Ce2pres ut

Financial Frictions and Investment: A

Requiem in Q

Russell W. Cooper

University of Texas

Joao Ejarque

Institute of Economics, University of Essex

Question: Do financial factors matter for investment?

Answers:

• YES: Look at 1000 papers on Q investment regressions: profits are significant

• NO: this evidence could all be measurement error ( Erickson-Whited, Gomes) or market power (Cooper-Ejarque, Abel-Eberly)

Methodology

• theory: dynamic optimization at firm level with borrowing restrictions

• facts: Q investment regression coefficients and other mo-ments

• organize facts around these models

What this paper does not do:

• studies firm optimization problem; not an equilibrium analysis

Consider:

V (K, A) = max K0

π(K, A) − p(K0 − K(1 − δ)) − C(K0, K) +

βE_A0_|AV (K0, A0) ∀(K, A)

• π(K, A) is profit after maximization over flexible inputs

• C(K0, K) is a cost of adjustment function

• A is a stochastic process; firm and aggregate components

Q- theory

• CRS and perfect competition: π(K, A) = AK

• adjustment costs

C(K0, K) = γ 2

K0 − (1 − δ)K

K − ai0 − εit

!2

K.

• optimality implies

p + γ (I/K_it − ε_it − a_i0) = βEV (K_it+1, A_it+1)/K_it+1

Evidence from Q-Theory based on:

(I/K)_it = a_i0 + a₁Eq¯_it+1 + a₂(π_it/K_it) + ε_it.

• Q-theory implies: a₁ = 1/γ, a₂ = 0

• Generally find (Table 1):

– a₁ is small “implying” γ large

– a₂ is significant “implying” financial frictions

Table 1: Q Regression Results and Other Moments

study a1 a2 mean(¯q) std (¯q) std(I/K) std(π/K) sc(I/K)

GH95 0.03 0.242 2.95 2.28 0.132 0.257 0.4 FHP88(low) 0.0008 0.46 3.8 na 0.17 0.2 na

FHP88(high) 0.002 0.23 1.6 na 0.06 0.06 na

G01 0.06 0.14 1.56 na 0.139 na 0.239

Cooper-Ejarque:

No! Hold It!

• let π(K, A) = AKα, α ≤ 1

• consider min

Θ J(Θ) = (Ψ

d _{− Ψ}s_(Θ))0_W(Ψd _{− Ψ}s_(Θ))

where

– Ψd = (a₁, a₂, sc(I/K), std(π/K),q¯)

– Ψs(Θ): corresponding simulation moments from solving dynamic optimization problem

Cooper-Ejarque reproduce Q-theory results without financial fric-tions :

• α < 1 and no borrowing restrictions matches moments except for serial correlation of investment rates

• small a₁ does not reflect large adjustment costs as γ is rela-tively small

Table 2a: Structural Parameter Estimates by Model Model Structural Parameter Estimates (Θ)

α γ ρ σ

Unconstrained 0.699 0.1647 0.111 0.857

(0.01) (0.017) (0.007) (0.029)

Internal 0.6967 0.2307 0.1053 0.8382

(0.01) (0.02) (0.01) (0.03)

Table 2b: Moments by Model

Model Reduced Form Coefficients and Moments

a₁ a₂ sc( I

K) std(

π

K) q¯ J(Θ)

GH95 0.03 0.24 0.4 0.25 3.0 na

Could a model with financial frictions improve the fit?

• Gilchrist-Himmelberg and Euler equations find support for market power and frictions

• perhaps the market power is just substituting for the financial frictions: identification is important

• But: why doesn’t average Q reflect financial frictions (Chirinko)?

Internal Finance: Theory

V (K, A) = max

K0 π

(K, A) − p(K0 − K(1 − δ)) − C(K0, K) +

βE_A0_|AV (K0, A0), with I ≤ π(A, K)

• “ constraint was violated” in about 20% of unconstrained observations

• allow for market power

• maintain quadratic costs

Internal Finance: Evidence

• estimate Θ as before

• market power still evident

• fit is not better

Costly External Finance: Theory

V (K, A) = maxnV e(K, A), V i(K, A)o

V e(K, A) = max

K0 d − φ0

+ βE_A0_|AV (K0, A0) and

V i(K, A) = max

K0≤π(K,A)+(1−δ)K

d + βE_A0_|AV (K0, A0)

where

d ≡ π(K, A) − (K0 − (1 − δ)K) − C(K0, K)

• φ₀: fixed costs for external finance

External Finance: Evidence in Table 3

• estimate 5 parameters, using six moments

• fit is no better when φ₀ 6= 0 is allowed

Table 3a: Structural Parameter Estimates: Costly External

Finance

Model Structural Parameter Estimates (Θ)

α γ ρ σ ˜φ₀

Costly 0.6956 0.1331 0.0976 0.8932 0

(0.01) (0.04) (0.02) (0.03) (0.05)

Table 3b: Moments by Model

Model Reduced Form Coefficients and Moments

a₁ a₂ sc( I

K) std(

π

K) q¯ Ext. Frac. J(Θ)

Moments 0.03 0.24 0.4 0.25 3.0 0.25 na

Implications for investment behavior:

• investment is a convex function of average Q

• profits still significant even in nonlinear Q-regression

• investment bursts in only 1% of observations

Costly finance with financial assets (in process)

V (K, A, B, D) = maxnV e(K, A, B, D), V i(K, A, B, D)o where

V i(K, A, B, D) = max K0,B0,D0≤D

d + βE_A0_|AV (K0, A0, B0, D0)

V e(K, A, B, D) = max K0,B0,D0≥0

d − φ₀ + βE_A0_|AV (K0, A0, B0, D0)

for all (K, A, B ≥ 0, D ≥ 0).

• here B represents funds in the ”bank” and D is debt

• allow Rb > Rl

• lumpy financial market participation distinct from investment behavior

• if internal, firm may not be constrained

• d ≥ 0 so that firm must pay fixed cost to borrow

Conclusions:

• estimated model allows for both financial frictions and market power

• fit of model reflects market power of firms not capital market imperfections

• results from Q-regressions do not reflect capital market im-perfections