Aggregate consequences of limited contract enforceability Thomas F. - - PowerPoint PPT Presentation

Aggregate consequences of limited contract enforceability

Thomas F. Cooley New York University Ramon Marimon Universitat Pompeu Fabra Vincenzo Quadrini University of Southern California New York University

MOTIVATION

• Recent studies have emphasized the importance of institutions for the

structure of the financial system. See La-Porta, Lopez-de-Silanes, Shleifer & Vishny (1998).

• Formal and informal institutions affect the enforceability of contracts.
• Enforceability affects the investment behavior of firms which in turn may

have important consequences for the aggregate economy.

OBJECTIVE

Studying how limited contract enforceability affects:

• The propagation of technological innovations.
• The efficiency of the macro allocation of resources.

THE APPROACH

• General Equilibrium: We study a general equilibrium model in which

entrepreneurs finance investment by signing long-term optimal contracts with a financial intermediary.

• Limited Enforcement: Entrepreneurs have the option to repudiate the

contract and financial frictions arise endogenously.

• No Market Exclusion: This is a key innovation relative to the existing

literature and it is important for the results.

MAIN RESULTS

• 1. Amplification: Limited enforceability amplifies the aggregate impact of

non-persistent technological innovations.

• 2. Delaying diffusion: Limited enforceability delays the aggregate impact
• f persistent technological innovations.
• 3. Efficiency: Limited enforceability distorts the allocation of resources.

The welfare cost is about 0.5% of consumption.

• 1. Amplification

KEYS: 1) No market exclusion; 2) State-contingent contracts.

• 2. Delaying diffusion

SOME RELATED LITERATURE

• Marcet-Marimon (1992):

Partial equilibrium with default leading to

• autarky. Also, agents are risk-averse, but not relevant.
• Albuquerque-Hopenhayn (1997):

Partial equilibrium with exogenous repudiation value. Exit is endogenous. See also Monge (2000) and Quintin (2000).

• Kiyotaki and Moore (1997): Contracts are not state-contingent. It is not
• bvious whether state-contingent contracts would lead to amplification.
• Phelan (1995): No market exclusion but only steady state.

THE MODEL

• There is a mass 1 of entrepreneurs and a mass m of workers.
• Workers are infinitely lived with utility:

E0

∞

• t=0
• 1

1 + r t (ct − ϕ(lt)) r = intertemporal discount rate ct = consumption ϕ(lt) = disutility from working

• Entrepreneurs are born in each period and they die with probability α. Their utility is:

E0

∞

• t=0

1 − α 1 + r t ct

• Entrepreneurs have the ability to implement and manage one of the available projects.
• A project generates revenues according to:

y = z · f(k, l) z = project-specific productivity; z ∈ {zL, zH}. k = input of capital (depreciating at rate δ). l = input of labor. f strictly concave.

• The set up of a new project requires a fixed investment I0, which is sunk.
• In each period Nt projects with high productive become available.
• Given St the number of entrepreneurs searching for a new project, the probability of

success is pt = Nt/St.

• Limited enforceability: By repudiating the contract, the entrepreneur is able to:

– Get utility from diverting the firm’s resources (capital). – Search for a new project and sign another contract (no market exclusion). – But if faces also a fixed cost from repudiating the contract. D(st, kt−1) = kt−1 + V (st) − κ V (st) = Value of searching. κ = Repudiation cost.

Start with kt−1 Observe Nt Repudiation Continuation Search for new project Production and choice of dt, kt

❆ ❆ ❆ ❆ ❆ ❆ ❆ ❆ ❆ ❆ ❆ ❆ ❆ ❆ ❯ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ☛

ASSUMPTIONS

• 1. The difference between zL and zH is not too large.
• This implies that the replacement of an existing project is not efficient.
• 2. Searching for a new project implies the loss of a previously managed project.
• This eliminates the possibility of renegotiation.
• 3. Entrepreneurial skills are lost if the entrepreneur remains inactive.
• This eliminates the possibility that newborn entrepreneurs wait for better investment
• pportunities.

THE OPTIMAL CONTRACT

V (z; st) = max

{dτ ,kτ ,lτ+1}∞ τ=t

Et

∞

• τ=t

βτ−tdτ subject to Eτ+1

∞

• j=τ+1

βj−τ−1dj ≥ D(kτ, sτ+1), for τ ≥ t Et

∞

• τ=t

βτ−t

• π(z; kτ, lτ+1, wτ+1) − dτ
• ≥ I0

dτ ≥ 0

RECURSIVE PROBLEM

W (z; s, µ) = min

µ(s′) max d,k,l′

• π(z; k, l′, w′) − (1 − µ)d

−βE(µ(s′) − µ)D(z; k, s′) + βEW (z; s′, µ(s′))

• subject to

d ≥ 0, µ(s′) ≥ µ s′ ∼ H(s) Aggregate states: 1) # of high productive projects N; 2) distribution over (z, µ).

VALUE OF SEARCHING

• The initial µ is such that the intermediary participates (zero-profit condition).
• Given the initial µ we determine the entrepreneur’s value V (z; s).
• The value of searching is:

V (s) = p · V (zH; s) + (1 − p) · V (zL; s) where p = N

α

REPUDIATION VALUE

D(s, k−1) = k−1 + V (s) − κ

FIRST ORDER CONDITIONS

µ(s′) : D(k, s′) ≤ Wµ(z; s′, µ(s′)), (= if µ(s′) > µ) d : µ ≤ 1, (= if d > 0) k : πk(z; k, l′, w′) = βE(µ(s′) − µ) l′ : πl(z; k, l′, w′) = 0

PROPERTIES OF THE CONTRACT

• There is an optimal input of capital ¯

k(z; s) in absence of enforceability problems.

• The state µ grows over time until it reaches 1.
• If µ < 1:

– Capital is smaller than ¯ k(z; s). – The entrepreneur gets zero payments.

• If µ = 1:

– Capital is always at the optimal level ¯ kz. – The entrepreneur’s payments are not determined.

CALIBRATION

Intertemporal discount rate r = 0.04 Disutility from working ϕ(l) ≡ A · l

1+ǫ ǫ

A = 0.001, ǫ = 1 Death probability of entrepreneurs γ = 0.05 Production technology ¯ z · (kνl1−ν)θ ¯ z = 0.012, θ = 0.85, ν = 0.294 Depreciation rate δ = 0.0579 Set-up investment I0 = 0.2 Cost of repudiation κ = 0.35

NON-PERSISTENT INNOVATION

INTUITION FOR AMPLIFICATION

The investment of constrained firms is determined by: D(s, k−1) = βD(s′, k)

• r

k−1 + V (s) − κ = β

• k + EV (s′) − κ

PERSISTENT INNOVATION

WELFARE CONSEQUENCES OF LIMITED ENFORCEABILITY

Limited Full Enforceability Enforceability Baseline Average size of firms (capital) 0.848 0.931 Change in working time 1.82% Steady state output gain 3.84% Welfare gain from transition 0.46%

Limited Full Enforceability Enforceability Low repudiation cost, κ = 0.25 Average size of firms (capital) 0.794 0.902 Change in working time 2.73% Steady state output gain 5.40% Welfare gain from transition 0.87% High repudiation cost, κ = 0.60 Average size of firms (capital) 0.941 0.978 Change in working time 0.61% Steady state output gain 1.48% Welfare gain from transition 0.08% High elasticity of labor, ǫ = 2.0 Average size of firms (capital) 0.848 0.942 Change in working time 3.33% Steady state output gain 4.91% Welfare gain from transition 0.46% Low elasticity of labor, ǫ = 0.5 Average size of firms (capital) 0.848 0.925 Change in working time 0.91% Steady state output gain 3.15% Welfare gain from transition 0.46%

CONCLUSION

• Limited enforceability of contracts amplifies the impact of certain technological

innovations and delays the diffusion of others.

• Two ingredients are key to generate the amplification result:
• 1. No market exclusion.
• 2. The use of optimal (state-contingent) contracts.
• Limited enforceability of contracts also distorts the allocation efficiency of the economy

with significant welfare consequences.

• The model is sufficiently rich that allows for the study of other interesting issues. For

example, the change in the degree of enforcement induced by the international mobility

• f capital and entrepreneurs.