Labor Market Flexibility and Growth.

Transcription

1 Labor Market Flexibility and Growt. Enisse Karroubi May 9, 006. Abstract Tis paper studies weter exibility on te labor market contributes to output growt. First I document two stylized facts concerning te relationsip between output growt and labor market institutions. Speci cally, labor market exibility is sown to be on te one and positively associated wit iger total factor input (TFI) growt but on te oter and negatively associated wit total factor productivity (TFP) growt. Second in a model were bot rms and workers face imperfect capital markets, I sow tat labor market exibility relaxes rms borrowing constraints but raises rms incentives to invest in low productivity projects. Moreover labor market exibility as a positive impact on workers precautionary savings and raises tereby te volume of global savings. As a result, te economy exibits multiple equilibria: one wit in exible labor contracts low savings and low investment but ig productivity and ig interest rate and one wit exible labor contracts ig savings and ig investment but low productivity and low interest rate. Te model terefore rationalizes te empirical observations on te relationsip between labor market exibility and te di erent sources of growt. Finally te model sows tat te negative e ect on TFP can o set te positive e ect on TFI, te ig exibility equilibrium being ten dominated in terms of bot welfare and growt. Preliminary Version. Comments Welcome. Banque de France. Address:, rue de la Vrillière Paris cedex 0. rstname.surname(at)banque-france.fr. I tank Gilbert Cette, Henri Pages and seminar participants at PSE. Usual disclaimers apply.

2 . Introduction. Since its creation, te Euro Zone as been lagging beind te United States in terms of output growt. As illustrated in gure, from 99 to 005, te US business sector as been steadily growing at a 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 grows eac year.4 percentage point faster tan te Euro Zone. Not witstanding tis worrying picture for te Euro Zone, a similar pattern emerges from a rapid comparison of te respective productivity growt performances. Comparing te growt rate of output per worker, te growt gap between te US and te Euro Zone is still more tan one percentage point in te business sector and 0.8% percentage point for te wole economy. 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 ). Moreover te investment to output ratio as been on average pretty larger in te Euro Zone tan in te US (6.% to.9% on ). Finally adding 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 propose to revisit te interactions between labor market institutions and growt. Speci cally, I ask two questions. First can labor market institutions be eld responsible for te US-Euro Zone growt gap? In oter words, does labor market exibility enance growt and ow? Second 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 adere 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 wat are te economic policy recommendations tat come out of te set of answers delivered to te rst questions? 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. To do so, I am going to sow tat labor market institutions namely, labor contracts can a ect capital accumulation and growt troug te interactions between labor and nancial markets at te rm level. Solving te problem of te rm will terefore prove to be elpful in understanding ow rms optimally coose teir labor contracts, teir nancial contracts and teir tecnology and weter more exibility in optimal labor contracts is associated at te macro level wit faster capital accumulation, more productive tecnologies and eventually wit iger or lower growt. Te basic claim of te model consists in sowing tat labor market exibility can elp rms reduce borrowing constraints and ence elp te economy accumulate production factors at a faster pace. Labor market exibility is terefore positively associated wit growt. However, te model also sows tat labor market exibility gives incentive to rms to invest in less risky but also less productive tecnologies. Hence labor market exibility can also be associated wit lower growt... Decomposing growt and labor market e ects. Output growt or labor productivity growt can be decomposed along te usual growt accounting partition. To grow, an economy can accumulate production factors suc as capital and labor. We will refer to tis 5

6 rst source of growt as total factor input growt (TFIG). To grow an economy can also improve its tecnology, i.e. improve te way it combines production factors to produce more output wit te same volume of production factors. We will refer to tis second source of growt as total factor productivity growt (TFPG). We consider a sample of fteen European countries and te US on te period. We get data on TFI and TFP from te GGDC Total Economy Growt Accounting Database 4. As to labor market exibility indicators we consider te Botero et al. [004] database 5. Ten we carry out a simple exercise. We divide our country sample into two categories, countries wit low employment protection or employment rigidity and countries wit ig employment protection or ig employment rigidity. In eac of tese two sub samples, we compute te average TFI growt rate and te average TFP growt rate and compare te gures obtained for eac category of countries. It appears tat average total factor input growt for te period as been larger in countries wit low employment rigidity (low ER) wile total factor productivity growt as been larger in countries wit large employment rigidity (large ER). Low ER Large ER TFIG,38%,4% TFPG 0,9%,0% Table. Source: Autor s calculations 6. Wile labor market exibility is correlated wit te di erent sources of growt according to table, tere exists a number of oter structural conditions wic a ect knowledge and production factors accumulation. On top of tese structural conditions comes te quality of te nancial sector or nancial development. Conducting a similar exercise to wat as been done iger, it appears tat nancial development measured from te Djankov et al. [006] database 7 (CP stands for creditor protection) is always associated wit larger growt bot in terms of total factor productivity and total factor input. 4 More details about te database, te sample and te variables can be found at te address ttp:// 5 More details on tese data can be found on te web site ttp:// 6 A country is de ned as belonging to te low (resp. large) ER index category if and only if it ER index is lower (resp. larger) tan te median ER index in te sample. Altoug te reader may legitimately question te statistical signi nance of tese di erences, te evidence sown simply aims at being suggestive of te labor market regulation di erentiated impact. 7 More details on tese data can be found on te web site ttp:// 6

7 Low CP Large CP TFIG,%,40% TFPG 0,6%,8% Table. Source: Autor s calculations 8. Now as tese two sets of comparisons are only indicative, we go one step furter and carry out regressions on te respective determinants of TFI and TFP growt. TFIG TFPG TFIG TFPG Lagged dep. variable 0, Employment Rigidity -,07 0,76-0,83 0,3 Creditor Protection -4,97 7,76 3,33 0,04 Time e ects yes yes yes yes NT Table 3. Source: Autor s calculations 9. Te results are similar to te rst ones: labor market exibility is associated every ting else equal wit iger total factor input growt but lower total factor productivity growt. Terefore it seems tat countries wit more exible (less regulated) labor markets tend to accumulate production factors at a iger speed. However it also seems tat countries wit more exible (less regulated) labor markets tend to improve more slowly teir tecnology 0... 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 8 A country is de ned as belonging to te low (resp. large) CP index category if and only if it CP index is lower (resp. larger) tan te median CP index in te sample. 9 On te rst row appear te left and side variables. On te rst column appear te rigt and side variable wit "lagged dep. variable" representing te lagged dependent variable. All estimations contain time e ects and ave been carried out under te assumption of eteroscedactic residuals. Te time span in Countries in te sample are : Austria, Belgium, Germany, Denmark, Spain, Finland, France, Great Britain, Greece, Ireland, Italy, Neterlands, Portugal, Sweden, USA. 0 Tis conclusion is owever subject to a serious data limitation: tere is no available data on time variations in labor market regulation: labor market regulation indicators are only available on a cross-country base. It terefore constitutes a caveat tat it is still ard to deal wit. 7

8 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 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. 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 e cient 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. 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. However te wage contract rms agree upon wit workers also as an in uence on te tecnology tey invest in. 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 if te rm were to invest in a igly productive tecnology, it would loose te gain in terms of increased borrowing capacity since its productivity in te bad state is very low (due to te correlation between average productivity and productivity volatility) wile it would still pay a premium on its wage bill. Consequently, 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, wage risk and employment risk 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. Equivalently, wen rms adopt a contingent labor compensation sceme, tis reduces te risk premium of its nancial liabilities, teir volume being given. 8

9 te coice to provide workers wit contingent contracts would certainly be costly wile it would not generate any gain for te rm. Terefore rms optimally invest in less risky and less productive tecnologies wen tey provide contingent wage contracts. On te contrary, rms wic propose uncontingent wage contracts coose to invest in more volatile and terefore more productive tecnologies. Put di erently, wen rms can coose te optimal degree of insurance tey provide workers wit, ten tere exists a complementarity between providing more contingent wage contracts and investing in safer, yet less productive tecnologies. As a result, labor market exibility is associated wit iger growt troug more rapid capital accumulation. But it also associated wit lower growt troug lower average total factor productivity. Now from a macroeconomic point of view, te capacity of rms to coose teir optimal wage contract creates a strategic complementarity. On te one and, rms borrowing capacity is negatively related to te degree of wage insurance in contracts provided to workers rst because transferring risks to workers raises rms pro ts before debt repayments and second because rms invest in less productive and less risky projects. On te oter and, assuming tat workers do not ave access to insurance markets, i.e. instruments to edge labor income uctuations, and assuming tat workers consumption is not perfectly substitutable in time, ten due to precautionary motives, workers savings are negatively related to degree of wage insurance in contracts provided by rms. Under te above assumptions, workers prefer to increase teir ex ante savings so as to bene t from a larger ex post consumption in case a bad state of nature appens. Terefore bot rms demand for capital and workers savings are decreasing functions of wage insurance and te economy can end up wit two stable equilibria. In te rst equilibrium, rms provide uncontingent wage contracts to workers and invest in relatively productive tecnologies. As a result, tey face tigt borrowing constraints. Because rms provide wage insurance to workers and invest in relatively productive tecnologies, workers savings are low due to te absence of wage income uctuations and deu to relatively ig future labor income. If te capital supply i.e. workers savings, is su ciently low, ten te equilibrium interest rate is large. Wit a large equilibrium interest rate rms optimally provide an uncontingent wage contract because tey do not need to borrow a large amount of capital due decreasing marginal returns on capital. Consequently, tey also invest in 9

10 relatively risky and productive tecnologies. In te second equilibrium, rms provide contingent wage contracts to workers and invest in relatively unproductive tecnologies. As a result, tey face slack borrowing constraints. Because rms provide workers wit contingent contracts and invest in relatively unproductive tecnologies, workers savings are ig due to te presence of wage income uctuations and due to relatively low future labor income. If te capital supply i.e. workers savings, is su ciently large, ten te equilibrium interest rate is low. Wit a low equilibrium interest rate rms optimally provide a state contingent wage contract because tey need to borrow a large amount of capital due to decreasing marginal returns on capital. Consequently, tey also invest in relatively safe and unproductive tecnologies. However wen te economy exibits multiple equilibria, we sow tat bot te Pareto optimal equilibrium and te ig growt equilibrium correspond to te low exibility-ig insurance equilibrium..3. Related literature. To be written..4. 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. 0

11 . 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... 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+ ) (.) 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 (.) 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 (.3).. 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+ ) (.4)

12 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 (.5) 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 A te mean of A s, A = A +A l, te standard deviation of A s, = A A l, and te ratio between te standard deviation and te mean A. Finally we on average more productive tan oters. However tey also embed more volatile socks. > 0: some projects are 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 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 (.6) 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 (.7)

13 .3. 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 claims be tey on te labor or on te capital market at some cost. Assuming tat tese costs are su ciently large, no entrepreneur will nd useful to issue contingent debt contracts because te interest rate carged on suc contracts would be too large compared to te gain in terms of increased borrowing capacity. We terefore focus on risk free debt contracts 3. 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 te totality of teir wage bill and teir debts. In tis case conditional on state s appening, tey earn ;s = ( ) y s (d; 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 + w s l y s (d; l) (.8) 3 See appendix 7.3 for a formal examination of te uselessness of contingent contracts. 3

14 3. Agents decisions. 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. Teir program writes as max (c t ) E s (c s;t+ ) c t;c s;t+ s.t. c s;t+ w s ( + r) c t (3.) At time t, workers ave no resource and are compelled to borrow on te capital market to nance teir consumption. At time t +, tey use teir labor income to nance teir consumption and pay back teir debts. Noting c t te optimal time t consumption, te rst order condition of te problem (3.) ten writes as w ( + r) c t ( + r) c = t w l w w l ( + r) c t ( + r) c (3.) t In te case were =, te last condition simpli es as ( + r) c t = w w + w l w l (3.3) 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 (3.4) 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 4

15 compromise teir future consumption. Te expected indirect utility of consumers ten writes as V w = wl w + r (3.5) 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 (3.6) 3.. Entrepreneurs and lenders optimal consumption coices. 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. More precisely teir program writes as max (b t+ ) (c t+ ) b t+;c t+ s.t. c t+ + b t+ + i;s ki (3.7) were i;s is te return on entrepreneurs or lenders assets. 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+ 5

16 and te optimal consumption c t+ write as b t+ = + i;s ki c t+ = ( ) + i;s ki (3.8) Assuming as previously tat =, entrepreneurs and lenders expected indirect utility ten writes as V e = E + i;s ki (3.9) 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 A () tey want to invest in 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 ) = A () (k i + d i ) l i Ew s l i ( + r) d i (3.0) 6

17 Te solution to tis problem ( rm i optimal demand for labor) ten writes as ( ) A () (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 ) = A () (k i + d i ) l i Ew s l i ( + r) d i d i 8 >< ( ) A () (k i + d i ) li = Ew s s.t. >: 8s, A s (k i + d i ) l i w s l i + ( + r) d i (3.) Introducing rm i optimal labor demand (3.) in bot te objective function (3.0) and te borrowing constraints A s (k i + d i ) l i w s l i + ( + r) d i we can rewrite (3.) as te following problem Ew s A () i maxe (d i ) = A () (k i + d i ) ( + r) d i d i i i (3.3) s.t. 8s, Ew s A () A s ( ) A() Ew s w s (k i + d i ) ( + r) d i Tere are ten two di erent cases: if A () Ew s A () 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 te i labor contract nor on te tecnology cosen. On te contrary wen A () Ew s A () > + r ten rm i optimal expected pro ts write as A () E = ( + r) Ew s ( )A() i A j ( ) wj Ew s A () i A j ( ) wj Ew s A () i ( + r) k i were j is te state of nature for wic te borrowing constraint is binding: j = arg min A p ( ) w p A () p Ew s 7

18 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 > + Ten rms expected pro ts write as E (; ) = + ( ) + ( ) ii + + +r A() ii ( + r) k i w ( )A() + 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. As long as log (A ()) is concave is, te optimal tecnology is suc tat is a decreasing function of te di erence w w l. Proof. c.f. appendix 7. for a proof of proposition. As concerns proposition, te rst order condition 8

19 determining te optimal wage contract writes as + r w + A () ( ) A () ( ) 4 + i3 5 = wile te rst order condition determining te optimal tecnology writes as + r w + A () ( ) A () 4 + A0 () A () + ( ) + i3 5 = Terefore rms individually coose wage contracts and tecnologies suc tat + r w A () A () A 0 () A () = 4 4 i A0 () + ( ) = ( ) A () Ten as long as A0 () A() is a decreasing function of, i.e. as long as log (A ()) is a concave function of, te rst condition de nes a positive relationsip between and wile te second condition de nes a negative relationsip between and. Tese two conditions terefore determine a unique couple ( ; ) wic maximizes rms expected pro ts. δ large interest rate low interest rate η 9

20 Figure 5: Firm optimal strategies in partial equilibrium. 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. Let us 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 constraint is binding. Ten on te one and tere is a strictly positive cost to being unable to borrow more capital. On te oter and providing contingent wage contracts could elp increase te volume of capital it is possible to borrow 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 on 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 te igly productive tecnology is very unproductive 0

21 in te case of a bad sock. Terefore rms prefer to invest in low productivity tecnologies wen tey provide exible labor compensation contracts. 4. Te general equilibrium of te economy. 4.. 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 = Ew s ( )A() ) A () (ki + d i ) Ew s A l ( ) A () i + A l ( ) A () 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 i A l + ( ) A () = + + i ( + r) A l ( ) A () Ew s ( )A() i k 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

22 Ew s is ten equal to te expected marginal productivity of labor Ew s = ( ) A () (k + d) and te uncontingent wage rate writes as w = + ( ) A () (k + d) (4.) 4.3. 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 ( ) A () + (k + d) + + r (4.) were te aggregate volume of capital d rms borrow at te general equilibrium of te economy is suc tat ( + r) d = A l ( ) A () (k + d) (4.3) + Finally rm optimal tecnology is suc tat A 0 () A () = 4 4 (4.4) and te optimal labor contract rm propose to workers veri es + r w + A () ( ) A () 4 + A0 () A () + ( ) + i3 5 = (4.5)

23 Proposition. 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 (4.5) and (4.4) 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.) and (4.3) are veri ed. Proof. Evident. Corollary. Te equilibrium wage rate on te labor market w is suc (4.) is veri ed. Using tese last expressions and assuming tat A () = + a wit a <, te optimal labor contract veri es + a " ( ) + + " a + + ( ) ## 4 = (4.6) Proof. Introducing te expression for rms optimal tecnology (4.4) and for te equilibrium wage rate on te labor market (4.) into te rst order condition determining te individual optimal labor contract (4.5), we end up wit (4.6). α/ η l Hig Flexibility Equilibrium η Low Flexibility Equilibrium η Figure 6: Optimal labor contracts in general equilibrium. 3

24 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 tecnologies. Workers ave a low contemporary consumption and rms borrow te bulk of available capital 4

25 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 7: Equilibrium of te capital market. 5

26 5. 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 (4.) and (4.) te di erent individual welfare functions V i write as V w = V f = V l = ( ) A () (k + d) + ( + r) A () (k + d) + ( ) + A () (k + d) ( ) + + Terefore te utilitarian social welfare criterion can write as W util = + + p + r + ( + ) A () (k + d) (5.) Proposition. 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 6

27 (4.) k = + ( + ) A () (k + d) + r Terefore from expression (5.) te utilitarian social welfare can be simpli ed as W util (; r) = i + p + + r i k p + r (5.) 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. It elps in particular get rid of te e ects tat play in opposite direction. Form expression (5.), it is obvious tat a larger interest rate r increases every ting else equal, te utilitarian social welfare criterion. As to te e ect of labor market exibility, te utilitarian social welfare criterion can be written as W util (; r) = N () k p + r 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 is maximized at te low labor market exibility equilibrium. Te intuition for tis result is fairly simple: social welfare is maximized at te low exibility equilibrium because tis equilibrium allocates risk to agents wic are te least risk averse in te economy and capital to tose wic ave no oter means to raise teir utility. Put di erently from a social point of view, te capital distribution between workers and rms is irrelevant. On te contrary te productivity level of rm 7

28 investments is relevant and raises social welfare because it raises bot rms pro ts and workers labor income. Since rms make more productive investments wen labor market contracts are less exible, it is natural tat te Pareto optimal equilibrium is te low labor market exibility equilibrium. Now if we turn to te egalitarian social welfare criterion, it writes as W egal = max min ( + ; ( + r) + + ; + ) ( + ) A () (k + d) wic according to te capital market equilibrium condition (4.) writes as W egal = max min + ; (+r) + + ; i i + r k To be continued. 8

29 6. 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 4. 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. Noting k t te capital stock in te economy at te beginning of period t, and k s t+ te capital stock in te economy at te beginning of period t wen state s as appened at time t, te low of motion of te capital stock writes as k s t+ = s (k t ) + ( + r) k t were s (k t ) represents rms pro ts conditional on state s and ( + r) k t lenders pro ts. If te bad state of nature appens at time t, te capital stock at te beginning of period t +, k l t+ terefore writes as k l t+ = A l () k t + d ( ) A () + k t + d + (6.) Te rst part of te rigt and side A l () k t + d represents total output in te economy. Te second 4 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. 9

30 part of te rigt and side + ( ) A () k t + d represents te wage bill distributed to workers. Te nal part of te rigt and side + represents te sare of te wage bill workers dedicate to beginning of period loans repayments. Finally entrepreneurs and lenders bequest a sare = of teir nal wealt and consume a sare =. Similarly if te good state of nature appens at time t, te capital stock at te beginning of period t +, k t+, writes as k t+ = A () k t + d ( ) A () + k t + d + (6.) Tis expression is similar to te above one apart two distinct features. First te tecnological sock wic is good in te latter case and bad in te former case. Second te sare of te wage bill workers dedicate to consumption wic is large is te latter case and low in te former case. We ten establis te following result as regards expected growt. Proposition. Noting = +, te average growt rate of te economy s capital stock writes as E log ks t+ ( ) A () + = log + log ( ) log k t (6.3) k t + () log + + () log [ ] were and () veri es, d k = (6.4) A 0 () A () = 4 Proof. Using te capital market equilibrium condition (4.) and te equilibrium borrowing constraint for rms (4.3) it is straigtforward to obtain te equilibrium rm debt equity ratio (6.4). Ten plugging (6.4) into capital accumulation expressions for eac state of te world (6.) and (6.), te expected capital growt rate expression (6.3) becomes immediate to obtain. 30

31 Te expected growt expression (6.3) can be decomposed along classical growt determinants on te one and and labor contracts speci c e ects on te oter and. Among te classical determinants of growt, appears te standard catc-up e ect: due to decreasing marginal returns to capital, growt in te capital stock is bound to go to zero as te economy accumulates capital in te absence of any oter source of growt. "!# E log k s;t+ ( ) ( ) = log A () + log k t {z } ( ) log k t {z } {z } Catc-up e ect TFP e ect TFI e ect + () log + + log [ ] {z } Inter-temporal e ect Now apart from te standard catc up e ect, rms coices as to te optimal wage contract and te optimal tecnology tey adopt generate tree di erent sources of growt. Wen rms adopt more exible wage contracts, tat elps tem increase te volume of capital tey can borrow. Hence te volume of rms investment is larger wit more exible labor contracts. Te total factor input e ect of labor market exibility is terefore positive and te economy grows faster wit more exible labor contracts. On te contrary wen rms adopt more exible labor contracts, tey also optimally coose to invest in less productive tecnologies. Hence te total factor productivity e ect of labor market exibility is negative and te economy grows slower wit more exible labor contracts. Finally tere is a tird e ect: wen rms propose more exible labor contracts, workers reduce teir beginning-of-period consumption and increase teir average end-of-period consumption. Terefore wen rms propose more exible labor contracts, te volume of capital workers borrow at te beginning of te period is reduced wile te volume of consumption at te end of te period is increased. Now since workers need to pay back loans contracted at te beginning of period, workers beginning of period consumption acts as an investment wose productivity is equal to te interest rate r. On te contrary, workers end-of-period consumption acts to reduce te volume of capital in te economy at te end of te period. Terefore more exible labor market will tend to reduce capital accumulation because workers are less willing to borrow and more willing to rely on teir labor income to nance teir consumption. Tis is te inter-temporal e ect. 3