Labor Contracts, Credit Constraints and Growth. Enisse Kharroubi April 2008
Abstract This paper studies how the design of labor contracts a¤ect productivity growth in the presence of credit constraints. Assuming that …rms and workers face imperfect capital markets, ‡exibility in labor contracts is shown to have three e¤ects. It …rst contributes to relax …rms credit constraints. Second it positively in‡uences workers precautionary savings and thereby raises the volume of global savings. Finally it modi…es …rm incentives to make more risky and hence more productive investments. Based on these three e¤ect, the model brings two results. First the economy can exhibit multiple equilibria when capital market imperfections are large, the high ‡exibility equilibrium being always Pareto dominated. Second the model predicts that productivity growth should be positively associated with labor market ‡exibility for relatively low levels of capital market imperfections. We provide empirical evidence at the industry level which supports this last conclusion.
Banque de France. Address: 1, rue de la Vrillière 75049 Paris cedex 01. e-mail: …rstname.surname(at)banque-france.fr. I thank Henri Pages, Thierry Mayer, Mathias Thoenig, Etienne Wasmer and seminar participants at PSE (June 2006), Banque de France (July 2006) and CEPR ESSLE (Sept. 2006) and INFER Workshop (March 2008) for helpful discussions and comments. Usual disclaimers apply.
1
1
Introduction.
Since its creation, the Euro Zone has been lagging behind the United States in terms of output growth. The US has grown on average each year 1.4 pp faster than the Euro Zone. A similar pattern is observed for productivity growth: the di¤erence in output per worker growth is about 1 pp in the business sector and 0.8 pp for the whole economy in favor of the US. Why is this so? Looking at …gures for long run fundamental sources of growth, namely investment, R&D expenditures and employment evolutions, it turns out that employment has been increasing somewhat faster in the US than in Euro Zone (1.4% to 0.8% per year on 1992-2005) while the investment to output ratio has been on average pretty larger in the Euro Zone than in the US (16.1% to 12.9% on 1992-2005). Finally considering R&D expenditure …gures are roughly similar (around 2.5% of GDP) and the fact that catch-up e¤ects should be larger for the Euro Zone given that its initial productivity level is lower, a rapid calibration of a Solow growth model shows that this …gures should predict a productivity growth gap in favor of the Euro Zone not in favor of the US. Still business sector labor productivity growth has been growing on average 1 pp faster in the US than in the Euro Zone on 1992-2005. If traditional growth determinants cannot account for the output - productivity growth gaps, then this begs the question of whether any stark structural di¤erence between these two economies can help understanding this long run growth performance gap.1 On the list of possible culprits or suspects, the labor market and its regulations have been given high priority. Indeed, the assumed lack of ‡exibility in Euro Zone labor markets has been set responsible for the poor growth performance relative to the US.2 However it is important to note that labor market regulation does not have a priori any direct impact on growth, at least according to standard growth models because it does not a¤ect directly fundamental sources for capital accumulation such as savings, investment, education or research and development activities, which are the primary sources of long run growth. It therefore remains a question to understand how such a pattern whose in‡uence is 1 The
capital market is also a possibility but this is precisely the point of this paper. is a widespread agreement on this view: ”To enjoy strong GDP growth, developed economies need, as a priority, policy frameworks that encourage competitive intensity. This means [...] encouraging labor market ‡exibility”. (IMF, Finance & Development, march 2006).”[...] institutional structures and policy settings that favour competition and ‡exibility in capital and labour markets [...] also make a key di¤erence to growth prospects. In particular, many of our countries need more competitive product markets; labour markets that adjust better and more rapidly to shocks”. (OECD. The Sources of Economic Growth in OECD Countries [2003]). Last but not least, the Kok report on employment policy (2003) underlines the need for more ‡exibility in labor markets as a means to enforce the Lisbon agenda designed to make Europe the most competitive economic area in the world. 2 There
2
mostly indirect (i.e. second order) can have that large (i.e. …rst order) impact as to be a valid explanation for the Euro Zone - US growth gap. In this paper I push forward the idea that labor market institutions can account for sizeable gaps in productivity growth when interactions between labor and credit markets are taken into account. The basic claim of the model consists in showing that labor market ‡exibility can decrease (resp. increase) …rm incentives to invest in high total factor productivity projects when …rms face tight (resp. wide) borrowing constraints. Labor market ‡exibility will therefore be positively associated with productivity growth if and only if capital markets are su¢ ciently well developed. This conclusion will prove to be con…rmed through empirical evidence.
1.1
Mechanism of the model.
In a simple framework with risk neutral …rms and risk averse workers, …rms should optimally provide …xed wage contracts to workers with full insurance against ex post ‡uctuations in labor productivity. Now we consider a modi…ed framework along two di¤erent lines. First …rms and workers are assumed to face capital market imperfections due to ex post imperfect enforceability. Second, …rms are allowed to choose an investment project among di¤erent technologies, with higher average productivity technologies also embedding more volatile productivity shocks. The model then brings two results. First when …rms cannot issue contingent debt (or more generally when the degree of capital market imperfection is su¢ ciently large), then the economy can experience multiple equilibria.3 Facing a low interest rate (i.e. low cost to borrow), …rms have incentives to increase their borrowing and hence to provide contingent or ‡exible wage contracts because providing ‡exible wage contracts raises pro…ts before debt repayments in the bad states of nature and hence raises the borrowing capacity.4 Moreover the …rm has incentives to invest in relatively safe assets, because investment in risky assets would hurt the borrowing capacity due to a lower productivity in the bad state of nature. To put it brie‡y, a low interest rate typically raises the cost to being 3 Credit market imperfections a¤ect here the capacity of capital providers to smooth bad outcomes with good ones. When …rms cannot issue contingent debt, the …nancial cost to take risky investments is indeed very large. 4 Equivalently, the volume of capital borrowed being given, a …rm which adopts a contingent labor compensation scheme bene…ts from a reduced risk premium on its …nancial liabilities.
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unable to borrow large amounts of capital. Hence …rms use both labor contracts and technological choices to expand their borrowing capacity. Now since workers savings depend positively on the ‡exibility of their compensation (due to precautionary savings) and negatively on the productivity of …rms investment (due to inter-temporal consumption smoothing), the volume of workers savings is large when …rms provide ‡exible wage contracts and invest in relatively safe projects. As a result, the interest rate …rms face is low. This situation is therefore an equilibrium. On the contrary, if the interest rate is large, …rms have few incentives to provide contingent-‡exible contracts on the labor market because the implied increase in labor costs due outweighs bene…ts of increased borrowing capacity. Moreover the …rm has incentives to invest in risky assets because the marginal cost to reduce the borrowing capacity is small (due to the large interest rate) while the marginal gain in terms of expected pro…ts is relatively larger. Now since workers savings depend positively on the ‡exibility of their compensation (due to precautionary savings) and negatively on the productivity of …rms investment (due to inter-temporal consumption smoothing), the volume of workers savings is low. Hence the interest rate …rms face is large and this situation is another equilibrium. The second result the model brings concerns the relationship between investment productivity and labor market ‡exibility: the relationship is more likely to be positive when …rms face fewer credit market imperfections. When lenders can more easily (less costly) smooth bad and good states of nature, the credit constraint the …rm faces is less dependent on the technological choice it makes. Therefore the …rm can more easily raise the productivity of its investments without reducing its borrowing capacity. As a result, a larger possibility to smooth bad and good states of nature raises the likelihood that an increase in labor market ‡exibility be positively associated with higher productivity.
1.2
Related literature.
This paper builds on a large body of theoretical and empirical literature on the macroeconomic consequences of labor market regulations to which we cannot hope do full justice. However we can mention three important strands of this literature, our paper is related to. First this paper relates to the implicit contract literature (based on the pioneering work of Azariadis[1978] and Azariadis and Stiglitz [1983]) according to which …xed
4
or rigid wages contracts can be an equilibrium phenomenon illustrating e¢ cient risk sharing between …rms and workers. Adopting this approach, we go one step further in this paper to assess the macroeconomic impact of risk sharing or risk allocation between …rms workers and capital providers as concerns …rm performance and productivity growth. Building on these pioneering papers, I large literature has developed which studies the role insurance on the labor market: Baker, Gibbs and Hölmström [1994] provide empirical evidence that workers are partly shielded from changes in the external conditions the …rm operates in. Acemoglu and Shimer [1999] build a model in which the decentralized equilibrium is ine¢ cient without unemployment insurance because the labor market endogenously creates jobs that provide risk-averse workers with low unemployment risk and low wages. More recently, Pissarides [2001] assets that a proper evaluation of Employment protection legislation requires a model where there is need for it, for instance in the absence of perfect insurance markets. Within this context, he shows that the standard results of the labor economics literature do not hold; in particular optimally chosen employment protection does not reduce job creation. Similarly, Bertola [2004] shows that in the absence of perfect …nancial market access, redistribution of aggregate income towards wages and protection from labor income risk are important determinants of the economic desirability of collective wage bargaining, unemployment insurance, and employment protection legislation. The second strand of literature this paper is related to the literature on the macroeconomic consequences of hiring and …ring costs. Bentolila and Saint-Paul [1992] study the impact of ‡exible (low …ring costs) labor contracts on aggregate labour demand. Bentolila and Bertola [1990] show that labour adjustment costs e¤ects on …rm hiring decisions are rather small. Nickell [1997] makes a similar point: many labor market institutions that conventionally come under the heading of rigidities have no observable impact on unemployment and may otherwise serve a useful purpose. Finally Blanchard and Wolfers [2000] show that interactions between shocks and institutions can account for the increase in European unemployment. Finally this paper is related to the burgeoning literature on the interactions between labour and …nance. Wasmer and Weil [2004] study how combining credit and labor market imperfections can better explain unemployment in Continental Europe and di¤erences between Europe and the US. Michelacci and Quadrini [2005] show that …rms facing …nancing constraints propose wage contracts to their workers where
5
the dynamics of wages basically consists in borrowing from the employees at …rst stages to accommodate the credit constraints. Belke and Fehn [2000] show that capital market imperfections exacerbate structural unemployment caused by labour market rigidities. Finally Rendon [2004] shows that job creation is limited by …nancing constraints even in the presence of a ‡exible labour market.
1.3
Road map of the paper.
The paper is organized as follows. The following section lays down the model and its main assumptions. Section 3 focuses on …rm behavior and describes the strategies …rms can adopt when …nancial contracts are limited to uncontingent contracts. In section 4, we extend the previous framework to the case of contingent …nancial contracts. The growth e¤ects of labor market ‡exibility are derived in section 5 as well as the relevant empirical evidence. Conclusions are eventually drawn in section 6.
6
2
The framework.
We consider a single good economy with three types of agents, entrepreneurs, lenders and workers. All agents live for two periods t and t + 1. There is a continuum of unit mass of each of type of agent.
2.1
Entrepreneurs and lenders.
Entrepreneurs and lenders have a capital endowment at time t. Their preference writes as
1
Ue = (bt+1 ) (ct+1 )
(1)
where bt+1 is the time t + 1 bequest an entrepreneur makes to its o¤-spring and ct+1 is the time t + 1 consumption. Lenders can lend their capital on the capital market. Entrepreneurs have access to a set of constant returns to scale technologies. Noting k the capital stock invested (be it entrepreneurs own funds or …nancial liabilities entrepreneurs have contracted) and l the number of workers hired, entrepreneurs’ technologies write as ys = As k l1
(2)
Entrepreneurs’ technology is subject to a macroeconomic shock s, There are two states of nature, a good s = h and a bad one s = l with Ah > Al . Both states of nature are equiprobable. We note m the average productivity, m =
Ah +Al 2
and
the standard deviation,
=
A h Al . 2
are more productive on average also embed more volatile shocks;
@m @
Finally we assume that projects which > 0.
Entrepreneurs and lenders program therefore writes as
1
max (bt+1 ) (ct+1 )
bt+1 ;ct+1
(3)
s.t. ct+1 + bt+1
where ki is agent i initial capital endowment and i;s
i;s
1+
i;s
ki
is the real interest rate if the agent i is a lender and
is the …rm’s return on asset in state s if agent i is an entrepreneur. Given that entrepreneurs and lenders
7
know the return
i;s
when they choose how much to consume and how much to bequeath, the optimal
bequest bt+1 and the optimal consumption ct+1 write as
bt+1 = ct+1 = (1
Assuming that
1+
ki
i;s
) 1+
i;s
(4) ki
= 12 , entrepreneurs and lenders expected indirect utility then writes as Ve = 12 E
1+
i;s
ki .
Lenders optimal decision then consists in lending their capital k on the capital market while entrepreneur’s problem consists in maximizing its expected pro…t.5 This will be the focus of section 3.
2.2
Workers.
At time t, workers have a labor endowment equal to one but no capital endowment. Their preference writes as 1
Uw = (ct ) (ct+1 )
(5)
Workers need to borrow capital to …nance their time t consumption ct . At time t + 1, they use their labor income to …nance their time t + 1 consumption ct+1 and pay back the loans contracted at time t. Workers’ program therefore writes as 1
max (ct ) E (cs;t+1 )
ct ;cs;t+1
s.t. cs;t+1
(6) ws
(1 + r) ct
where ws is a worker’s time t + 1 labor income when state s happens at time t + 1, and r is the real interest rate on loans. Noting ct the optimal time t consumption, the …rst order condition of the problem (6) then writes as wh wh (1 + r) ct = (1 + r) ct wl wl 5 Since
each lender is in…nitely small, the return
(1 + r) ct (1 + r) ct
is independent of each lender’s decision.
8
(7)
In the case where
= 12 , the last condition simpli…es as
(1 + r) ct =
wh wl wh + wl
(8)
Therefore the optimal time t + 1 consumption cs;t+1 is always strictly positive and writes as
cs;t+1 =
ws ws wh + wl
(9)
Optimal …rst period consumption decreases, every thing else equal, with any mean preserving spread in the wage contract fws gs due to the standard precautionary savings motive.6 Then workers expected indirect utility writes as Vw =
1 2
w l wh 1+r
1 2
. Workers are therefore indi¤erent between two di¤erent wage contracts
fws gs and fw1;s gs if and only if they yield the same level of indirect utility. Assuming for instance that fw1;s gs is a …xed wage contract, i.e. w1;l = w1;h = w while fws gs is a strictly contingent contract, i.e. wl 6= wh , the indi¤erence condition simpli…es as wl wh = w2 .
2.3
Markets.
At the beginning of each period, there are two di¤erent markets which open one after the other. The …rst market on which transactions take place is the capital market. On this market, entrepreneurs and workers sign one period contracts with lenders. We assume that entrepreneurs face ex post imperfect enforceability. They can default on their …nancial claims at some cost. The second market on which transactions take place is the labor market. The labor market is competitive. At the end of the period, …rms pay wages to workers and …nancial contracts are paid back. An entrepreneur pro…ts in state s write as
1;s
= As (k + d) l1
ws l
(1 + r) d
6 This precautionary saving motive comes from the impossibility for workers to borrow through …nancial contracts where interest rates would be contingent to their income.
9
where k is the volume of entrepreneur own funds, d is the volume of capital the entrepreneur has borrowed and l is the number of workers he has hired. Since transactions are imperfectly enforceable, …rms can always retain a fraction
of their output and abstract from paying their debts. In this case conditional on state s
happening, they earn 2;s
with
=
As (k + d) l1
ws l
1. To be incentive compatible the face value of the entrepreneur …nancial liabilities (1 + r) d and
the wage bill ws l must be such that the cost to pay back one’s liabilities is lower than the cost to default. If …rms cannot or do not want to issue contingent debt, then …rm liabilities must be such that
(1 + r) d
(1
) min As (k + d) l1 s
ws l
(10)
On the contrary if the …rm is willing and is able to issue contingent debt, then the borrowing constraint writes as (1 + r ) d
(1
) max As (k + d) l1 s
ws l
(11)
where r is the interest rate on contingent debt and s is a given state of nature.
3 3.1
The no contingent debt economy. Firms optimal behavior.
Given that …rm decisions are sequential, the program of a representative …rm can be solved with backward induction. Assuming that the …rm satis…es workers participation constraint, …rm i program …rst consists in choosing the number of worker li such that
maxE (li ) = m ( ) (ki + di ) li1 li
10
Ews li
(1 + r) di
(12)
The solution to this problem (…rm i optimal demand for labor) then writes as
(1
) m ( ) (ki + di ) li
= Ews
Secondly …rm i problem consists in determining its optimal amount of debt …nance di . Assuming that the …rm cannot issue contingent debt, this amounts to solve the following problem
maxE (di ) = m ( ) (ki + di ) li1 Ews li (1 + r) di di 8 > > < (1 ) m ( ) (ki + di ) li = Ews s.t. > > : 8s, (1 + r) di (1 ) As (ki + di ) li1 ws li There are then two di¤erent cases: if
m( )
h
1 Ews m (
i1 )
(13)
1 + r, then …rms simply lend their capital
on …nancial markets because lending is more pro…table than investing in the …rm. Firms expected pro…ts h i1 1 write as E = (1 + r) k. On the contrary if m ( ) Ew m ( ) > 1 + r then …rm i optimal expected s
pro…ts write as
m( ) E
= (1 + r)
h
(1
Ews )m( )
(1 i1
h ) Aj
i w (1 ) Ewjs m ( ) h i (1 + r) ki wj ) Aj (1 ) Ews m ( )
(1
where j is the state of nature for which the borrowing constraint is binding. In this case, …rm i problem …nally consists in determining the optimal labor contract fws gs and the optimal technology
which solve
the following problem w
m( ) (1 )[Aj (1 ) Ewjs m( )] (1 + r) ki max E ( ; fws gs ) = 1 w Ew s ;fws gs (1 )[Aj (1 ) Ewjs m( )] 8 (1+r)[ (1 )m( ) ] i h > w > < j = arg min Ap (1 ) Ewps m ( ) p s.t. > > : wh wl w2
(14)
where w is the equivalent certain wage rate that is being proposed on the labor market. The labor contract fwl ; wh g has two di¤erent e¤ects on …rm expected pro…ts. An increase in the volatility 11
of labor compensation raises the cost of labor and reduces the productivity of the …rm because the …rm faces a less favorable e¢ ciency frontier. On the contrary an increase in the volatility of labor compensation can raise pro…ts before debt repayments and hence increase the borrowing capacity of the …rm. Similarly, an increase in the volatility of technological shocks
raises on the one hand the …rm average productivity while
it reduces on the other hand the productivity of the …rm conditional on a bad state of nature and hence reduces the …rm borrowing capacity. The next propositions then derive the main properties of the optimal wage contract and the optimal technology in this last context. Proposition 1 When …rms face a binding credit constraint and cannot issue contingent debt, noting " (y) = @y @ y,
the optimal technology
is an increasing function of optimal wage contract insurance (wl =wh ) if and
only if "
Proof.
@m @
< " (m) [" (m)
1]
cf. appendix 7.2 for a proof of proposition 1. As concerns proposition 2, the …rst order condition
determining the optimal wage contract (wl ; wh ) writes as 2
1
=
1+r Ews m (1 )m
41 + 1 wh 4 wl
wl wh
(1
while the …rst order condition determining the optimal technology 1
=
where " (y) =
1+r Ews m (1 )m
@y y @ .
2
41 + m
1
" (m) " (m)
(1
h ) 1
m
(1
wl ) Ew s
i3 5
(15)
writes as h ) 1
m
(1
wl ) Ew s
i3 5
(16)
Therefore the individually optimal wage contract and the individually optimal technology
verify the following condition that m
The optimal technology
" (m) 1 wh = 1 " (m) 4 wl
wl wh
is therefore an increasing function of the optimal wage contract insurance
12
(17) wl wh
if
and only if @ @
m
" (m)
" (m ( )) [1 " (m)
" (m)] [" (m) + (1
" (m)) (1
) X ( ; )]
where 1
1+ (1 )m( ) X( ; )= + m m( ) 1+r w( ) Proof.
At the individual optimum, …rms technology and workers labor contracts are determined through
the condition 1
1+r w( ) m ( ) (1 )m( )
wh wl
wl wh
22
@m ( ) m ( ) @ m 1
1 = " (m)
1
2
As is clear the left hand side of this expression unambiguously decreases in are ambiguous. Taking the …rst derivative of this left hand side w.r.t.
wl wh
while the variations w.r.t.
and after some tedious algebra we
end up with the following condition: the left hand side expression increases in
"
@m @
>
" (m ( )) [" (m) " (m)
where X( ; )=
"
1] [" (m) + (1
" (m)) (1
) X ( ; )]
1
m1+ (1 )m( ) 1 + m( ) 1+r w( )
if and only if
#
Corollary 6 When …rms can issue contingent debt then an exogenous increase in labor market ‡exibility is more likely to be associated with an increase in …rms average productivity than in the case where …rms cannot issue contingent debt. Proof. When …rms cannot issue contingent debt, labor market ‡exibility is associated with less productive investments if and only if "
@m @
0, a su¢ cient condition which ensures that labor market ‡exibility is more likely to be associated with an increase in …rm average productivity in the case where contingent debt is not available writes as " (m ( )) > " (m). This simpli…es as " (m) < 1 and this condition is always true since " (m) = de…nition Al = m
> 0, i.e.
m
< 1 and
@Al @
=
@m @
23
1 < 0 i.e.
@m @
< 1.
@m @ m
and by
(wl/wh )
(wl/wh)1 (wl/wh)2 σ1
σ2
σ
Figure 2: Firm optimal strategies when contingent debt is available.
4.2 4.2.1
The general equilibrium of the economy. The equilibrium of the capital market.
Up to now the risk free interest rate has been taken to be exogenous. To determine the equilibrium interest rate that prevails in the economy, one simply needs to equal the supply for capital provided by lenders and the demand for capital expressed by entrepreneurs and consumers. Put di¤erently the equilibrium interest rate is determined through kl = d + l (ct )1 + (1
l) (ct )2
where kl represents lenders capital supply, d …rms aggregate demand for capital; l …rms aggregate demand for labor, (ct )1 is the …rst period consumption of workers hired by entrepreneurs and (ct )2 is the …rst period consumption of workers who have not been hired by entrepreneurs. Given entrepreneur i labor and capital demand, the equilibrium of the capital market simpli…es as
kl
1 w = 1+r 2
m ( ; ) (1 w()m( ) h i1 ) 2 (1 + r) (1 w()m( ) 24
)
h
w ( ; ) 2 wwhl h m ( ; ) (1
hp
wh wl wh +wl
1 2
ii
; ) ) m ( ) w( w( )
ik
4.2.2
The equilibrium of the labor market.
At the equilibrium of the capital market, labor demand balances labor supply. Given that entrepreneurs are all identical, noting k …rms aggregate capital stock and d …rms aggregate borrowing, the expected wage rate Ews is then equal to the expected marginal productivity of labor
w ( ) = (1
) m ( ) (k + d)
and the uncontingent wage rate writes as
w=
4.2.3
p
wh wl (1 wh + wl
) m ( ) (k + d)
(27)
General Equilibrium.
The general equilibrium of the economy corresponds to the situation where all markets, the capital and the labor market, balance supply and demand. To determine the properties of this situations, one simply need to plug the two last expressions in the capital market equilibrium condition, we end up with an equilibrium interest rate r being de…ned through
kl =
m( ; ) 1 + (1 2 2
)
m( ) wl wh wh + wl wh + wl
w( ; )
(k + d) 1+r
(28)
where the aggregate volume of capital d …rms borrow at the general equilibrium of the economy is such that
(1 + r) d =
1 m( ; ) 2
(1
)m( )
w( ; ) (k + d) w( )
(29)
Finally …rm optimal technology is such that 1
w( ) 1+r m ( ) (1 )m( )
wh wl
wl wh
25
@m ( ) m ( ) @ m( ) 1
1 = " (m)
1
2
(30)
and the optimal labor contract …rms propose to workers veri…es
W 1
1 2
wh wl
wl V wh 1
= U+
V
(1
)
Proposition 7 The general equilibrium of the economy is represented by the vector ( wwhl ; w; ; r; d). Firms choose the labor contract optimal insurance
wl wh
and their optimal technology
respectively such that (??)
and (30) are veri…ed. The equilibrium interest rate on the capital market r and the volume of capital d …rms are able to borrow are respectively such that (28) and (29) are veri…ed. Proof. Straightforward.
5
Growth e¤ects of labor market ‡exibility.
We embed the framework considered in the previous sections into a dynamic AK model. At each point in time there is a continuum of unit mass of workers, a continuum of mass 2 of agents who can be entrepreneurs or lenders with equal probability.8 At the beginning of each period, entrepreneurs hire workers and agree on labour contracts with them. They borrow capital from lenders to …nance investment and they choose a technology and engage in production. Workers supply labour to entrepreneurs and agree on labour contracts with them. They borrow capital from lenders to …nance beginning of period consumption. Lenders lend capital to …rms to …nance investment. They lend capital also to workers to …nance consumption. At the end of each period, entrepreneurs pay workers according to the labour contracts they agreed upon. They pay back lenders for beginning of period loans and they divide their pro…ts between consumption and bequest. Workers are paid according to the wage contract they agreed upon with entrepreneurs. They pay back lenders for beginning of period loans and consume their labour income net of loan repayments. Lenders are paid back on beginning of period loans extended to workers and entrepreneurs and they divide their …nal capital income between consumption and bequest. Finally the total factor productivity of …rm technology 8 This assumption helps simplify the exposition of the model since …rms beginning of period aggregate capital stock k is f always equal to lenders beginning of period aggregate capital stock kl which is half the economy’s beginning of period aggregate capital stock kt .
26
As is assumed to write as As = Bs
k 2
+ d where k is the aggregate capital stock …rms of the economy and
d is the volume of capital …rms are able to borrow from lenders,
k 2
+ d therefore represents the aggregate
s volume of capital …rms are able to invest in production. Let us then note kt+1 the aggregate capital stock in
the economy at the beginning of period t + 1 when state s has happened at time t. Then if the good state h of nature happens at time t, the aggregate capital stock at the beginning of period t + 1, kt+1 writes as
h kt+1
where m ( ) =
1 = 2
1 2
8 > >
2 > : Bh (1
( Bl + Bh ) and w ( ) =
1 2
) wh m( w(
) )
h
h
) wh m(1) w(1) 1
wl wh +wl
1
wl wh +wl
i
i
with contingent debt (31)
without contingent debt
( wl + wh ). The …rst part of the right hand side Bh
1 2 kt
+d
h ) whw+w m( ) l
1 2 kt
+d
represents total output in the economy. The second part of the right hand side (1 or alternatively (1
h ) whw + wl m ( )
1 2 kt
+ d represent the wage bill distributed to workers in the case where
…rms cannot issue contingent debt and the case where …rms can do so. The …nal part of the right hand side 1
wl wh +wl
represents the share of the wage bill workers dedicate to beginning of period loans repayments.
Finally entrepreneurs and lenders bequest a share
=
1 2
of their …nal wealth and consume a share 1
= 12 .
Similarly, if the bad state of nature happens at time t, the capital stock at the beginning of period t + 1, l kt+1 therefore writes as
l kt+1
1 = 2
8 > > < ( + ) Bl
1 kt + d > 2 > :
Bl
(1
(1
) wl m( w( h
) )
) wl m(1) w(1) 1
h
+ wh wh +wl
i
wh wh +wl
i
with contingent debt (32)
without contingent debt
This expression is similar to the above one apart three distinct features. First when contingent debt is available …rms default in the bad state of nature and recoup only a fraction are able to seize a fraction
of their output while lenders
of this output, the di¤erence between + and one being the social loss coming
from default. Second, the technological shock is good in the latter case and bad in the former case. Third the share of the wage bill workers dedicate to consumption which is large is the latter case and low in the former case. We then establish the following result as regards expected growth. Proposition 8 When …rms can issue contingent debt, the average growth rate of the economy’s capital stock 27
writes as E log
where
log m + log (1 + ) + log
represents the equilibrium …rm debt equity ratio, i.e.
( ; )=
with Y = (1 with
s kt+1 kt
= 1 and
Proof.
) m( w(
1 ( + ) Bl m2
) wl wh ) wh +wl .
(1
) wl
( ; )
(33)
, 2 kdii and
m( ) +Y w( )
Bh
(1
) wh
m( ) +Y w( )
The same expressions apply to the case where contingent debt is not available
= 0.
Using the (32) and (31), the expected capital growth rate expression (33) is immediate to obtain.
The expected growth expression (33) can be decomposed into three parts, the total factor productivity growth, the total factor input growth and an heterogeneity e¤ect
E log
ks;t+1 = log m ( ) + log (1 + ) + log ( ; ) | {z } | {z } | {z } kt TFP e¤ect
TFI e¤ect
Heterog. e¤ect
Firms choices as to the optimal wage contract and the optimal technology they adopt generate three di¤erent sources of growth. When …rms adopt more ‡exible wage contracts, that helps them increase the volume of capital they can borrow. Hence the volume of …rms investment is larger with more ‡exible labor contracts. The total factor input e¤ect of labor market ‡exibility is therefore positive and the economy grows faster with more ‡exible labor contracts. On the contrary when …rms adopt more ‡exible labor contracts, they more likely to optimally invest in less productive technologies the lower the …nancial development. Hence the total factor productivity e¤ect of labor market ‡exibility depends positively on …nancial development, here the capacity of …rms to issue contingent debt. Finally there is a third e¤ect called heterogeneity e¤ect: when …rms propose more ‡exible labor contracts, workers reduce their beginning-of-period consumption and increase their average end-of-period consumption. Therefore with more ‡exible labor contracts, the volume of capital workers borrow at the beginning of the period is reduced while the volume of consumption at the
28
end of the period is increased. Now since workers propensity to save is zero, workers beginning of period consumption acts as an investment whose productivity is equal to the interest rate r. On the contrary, workers end-of-period consumption acts to reduce the volume of capital in the economy at the end of the period. Therefore more ‡exible labor market will tend to reduce capital accumulation because workers are less willing to borrow and more willing to rely on their labor income to …nance their consumption.
6
Empirical Evidence.
We carry out two di¤erent types of estimations. First we consider a macro approach in which we aim at determining the impact for labour market institutions on productivity growth at the macro level. To do so we elaborate on the standard growth regressions "à la Barro" by adding three di¤erent terms, …rst a indicator for capital market development, second an indicator for labour market ‡exibility (or rigidity) and …nally an interaction term between these two variables. The basic regression we carry out is the following
gi;t =
i
+
t
+ Xi;t
1
+ (epl)i;t
1
+ (km)i;t
1
+ (epl)i;t
1
kmi;t
1
+ "i;t
The dependent variable gi;t is the growth rate of GDP per workerin country i at time t. Standard growth regressors are included in the vector Xi;t . Explanatory variables are all lagged one period. Labor market rigidity or ‡exibility indicators are represented by the (epl)i;t development variable. Finally (epl)i;t
1
kmi;t
1
1
variable and kmi;t
1
represents the …nancial
represents the interaction e¤ect of these two variables.
To carry out this …rst exercise, we consider data from four di¤erent sources. Data for standard macroeconomic variables comes from OECD Economic Outlook. Data on …nancial development comes from the World Bank database on …nancial structure. Finally data on the labor market comes from Allard [2003] from which we obtain time varying measures for Employment Protection Legislation. We compute our estimations on the 1987-2005 period for twently countries.9 9 List of countries for estimations on macro data: Australia, Austria, Belgium, Canada, Switzerland, Germany, Denmark, Spain, Finland, Great-Britain, France, Japan, Ireland Italy, Netherlands, New-Zealand, Norway, Portugal, Sweden and United States.
29
In table 1, we consider the e¤ect of employment protection legislation on the growth rate of GDP per worker. The labor market indicator is the EPL index from Allard [2003] and the …nancial development indicator is the volume of private credit to GDP. The regressions show that a larger EPl index is positively associated with GDP per worker growth. However this positive e¤ect is mitigated by …nancial development up to the point where the growth e¤ect of EPL can become negative for su¢ ciently large levels of …nancial development. The threshold above which …ring di¢ culties become detrimental to growth is computed at the bottom of table 1.A. [Insert table 1.A here]
The next three tables (table 1.B-3.B) aim at exploring the growth consequences of employment protection at a sectoral level. To do so we use an augmented version of the Rajan-Zingales methodoly as follows
gi;k =
i
+
k
+ Xi;k + (F D)k
(epl)i + (F D)k
(epl)i
(km)i + "i;t
The dependent variable gi;k is the average growth rate of GDP per worker in secotr k in country i. Sector and country dummy variables are represented by
i
and
k,
the share of sector k output in total output
is Xi;k . As previously (epl)i and (km)i represent respectively the employment protection index and the …nancial development level. Finally (F D)k represents the …nancial dependence indicator of sector k in the United States. The data we use is the Rajan and Zingales dataset which we restrict to OECD countries.10 To avoid endogeneity issues, employment protection legislation index is measured in 1980 while the di¤erent …nancial development variables are similar to those of Rajan and Zingales [1998].
[Insert table 1.B here]
The two …rst columns of Table 1.B replicate the regressions of Rajan and Zingales for the sub-group of OECD countries we consider. Surprisingly, we observe a negative coe¢ cient for interaction between sectorial 1 0 List of countries for estimations on sectorial data: Austria, Australia, Belgium, Canada, Denmark, Finland, France, GreatBritain, Germany, Italy, Japan, Netherlands, Norway, New-Zealand, Sweden.
30
…nancial dependence and …nancial development. However it is not signi…cant when …nancial development is measured as the ratio of private domestic credit to GDP. The next three columns (3, 4 and 5) show that introducing the EPL variable does not modify the results of the previous regressions, in terms of the sign and the signi…cance of the coe¢ cients. Moreover employment protection does not play any explanatory role in the regression. However the two last columns (6 and 7) show that introducing an interaction term between employment protection legislation and …nancial development radically modi…es the results. First the EPL variable on its own becomes signi…cant and positive. Hence raising employment protection every thing else equal raises the growth rate of sectors with higher external …nancial dependence. Second this positive e¤ect is dampened when …nancial development is larger since the last interaction term has a negative and signi…cant coe¢ cient. Hence raising employment protection legislation can be detrimental to growth when …nancial development is su¢ ciently large. This is true both when …nancial development is measured as stock market capitalization to GDP or private credit to GDP. Table 2.B carries out a similar exercise to the one carried out in table 1.B but uses for the …nancial dependence indicator the …nancial dependence of young …rms or alternatively the …nancial dependence of old …rms.
[Insert table 2.B here]
The results are essentially the same in the sense that the growth e¤ect of employment protection legislation is positive when …nancial development is low and is more likely to become negative as …nancial development increases.
7
Conclusion.
We have built a model in which the structure of workers compensation and …rms productivity are endogenous. This has enabled us to build a theory of the labor market ‡exibility e¤ects of growth. To be completed....
31
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36
Table 1.A Growth effects of Employment Protection Legislation. Dependent variable: GDP per worker Growth Estimation: IV/TSLS with White Period heteroscedasticity correction Employment Protection Legislation
0.044**
0.060***
0.045*
Private Credit to GDP
0.057
0.092*
0.080*
Employment Protection Legislation × Private Credit to GDP
-0.045**
-0.068**
-0.057**
Control Variables Investment to GDP
0.061
Schooling
0.057*
0.043
Labor Force Growth
0.400
0.505*
0.511*
Lagged GDP per worker
-0.600***
-0.627***
-0.638***
Exports and Imports to GDP
0.257***
0.243***
0.210***
Inflation
-0.118
-0.072
-0.007
Terms of Trade Shocks
0.058
0.063
-0.074
Time Effects/ Fixed Effects
yes/yes
yes/yes
yes/yes
1987-2005
1985-2005
1985-2005
20/311
20/311
20/311
Private Credit to GDP larger than
0.98
0.88
0.80
Would France significantly gain from reducing EPL?
no
no
no
Time Span No. countries/No. observations Turning point for productivity growth reducing effects of labor market rigidity
37
Table 1.B - Industry Growth and Various Measures of Development -0.124 -0.151 -0.134 -0.158 Industry's share of total value (-1.08) (-1.30) (-1.17) (-1.36) added in manufacturing in 1980
-0.163 (-1.40)
-0.139 (-1.208)
-0.162 (-1.39)
Interaction (external dependence × Employment Protection Legislation)
0.006 (1.45)
0.061** (2.26)
0.027** (2.08)
Interaction (external dependence × Total capitalization)
0.005 (1.18) -0.043** (-2.41)
0.006 (1.52)
-0.040** (-2.25)
Interaction (external dependence × Domestic credit to private sector)
-0.003 (-0.16)
0.085 (1.32) -0.010 (-0.50)
0.086 (1.36)
Interaction (external dependence × Total Capitalisation × Employment Protection Legislation)
-0.064** (2.19)
Interaction (external dependence × -0.051* Domestic credit to private sector × (1.82) Employment Protection Legislation) 444 444 444 444 444 444 444 #observations (#Industry × (36×15) (36×15) (36×15) (36×15) (36×15) (36×15) (36×15) #Countries) Notes: Robust standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%. The dependent variable is the average growth rate of output in a given sector in a given year for the period 1980-1990. Share is the share of output in a sector in total manufacturing output. All specifications are estimated using OLS, and include time and industry dummies not reported in the table. Variable definitions and sources are described in detail in the text.
Table 2.B - Industry Growth and Various Measures of Development Young firms Financial Dependance
Old firms Financial Dependance
Industry's share of total value added in manufacturing in 1980
-0.115 (-0.97)
-0.115 (-0.97)
-0.100 (-0.85)
-0.099 (-0.85)
-0.145 (-0.97)
-0.163 (-1.40)
-0.139 (-1.208)
-0.162 (-1.39)
Interaction (external dependence × Employment Protection Legislation)
0.006 (1.55)
0.006 (0.69)
0.021 (1.19)
0.016** (3.18)
0.006 (1.55)
0.006 (1.45)
0.061** (2.26)
0.027** (2.08)
Interaction (external dependence × Total capitalization) Interaction (external dependence × Domestic credit to private sector)
0.013 (0.29)
0.085 (1.32)
-0.001 (-0.02)
0.06 (0.02)
Interaction (external dependence × Total Capitalisation × Employment Protection Legislation)
-0.024 (-1.24)
-0.018*** (-3.52)
0.086 (1.36) -0.064** (2.19)
Interaction (external dependence × -0.010 -0.010* -0.070 -0.070* -0.051* Domestic credit to private sector × (-0.52) (-1.76) (-0.52) (-0.52) (1.82) Employment Protection Legislation) 420 420 420 420 420 420 420 420 #observations (#Industry × (34×15) (34×15) (34×15) (34×15) (34×15) (34×15) (34×15) (34×15) #Countries) Notes: Robust standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%. The dependent variable is th average growth rate of output in a given sector in a given year for the period 1980-1990. Share is the share of output in a sector in tot manufacturing output. All specifications are estimated using OLS, and include time and industry dummies not reported in the table. Variab definitions and sources are described in detail in the text.
38
