Labor Market Flexibility and Growth.

Transcription

1 Labor Market Flexibility and Growt. Enisse Karroubi July 006. Abstract Tis paper studies weter exibility on te labor market contributes to output growt. Under te assumption tat rms and workers face imperfect capital markets, I sow tat labor market exibility as tree types of e ects. It rst contributes to relax rms credit constraints. Second it can prompt rms to make more productive investments but te more likely so if capital market imperfections are low. Finally it positively in uences workers precautionary savings and tereby raises te volume of global savings. Based on tese tree e ect, te model brings two results. First te economy can exibit multiple equilibria wen capital market imperfections are large, te ig exibility equilibrium being always Pareto dominated. Second te model predicts tat productivity growt sould be positively associated wit labor market exibility for relatively low levels of capital market imperfections. We provide macro empirical evidence wic supports tis last conclusion. Preliminary and Incomplete. Banque de France. Address:, rue de la Vrillière Paris cedex 0. rstname.surname(at)banque-france.fr. I tank Henri Pages, Tierry Mayer, Matias Toenig and seminar participants at PSE for elpful discussions and comments. Usual disclaimers apply.

2 . Introduction. Since its creation, te Euro Zone as been lagging beind te United States in terms of output growt. From 99 to 005, te US business sector as been growing signi cantly faster pace tan its Euro Zone counterpart, year 00 being te sole signi cant exception. Moreover wile tis growt gap seemed to be on a disappearing trend by te end on te 990 s, te rst years of te 000 s decade ave witnessed a resurgence in tis growt gap wit a steady expansion from 0.7 in 00 to about.5 percentage points in % 4% 3% U.S.A % % Euro Zone 0% % Figure : Business Sector GDP Growt. Source: OECD Economic Outlook. A broader focus on te wole economy (and not only on te business sector) yields a very similar view as to te Euro Zone-USA growt gap: on average, te US as grown eac year.4 percentage point faster tan te Euro Zone on Not witstanding tis worrying picture for te Euro Zone, a similar pattern emerges from a rapid comparison of te respective productivity growt performances. Te di erence in output per worker growt is still more tan one percentage point in te business sector and 0.8% percentage point for te wole economy in favor of te US. Wy is tis so? Wy as te U.S. grown, over te last years, signi cantly faster tan te Euro Zone? Were does te growt gap between te Euro Zone and te US come from? Providing an answer to tis question is not an easy task: looking at gures for long run fundamental sources of growt, namely investment

3 and employment evolutions, it turns out tat employment as been increasing somewat faster in te US tan in Euro Zone (.4% to 0.8% per year on ) wile te investment to output ratio as been on average pretty larger in te Euro Zone tan in te US (6.% to.9% on ). Finally considering te fact tat catc-up e ects sould be larger for te Euro Zone given tat its productivity is lower, a rapid calibration of a Solow growt model sows tat tis gures sould predict a productivity growt gap in favor of te Euro Zone not in favor of te US. Still business sector labor productivity growt as been growing on average percentage point faster in te US tan in te Euro Zone on ,5%,0%,5% U.S.A. U.S.A.,0% EMU EMU 0,5% 0,0% Business Sector Productivity Growt Wole Economy Productivity Growt Figure : Average Productivity Growt. Source: OECD Economic Outlook. Terefore if traditional growt determinants cannot account for te output - productivity growt gaps, ten tis begs te question of were tese gaps come from and weter any stark structural di erence between tese two economies can elp understanding tis long run growt performance gap? On te list of possible culprits or at least of suspects, te labor market and its regulation ave been given very ig priority. Put di erently, given te gures for capital accumulation and employment growt in te US and te Euro Zone, te di erence in TFP needed to rationalize te di erence in growt rates is inconsistent wit empirical estimates of TFP growt. All te gures stated ere ave been taken out of te OECD economic outlook. Te employment variable (ETB) is named "employment of te business sector", te output variable (GDPBV) is named "gross domestic product business sector volume factor cost" and te investment variable (IBV) is named "private non-residential xed capital formation volume". 3

4 EMU 0 EMU EMU 0 0 USA USA USA Firing Difficulty Index Employment Rigidity Index Hiring Costs Index Figure 3: Labor Regulation Indexes. Source: Botero et al. [004]. Indeed, a large number of commentators ave pointed in te direction of te labor market, regarded as te driving element of tis growt gap. More precisely, te supposed lack of exibility in Euro Zone labor markets as been set responsible for te poor growt performance relative to te U.S. 3. However it is important to note tat labor market regulation does not ave a priori any direct impact on growt, at least according to standard growt models because it does not a ect directly fundamental sources for capital accumulation suc as savings and investment. Nor does te functioning of te labor market a ect education or te capacity to carry out researc and development activities, wic are te primary sources of endogenous long run growt. It terefore remains a question to understand ow suc a pattern wose in uence is mostly indirect (i.e. second order) can ave tat uge (i.e. rst order) impact so as to be a valid explanation for te Euro Zone - US growt gap. In tis paper I ask two questions. First (ow) can labor market institutions a ect productivity growt? Put di erently, does labor market exibility enance growt and ow? Second wat are te policy implications tat come out of te set of answers delivered to te rst questions? 3 Recently (marc 006), te president of te ECB, Jean-Claude Tricet, endorsed tis view, in an interview declaring anyting tat elps raising exibility is good to gt joblessness in today s world. Bot te IMF and te OECD also sare to a similar belief: To enjoy strong GDP growt, developed economies need, as a priority, policy frameworks tat encourage competitive intensity. Tis means [...] encouraging labor market exibility. (Finance & Development, marc 006). [...] institutional structures and policy settings tat favour competition and exibility in capital and labour markets [...] also make a key di erence to growt prospects. In particular, many of our countries need more competitive product markets; labour markets tat adjust better and more rapidly to socks. (Te Sources of Economic Growt in OECD Countries [003]) Last but not least, te Kok report on employment policy (003) underlines te need for more exibility in labor markets as a means to enforce te Lisbon agenda designed to make Europe te most competitive economic area in te world. 4

5 3,5 3,5,5 EMU EMU 0,5 0 USA Overall strictness of labor market regulation late 980's USA Overall strictness of labor market regulation late 990's Figure 4: Labor Market Regulation. Source: OECD Employment Outlook. Te idea I will pus forward in tis paper consists in claiming tat labor market institutions can account for sizeable productivity growt gaps in general and te for te US-Euro Zone productivity growt gap in particular wen interactions between labor and credit markets are taken into account. Te basic claim of te model consists in sowing tat on te one and labor market exibility always elps rms reducing teir borrowing constraints. On te oter and owever, labor market exbility can decrease (resp. increase) rms incentives to invest in ig total factor productivity projects wen rms face tigt (resp. wide) borrowing constraints. Labor market exibility will terefore be positively associated wit productivity growt if and only if capital markets are su ciently well developed. Tis conclusion will nally prove to be con rmed troug empirical evidence... Mecanism of te model. We model labor market exibility as te possibility for rms to propose wage contracts contingent to te ex post marginal productivity of labor. Wen te labor market is exible, ten rms do not provide any insurance to workers against ex post uctuations in labor productivity: labor compensation is ten contingent to ex post e ective labor productivity. On te contrary, wen te labor market is said to be in exible, ten rms provide insurance to workers against ex post uctuations in labor productivity and labor compensation 5

6 is ten related to te ex ante average and not te ex post e ective productivity of labor. Put di erently, labor market exibility is inversely related to te degree of wage insurance provided by rms to workers 4. In a simple model wit risk neutral rms and risk averse workers, rms sould optimally provide xed wage contracts to workers wit full insurance against ex post uctuations in labor productivity. Now let us make two assumptions. First rms face capital market imperfections in te form of ex post imperfect enforceability. Second, rms can coose te project tey invest in among di erent tecnologies wit more productive tecnologies also embedding more volatile socks. Ten te wage contract tey agree upon wit workers as an in uence on teir borrowing capacity. Namely if rms provide contingent wage contracts -(part of) labor productivity risk is transferred to workers- ten tat can raise rms pro ts before debt repayments in te bad states of te world and tereby raise rms borrowing capacity 5. As soon as rms marginal productivity of capital is larger tan te risk free interest rate, ten te policy consisting for rms to provide contingent wage contracts in order to alleviate borrowing constraints can raise expected pro ts. Moreover te wage contract rms provide workers wit modi es rm incentives for investment: wen a rm decides to propose contingent wage contracts, it bene ts on te one and from an increase in its borrowing capacity wile on te oter and, it as to pay a premium on its wage bill. Ten wen capital markets imperfections are large, if te rm invests in a igly productive tecnology, it looses te gain in terms of increased borrowing capacity since its productivity in te bad state is very low (because more productive projects are also more volatile). On te contrary, wen capital markets imperfections are low, if te rm invests in a igly productive tecnology, altoug its productivity in te bad state is very low, it does not loose as muc of its gain in terms of increased borrowing capacity because lenders are able somewat to smoot (imperfectly) bad and good states of nature. As a result at te individual optimum, labor market 4 One may argue tat altoug wage exibility is important, it remains a second order issue relative to employment exibility as long as workers are more concerned wit loosing teir jobs tan undergoing a wage cut. Altoug tis point is well-taken, it is important to note tat under te assumption tat a Walarasian spot labor market exists at eac date, compensation and employment risks are isomorpic at te aggregate level since at any date, te labor market balances supply from (previously sacked) workers and demand from rms, te wage rate being te equilibrium variable. Terefore under te assumption tat a set of complete labor markets exists te dicotomy between wage and employment exibility is irrelevant and one can focus on wage risk as long as it simpli es te analysis. Te model focusing on "wage risk" is in particular more tractable insofar as one can rely on a static ex ante ex post model wile te "employment risk" model de nitely needs some type of time-to-build tecnology as to de ne a non degenerate coice for rms between sort and long term labor contracts. 5 Equivalently, wen a rm adopts a contingent labor compensation sceme, tis reduces te risk premium on its nancial liabilities, te volume of capital borrowed being given. 6

7 exibility is more likely to be associated wit iger total factor productivity, te lower te capital market imperfections, i.e. te iger te degree of nancial development. To sum up, wen capital imperfections are large, labor market exibility is associated wit more rapid capital accumulation but wit lower total factor productivity. Wen capital imperfections are large, labor market exibility is associated wit iger growt troug more rapid capital accumulation and troug iger total factor productivity... Related literature. To be written..3. Road map of te paper. Te paper is organized as follows. Te following section lays down te model and its main assumptions. Section 3 describes te di erent strategies agents adopt as regards te labor and te capital market. In section 4, we build te general equilibrium of te economy. Te individual and social optimality properties for te di erent possible equilibria are derived in section 5. Te main results of te model as regards growt and labor market exibility can ten be found in section 6. Conclusions are eventually drawn in section 7. 7

8 . Te framework. We consider a single good economy wit tree types of agents, entrepreneurs, lenders and workers. All agents live for two periods t and t +. Tere is a continuum of unit mass of eac of type of agent... Entrepreneurs and lenders. Entrepreneurs and lenders do not ave any labor endowment but tey ave a capital endowment k at time t. Teir preference writes as U e = (b t+ ) (c t+ ) (.) were b t+ represents te time t + bequest an entrepreneur makes to its o -spring and c t+ represents te time t + consumption. lenders can lend teir capital k on te capital market. Entrepreneurs ave access to a set of constant returns to scale tecnologies. Noting k te capital stock invested (be it entrepreneurs own funds or nancial liabilities entrepreneurs ave contracted) and l te number of workers ired, entrepreneurs tecnologies write as y s = A s k l (.) Entrepreneurs tecnologies are subject to a macroeconomic sock s, Tere are two states of nature, a good s = and a bad one s = l wit A > A l. Bot states of nature are equiprobable. We adopt te following notations: we note m te mean, m = A +A l and te standard deviation, = A A l. Finally we > 0: projects wic are more productive on average also embed more volatile socks. An entrepreneur is faced wit te following budget constraints: At time t, it can invest its own capital and borrow from capital markets to invest in its rm. Similarly, at time t lenders can lend teir capital on te loan market. At time t +, entrepreneurs and lenders divide teir nal income between consumption and bequest to te next generation of entrepreneurs. Noting s te volume of capital invested at time t, and 8

9 k i agent i initial capital endowment, an entrepreneur or a lender faces te following budget constraints: s t k i c t+ + b t+ + i;s st (.3) were i;s = r if te agent i is a lender and i;s is te rm s return on asset in state s if agent i is an entrepreneur. Entrepreneurs and lenders program terefore writes as max (b t+ ) (c t+ ) b t+;c t+ s.t. c t+ + b t+ + i;s ki (.4) Once production as taken place and liabilities ave been paid back, entrepreneurs and lenders problem consists in coosing te volume of goods tey want to devote to bequest and consumption given teir nal income. Given tat entrepreneurs and lenders know te return i;s wen tey coose ow muc to consume and ow muc to bequeat, te optimal bequest b t+ and te optimal consumption c t+ write as b t+ = + i;s ki c t+ = ( ) + i;s ki (.5) Assuming as previously tat =, entrepreneurs and lenders expected indirect utility ten writes as V e = E + i;s ki (.6) In te case of a lender te optimal decision consists in lending its capital k on te capital market. On te contrary, in te case an entrepreneur, its problem consists in maximizing its expected pro t, i.e. E + i;s ki. To do so, entrepreneurs take two types of decisions: on te one and tey determine te volume of labor l and te amount of capital d tey want to invest. On te oter and, tey coose te labor contract fw s g s tey o er to workers and te tecnology m () tey want to invest in. 9

10 .. Workers. At time t, workers ave a labor endowment equal to one but no capital endowment. Teir preference writes as U w = (c t ) (c t+ ) (.7) Workers borrow capital to nance teir time t consumption c t. Tey also provide teir labor endowment to rms. At time t +, tey use teir labor income to nance teir time t + consumption c t+ and pay back te loans contracted at time t. Let us note w s, a worker s time t + labor income wen state s appens at time t +, ten te budget constraints eac worker faces write as c t d t c t+ w s ( + r) d t (.8) were d t is te amount of debt a worker contracts at time t and r is te interest rate on period t loans due at time t +. Workers program terefore writes as max (c t ) E (c s;t+ ) c t;c s;t+ s.t. c s;t+ w s ( + r) c t (.9).3. Workers optimal consumption coices. Te problem for workers consists in coosing te optimal consumption pat (c t ; c s;t+ ) given te interest rate on te capital market r, and te wage contract fw s g s tey ave agreed on wit entrepreneurs. Noting c t te optimal time t consumption, te rst order condition of te problem (??) ten writes as w ( + r) c t ( + r) c = t w l w w l ( + r) c t ( + r) c (.0) t 0

11 In te case were =, te last condition simpli es as ( + r) c t = w w + w l w l (.) Tis means tat consumers optimal rst period consumption is suc tat its second period cost is equal to a given fraction of te lowest second period wage income. Tereby te optimal time t + consumption c s;t+ is always strictly positive: c s;t+ = w s w + w l w s (.) One can also note tat te optimal rst period consumption decreases, every ting else equal, wit any mean preserving spread in te wage contract fw s g s. Tis corresponds to a standard precautionary savings motive: wen income volatility increases and in te absence of any nancial instrument to edge income uctuations, workers decide to reduce te amount of capital borrowed from capital market in order not to compromise teir future consumption. Te expected indirect utility of consumers ten writes as V w = wl w + r (.3) As expected, consumers expected indirect utility decreases wit te interest rate and increases wit te income w s. Moreover consumers are indi erent between two di erent wage contracts fw ;s g s and fw ;s g s if and only if for tey yield te same level of indirect utility, every ting else equal. Tis ten writes as w ;l w ; = w ;l w ; Assuming for instance tat fw ;s g s is a xed wage contract, i.e. w ;l = w ; = w wile fw ;s g s is a strictly contingent contract, i.e. w ;s = s w wit l 6=, ten te last condition simpli es as = l (.4)

12 .4. Markets. At te beginning of eac period, tere are two di erent markets wic open one after te oter. Te rst market on wic transactions take place is te capital market. On tis market, entrepreneurs and workers sign one period contracts wit lenders. We assume tat entrepreneurs face ex post imperfect enforceability. Tey can default on teir nancial claims at some cost. Te risk free interest rate is noted r. Te second market on wic transactions take place is te labor market. Te labor market is competitive. At te end of te period, rms pay wages to workers and nancial contracts are paid back. An entrepreneur pro ts in state s write as ;s = y s (d; l) w s l ( + r) d were d is te volume of capital te entrepreneur as borrowed from te capital market and l is te number of workers e as ired. Since transactions are imperfectly enforceable, rms can always retain a fraction of teir output and abstract from paying teir debts (te marginal cost to default is in tis case equal to ). In tis case conditional on state s appening, tey earn ;s = (y s (d; l) w s l) wit. To be incentive compatible te face value of te entrepreneur nancial liabilities ( + r) d and te wage bill w s l must be suc tat te cost to pay back one s liabilities is lower tan te cost to default. Ten a rm liabilities must be suc tat ( + r) d ( ) (y s (d; l) w s l) (.5) Tis constraint is valid only as long as rms are not able to issue contingent debt. In te case were rms can issue contingent debt, ten te borrowing constraint rms face writes as ( + r ) d ( ) max (y s (d; l) w s l) (.6) s

13 were r is te interest rate on risky debt. 3. Te no contingent debt economy. 3.. Firms optimal beavior. Given tat rm decisions are sequential, te program of a representative rm can be solved wit backward induction. First we determine te strategy of te representative rm as regards te volume of labor it ires, ten we turn to te capital demand of te representative rm and nally we determine te optimal wage contract and te optimal tecnology. Let us consider a rm i wic as cosen a given compensation sceme fw l ; w g wen oter rms coose to propose an equivalent certain wage rate w. Ten assuming tat te compensation sceme fw l ; w g veri es workers participation constraint, i.e. w l w w, were w is te certain equivalent wage rate proposed on te labor market, rm i program rst consists in coosing te number of worker l i suc tat it solves max l i E (l i ) = m () (k i + d i ) l i Ew s l i ( + r) d i (3.) Te solution to tis problem ( rm i optimal demand for labor) ten writes as ( ) m () (k i + d i ) li = Ew s (3.) Now one can solve te problem consisting for rm i in determining its optimal amount of debt nance d i. Tis amounts to solve te following problem maxe (d i ) = m () (k i + d i ) l i Ew s l i ( + r) d i d i 8 >< ( ) m () (k i + d i ) li = Ew s s.t. >: 8s, ( + r) d i ( ) A s (k i + d i ) l i w s l i (3.3) 3

14 Introducing rm i optimal labor demand (3.) in bot te objective function (3.) and te borrowing constraints ( ) A s (k i + d i ) l i w s l i ( + r) di we can rewrite (3.3) as te following problem maxe (d i ) = m () d i s.t. 8s, ( + r) d i ( ) Ew s m () Ew s m () i i (k i + d i ) ( + r) d i A s ( ) m() Ew s w s i (k i + d i ) (3.4) Te labor contract fw s g s as two di erent e ects on te borrowing capacity of te rm. An increase in te volatility of labor compensation raises te cost of labor and as a matter of fact reduces te productivity of te rm because te e ciency frontier te rm faces is less favorable. On te contrary owever, an increase in te volatility of labor compensation can raise pro ts before debt repayments and ence raise te cost for te rm to default and tereby increase te borrowing capacity of te rm. Similarly, te coice of te tecnology as two di erent e ects on te borrowing capacity of te rm. On te one and an increase in te volatility of tecnological socks raises by de nition te rm average productivity. On te oter and owever, an increase in te volatility of tecnological socks reduces te productivity of te rm conditional on a bad state of nature. Moreover for a given compensation sceme fw s g s an increase in te volatility of tecnological socks increases te rm demand for labor and ence furter reduces pro ts before debt repayments conditional on a bad state of nature. Tere are ten two di erent cases: if m () Ew s m () i + r, ten rms simply lend teir capital on nancial markets because lending is more pro table tan investing in te rm. Firms expected pro ts write as E = ( + r) k. As is clear te expected pro ts of rm i do not depend upon nor on te type of i te labor contract nor on te tecnology cosen. On te contrary wen m () Ew s m () > + r ten rm i optimal expected pro ts write as E = ( + r) m () ( ) Ew s ( )m() i i A j ( ) wj Ew s m () ( ) A j ( ) wj Ew s m () i ( + r) k i 4

15 were j is te state of nature for wic te borrowing constraint is binding: j = arg min A p ( ) w p m () p Ew s Assuming for now on tat =, noting w s = s w, and simplifying te last expression, we obtain tat te state of nature for wic te borrowing constraint is binding is te bad state, i.e. j = l, if and only if l > ( ) m ( ) m + Ten rms expected pro ts write as E (; ) ( + r) k i = ( ) m ( ) i ( ) m ( ) +r + m + i w ( )m + i were for now on stands for l. As is clear in tis last case, te expected pro ts of rm i do depend upon on te type of te labor contract and te tecnology cosen. Firms expected pro ts can be positively or negatively related to wage variability since on te one and wage variability raises labor costs and terefore reduces te rm s productivity wile on te oter and, wage variability can ease te rm s borrowing constraints by increasing minimum pro ts before debt repayments. Similarly, coosing a more productive tecnology raises expected pro ts on te one and because total factor productivity is larger. On te oter and owever, coosing a more productive tecnology means every ting else equal a lower borrowing capacity due to more volatile socks. Te next propositions ten derive te main properties of te optimal wage contract and te optimal tecnology in tis last context. Proposition. As long as rms credit constraint is binding, te optimal wage contract fwl ; w g is suc tat w l < w < w. Moreover te di erence w w l decreases wit te risk free interest rate r. Proposition. Wen rms cannot issue contingent debt, noting " (y) te elasticity of y wrt to, te 5

16 optimal tecnology is an increasing function of te optimal wage contract if and only if < " (m) [" (m) Proof. c.f. appendix 7. for a proof of proposition. As concerns proposition, te rst order condition determining te optimal wage contract writes as = + r m Ew s ( ) m ( ) m ( ) + i 3 5 wile te rst order condition determining te optimal tecnology writes as = + r m Ew s ( ) m 4 + m " (m) ( ) m ( ) " (m) + i 3 5 were " (y) Terefore te individually optimal wage contract and te individually optimal tecnology verify te following condition tat " (m) = 4 4 " m m Te optimal tecnology is terefore an increasing function of te optimal wage contract if and only if " " m m # < 0 Applying te following = " " (m) + te last < 0 ends up being equivalent to "( m) m < " (m) [" (m) 6

17 In tis case, te condition " (m) = 4 4 " m m de nes a positive relationsip between and wile te condition = + r m Ew s ( ) m 4 + " (m) " (m) 4 + m ( ) ( ) i de nes a negative relationsip between and. Tese two conditions terefore determine a unique couple ( ; ) wic maximizes rms expected pro ts. η η η σ σ σ Figure 5: Firm optimal strategies in partial equilibrium wen contingent debt is not available. In tis proposition, we ave tree di erent properties. Te rst one states tat te situation were rms are not able to borrow capital up to te point were te expected marginal productivity of capital is equal to te risk free interest rate is a necessary and su cient condition for rms to provide contingent compensation scemes to workers. Tis property is very natural: consider a rm wic provides xed wage contracts and faces a binding borrowing constraint in te sense tat its expected marginal productivity of capital is larger tan te interest rate on te capital market wen te borrowing capacitty is exausted. Ten on te one and tere is a strictly positive cost to being unable to borrow a larger volume of capital. On te oter and providing contingent wage contracts could elp increase te volume of capital it is possible to borrow 7

18 wile te marginal increase in labor cost is zero wit xed wage contracts = + = = = 0 Terefore as soon as rms are credit constrained, tey ave incentives to provide contingent wage contracts basically because a binding credit constraint is always marginally costly wile providing exible labor contracts is always marginally cost free. Secondly proposition states tat a large interest rate reduces rms incentives to provide contingent labor compensation scemes. Tis is natural since a large interest rate reduces rms demand for capital and terefore reduces te need to provide contingent labor contracts. Finally proposition sows tat rms wic coose to provide workers wit more exible labor contracts also coose to invest in less productive tecnologies. Once again tis is very natural: if a rm decides to provide exible labor contracts in order to alleviate its credit constraints, it also undergoes an increase in labor costs due to te risk premium it pays to workers. Now investing in a igly productive tecnology also means accepting large uctuations in te rm s productivity. Given tat lenders compute te borrowing constraint tey impose to rms w.r.t. te bad state of nature, investing in a igly productive tecnology and providing exible labor contracts would mean tat te rm would pay for a risk premium on workers wages witout bene ting from an increased borrowing capacity since a igly productive tecnology is very unproductive wen te bad state appens. Terefore rms prefer to invest in low productivity tecnologies wen tey provide exible labor compensation contracts. For instance wen m () = m wit m > 0 and 0 < < ten te labor market exibility is always TFP reducing since " (m) = = < 0 wic implies tat te condition < " (m) [" (m) is always satis ed. 8

19 3.. Te general equilibrium of te economy Te equilibrium of te capital market. Up to now te risk free interest rate as been taken to be exogenous. To determine te equilibrium interest rate tat prevails in te economy, one simply needs to equal te supply for capital provided by lenders and te demand for capital expressed by entrepreneurs and consumers. Put di erently te equilibrium interest rate is determined troug k l = d + l (c t ) + ( l) (c t ) were k l represents lenders capital supply, d rms aggregate demand for capital; l rms aggregate demand for labor, (c t ) is te rst period consumption of workers ired by entrepreneurs and (c t ) is te rst period consumption of workers wo ave not been ired by entrepreneurs. Entrepreneur i labor demand l i and capital demand d i respectively write as d i = ( + r) Ews ( )m ( ) m l i = (ki + d i ) Ew s A l ( ) m i + i k i A l ( ) m () + Given tat entrepreneurs are identical, tat w s = s w wit w l w = w, te equilibrium of te capital market simpli es as w k l + r A l + ( ) m () = i ( + r) Ew s ( )m + + i k A l ( ) m + i 3... Te equilibrium of te labor market. At te equilibrium of te labor market, labor demand balances labor supply. Given tat entrepreneurs are all identical, noting k rms aggregate capital stock and d rms aggregate borrowing, te expected wage rate Ew s is ten equal to te expected marginal productivity of labor Ew s = ( ) m (k + d) 9

20 and te uncontingent wage rate writes as w = + ( ) m (k + d) (3.5) General Equilibrium. Te general equilibrium of te economy corresponds to te situation were all markets, te capital and te labor market, balance supply and demand. To determine te properties of tis situations, one simply need to plug te two last expressions in te capital market equilibrium condition, we end up wit an equilibrium interest rate r being de ned troug k l = A l ( ) m + (k + d) + + r (3.6) were te aggregate volume of capital d rms borrow at te general equilibrium of te economy is suc tat ( + r) d = A l ( ) m (k + d) (3.7) + Finally rm optimal tecnology is suc tat m " (m) " (m) = 4 4 (3.8) and te optimal labor contract rm propose to workers veri es + r m Ew s ( ) m 4 + m " (m) ( ) m ( ) " (m) + i 3 5 = (3.9) Proposition 3. Te general equilibrium of te economy is represented by te vector (; ; r; d; w). Firms coose teir optimal labor contract and teir optimal tecnology respectively suc tat (3.9) and (3.8) are veri ed. Te equilibrium interest rate on te capital market r and te volume of capital d rms are able to borrow are respectively suc tat (3.6) and (3.7) are veri ed. 0

21 Proof. Straigtforward. A few remarks ere are in order. First rms borrowing capacity decreases wit te interest rate. Tis is due rst to larger debt repayments second because rms coose optimally to propose less contingent compensation scemes to workers and tird because rms optimally coose to invest in more productive, yet more risky tecnologies on te oter and. As a result of tese tree e ects, rms demand for capital is walrasian: it decreases wit te cost of capital. Second, workers demand for capital decreases wit te interest rate as a basic trade-o between contemporary and future consumption. Tis is due a standard substitution e ect. However an increase in te interest rate also as an income e ect: it modi es workers future labor income and terefore a ects workers contemporary consumption and tereby workers demand for capital. On te one and rms raise fewer capital wen te cost of capital increases. Since capital and labor are complements in rms production function workers demand for capital decreases wit te interest rate according to tis rst e ect. On te oter and owever, rms invest in more productive tecnologies wen te interest rate increases. Tis second e ect raises every ting else equal, te marginal productivity of labor. Hence workers future labor income is raised and workers increase teir contemporary consumption. Terefore te income e ect is a priori ambigious since labor income can increase or decrease following an cange in te cost of capital. However workers contemporary consumption (i.e. demand for capital) is a ected in a tird manner. Wen te cost of capital increases, rms provide less contingent labor compensation scemes to workers. Terefore te need for workers to reduce teir consumption as a edging device against labor income uctuations is reduced. Terefore, workers demand for capital increases as te cost of capital increases according to tis last e ect. To sum up, workers demand for capital can well be increasing in te cost of capital if te last two e ects dominate te rst one. Ten if te increase in workers demand for capital compensates for te decrease in rms demand for capital, tere can exist a range of interest rates for wic te global demand for capital increases wit te interest rate due to te fact tat te reduction in rms demand for capital is more tan o set by te increase in workers demand for capital. As a result, tere can be multiple equilibria. In te rst one te interest rate is low, rms propose relatively exible labor contracts to workers and invest in relatively unproductive

22 tecnologies. Workers ave a low contemporary consumption and rms borrow te bulk of available capital on te credit market. In te second equilibrium te interest rate is large, rms propose relatively xed labor contracts to workers and invest in relatively productive tecnologies. Workers ave a large contemporary consumption and rms borrow only a relatively small sare of available capital on te credit market, te bulk of available capital being used to nance workers consumption. It is terefore unclear wic of te low or te large labor market exibility equilibrium is te Pareto optimal equilibrium. Nor is it clear if te Pareto optimal equilibrium is te also ig growt equilibrium or not. However te model clearly sows tat di erent labor market institutions can emerge and remain existent in a general equilibrium framework as long as some market imperfections are being introduced. Te view tat te supposed lack of exibility in Continental European labor markets is an out-of-equilibrium penomenon, or put di erently, is a pure political economy equilibrium is terefore not necessarily completely relevant. Structural cross-country di erences in labor market institutions can well be an equilibrium penomenon entirely based on pure economic mecanisms. S D r Figure 6: Equilibrium of te capital market.

23 3.3. Te welfare analysis. Given tat te economy is populated by eterogenous agents, te welfare analysis can be carried out using two di erent welfare criteria: te utilitarian or te egalitarian social welfare. In te case of te utilitarian welfare criterion, social welfare is simply te sum of individual welfare weigted by eac type of agents weigt in te total population. Since lenders, workers and entrepreneurs ave identical weigts in te economy, noting W util te utilitarian welfare criterion, we ave W util = V w + V f + V l were V w represents workers welfare, V f represents rms welfare and V l represents lenders welfare. At te general equilibrium of te economy, using in particular expressions (3.5) and (3.6) te di erent individual welfare functions V i write as V w = V f = V l = ( ) m () (k + d) + ( + r) m () (k + d) + ( ) + m () (k + d) ( ) + + Terefore te utilitarian social welfare criterion can write as W util = + + p + r + ( + ) m () (k + d) (3.0) Proposition 4. Wen te economy exibits multiple equilibria, ten te socially optimal equilibrium is te low labor market exibility equilibrium. Proof. At at te general equilibrium of te economy, te interest r, te optimal labor contract, te volume of debt d rms borrow and rms optimal tecnology verify te capital market equilibrium condition 3

24 (3.6) k = + ( + ) m () (k + d) + r Terefore from expression (3.0) te utilitarian social welfare can be simpli ed as W util (; r) = i + p + + r i k p + r (3.) As is clear tis expression is useful since it only depends upon te cost of capital r and te labor contract wic are positively correlated across equilibria: te ig labor market exibility equilibrium is also te low interest rate equilibrium. From expression (3.), it is clear tat a larger interest rate r increases every ting else equal, te utilitarian social welfare criterion. As to te e ect of te labor contract, te utilitarian social welfare criterion can be written as W util N () =D () wit " # N () = + p + r D () = + As is clear, te numerator N () is strictly increasing in and r. As to te denominator D (), it is a strictly decreasing function of. Terefore social welfare under te utilitarian criterion increases wit and r. Tis implies tat te low labor market exibility equilibrium maximizes social welfare. Te intuition for tis result is fairly simple: social welfare is maximized at te low exibility equilibrium for tree reasons. First because tis equilibrium allocates risk to agents wic are te least risk averse in te economy. Second because it allocates capital to tose wic ave no oter means to raise teir utility. Tird because it gives incentives to rms to invest in projects wit ig productivity wic bene ts all agents in te economy, workers and lenders in particular. For tese tree reasons, wen te economy faces multiple equilibria, te Pareto optimal equilibrium is always te low labor market exibility equilibrium. 4

25 4. Te contingent debt economy. 4.. Firms optimal beavior. Up to now, we ave restricted rms coices as concerns nancial liabilities to uncontingent debt. Now let us assume tat rms can issue contingent debt. Te borrowing constraint tey face now writes as ( ) min (y s (d; l) w s l) < ( + r ) d ( ) max (y s (d; l) w s l) (4.) s s were r represents te interest rate on contingent debt. Moreover let us assume witout generality tat te rm defaults in te bad of nature s = l and pays back its debts in te good state of nature, s =. Ten te program of tis rm writes as max l i E (l i ) = A (k i + d i ) l i w l i ( + r ) d i + Al (k i + d i ) l i w l l i (4.) Noting m () = A + A l, m (; ) = ( ) A + A l, w () = w + w l, w (; ) = ( ) w + w l, and solving te problem of te rm similarly to wat as been done in te previous section, te rm labor demand rst writes as ( ) m () (ki + d i ) = l i (4.3) w () Now as concerns lenders, we can derive te risk premium on contingent debt r r (r being te risk free interest rate) from a no arbitrage condition. Since lenders are risk neutral, te risk free interest rate r and te interest rate on contingent debt r verify te following condition ( + r) d = ( + r ) d + Al (k i + d i ) l i w l l i (4.4) 5

26 were is te fraction of net output lenders are able to seize in case of default. Assumuing tat < we can rule out te case were te seized output would be larger tan te face value of rms debts: A l (k i + d i ) l i w l l i < ( + r ) d Terefore introducing te labor demand (4.3) into te expected pro t function (4.), we end up wit te following expressions: wen rms want to issue contingent debt, tere expected pro ts write as ( E (d i ) = ) m () w () m () (k i + d i ) ( + r ) d i Similarly, introducing te labor demand (4.3) into te no arbitrage condition (4.4) we end up wit te following expressions: wen rms want to issue contingent debt, te capital supply function linking te volume of capital d tey raise to te risk free interest rate r and te risk premium r r writes as ( + r) d i = ( + r ) d i + ( ) m () ( A l w l w () ) m () w () (ki + d i ) (4.5) Finally introducing te no arbitrage condition (4.5) into te borrowing constraints (4.) te program wic determines te rm optimal capital demand terefore writes as maxe (d i ) = d i s.t. ( + ) ( )m() w() i A l ( )m() w() w l i < ( + r) ii m () + A l ( ) m () w l w() (k i + d i ) ( + r) d i i w() ( )m() d i k i+d i < m (; ) ( ) m () w(;) w() (4.6) Te labor contract fw s g s as tree di erent e ects on te borrowing capacity of te rm. First, as previously an increase in te volatility of labor compensation raises te cost of labor and as a matter of fact reduces te productivity of te rm because te e ciency frontier te rm faces is less favorable. Secondly, owever, an increase in te volatility of labor compensation (in te sense of an increase in w and a decrease in w l ) can raise te volume of capital lenders can seize in case of default (in te bad state of nature). Finally an increase in te volatility of labor compensation (in te sense of an increase in w and a decrease in w l ) 6

27 reduces rms pro ts before debt repayments in te good state of nature, and ence te rm borrowing capacity. Similarly, te coice of te tecnology as two di erent e ects on te borrowing capacity of te rm. On te one and an increase in te volatility of tecnological socks raises by de nition te rm average productivity. On te oter and owever, an increase in te volatility of tecnological socks raises te rm borrowing capacity because te rm borrowing constraint is not computed anymore w.r.t. te sole bad state of nature (in wic case te rm borrowing capacity would ave oterwise been reduced). Finally for a given compensation sceme fw s g s an increase in te volatility of tecnological socks increases te rm demand for labor and ence reduces pro ts before debt repayments conditional on a bad state of nature. Ten assuming tat raising capital is pro table for te rm, i.e. ( ) m () w () m () m () + A l ( ) w l > ( + r) w () te expected pro t of te rm writes as E ( + r) k i = +r m() i ( ) A m() ( ) w w() w() ( )m() i m(;) m() ( ) w(;) w() i We can ten derive te following proposition. Proposition. Wen rms can issue contingent debt, ten tey optimally coose rms te optimal labor contract and te optimal tecnology so as to verify + r w () m () ( ) m () m () m # " (m) = were " (m) is te elasticity of m w.r.t. " m 7

28 Proof. Computing te rst order condition determining te optimal labor contract we nd tat veri es W " # V = V + [U + V ] ( ) wile te optimal tecnology is determined by te following condition m () m V = V " (m) + [U + V ] wit te following notations U = m () ( ) m () + m + V = ( ) m () + W = + r w + m () ( ) m () Ten taking te di erence between te two rst order conditions, we end up wit + r w () m () ( ) m () m () m # " (m) = One can note tat te relationsip between te optimal tecnology and te optimal labor contract in te contingent debt case is essentially similar to te uncontingent debt case. Basically, te uncontingent debt case is a special case of te contingent debt case if considered wit =. Corollary. Wen rms can issue contingent debt, ten te optimal tecnology is a decreasing function of te optimal labor contract if and only if " (m ()) > [" (m) ] [" (m) + ( " (m)) ( ) X (; " (m) 8

29 were X (; ) = m () + m + ( + r ) m () w () Proof. At te individual optimum, rms tecnology and workers labor contracts are determined troug te condition + r w () m () ( ) m () m () m # " (m) = As is clear te left and side of tis expression unambigiously decreases in wile te variations wrt are ambigious. Taking te rst derivative of tis left and side wrt and after some tedious algebra we end up wit te following condition: te left and side expression increases in if and only if " (m ()) > [" (m) ] [" (m) + ( " (m)) ( ) X (; " (m) were X (; ) = m () + m + ( + r ) m () w () Corollary 3. Wen rms can issue contingent debt ten an exogenous increase in labor market exbility is more likely to be associated wit an increase in rms average productivity tan in te case were rms cannot issue contingent debt. Proof. Wen rms cannot issue contingent debt, labor market exibility is associated wit less productive investments if and only if < " (m) [ " 9

30 Similarly wen rms can issue contingent debt, labor market exibility is associated wit more productive investments if and only if " (m ()) " (m) [ " (m)] [" (m) + ( " (m)) ( ) X (; )] Since X > 0, a su cient condition wic ensures tat labor market exibility is more likely to be associated wit an increase in rms average productivity in te case were contingent debt is not available writes as " (m ()) > " (m) wic simpli es wic is always true since by de nition A l = m > 0 @ < 0 η η η σ σ σ Figure 7: Firm optimal strategies wen contingent debt is available. 30

31 4.. Te general equilibrium of te economy Te equilibrium of te capital market. Up to now te risk free interest rate as been taken to be exogenous. To determine te equilibrium interest rate tat prevails in te economy, one simply needs to equal te supply for capital provided by lenders and te demand for capital expressed by entrepreneurs and consumers. Put di erently te equilibrium interest rate is determined troug k l = d + l (c t ) + ( l) (c t ) were k l represents lenders capital supply, d rms aggregate demand for capital; l rms aggregate demand for labor, (c t ) is te rst period consumption of workers ired by entrepreneurs and (c t ) is te rst period consumption of workers wo ave not been ired by entrepreneurs. Entrepreneur i labor demand l i and capital demand d i respectively write as d i = ( + r) ( l i = ) m () (ki + d i ) w () m (; ) ( ) m () w(;) w() ( )m() i w() m (; ) ( ) m () w(;) w() i k i Given tat entrepreneurs are identical, tat w s = s w wit w l w = w, te equilibrium of te capital market simpli es as w k l + r m (; ) = ( + r) w() ( )m() ( )m() w() i ii w (; ) + m (; ) ( ) m () w(;) w() i k 4... Te equilibrium of te labor market. At te equilibrium of te capital market, labor demand balances labor supply. Given tat entrepreneurs are all identical, noting k rms aggregate capital stock and d rms aggregate borrowing, te expected wage rate 3

32 Ew s is ten equal to te expected marginal productivity of labor w () = ( ) m () (k + d) and te uncontingent wage rate writes as w = + ( ) m () (k + d) (4.7) General Equilibrium. Te general equilibrium of te economy corresponds to te situation were all markets, te capital and te labor market, balance supply and demand. To determine te properties of tis situations, one simply need to plug te two last expressions in te capital market equilibrium condition, we end up wit an equilibrium interest rate r being de ned troug m (; ) k l = + ( ) m () w (k + d) w + w l + w (; ) + r (4.8) were te aggregate volume of capital d rms borrow at te general equilibrium of te economy is suc tat ( + r) d = m (; ) ( ) m () w (; ) (k + d) (4.9) w () Finally rm optimal tecnology is suc tat + r w () m () ( ) m () # m () m () " (m) = (4.0) and te optimal labor contract rms propose to workers veri es W " # V = V + [U + V ] (4.) ( ) 3

33 Proposition 4. Te general equilibrium of te economy is represented by te vector (; ; r; d; w). Firms coose teir optimal labor contract and teir optimal tecnology respectively suc tat (4.) and (4.0) are veri ed. Te equilibrium interest rate on te capital market r and te volume of capital d rms are able to borrow are respectively suc tat (4.8) and (4.9) are veri ed. Proof. Straigtforward. A few remarks ere are in order. To be continued Te welfare analysis. To be done. 33

34 5. Growt e ects of labor market exibility. We embed te framework considered in te previous sections into a dynamic model. At eac point in time tere is a continuum of unit mass of workers, a continuum of mass of agents wo can be entrepreneurs or lenders wit equal probability 6. At te beginning of eac period, entrepreneurs ire workers and agree on labour contracts wit tem. Tey borrow capital from lenders to nance investment and tey coose a tecnology and engage in production. Workers supply labour to entrepreneurs and agree on labour contracts wit tem. Tey borrow capital from lenders to nance beginning of period consumption. Lenders lend capital to rms to nance investment. Tey lend capital also to workers to nance consumption. At te end of eac period, entrepreneurs pay workers according to te labour contracts tey agreed upon. Tey pay back lenders for beginning of period loans and tey divide teir pro ts between consumption and bequest. Workers are paid according to te wage contract tey agreed upon wit entrepreneurs. Tey pay back lenders for beginning of period loans and consume teir labour income net of loan repayments. Lenders are paid back on beginning of period loans extended to workers and entrepreneurs and tey divide teir nal capital income between consumption and bequest. Let us note k t te capital stock in te economy at te beginning of period t, and kt+ s te capital stock in te economy at te beginning of period t wen state s as appened at time t. If te good state of nature appens at time t, te capital stock at te beginning of period t +, kt+, writes as k t+ = 8> < k t + d >: A + ( ) m () A + ( ) m () i + if no contingent debt i + oterwise (5.) Te rst part of te rigt and side A k t + d represents total output in te economy. Te second part of te rigt and side + ( ) m () k t + d or alternatively + ( ) m () k t + d represent te wage bill distributed to workers in te case were rms cannot issue contingent debt and te case were rms can do so. Te nal part of te rigt and side + represents te sare of te wage bill workers 6 Tis assumption elps simplify te exposition of te model since rms beginning of period aggregate capital stock k f is always equal to lenders beginning of period aggregate capital stock k l wic is alf te economy s beginning of period aggregate capital stock k t. 34