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

Aggregate consequences of limited contract enforceability Thomas F. Cooley Ramon Marimon New York University 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 of 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 obvious 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: � t ∞ � 1 � E 0 ( c t − ϕ ( l t )) 1 + r t =0 r = intertemporal discount rate c t = consumption ϕ ( l t ) = disutility from working • Entrepreneurs are born in each period and they die with probability α . Their utility is: � 1 − α � t ∞ � E 0 c t 1 + r t =0

• 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 ∈ { z L , z H } . 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 I 0 , which is sunk. • In each period N t projects with high productive become available. • Given S t the number of entrepreneurs searching for a new project, the probability of success is p t = N t /S t .

• 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 ( s t , k t − 1 ) = k t − 1 + V ( s t ) − κ V ( s t ) = Value of searching. κ = Repudiation cost.

Start with k t − 1 Observe N t ✁ ❆ ✁ ❆ ✁ ❆ ✁ ❆ ✁ ❆ Repudiation ✁ ❆ Continuation ✁ ❆ ✁ ❆ ✁ ❆ ✁ ❆ ✁ ❆ ✁ ❆ ✁ ✁ ☛ ❯ ❆ ❆ Search for Production and new project choice of d t , k t

ASSUMPTIONS 1. The difference between z L and z H 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 opportunities.

THE OPTIMAL CONTRACT ∞ β τ − t d τ � V ( z ; s t ) = max E t { dτ ,kτ ,lτ +1 }∞ τ = t τ = t subject to ∞ � β j − τ − 1 d j ≥ D ( k τ , s τ +1 ) , E τ +1 for τ ≥ t j = τ +1 ∞ � � β τ − t � E t π ( z ; k τ , l τ +1 , w τ +1 ) − d τ ≥ I 0 τ = t d τ ≥ 0

RECURSIVE PROBLEM � π ( z ; k, l ′ , w ′ ) − (1 − µ ) d W ( z ; s , µ ) = min µ ( s ′ ) max d,k,l ′ � − βE ( µ ( s ′ ) − µ ) D ( z ; k, s ′ ) + βEW ( z ; s ′ , µ ( s ′ )) subject to µ ( s ′ ) ≥ µ d ≥ 0 , 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 ( z H ; s ) + (1 − p ) · V ( z L ; s ) where p = N α

REPUDIATION VALUE D ( s , k − 1 ) = k − 1 + V ( s ) − κ

FIRST ORDER CONDITIONS µ ( s ′ ) : D ( k, s ′ ) ≤ W µ ( z ; s ′ , µ ( s ′ )) , ( = if µ ( s ′ ) > µ ) d : µ ≤ 1 , ( = if d > 0 ) π k ( z ; k, l ′ , w ′ ) = βE ( µ ( s ′ ) − µ ) k : l ′ : π l ( 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 ¯ k z . – The entrepreneur’s payments are not determined.

CALIBRATION Intertemporal discount rate r = 0 . 04 1+ ǫ ǫ Disutility from working ϕ ( l ) ≡ A · l A = 0 . 001 , ǫ = 1 Death probability of entrepreneurs γ = 0 . 05 z · ( k ν l 1 − ν ) θ Production technology ¯ z = 0 . 012 , θ = 0 . 85 , ν = 0 . 294 ¯ Depreciation rate δ = 0 . 0579 I 0 = 0 . 2 Set-up investment 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 ) or � � k + EV ( s ′ ) − κ k − 1 + V ( s ) − κ = β

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 of capital and entrepreneurs.