Innovation and Growth in Imperfect Financial Markets · Innovation and Growth in Imperfect...

Innovation and Growth in Imperfect Financial Markets

Maurizio Iacopetta, SKEMA and OFCE (Sciences Po)Raoul Minetti, Michigan StatePietro F. Peretto, Duke

January 2013

Iacopetta, Minetti, Peretto () Finance and growth January 2013 1 / 35

What we do

Schumpeter (1911, Theory of Economic Development) emphasized thatinnovation requires credit. A massive literature studies the role of �nancialmarkets in the growth process. However, not much has been done tounderstand role of �nance in Schumpeterian theory of innovation-drivengrowth.

We elaborate on Schumpeter�s vision as follows:1 Two dimensions of innovations:

creation of new products/�rms;in-house incremental innovation by existing �rms.

2 Moral Hazard: a source of �nancial frictions that can bite bothwhen new �rms enter the marketand when incumbent �rms innovate in-house.

3 How do frictions a¤ect growth and market structure?We study both direct (household) and bank �nancing.Important insight: interdependence of decisions on two margins ofinnovation.


Why is this important?

Crisis highlighted critical role of �nancial markets in economic activity, ledto calls for far-reaching reforms. But,

do we know what we are doing?

Example � Financial market reforms may generate undesirable long-rune¤ects: �nancial stability induced by reforms may come at the cost ofmore rigidity or unforseen frictions in �nancing �rms, especially innovativeones (Economist, 2012).

Our question: What role do imperfect �nancial markets play in growthprocess led by �rms�innovation?

A necessary �rst step toward understanding the more general issues ofreform and regulation.


Model structure

Final producers: Homogeneous good that is consumed, used to produceintermediate goods, or invested in R&D. (One-sector structure.) Thisgood is the numeraire, so PY � 1.

Intermediate producers: Develop new goods and set up operations to servemarket (variety innovation or entry) and, when already in operation, investin R&D internal to �rm (quality innovation).

Households: Consume and save.


Households

To focus analysis on �nancing of innovation, simplest possiblecharacterization of consumption/saving:

representative household chooses C (t) to maximize

U (0) =Z ∞

0e�ρtL (t) log

�C (t)L (t)

�dt, L (t) = eλt , ρ > λ > 0

subject toA = rA+ wL� C ;

resulting consumption/saving plan is

r = ρ+CC� λ.


Final producers: technology

Y =Z N

0X θi

�Z αi Z

1�α LN1�σ

�1�θ

, Z �Z N

0(Zj/N) dj

where:

0 < θ, α, σ < 1;

Z αi Z

1�α vertical technology index, with α measure of private returnsto quality and 1� α measure of social returns to quality;

N horizontal technology index, with σ measure of social returns tovariety.


Final producers: behavior

Demand for good i :

Xi = Nσ�1�

θ

Pi

� 11�θ

Z αi Z

1�αL.

Factor payments:

N � PX =Z N

0PiXidi = θY ;

wL = wZ N

0Lidi = (1� θ)Y .


Intermediate producers: technologies

Production:Costi = 1 �

�Xi + φZ α

i Z1�α�,

where both the variable and the �xed cost are in units of �nal output.

Corporate innovation:Zi = Ii ,

where Ii is in units of �nal output.

Entrepreneurial innovation:

N =N

βY� E ,

where E is in units of �nal output.


Intermediate producers: equilibrium concept (i)

Value maximization: �rm i chooses paths Pi (t) and Ii (t) to maximize

Vi (0) =Z ∞

0e�

R t0 r (s)dsΠi (t) dt,

whereΠi = Xi (Pi � 1)� φZ α

i Z1�α � Ii ,

subject to the incremental innovation technology and the demand curvecoming from the �nal sector.

Free entry: the anticipated maximized value of the �rm must equal theentry cost:

Vmaxi (0) =βY (0)N (0)

.


Intermediate producers: equilibrium concept (ii)

Looking at incentives on intensive and extensive margins:

existing �rm,

r =∂Πi/∂Ziqi

+qiqi

and qi = 1;

new �rm,

r =Πi

Vi+ViVi

and Vi =βYN.

In symmetric equilibrium:

r = α

�X (1/θ � 1)

Z� φ

�� rZ ;

r =[X (1/θ � 1)� φZ � I ]N

βY+YY� NN� rN .


General equilibrium: output and role of �rm size (i)

Symmetry plus factor markets equilibrium yields

Y = θ2θ1�θ �NσZ � L.

Returns to innovation are functions of

x � X (P � 1)Z

=gross cash �ow

quality= ��rm size�,

where in equilibrium

x = θ (1� θ) � YNZ

= θ (1� θ) θ2θ1�θ � L

N1�σ.


General equilibrium: output and role of �rm size (ii)

Subtracting from �nal output cost of intermediate production yields

GDP � G = (1� θ)

�θ

�1� φ

x

�+ 1

�| {z }

unit cost of intermediate �rmfalls as scale of operation rises

� Y .

Taking logs and time derivatives,

GG=YY+ ξ (x)

xx, ξ (x) � θφ

(1+ θ) x � θφ.


General equilibrium: returns and saving behavior

Returns to innovation now read:

r = α (x � φ) ;

r =x � φ

πx+ z

�1� 1

πx

�+xx,

where z � Z/Z = I/Z and

π � β

θ (1� θ)=

βY /NX (P � 1) =

entry costgross cash �ow

.

Assets market equilibrium requires

A = NV = βY .

Then, household budget yields

0 = ρ� λ+

�CC� YY

�+1� θ � (C/Y )

β) CY= (ρ� λ) β+ 1� θ.


General equilibrium: dynamics

There exist threshold xN of �rm size that triggers variety innovation andthreshold xZ of �rm size that triggers quality innovation.

We study economy in the region x > max fxZ , xNg > φ and approximateσ/x ! 0 so that �rm size evolves according to linear di¤erential equation:

x = ν � (x� � x) ,

where:

ν � (1� σ) φ

πx�; x� =

(1� α) φ��ρ+ σλ

1�σ

�1� α� π

�ρ+ σλ

1�σ

� .Closed-form solution:

x (t) = x0e�νt + x��1� e�νt� ,

where x0 is initial condition.Iacopetta, Minetti, Peretto () Finance and growth January 2013 14 / 35

The steady state: innovation rates and economic growth

Variety growth:

n� ��NN

��=

λ

1� σ> 0.

Quality growth:

z� ��ZZ

��=

"α (φπ � 1)

1� α� π�ρ+ σλ

1�σ

� � 1#�ρ+σλ

1� σ

�> 0.

Final output and GDP per capita growth:�YY

�� λ =

�GG

�� λ =

σλ

1� σ+ z�.


The steady state: comparative statics (i)

From saving behavior of household:

r � = ρ+σλ

1� σ+ z�.

Manipulate returns to innovation to get:

z� = α � (x� � φ)��

ρ+σλ

1� σ

�; (CI)

z� = x��1� π �

�ρ+

σλ

1� σ

�� φ. (EI)

Key concept: no-arbitrage.


The steady state: comparative statics (ii)

When either α " or π " we have z� " and x� ".


Welfare

Utility �ow is

log�C (t)L (t)

�=

�σλ

1� σ+ z�

�t| {z }

steady-state growth

+

�σ

1� σ+

α

νx0

��1� x

�

x0

� �1� e�νt�| {z }

transitional dynamics

.

Substituting in welfare functional and integrating yields:

U =1

ρ� λ

��σλ

1� σ+ z�

�1

ρ� λ+

σν1�σ + αx0ρ� λ+ ν

�1� x

�

x0

��.

Note: there is a growth/variety tradeo¤ here, because

logN� (t) =1

1� σlog�

θ (1� θ) θ2θ1�θL (t)x�

�.


Introducing �nancial frictions

Firms need external �nance:

creation of new varieties, i.e., foundation of new �rms;

incremental innovation within existing �rms.

Two cases:

borrow directly from households;

borrow from banks. (Not today since analysis not �nished yet.)

We consider moral hazard: agents (i.e., founders, entrepreneurs,managers, CEOs, whatever else we want to call them) can abscond loan of�nancier and use it to produce private bene�t.


The frictions: foundation

Extraction of entrepreneur�s private bene�t occurs according to

γ � βY (0)N (0)| {z }

size of loan

, γ 2 [0, 1] .

If entrepreneur �runs away�with loan, �rm does not start and Vi (0) = 0.Then, value of entrepreneurial project is Vi (0)� βY (0)

N (0) = �βY (0)N (0) .

Outside option of �nancier (household) is to consume funds.


The frictions: management

Manager can commit to optimal price plan but not to optimal R&D plan.

Extraction of manager�s private bene�t occurs according to

δ � Ii (t)|{z}size of loan

, δ 2 [0, 1] .

If manager �runs away�with loan at time t, innovation does not occurand qi (t) = 0. Then, value of R&D project is Ii (t) � [qi (t)� 1] = �Ii (t).

Outside option of �nancier (household) is to consume funds.

Given capital-theoretic structure of incremental innovation, we can focuson marginal values.


The incentives (i)

Key: Interdependence of incentive and participation constraints onextensive and intensive margins.

Need to solve simoultaneously moral hazard problems in foundation andmanagement.


The incentives (ii)

Incentive constraint of entrepreneur:

γ � βY (0)N (0)| {z }

private bene�tof entrepreneur

� (1� ai (0))| {z }equity shareof entrepreneur

� Vi (0)| {z } .present valueof �rm at entry

Participation constraint of �nancier:

βY (0)N (0)| {z }

outside optionof �nancier

� ai (0)| {z }equity shareof �nancier

� (1� bi (t))| {z }equity shareof manager

� Vi (0)| {z } .present valueof �rm at entry


The incentives (iii)

Incentive constraint of manager:

δ � 1|{z}private bene�tof manager


� (1� bi (t))| {z }equity shareof manager

� qi (t)|{z} .present valueof project

Participation constraint of �nancier:

1|{z}outside optionof �nancier


� bi (t)| {z }equity shareof �nancier

� qi (t)|{z} .present valueof project


The incentives (iv)

Bang-bang solution for manager/�nancier problem plus free entry forentrepreneur/�nancier problem imply that all constraints hold withequality.

From manager/�nancier constraints:

δ =1� bi (t)bi (t)

) bi (t) =1

1+ δ.

From entrepreneur/�nancier constraints:

γ =(1� bi (t)) ai (0)

1� ai (0)) ai (0) =

1

1+ γδ1+δ

.


The incentives (v)

From �rst-order condition:

δ

(1� bi (t)) ai (0)� 1| {z }

e¤ective innovation cost

= qi (t) ) (1+ γ+ γδ) � 1 = qi (t).

From free-entry condition:

γ

1� ai (0)� βY (0)N (0)| {z }

e¤ective entry cost

= Vi (0) ) (1+ γ+ 1/δ) � βY (0)N (0)

= Vi (0).


Returns to innovation and saving behavior with frictions

Returns to corporate and entrepreneurial innovation are:

r = αf � (x � φ) , αf �α

1+ γ+ γδ;

r =x � φ

πf x+ z

�1� 1

πf x

�+xx, πf �

βfθ (1� θ)

, βf � β (1+ γ+ 1/δ) .

Wealth/output and consumption/output ratios are:

AY= βf and

AG=AYYG=

βf

(1� θ)hθ�1� φ

x

�+ 1

i ;CY= (ρ� λ) βf + 1� θ and

CG=CYYG=

ρ�λ1�θ βf + 1

θ�1� φ

x

�+ 1

.


General equilibrium dynamics with frictions

Again, we study economy in the region x > max fxZ , xNg > φ andapproximate σ/x ! 0 so that �rm size evolves according to lineardi¤erential equation:

x = νf � (x�f � x) ,where:

νf �(1� σ) φ

πf x�f; x�f =

(1� αf ) φ��ρ+ σλ

1�σ

�1� αf � πf

�ρ+ σλ

1�σ

� .Using explicit solution for path x (t), we obtain welfare:

Uf =1

ρ� λ

"�σλ

1� σ+ z�f

�1

ρ� λ+

σνf1�σ + αf x0ρ� λ+ νf

�1� x

�f

x0

�#.


The "delta" friction: steady state


The "delta" friction: dynamics

Because πf = (1+ γ+ 1/δ)π and αf = α/ (1+ γ+ γδ), the δ frictionraises the return to entry and lowers the return to in-house innovation.The interaction of the two margins yields that:

steady-state �rm size falls (intuition: �rms can service debtcontracted at foundation with smaller gross pro�t �ow because theydo less in-house R&D);

the eigenvalue of the dynamics is larger so that economy exhibitsfaster mean reversion (intuition: ?????);

steady-state growth falls and the path of the mass of �rms is higher(because of more entry in transition);

overall, ambiguous change in welfare (but good reasons to think it isnegative, see expression above).


The "gamma" friction: steady state


The "gamma" friction: dynamics

Because πf = (1+ γ+ 1/δ)π and αf = α/ (1+ γ+ γδ), the γ frictionlowers both the return to entry and to in-house innovation. Theinteraction of the two margins yields that all e¤ects are, in principle,ambiguous. Let�s take �gure at face value and say that:

steady-state �rm size rises;

eigenvalue of the dynamics is larger so that economy exhibits fastermean reversion (intuition: ?????);

steady-state growth falls but the path of the the mass of �rms ishigher;

overall, they yield an ambiguous change in welfare.


Welfare: a more re�ned exercise (i)

What is the welfare cost of �nancial frictions?

We can think about this as follows:

the baseline path is the case with frictions;

the welfare gain of eliminating frictions is the expression for the casewithout frictions calculated using x0 = x�f , that is,

U � U�f =1

ρ� λ

�z� � z�fρ� λ

+σν1�σ + αx�fρ� λ+ ν

�1� x

�

x�f

��.

The graphical analysis suggests that γ and δ push the EI line inopposite directions. Say that they roughly cancel out and think ofdynamics when EI line does not move while CI line shifts up.


Welfare: a more re�ned exercise (ii)


Welfare: a more re�ned exercise (iii)

Hence, z� > z�f and x� > x�f .

Welfare change from elimination of frictions:

U � U�f =1

ρ� λ

26664z� � z�fρ� λ| {z }>0

+σν1�σ + αx�fρ� λ+ ν

�1� x

�

x�f

�| {z }

<0

37775 .

Conclusion: Elimination of frictions allows faster quality growth and largermass of �rms.


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