"A Theory of Financing Constraints and Firm Dynamics" G.L. Clementi and H.A. Hopenhayn (QJE, 2006) Cesar E. Tamayo Econ612- Economics - Rutgers April 30, 2012 1/21
Program I Summary I Physical environment I The contract design problem I Characterization of the optimal contract I Firm growth and survival I Contract maturity and debt limits 2/21
What they do in a nutshell I The paper develops a theory of endogenous …nancing constraints. 3/21
What they do in a nutshell I The paper develops a theory of endogenous …nancing constraints. I Repeated moral hazard problem 3/21
What they do in a nutshell I The paper develops a theory of endogenous …nancing constraints. I Repeated moral hazard problem I The optimal contract (under asymmetric info) determines non-trivial stochastic processes for …rm size, equity and debt. 3/21
What they do in a nutshell I The paper develops a theory of endogenous …nancing constraints. I Repeated moral hazard problem I The optimal contract (under asymmetric info) determines non-trivial stochastic processes for …rm size, equity and debt. I This in turn implies non-trivial …rm dynamics even under simple i.i.d. shocks. 3/21
Physical environment: I At t = 0 entrepreneur ( E ) has a project that requires initial investment I 0 > M where M in his net worth. 4/21
Physical environment: I At t = 0 entrepreneur ( E ) has a project that requires initial investment I 0 > M where M in his net worth. I Borrower ( E ) and lender ( L ) are risk neutral, discount future at δ . 4/21
Physical environment: I At t = 0 entrepreneur ( E ) has a project that requires initial investment I 0 > M where M in his net worth. I Borrower ( E ) and lender ( L ) are risk neutral, discount future at δ . I Both agents can fully commit to a long term contract. 4/21
Physical environment: I At t = 0 entrepreneur ( E ) has a project that requires initial investment I 0 > M where M in his net worth. I Borrower ( E ) and lender ( L ) are risk neutral, discount future at δ . I Both agents can fully commit to a long term contract. I At each t � 1, E can re-scale the project by investing additional k t . 4/21
Physical environment: I At t = 0 entrepreneur ( E ) has a project that requires initial investment I 0 > M where M in his net worth. I Borrower ( E ) and lender ( L ) are risk neutral, discount future at δ . I Both agents can fully commit to a long term contract. I At each t � 1, E can re-scale the project by investing additional k t . I Returns are stochastic and equal to R ( k t ) if state of nature is H (with prob. p ) and zero if state is L (prob. 1 � p ) 4/21
Physical environment: I At t = 0 entrepreneur ( E ) has a project that requires initial investment I 0 > M where M in his net worth. I Borrower ( E ) and lender ( L ) are risk neutral, discount future at δ . I Both agents can fully commit to a long term contract. I At each t � 1, E can re-scale the project by investing additional k t . I Returns are stochastic and equal to R ( k t ) if state of nature is H (with prob. p ) and zero if state is L (prob. 1 � p ) I At the begining of each t , project can be liquidated ( α t = 1 ) yielding S � 0 and resulting in payo¤s Q to E and S � Q to L 4/21
Physical environment: I At t = 0 entrepreneur ( E ) has a project that requires initial investment I 0 > M where M in his net worth. I Borrower ( E ) and lender ( L ) are risk neutral, discount future at δ . I Both agents can fully commit to a long term contract. I At each t � 1, E can re-scale the project by investing additional k t . I Returns are stochastic and equal to R ( k t ) if state of nature is H (with prob. p ) and zero if state is L (prob. 1 � p ) I At the begining of each t , project can be liquidated ( α t = 1 ) yielding S � 0 and resulting in payo¤s Q to E and S � Q to L I If project is not liquidated, E repays τ to L . 4/21
Physical environment: I Assumption : R ( � ) is continuous, increasing and strictly concave. 5/21
Physical environment: I Assumption : R ( � ) is continuous, increasing and strictly concave. I Assumption: R ( � ) is private information; the state of nature at t is θ t 2 Θ � f H , L g but E reports ˆ θ t . 5/21
Physical environment: I Assumption : R ( � ) is continuous, increasing and strictly concave. I Assumption: R ( � ) is private information; the state of nature at t is θ t 2 Θ � f H , L g but E reports ˆ θ t . I Assumption : E consumes all proceeds R ( k t ) � τ (i.e. no storage) 5/21
Physical environment: De…nition (reporting strategy) � ˆ � θ t �� ∞ t = 1 where θ t = ( θ 1 , θ 2 , ..., θ t ) A reporting strategy for E is ^ θ = θ t 6/21
Physical environment: De…nition (reporting strategy) � ˆ � θ t �� ∞ t = 1 where θ t = ( θ 1 , θ 2 , ..., θ t ) A reporting strategy for E is ^ θ = θ t De…nition (contract) � � h t � 1 � � h t � 1 � � h t � 1 � � , τ t ( h t ) A contract is a vector σ = α t , Q t , k t � ˆ � where h t = θ 1 , ..., ˆ θ t 6/21
Physical environment: De…nition (reporting strategy) � ˆ � θ t �� ∞ t = 1 where θ t = ( θ 1 , θ 2 , ..., θ t ) A reporting strategy for E is ^ θ = θ t De…nition (contract) � � h t � 1 � � h t � 1 � � h t � 1 � � , τ t ( h t ) A contract is a vector σ = α t , Q t , k t � ˆ � where h t = θ 1 , ..., ˆ θ t De…nition (feasible contract) � � � 0 , h t � 1 , L A contract σ is feasible if α t 2 [ 0 , 1 ] , Q t � 0 , τ t � � � R ( k t ) . h t � 1 , H τ t 6/21
Physical environment: De…nition (reporting strategy) � ˆ � θ t �� ∞ t = 1 where θ t = ( θ 1 , θ 2 , ..., θ t ) A reporting strategy for E is ^ θ = θ t De…nition (contract) � � h t � 1 � � h t � 1 � � h t � 1 � � , τ t ( h t ) A contract is a vector σ = α t , Q t , k t � ˆ � where h t = θ 1 , ..., ˆ θ t De…nition (feasible contract) � � � 0 , h t � 1 , L A contract σ is feasible if α t 2 [ 0 , 1 ] , Q t � 0 , τ t � � � R ( k t ) . h t � 1 , H τ t De…nition (equity and debt) Expected discounted cash ‡ows for E is called equity , V t ( σ , ^ θ , h t � 1 ) and for L is called debt , B t ( σ , ^ θ , h t � 1 ) 6/21
Physical environment: De…nition (reporting strategy) � ˆ � θ t �� ∞ t = 1 where θ t = ( θ 1 , θ 2 , ..., θ t ) A reporting strategy for E is ^ θ = θ t De…nition (contract) � � h t � 1 � � h t � 1 � � h t � 1 � � , τ t ( h t ) A contract is a vector σ = α t , Q t , k t � ˆ � where h t = θ 1 , ..., ˆ θ t De…nition (feasible contract) � � � 0 , h t � 1 , L A contract σ is feasible if α t 2 [ 0 , 1 ] , Q t � 0 , τ t � � � R ( k t ) . h t � 1 , H τ t De…nition (equity and debt) Expected discounted cash ‡ows for E is called equity , V t ( σ , ^ θ , h t � 1 ) and for L is called debt , B t ( σ , ^ θ , h t � 1 ) De…nition (incentive compatibility) � σ , θ , h 0 � � V 1 ( σ , ^ A contract σ is incentive compatible if 8 ^ θ , h 0 ) θ , V 1 6/21
The …rst-best (symmetric info) I Since both are risk neutral and share δ , the optimal contract maximizes total exp. discounted pro…ts of the match ( E , L ) . 7/21
The …rst-best (symmetric info) I Since both are risk neutral and share δ , the optimal contract maximizes total exp. discounted pro…ts of the match ( E , L ) . I In equilibrium L provides E with the unconst. e¤cient k in every t : max [ pR ( k ) � k ] (1) k 7/21
The …rst-best (symmetric info) I Since both are risk neutral and share δ , the optimal contract maximizes total exp. discounted pro…ts of the match ( E , L ) . I In equilibrium L provides E with the unconst. e¤cient k in every t : max [ pR ( k ) � k ] (1) k I So that R ( � ) strictly concave ) 9 unique k � � 0 that solves (1). 7/21
The …rst-best (symmetric info) I Since both are risk neutral and share δ , the optimal contract maximizes total exp. discounted pro…ts of the match ( E , L ) . I In equilibrium L provides E with the unconst. e¤cient k in every t : max [ pR ( k ) � k ] (1) k I So that R ( � ) strictly concave ) 9 unique k � � 0 that solves (1). I Assume k � > 0 so that per-period total surplus is: π � = max [ pR ( k ) � k ] = pR ( k � ) � k � k 7/21
The …rst-best (symmetric info) I Since both are risk neutral and share δ , the optimal contract maximizes total exp. discounted pro…ts of the match ( E , L ) . I In equilibrium L provides E with the unconst. e¤cient k in every t : max [ pR ( k ) � k ] (1) k I So that R ( � ) strictly concave ) 9 unique k � � 0 that solves (1). I Assume k � > 0 so that per-period total surplus is: π � = max [ pR ( k ) � k ] = pR ( k � ) � k � k I And PDV of total surplus is W � = π � 1 � δ > S by assumption. 7/21
Recommend
More recommend
