A Theory of Financing Constraints and Firm Dynamics Gian Luca Clementi and Hugo Hopenhayn forthcoming on the Quarterly Journal of Economics A Theory of Financing Constraints and Firm Dynamics – p. 1/16 Introduction Objective: Study the effect of borrowing constraints on firms’ growth and survival. Framework: Long-term contractual relationship between an entrepreneur (borrower) and an investor (lender) with asymmetric information. Results: Borrowing constraints as endogenous "products" of the optimal contract; less stringent the higher the entrepreneur’s share of total firm value (Equity); Optimal contract generates firm dynamics that match stylized facts qualitatively. A Theory of Financing Constraints and Firm Dynamics – p. 2/16 Model I Time: Discrete; infinite horizon. Players: A risk-neutral entrepreneur has a project "in mind" at t = 0. She owns M but needs I0 > M to start. If started, the project takes working capital kt as input and returns output y˜t , ∀t ≥ 1. A risk-neutral investor (with the same discount factor as the entrepreneur) covers the start-up cost and provides working capital. She cannot monitor the project, must rely on entrepreneur’s reports. Liquidation: The project can be scrapped at any time, generating value S . A Theory of Financing Constraints and Firm Dynamics – p. 3/16 Model II Productivity shocks: θ ǫ Θ ≡ {H, L}; θ takes value H with probability p. Accordingly, ( R(kt ) with prob. p y˜t = 0 with prob. 1 − p Reporting strategy: θˆ = {θˆt (θt )}∞ t=1 , where θt = (θ1 , . . . , θt ); history of reports thus ht = (θˆ1 , . . . , θˆt ). Contract: At t = 0, the investor offers a contract to the entrepreneur. The terms specify liquidation policy, payments and capital advancements and are made contingent on common information: σ = {αt (ht−1 ), Qt (ht−1 ), kt (ht−1 ), τt (ht )} A Theory of Financing Constraints and Firm Dynamics – p. 4/16 Timing A Theory of Financing Constraints and Firm Dynamics – p. 5/16 Equity and Debt σ feasible if, ∀t ≥ 1 and ∀ht−1 ǫ Θt−1 αt (ht−1 ) ǫ [0, 1]; Qt (ht−1 ) ≥ 0; τt (ht−1 , H) ≤ R(kt (ht−1 )) and τt (ht−1 , L) ≤ 0. ˆ implies expected discounted cash ∀ht−1 , the pair (σ, θ) flows for: ˆ ht−1 ) or Equity; Entrepreneur: Vt (σ, θ, ˆ ht−1 ) or Debt. Investor: Bt (σ, θ, σ incentive compatible if, ∀θˆ ˆ σ, h0 ) V1 (θ, σ, h0 ) ≥ V1 (θ, A Theory of Financing Constraints and Firm Dynamics – p. 6/16 Pareto Frontier Set of equity values that can be generated by feasible and incentive compatible contracts: V ≡ {V |∃ σ s.t. feas., i.c. and V1 (θ, σ, h0 ) = V } Can define a Frontier of values thus: for any V ǫV , the optimal contract such that B(V ) = sup{B|∃ σ s.t. V1 (θ, σ, h0 ) = V and B1 (θ, σ, h0 ) = B} Each point on the frontier corresponds to a capital structure (V, B(V )). In general, the Modigliani-Miller Theorem does not hold: W (V ) = V + B(V ) not invariant to capital structure. A Theory of Financing Constraints and Firm Dynamics – p. 7/16 Symmetric Information Benchmark: With symmetric information, the contract simply maximizes the expected discounted surplus of the project: k ∗ = arg max pR(k) − k k π ∗ = pR(k ∗ ) − k ∗ ∗ π ˜ = π ∗ [1 + δ + δ 2 + . . .] = W 1−δ ˜ > I0 . Any division of W ˜ The project is undertaken if W between investor and entrepreneur is feasible as long as the latter gets a nonnegative value. A Theory of Financing Constraints and Firm Dynamics – p. 8/16 Asymmetric Information I Suppose liquidation has not occurred at the beginning of the period. The problem is then: ˆ (V ) = W max [pR(k) − k] + δ[pW (V H ) + (1 − p)W (V L )] k,τ,V H ,V L subject to PK: V = [pR(k) − τ ] + δ[pV H + (1 − p)V L ] IC: R(k) − τ + δV H ≥ R(k) + δV L LL: τ ≤ R(k) V H, V L ≥ 0 A Theory of Financing Constraints and Firm Dynamics – p. 9/16 Asymmetric Information II Step back at the beginning of the period. Liquidation decision to be made: ˆ (Vc ) W (V ) = max αS + (1 − α)W α,Q,Vc subject to PK: V = αQ + (1 − α)Vc Q, Vc ≥ 0 Solution: Set Q = 0 ⇒ α(V ) = Vc (V )−V Vc (V ) ; Set Vc (V ) = Vr such that 0 ≤ α(V ) ≤ 1, for V ≤ Vr ; Three regions emerge (see graph below). A Theory of Financing Constraints and Firm Dynamics – p. 10/16 Value Function W (V ) linear for V ≤ Vr , where random liquidation occurs; pR(k ∗ ) ˜ ˜ ˜ . strictly incr. for V < V and equal to W for V ≥ V ≡ (1−δ) A Theory of Financing Constraints and Firm Dynamics – p. 11/16 Optimal Contract I Capital Advancement: k(V ) single valued and continuous; for V < V˜ , k(V ) < k ∗ , i.e. borrowing constraint binds; for V ≥ V˜ , k(V ) = k ∗ ; Intuition when R(k) = τ : in this case IC binds, i.e. R(k) = δ(VH − VL ). Higher capital advancement requires higher spread in equity values: as standard with moral hazard, the lender wants to make the borrower more sensitive to the realization of output. Given the concavity of W (V ), this spread is costly for the investor. Borrowing constraints stem from this trade-off. A Theory of Financing Constraints and Firm Dynamics – p. 12/16 Optimal Contract II Repayment: For V < V˜ , given risk neutrality and the common discount factor δ , it is optimal for both the entrepreneur and the investor to set R(k) = τ until V reaches V˜ and providing the efficient level of capital k ∗ becomes incentive compatible. (For V H < V˜ , R(k) = τ is necessary for optimality). Intuition: For given k and V L , there are infinite combinations of τ and V H that are feasible and incentive compatible. Instantaneous profits are not affected by the choice. Continuation value, though, is weakly increasing in V H . A Theory of Financing Constraints and Firm Dynamics – p. 13/16 Optimal Contract III Evolution of Equity when R(k) = τ and Vr ≤ V < V˜ : VL <V <VH (V L = V −pR(k) , δ VH = V +(1−p)R(k) ); δ V < pV H + (1 − p)V L . A Theory of Financing Constraints and Firm Dynamics – p. 14/16 Simulation A Theory of Financing Constraints and Firm Dynamics – p. 15/16 Conclusions Borrowing constraints emerge endogenously from the optimal contract; tend to be less stringent the higher the entrepreneur’s share of total firm value (V ); Optimal contract generates firm dynamics that match stylized facts qualitatively; in a regression of investment on some controls (Tobin’s average q ’s, cash flows, . . . ), would expect positive and significative cash flow coefficients. Extensions: "Hunger"; Multiple shocks; General equilibrium. A Theory of Financing Constraints and Firm Dynamics – p. 16/16

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