficient? Change in welfare (total surplus) that results from asset side adjustments: Direct effect
z Wc − Wb
=
{ }| T − Tb NPVadjusted T T − Tc − b [NPVoriginal − NPVadjusted ] T {z } | Dilution effect
Welfare gain: Suppose ∆ = 1 I
Direct effect > 0
I
Dilution effect = 0
Welfare loss: Suppose ∆ such that NPVadjusted = 0 I
Direct effect = 0
I
Dilution effect < 0
Are Firms’ Maturity Adjustments Efficient? Percentage change in surplus depends on dilution parameter ∆:
T
HWc -Wb LWb 0.2
10 Tcp 8
Tb
0.80
6 4
0.85
0.90
0.95
1.00
-0.2 -0.4
Tc
-0.6 2 -0.8 0.80
0.85
0.90
0.95
1.00
D
-1.0
Two observations: I
Increase in lending not sufficient statistic for increase in surplus
I
Asset side adjustments can be inefficient even if NPVadjusted > 0
D
Conclusion Integrated model of interaction between asset and liability sides I
Contracting frictions can lead to maturity rationing
Firms react by adjusting their asset side investments I
Endogenous short-termism driven by liability side frictions
I
Endogenous adverse selection leads to cross-firm externalities
Competitive equilibrium inefficiently short-term Firms’ privately optimal asset side adjustments: I Can amplify shocks I
Can be inefficient from a welfare perspective
