Volatility and Growth: Credit Constraints and the Composition of Investment Aghion, Angeletos, Banerjee and Manova

Meng Li

Universidad Carlos III de Madrid 9 March, 2015

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 1 / 32

Some motivating background

Ramey and Ramey (1995): document a negative correlation between volatility and mean rate of output growth in a cross-section of countries. Some explanations:

One-sector neoclassical growth model if risk discourages demand for investment more than it encourages the precautionary supply of savings; Neoclassical growth model with heterogenous agents and idiosyncratic investment risks; Models featuring nancial frictions; Feature: High volatility reduces average investment.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 2 / 32

Some motivating background

Above stories fail to reect the reality, because if it were true... ...one would expect that controlling for aggregate rate of investment would remove most of this correlation.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 3 / 32

Some motivating background

Another fact: credit access predicts both mean and volatility of growth rate, but not volatility of aggregate investment rate.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 4 / 32

What the Paper Does

Study how nancial frictions impact the composition of investment over the business cycle... ...and the implications that the composition aects both volatility and growth.

Carry on an empirical study to verify their results.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 5 / 32

Feature of Model

Firms engage in two alternative types of investment:

Short-term investment takes little time to build and therefore generates output quickly. Long-term investment takes more time to complete, but also contributes more to productivity growth. The overall supply of capital goods does not vary over the business cycle.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 6 / 32

Main Results

The share of long-term investment to total investment is countercyclical when nancial markets are perfect; This share may turn procyclical when rms face tight credit constraints. Tighter credit can lead to both higher volatility and lower mean growth. Evidence from a panel of countries provides support for the model's key predictions.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 7 / 32

Model

Economy

Populated by overlapping generations of a single type of agents, entrepreneurs; Each generation consists of a unit mass of entrepreneurs. Each entrepreneur lives for three periods... ... and is endowed with one unit of labor in each period of her life. There is a single consumption good and two types of capital goods.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 8 / 32

Model

Economy

Consider an entrepreneur born in period

t:

Her labor endowment, measured in eciency units, is denoted by

Ht .

Assumed to be xed over the productive life of an entrepreneur and to be exogenous to her production choices. The growth rate of

Ht

depends on the general equilibrium of the

economy through a certain type of intergenerational spillover eects.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, of 2015 Investment 9 / 32

Model

Agent

Preference of entrepreneur:

Ut = Ct,t + βCt,t+1 + β 2 Ct,t+2 . Period Period

t , transform eective labor to either of two t + 1 and t + 2, use stock of capital goods

types of capital goods; and endowment of labor

to produce consumption goods.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 10 / 32

Model

Agent

Production of capital goods at

t:

Labor is the only input in the production of capital goods; linear production functions. Short-term capital goods:

Kt = θk,t Hk,t ;

Long-term capital goods:

Zt = θz,t Hz,t .

Let

θk,t = θz,t = θ

for some xed

θ > 0.

Budget and borrowing constraints

Ct,t + qt (Kt + Zt ) = qt θHt + Bt,t

and

Bt,t ≤ µqt θHt .

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 11 / 32

Model

Agent

Production of consumption goods at

t + 1:

Only short-term investment available:

Yt,t+1 = At+1 F (Kt , Ht ). F

is assumed to be Cobb-Douglas:

F (K , H) = K α H 1−α , for some

α ∈ (0, 1).

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 12 / 32

Model

Agent

Entrepreneur may face an idiosyncratic ``liquidity'' risk:

t + 1, an Lt+1 ≥ 0. At

idiosyncratic shock hits the entrepreneur, denoted by

The shock incurs a random expense, in terms of consumption goods. Budget and borrowing constraints

Ct,t+1 + Lt+1 et,t+1 = Yt,t+1 + Bt,t+1 − (1 + Rt )Bt,t and

et,t+1 :

Bt,t+1 ≤ µYt,t+1 .

indicator function that takes the value 1 if the entrepreneur covers

this shock and 0 otherwise.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 13 / 32

Model

Agent

Production of consumption goods at

t + 2:

If covering this expense,

Yt,t+2 = At+2 F (Zt , Ht ). If unable to cover, output is zero.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 14 / 32

Model

Agent

Assume that if the entrepreneur covers the liquidity shock in period she recovers fully the associated expense in period

t +2

foregone interest: conditional on paying

Lt+1

in period

t + 1,

she receives

t + 1,

along with any

β −1 Lt+1

in period

t + 2. Budget and borrowing constraints

Ct,t+1 = (Yt,t+2 + β −1 Lt+1 )et,t+1 − (1 + Rt,t+2 )Bt,t+1 .

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 15 / 32

Model

Exogenous variables

Labor endowment:

Ht+1 = Γ(Ht , Z˜t , Kt ), where

Z˜t

denotes amount of long-term investment that survives the

liquidity shock; for any

H

and any given sum

assumed to increase with the ratio

Z + K , Γ(H, Z , K )

is

Z /K .

Productivity shock: log At

= ρ log At−1 + log vt , where ρ ∈ (0, 1).

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 16 / 32

Model

Exogenous variables

Ht . Lt+1 Ht denote normalized level of liquidity shock;

Liquidity shock: grow proportionately with let

`t+1 ≡

distribution of

`t+1 :

invariant over time;

let [0, `max ] be support of distribution and

Φ

its c.d.f.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 17 / 32

Model

Exogenous variables

`max is assumed to exceed vmax 1−ρ is the maximal productivity shock;

The maximal liquidity shock, where

Amax ≡

Amax F (θ, 1),

Assume a power-form specication:

Φ(`) =

  1

` `max

φ

when ` < `max , for some φ > 0; when ` ≥ `max .

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 18 / 32

Equilibrium composition of investment

Complete markets

Linearity of preferences

⇒

equilibrium interest rate

R t = β −1 .

Net present value of meeting the liquidity shock is

(Yt,t+2 + β −1 Lt+1 ) − Rt+1 Lt+1 = Yt,t+2 = At+2 F (Zt , Ht ) ≥ 0. Present value of entrepreneur's lifetime utility

Ut = Ct,t + βCt,t+1 + β 2 Ct,t+2

= qt (θHt − Kt − Zt ) + β(Yt,t+1 − Lt+1 ) + β 2 (Yt,t+2 + β −1 Lt+1 ) = qt (θHt − Kt − Zt ) + βAt+1 F (Kt , Ht ) + β 2 At+2 F (Zt , Ht ).

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 19 / 32

Equilibrium composition of investment

Complete markets

The optimal investment problem of entrepreneur max

Kt ,Zt Let

kt ≡

Et [βAt+1 F (Kt , Ht ) + β 2 At+2 F (Zt , Ht ) − qt Kt − qt Zt ].

Kt Ht and

zt ≡

Zt Ht denote the ``normalized'' levels of short- and

long-term investment. The entrepreneur's problem can then be restated max Et [βAt+1 f

kt ,zt

(kt ) + β 2 At+2 f (zt ) − qt kt − qt zt ].

F.O.C

βEt [At+1 f 0 (kt )] = qt

and

β 2 Et [At+2 f 0 (zt )] = qt .

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 20 / 32

Equilibrium composition of investment

Complete markets

Resource constraint

Kt + Zt = θHt ⇒kt + zt = θ.

Equilibrium composition of investment

Et [At+1 f 0 (θ − zt )] = βEt [At+2 f 0 (zt )]. To ensure that there are enough aggregate resources to pay for the liquidity shocks in each period, impose that

`mean < Amin f (θ − zmax ), where

zmax

and where

is the solution to FOC when

Amin

and

`mean

At = Amin ,

are, respectively, the minimum productivity level

and the mean liquidity shock.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 21 / 32

Equilibrium composition of investment

Complete markets

Proposition Suppose that credit markets are perfect. (i) The equilibrium exists and is unique. ∗ (ii) There exists a continuous function z : R+ → (0, θ) such that the equilibrium levels of short-term and long-term investment are given, respectively, by kt = θ − z ∗ (At ) and zt = z ∗ (At ). ∗ (iii) The function z is strictly decreasing. That is, the share of long-term investment decreases with a positive innovation in productivity.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 22 / 32

Equilibrium composition of investment

Complete markets

Implication: Prots anticipated in the near future are likely to be more procyclical than prots anticipated in the distant future. The return to short-term investment depends more heavily on prots in the near future, while the return to long-term investment depends more heavily on prots in the distant future. The return to short-term investment is likely to be more procyclical than the return to long-term investment and, therefore, the composition of investment is likely to shift towards a relatively higher share of long-term investment during recessions than during booms.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 23 / 32

Equilibrium composition of investment

Incomplete markets

Probability of failing to meet the liquidity shock is positive, the entrepreneur nds it strictly optimal to consume zero in the rst period of her life. The entrepreneur covers her liquidity shock if and only if

Lt+1 ≤ Xt+1 ,

where

Xt+1 ≡ (1 + µ)Yt,t+1 + Rt qt (θHt − Kt − Zt ). Present value of entrepreneur's lifetime utility

Ut = Ct,t + βCt,t+1 + β 2 Ct,t+2 = qt (θHt − Kt − Zt ) + βAt+1 F (Kt , Ht ) + β 2 At+2 F (Zt , Ht )et,t+1 .

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 24 / 32

Equilibrium composition of investment

Incomplete markets

Let

xt+1 ≡

Xt+1 Ht , the entrepreneur's problem can be restated

max Et [βAt+1 f

kt ,zt

where

λt+1 ≡ Φ(xt+1 )

(kt ) + β 2 λt+1 At+2 f (zt ) − qt kt − qt zt ],

is the probability that the entrepreneur will have

enough funds to cover the liquidity shock. 1

− λt+1

measures the ``liquidity

risk'' faced by the entrepreneur.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 25 / 32

Equilibrium composition of investment

Incomplete markets F.O.C

βEt [At+1 f 0 (kt )] + β 2 Et [

∂λt+1 At+2 f (zt )] = qt , ∂kt

β 2 Et [λt+1 At+2 f 0 (zt )] + β 2 Et [

∂λt+1 At+2 f (zt )] = qt . ∂zt

Combining two FOCs,

Et [At+1 f 0 (kt )] = βEt [(1 − τt+1 )At+2 f 0 (zt )], where

τt+1 ≡ (1 − λt+1 ) + ( ∂λ∂kt+t 1 −

∂λt+1 f (zt ) ∂zt ) f 0 (zt ) , the wedge that credit

frictions introduce between two types of investment.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 26 / 32

Equilibrium composition of investment

Incomplete markets

The wedge 1

τt+1

− λt+1

comprises two terms:

captures the probability of failure;

emerges even if the probability of failure were exogenous to the choices of the entrepreneur.

( ∂λ∂kt+t 1 −

∂λt+1 f (zt ) ∂zt ) f 0 (zt ) captures the marginal change in this probability

caused by a reallocation of investment from the long- term opportunity to the short-term one; highlights the endogeneity of the liquidity risk.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 27 / 32

Equilibrium composition of investment

Incomplete markets

When

xt+1 > `max ,

the entrepreneur has enough liquidity to meet even the highest possible liquidity shock, both terms are zero and the wedge vanishes.

xt+1 < `max , 0 0 t+1 f (kt ) − ∂λ∂zt+t 1 = Φ (xt+1 )(1`+µ)A > 0. max shifting a unit of capital from the long-term to the short-term investment opportunity necessarily reduces the probability of failure. τt+1 is strictly positive whenever xt+1 < `max . When

∂λt+1 ∂kt

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 28 / 32

Equilibrium composition of investment

Incomplete markets

Consider that credit constraints are suciently tight, that is, So let

∂λt+1 ∂kt

xt+1 < `max .

µ 0 solves (1 + µ ¯)Amax f (θ) = `max . φλt+1 f 0 (kt ) ∂λt+1 − ∂zt = . f (kt )

   At+2 f (zt ) 0 Et At+1 f (θ − zt ) 1 + βφλt+1 = βEt [λt+1 At+2 f 0 (zt )]. At+1 f (kt ) Ignore the underlying uncertainty about aggregate productivity momentarily,

τt+1 = 1 −

λt+1 A

f (z )

1+βφλt+1 At+2 f (kt ) t+1

which is decreasing in

,

t

λt+1

and increasing in the ratio

At+2 f (zt ) At+1 f (kt ) .

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 29 / 32

Equilibrium composition of investment

Incomplete markets

In a boom, one would expect 1

the probability of survivalλt+1 to be higher, because of the improved availability of liquidity.

2

the ratio

At+2 f (zt ) At+1 f (kt ) to be lower, because of the mean-reversion in the

business cycle. Prediction: the wedge

τt+1

to be lower in a boom than in a recession. This

countercyclicality of the wedge would tend to boost long-term investment during a boom. Conclusion: the share of long-term investment to be procyclical if and only if the countercyclicality of the wedge

τt+1

is suciently strong to oset the

countervailing opportunity-cost eect.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 30 / 32

Equilibrium composition of investment

Incomplete markets

Proposition Suppose that credit constraints are suciently tight that the liquidity risk is non-zero in all states of nature, which is necessarily the case if µ < µ¯. (i) The equilibrium exists and is unique. (ii) There exists a continuous function z such that the equilibrium composition of investment is given by kt = θ − z(At , µ) and zt = z(At , µ). (iii) This function satisesz(A, µ) < z ∗ (At ) for all (A, µ), and is decreasing in µ. That is, credit constraints depress the share of long- term investment below its complete-market value, and the more so the tighter they are. (iv) Suppose further that φ > 1 − ρ. Then the function z(A, µ) is increasing in A. That is, the share of long-term investment increases with a positive innovation in productivity.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 31 / 32

Conclusion

1

Identify a novel propagation mechanism in the impact of credit frictions on the cyclical composition of investment;

2

Show how the share of long-term investment turns from countercyclical under complete markets to procyclical under suciently tight credit constraints.

Meng Li (Universidad Carlos III de Madrid) Volatility and Growth: Credit Constraints and the Composition 9 March, 2015 of Investment 32 / 32