# On The Effects of Economic Fluctuations on Productivity Growth

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**WORKING PAPER SERIES**

**CEEAplA WP No. 05/2004**

**On The Effects of Economic Fluctuations**

**on Productivity Growth**

**António Gomes de Menezes**

**November 2004**

**Universidade dos Açores**

Universidade da Madeira

Universidade da Madeira

**On The Effects of Economic Fluctuations on**

**Productivity Growth**

**António Gomes de Menezes**

Universidade dos Açores (DEG)

e CEEAplA

Working Paper n.º 05/2004

Novembro de 2004

CEEAplA Working Paper n.º 05/2004

Novembro de 2004

**RESUMO/ABSTRACT**

**On The Effects of Economic Fluctuations on Productivity Growth**

We analyze the productivity effects of shocks to the real interest rate and to

demand and supply conditions in a world where productivity enhancing activities

are disruptive. The model predicts that temporary demand downturns may have

positive productivity effects if the real interest rate is not too countercyclical, and

that supply shocks do not affect productivity growth. The model is used to

derive refined novel empirical tests on the so-called Opportunity Cost View of

recessions (Aghion and Saint-Paul (1998)) vis à vis the competing theories of

learning-by-doing and capital market imperfections.

*JEL Code:*O4 - Economic Growth and Aggregate Productivity.

*Keywords:*Productivity Growth; Economic Fluctuations.

António Gomes de Menezes

Departamento de Economia e Gestão

Universidade dos Açores

Rua da Mãe de Deus, 58

9501-801 Ponta Delgada

On The E¤ects of Economic Fluctuations on Productivity Growth

António Gomes de Menezes

University of the Azores

November 2004

Abstract

We analyze the productivity e¤ects of shocks to the real interest rate and to demand and supply

conditions in a world where productivity enhancing activities are disruptive. The model predicts that

temporary demand downturns may have positive productivity e¤ects if the real interest rate is not too

countercyclical, and that supply shocks do not a¤ect productivity growth. The model is used to derive

re…ned novel empirical tests on the so-called Opportunity Cost View of recessions (Aghion and Saint-Paul

(1998)) vis à vis the competing theories of learning-by-doing and capital market imperfections.

JEL Code: O4 - Economic Growth and Aggregate Productivity.

Keywords: Productivity Growth; Economic Fluctuations.

Assistant Professor, Department of Economics and Management, University of the Azores. Rua da Mãe de Deus. 9501-801

Ponta Delgada, Portugal. E-mail: [email protected]

1

1

Introduction

Recently, several papers in the endogenous growth literature have studied the e¤ects of cyclical shocks

on productivity growth. However, there is little empirical evidence on the matter (Aghion and Howitt

(1998, Ch. 8)). This may owe to the di¢ culty of testing the existing competing theories. While, on the

one hand, there are theories that predict that temporary demand downturns have deleterious e¤ects on

productivity growth, such as learning-by-doing (Staedler (1990)) and capital market imperfections (Stiglitz

(1993)), on the other hand, theories in the spirit of the so-called Opportunity Cost View (Aghion and Saint-

Paul (1998)) argue that temporary demand downturns have positive e¤ects on productivity, since during the

downturns the opportunity cost in terms of foregone output and pro…ts of engaging in disruptive productivity

enhancing activities is low, and therefore …rms invest relatively more in such activities, which may include

job reallocation, managerial reorganizations and training. Clearly, all the above mentioned theories are well

rooted, and, thus, the e¤ects of cyclical shocks on productivity growth is, to be pragmatic, an empirical

question, which, in turn, calls for careful empirical work, with close guidance from theory.

By extending the work of Aghion and Saint-Paul (1998), we provide a novel set of theoretical results that

can be used to narrowly assess the empirical importance of the Opportunity Cost View of downturns vis-à-

vis the competing theories of learning-by-doing and capital market imperfections. In particular, we solve a

model where …rms invest in disruptive productivity enhancing activities and face shocks not only to demand

conditions but also to supply conditions and to the real interest rate. We …nd that: (i) temporary demand

downturns have positive e¤ects on productivity growth if the real interest rate is not too countercyclical and

(ii) supply shocks do not have e¤ects on productivity growth. Both results are meaningful, at an empirical

level, since they are useful in setting up empirical tests on the above mentioned competing theories. In

particular, from result (i) we can study the joint behavior of shocks to demand conditions and to the real

interest to test the unambiguous prediction that under the Opportunity Cost View productivity growth is

stronger after temporary contractionary demand shocks associated with decreases in the real interest rate

than after those associated with increases in the real interest rate. In addition, under the Opportunity Cost

View, and by result (ii), supply shocks do not matter for productivity growth, unlike what is predicted by

the competing theories of learning-by-doing and capital market imperfections, which are silent with respect

to the nature of the shocks. Hence, this result provides one extra dimension to test these competing theories,

and, concomitantly, to improve on the evidence gathered by, among others, Gali and Hammour (1992) and

Saint-Paul (1993).

This paper is organized as follows. Section 2 solves a highly stylized model that extends Aghion and

Saint-Paul (1998). Section 3 concludes.

2

The Model

The Goods Market and the Firm’s Problem

We consider an open economy that produces a variety

of export goods indexed by i and consumes a homogeneous imported good. Demand for home good i, Dit, is

a function of an index of nominal world demand, yt, an aggregate price index for home goods, pt, and good

i’s price, pit and is written as:

Dit = (yt=pt) (pit=pt)

(1)

The aggregate price index for home goods is given by:

pt = (Z Nt p1 di)1=(1 )

(2)

it

0

where Nt is the number of varieties produced at home, and

> 1 is assumed.

Each home good i is produced by a monopolistic competitor of …xed size, characterized by its productivity

level, x

dxit

it, which increases at rate vit

: a choice variable involving a trade-o¤ between a current cost

dt

and a higher future net present value of the …rm. More speci…cally, to increase productivity by vit, …rm i

must sacri…ce a fraction k(vit) of its current output, with k0

0, k00 > 0, and k(0) = 0. Let it

(1

k(vit))

be the share of …rm i’s output not sacri…ced by the implementation of the disruptive productivity enhancing

activities. Hence, …rm i’s net output, zit, reads:

zit = exite i

it

it

2

where eit is the level of an input, and i is a …rm speci…c parameter between 0 and 1. The …rm chooses e so

as to maximize nominal pro…ts

it:1

it = pitexit e i

it

it

peteit

where pit is the exogenous price of the input e. In equilibrium, the marginal revenue product of the input

equals its price and the goods markets clear. After imposing the goods market clearing condition (zit = Dit),

we determine the optimal eit, e :

it

e

(

1)=ai

it = y1=ai

t

p(

1)=ai

t

p

=ai

et

exit(

1)=ai

b =ai

it

i

where ai

(1

i) +

i, and bi

i(

1)= . We now evaluate nominal pro…ts at the optimal input level,

:

it

(ai

)

1

(

1)

(

1)

(

1)

(

a

a

a

i )

i

i

ai

ai

a

a

i

a

it = pe

y

i

(

a

i

t

t

pt

exit

it

i)

The optimal investment rate in productivity enhancing activities, v, solves the following recursive expression:

Vt[xit] = itdt + (1

rdt)EtVt+dt[xit + vitdt]

(3)

where Vt[xit] is the current value of the …rm. The …rst-order condition for v is given by:

1

@Vt+dt

(4)

a

ith(vit) = Et

i

@xit

where h(:) is de…ned as (k0=(1

k)), or the absolute percentage change in the share of output that survives

to a marginal productivity enhancing activity. Finally, we obtain an expression for the RHS of (4) by

di¤erentiating (3) with respect to xit:

@Vt

@V

=

1

t+dt

(5)

@x

a

itdt + (1

rdt)Et

i

it

@xit

Entry and Exit

To close the model, we follow Aghion and Saint-Paul (1998) and assume that the

liquidation value of exiting …rms is given by

Ce xit e

xt , where C is the entry cost,

is a parameter

between 0 and 1,

is a free parameter, and xt is the average level of productivity. This ensures that entry

and exit decisions do not in‡uence the decision on v.

Goods Market Equilibrium

We focus on the symmetric equilibrium where vit = vt, xit = xt, and

it =

t. From (2), (1), and the goods market clearing condition (zit = Dit ), we obtain:

p

1

t = ytN

=(

1)

t

e xt e

i

it

t

(6)

pit = yte xte

i =(N

it

t

t)

(7)

We use (6) and (7) to rewrite optimal purchases of the input, e , and nominal pro…ts,

:

it

it

eit = biyt=(petNt)

(8)

ai yt

it =

(9)

Nt

1 Supply shocks are shocks to the price of the input, pet. We obtain the same results if we introduce supply shocks as

exogenous productivity shocks to the net production function:

zit = exit e it it

where

it is the productivity shock.

3

Steady State

In the steady state, pro…ts, the number of …rms, and the marginal value to the …rm of

an increase in x, @V , are all constant. Using (5) and (9) we obtain an expression for @V :

@x

@x

@V

1 y

=

(10)

@x

a

rN

Equations (4) and (10) determine the steady state value of v as follows:

rh(v) = 1

(11)

To close the model, we assume that the economy is always on the margin of entry, i.e., V = C, which

translates into the following free entry condition (using (3)):

= rC

(12)

Finally, we use (9) and (12) to determine the number of …rms in steady state (N ):

a y

N =

(13)

rC

Economic Fluctuations

The economy can be in one of two regimes: in expansion, E, with (yE; rE; pE

e ),

or in recession, R , with (yR; rR; pR

e ). While yE > yR is naturally assumed, no relation between rE and rR

and between pE

e and pR

e is assumed. The economy may switch from the E regime to the R regime with ‡ow

probability , and from the R regime to the E regime with ‡ow probability ".

Solution, Remarks and Interpretations

Let uj denote @Vj and d

@x

j the demand that …rms face

(dj = yj =

N j

j ), j = E, R. Then, we write uR and uE as follows:

(

1)d

u

R=a + "uE

R =

(14)

rR + "

(

1)d

u

E =a +

[(N R=N E)uR + (1

N R=N E)

C]

E =

(15)

rE +

The last expression in (15) re‡ects the existence of an exit e¤ect: the expected capital gain includes the

probability of exiting, (1

N R=N E), and associated value,

C. It can be shown that if

= (

1)= then

the exit e¤ect vanishes and the above system reduces to:

(

(rE + )d

u

R +"dE

R = (

1)dR=a+"uE

rR+"

(rR+")(rE + )

u

() ( uR = 1a (rR+")dE+ dR

E = (

1)dE =a+ uR

rE +

uE =

1

a

(rR+")(rE + )

The …rst order conditions are given by:

1 djh(vj) = uj; j = E;R

(16)

a

Replacing the RHS of the …rst order conditions with the relevant expressions for uj, we obtain:

(rE + ) + "d

h(v

E =dR

R) =

(17)

(rR + ")(rE + )

(rR + ") + d

h(v

R=dE

E ) =

(18)

(rR + ")(rE + )

Finally, to close the model, we use the free entry-exit conditions, together with the assumptions that in

recessions there is exit (V R = C) and in expansions entry occurs (V E = C). Hence, the following relations

must hold in equilibrium (recall that dj = j):

dR = [rR + "(

1)]C

(19)

dE = [rE + (1

)]C

(20)

We are …nally in position to study the cyclical behavior of productivity growth, i.e., the relation between

vR and vE. To do so, we only have to analyze the system of equations (14), (15), (19), and (20). We

summarize the main implications of the model below, in form of remarks, accompanied by the relevant

proofs, and followed by an interpretation at a rather intuitive level.

4

Remark 1 Shocks to supply conditions have no productivity e¤ ects. Inspection of the system (14), (15),

(19), and (20) reveals that vR and vE are determined without reference to the price of the input, pe, the

object through which supply shocks operate in the model.

Remark 2 If

< 1 and rE

rR, then vR > vE. Since h0 > 0 always obtains given the assumptions made

on k, to compare vR and vE it su¢ ces to compare the RHSs of (14), (15), (19), and (20).

Remark 3 If

< 1 and rE < rR then there exists a

such that if

2 ( " ; ), then v

rR+"

R > vE , and if

2 ( ;1], then vR < vE. From the above argument we know that vR > vE obtains if and only if the following

condition holds:

d

d

"( E

1) + (1

R ) > rR

rE

dR

dE

When

=

"

, dE becomes +

+ . The

rR+"

dR

1 and the above inequality will hold. Now consider 0 = "

rR+"

above inequality will also hold as we make

an arbitrarily small positive number, by a limit argument.

The intuition for the above results is straightforward. Supply shocks a¤ect an intra-temporal problem, but

not the productivity investment problem, which is, of course, an inter-temporal problem. The productivity

investment problem is a¤ected, in turn, by the following two e¤ects: an opportunity cost e¤ect, associated

with ‡uctuations in demand, and a real interest rate e¤ect, as with any other investment problem. If the

real interest rate is procyclical, then both e¤ects reinforce each other and productivity unambiguously grows

after a transitory demand downturn. If the real interest rate is countercyclical, then the opportunity cost

e¤ect and the real interest rate e¤ect work in opposite directions. However, if the real interest rate is not

too countercyclical and / or the opportunity cost e¤ect is strong enough, then productivity may grow after

a transitory demand downturn despite an increase in the real interest rate. Nevertheless, it is clear that

the smaller the increase in the real interest rate during the transitory demand downturn, the stronger the

productivity growth after the transitory demand downturn.

3

Final Remarks

We extend the work of Aghion and Saint-Paul (1998) and provide novel theoretical guidance to much needed

tests of the empirical relevance of the Opportunity Cost View of downturns vis à vis the competing theories

of learning-by-doing and capital market imperfections as empirically relevant theories on the relationship

between cyclical shocks and productivity growth.

Future work should capitalize on the results we present here and seek to establish the empirical relevance

of the surveyed competing theories on the relationship between cyclical shocks and productivity growth.

References

[1] Aghion, P., Howitt, P., 1998, Endogenous Growth (MIT Press).

[2] Aghion, P., Saint-Paul, G., 1998, Virtues of bad times: interaction between productivity growth and

economic ‡uctuations, Macroeconomic Dynamics 2, 322-344.

[3] Gali, J., and Hammour, M., 1992, Long-run e¤ects of business cycles, Mimeo, Columbia University.

[4] Saint-Paul, G., 1993, Productivity growth and the structure of the business cycle, European Economic

Review 37(4), 861-883.

[5] Stadler, G., 1990, Business cycles models with endogenous technology, American Economic Review 80(4),

763-778.

[6] Stiglitz, J., 1993. Endogenous growth and cycles, NBER Working Paper 4286.

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