The Macroeconomics of Credit and Labor Markets Imperfections Etienne Wasmer, Philippe Weil

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Etienne Wasmer, Philippe Weil. The Macroeconomics of Credit and Labor Markets Imperfections. American Economic Review, American Economic Association, 2004, 94 (4), pp.944-963. hal-01020132

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HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Macroeconomics of Labor and Credit Market Imperfections

By ETIENNE WASMER AND PHILIPPE WEIL*

Credit market imperfections influence the labor market and aggregate economic activity. In turn, macroeconomic factors have an impact on the credit sector. To assess these effects in a tractable general-equilibrium framework, we introduce endogenous search frictions, in the spirit of Peter Diamond (1990), in both credit and labor markets. We demonstrate that credit frictions amplify macroeconomic volatility through a financial accelerator. The magnitude of this general-equilibrium accelerator is proportional to the credit gap, defined as the deviation of actual output from its perfect credit market level. We explore various extensions, notably endogenous wages. (JEL J64, G24, E51)

Labor market frictions and wage rigidities are the development of new sectors and products. not the only deviation from the Arrow-Debreu Note, however, that the causality between fi- paradigm. Modern economies are plagued with nance and macroeconomic activity might run in a variety of informational imperfections in fi- reverse. For instance, Joan Robinson (1952, p. nancial markets. These imperfections, which 86), cited by Ross Levine (1997), suggests that may stem from moral hazard, adverse selection, “where enterprise leads, finance follows.”2 On and search externalities, are relevant not only the other hand, financial intermediation gener- for corporate finance—an area in which they ates macroeconomic volatility. In particular, have extensively been studied—but also for Nobuhiro Kiyotaki and John Moore (1997) and macroeconomics. This is, of course, the foun- Bernanke et al. (1999) argue that a “financial dation of the credit channel view of the trans- accelerator” amplifies macroeconomic fluctua- mission of monetary policy: new businesses, tions as the value of collateral varies over the having poor access to credit markets, are the cycle. primary victims of monetary contractions.1 The objective of this paper is to build a sim- Beyond monetary issues, the financial sector ple macroeconomic model of credit and labor plays a crucial role in the determination of eco- market imperfections which sheds light, in a nomic activity. On the one hand, finance con- tractable way, on the interaction between mac- tributes, in a Schumpeterian view of growth, to roeconomic activity and finance, and to demonstrate the existence of a financial accelerator based on the general-equilibrium feedback be- * Wasmer: De«partement des sciences e«conomiques, Uni- tween credit and labor markets. To that effect, versite« du Que«bec a` Montre«al, Case postale 8888, Succur- we develop a theory of job creation and job sale Centre-Ville, Montre«al (Que«bec), Canada H3C 3P8, destruction in an environment in which new ECARES (ULB), GAME (Universite« de Metz), CEPR, and entrepreneurs have no wealth of their own, and IZA (e-mail: [email protected]); Weil: European Center for Advanced Research in Economics and Statistics (Universite« Libre de Bruxelles), 39 Avenue Franklin D. Roosevelt, CP114, Brussels 1050, Belgium, IEP Paris, 2 There have been several attempts to clarify empirically CEPR, and NBER (e-mail: [email protected]). The the links between finance and growth. Robert G. King first version of this paper was written in November 1998, and Levine (1993) examine cross-country evidence on the and presented at the CEPR European Summer Symposium role of financial intermediaries in capital accumulation. on Macroeconomics (Sintra, May 1999). We are grateful to Raghuram G. Rajan and Luigi Zingales (1998) argue that anonymous referees for their useful comments and sugges- causality goes both ways, but establish that the growth of tions. We thank the Belgian Fonds national de la recherche employment due to the number of establishments is twice as scientifique for financial support. large as the growth due to existing firms. This suggests that 1 See, for instance, Ben S. Bernanke and Mark Gertler financial intermediaries indeed mitigate informational (1989) and Gertler and Simon Gilchrist (1994). asymmetries, and thus contribute to growth. 944 VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 945 must raise funds on imperfect credit market Furthermore, Mitchell A. Petersen and Rajan before they enter the labor market to search for (2002) document how “information closeness” workers. impinges on the efficiency of credit markets. To introduce credit market imperfections, we In addition, the survey of Levine (1997, p. use a modeling strategy that has proved tractable 715) indicates that “the durability of the bank- and fruitful in thinking about the macroeconomics borrower relationship is valuable.” We take of labor markets: search theory. We focus on the this as evidence of match specificity which is credit and labor rationing that arises, when agents most simply modeled as the outcome of a are imperfectly aware of economic opportunities, search-matching process. Finally, Giovanni from the stochastic matching between creditors Dell’Ariccia and Pietro Garibaldi (2000) argue and borrowers, and between workers and entre- that matching models of the capital market are a preneurs. Thus, we take a leaf from the macro- promising way to rationalize the empirical evi- labor literature, and follow, in the credit market, dence on gross credit flows. the lead taken by Christopher A. Pissarides (2000) Our symmetrical model of credit and labor in the labor market. Accordingly, we model cap- market imperfections is parsimonious, yet rich. ital market imperfections and labor market imper- It enables us to show, in a framework reminis- fections in a perfectly symmetric way, and cent of IS/LM, that financial imperfections in- summarize at an abstract level the properties of the crease volatility, in the sense that they magnify credit and labor matching processes by a pair of the response of the economy to exogenous matching functions. shocks. This amplification mechanism is not The benefit of our symmetric, search-theoretical based, as it is in Bernanke et al. (1999) or formalization is that it eschews the microeco- Kiyotaki and Moore (1997), on fluctuations in nomic detail associated, often at the cost of sub- the value of collateral, but instead on a general- stantial complexity, with macroeconomic models equilibrium interaction: the state of the credit that introduce credit market imperfections through market affects the state of the labor market, but moral hazard and/or adverse selection.3 the state of the labor market itself affects the Several pieces of empirical evidence can be state of the credit market. We summarize this adduced for our formalization of credit markets interaction by providing a simple measure of the imperfections. David G. Blanchflower and An- financial accelerator, which depends on the drew J. Oswald (1998) report that raising capital credit gap, defined as the percent deviation of constitutes the principal difficulty encountered actual output from the level that would prevail by potential entrepreneurs. For instance, 20 per- absent credit market imperfections. cent of the respondents of the 1987 U.K. Na- Beyond our basic framework, we extend the tional Survey of the Self-Employed report that model to endogenous wages and to endogenous where to get finance was the biggest obstacle to destruction. In the former case, the equilibrium self-employment.4 On top of that, 51 percent of outcome is crucially affected by the institutional the participants in the British Social Attitudes arrangement that govern bargaining between Survey who say they failed to become self- financiers, entrepreneurs, and workers—the employed report, over the period 1983Ð1986, central organizational problem of capitalism. that lack of capital or money was the main We establish, for instance, that financiers and culprit.5 Since 40 to 60 percent of jobs are held bankers have a common incentive to inflate the in small firms (less than 100 employees),6 firm’s debt beyond what is strictly necessary in a theory of job creation and unemployment order to decrease the wage that will ultimately must deal with difficulties in locating credit. be negotiated between entrepreneurs and workers,7 but that incentive compatibility considerations limit the use of debt as a strategic 3 See, for instance, Joseph E. Stiglitz and Andrew Weiss variable. In the latter extension, we establish that (1981) for microeconomic foundations, and Carl Shapiro endogenous job destruction generates financial and Stiglitz (1984), or Philippe Aghion et al. (1999), for macroeconomic applications. 4 Blanchflower and Oswald (1998), Table 8. 5 Blanchflower and Oswald (1998), Table 6. 6 These numbers are based on industry and market ser- 7 See Stephen G. Bronars and Donald R. Deere (1991) vices. See OECD (1994). and Enrico C. Perotti and Kathryn E. Spier (1993). 946 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004 fragility, in the spirit of Wouter J. den Haan et matching workers to firms (which in principle al. (2003). involves heterogeneity, together with informa- The paper is organized as follows. Section I tional difficulties) into a simple constant-returns- introduces the model. Section II presents the to-scale technology h(ᐁ, ᐂ) that “produces” a model and derives the long-run equilibrium flow of matches between firms and workers with exogenous wages. Section III highlights with two “inputs:” job vacancies ᐂ posted by the existence of a financial accelerator. Section firms, and available (i.e., unemployed) workers IV extends the basic model by examining the ᐁ.9 Measuring labor market tightness (from the effects of endogenous wages, and of endoge- point of view of firms) by the index ␪ ϭ ᐂ/ᐁ, nous destruction. The conclusion summarizes the instantaneous probability that an entrepre- and outlines directions for future research. neur will find a worker is thus

I. The Model h͑ᐁ, ᐂ͒ ϭ h͑␪Ϫ1,1͒ ϵ q͑␪͒. In this section, we first describe the three ᐂ types of agents in our economy. We then characterize optimal behavior during the four stages The tighter the labor market, the less probable it of the life of a firm. is that an entrepreneur meets an available worker (qЈ(␪) Ͻ 0). A. Entrepreneurs, Workers, and Financiers Financiers and Entrepreneurs.—Since an There are three types of agents: entrepre- entrepreneur must expend resources to search neurs, workers, and financiers. Entrepreneurs for a worker before production even starts, the have ideas but they cannot work in production, entrepreneur must be able to finance his recruit- and have no capital of their own. Workers, ment efforts. Traditional models of the labor who have neither entrepreneurial skills nor market, such as Pissarides (2000), focus solely capital, toil on the production line, and trans- on labor market frictions, and thus assume away form the entrepreneurs’ ideas into output. Fi- credit market frictions. As a result, entrepre- nally, financiers have access to the financial neurs have no problem whatsoever financing resources required for the concretization of the their search for a worker, whether they finance entrepreneurs’ ideas, but have no ideas and can- it on their own, or borrow the cost of posting not work on the production line.8 In the real vacancies on a perfect capital market. But if world, there is a bit of the entrepreneur, the credit markets are imperfect, an entrepreneur worker, and the financier in each agent, and with an idea but without any capital will en- people can choose in which activity they want counter some impediments when he turns to to specialize. In our model, however, this is not credit markets to find the funds required to post the case, and entrepreneurship, working, and a vacancy.10 financing are assigned, for simplicity, to mutu- We could try, in line with the rest of the ally exclusive and exogenously assigned types of agents.

Entrepreneurs and Workers.—Producing 9 We impose, as usual, that marginal products in match- output in a firm requires a team of one entre- Ͼ Ͼ Ͻ ing are positive but decreasing: h1 0, h2 0, h11 0, Ͻ preneur and one worker. There are labor market h22 0. Because of homogeneity, there is no scope for frictions, so that entrepreneurs and workers can- on-the-job search. 10 not meet easily. An entrepreneur must search This sequencing also captures the well-documented fact that financiers often play a crucial role in the compo- for the worker that will enable him to carry out sition of the management team of a firm, and that they thus his idea. We adopt the now standard device of have an essential role to play in production. Studying the Pissarides (2000), and subsume the process of reverse sequencing—labor search, then credit search—is interesting only in cases where credit frictions are relatively unimportant (e.g., the start-ups in the Silicon Valley where skilled labor was much scarcer than venture capital). Ac- 8 We will hereafter interchangeably refer to financiers or cordingly, we focus exclusively in this paper on the “credit bankers. search, then labor search” model. VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 947 literature,11 to describe in detail the microeco- B. Four Stages in the Life of a Firm nomic nature of these credit market frictions. Instead, we note that credit markets frictions do The life of a firm can be decomposed into not differ much from those encountered in labor four successive stages of stochastic length: fund markets: moral hazard, heterogeneity, and spec- raising, recruitment, creation, and destruction. ificity are the hallmark of both credit and labor markets imperfections. As a result, we chose to ● Fund-raising. In stage 0, prospective entre- describe credit market frictions symmetrically preneurs are looking, at a flow search cost c, to the way we model labor market frictions, and for a bank willing, in exchange for future introduce a credit market matching function.12 repayments, to finance the posting of a job Formally, let Ꮾ be the number of bankers vacancy. In line with the assumption that looking for entrepreneurs, and denote by Ᏹ the entrepreneurs have no wealth, the cost c is number of entrepreneurs looking for financing. assumed to be nonpecuniary, e.g., a private Each of these Ᏹ entrepreneurs is searching for sweat cost reflecting the time it takes an en- one the Ꮾ available bankers. trepreneur to find a financier. At the same The flow of loan contracts successfully time, financiers are searching for clients at a signed between financiers and entrepreneurs is flow search cost k. The probability of a determined by the constant-returns-to-scale credit match, and of moving on to the recruitment market matching function m(Ꮾ, Ᏹ).13 From the stage, is p(␾). point of view of firms, credit market tightness ● Recruitment. In stage 1, entrepreneurs have can be measured by ␾ ϭ Ᏹ/Ꮾ. Equivalently, found a financier and are looking (at a flow 1/␾ is an index (for firms) of the liquidity of the search cost ␥ borrowed from their financier) credit market.14 for the worker that will enable them to start The instantaneous probability that an entre- operating their firm. The probability that an preneur/borrower will find a suitable financier is entrepreneur meets a worker, and that the thus financing stage ends, is q(␪). The repayment ␳ that the entrepreneur will make to the en- m͑Ꮾ, Ᏹ͒ trepreneur once the firm starts operating is ϭ ͑␾Ϫ1 ͒ ϵ ͑␾͒ Ᏹ m ,1 p , negotiated between the financier and the entrepreneur. which is decreasing in credit market tightness ● Creation. In stage 2, the firm has found a (pЈ(␾) Ͻ 0). worker and is generating exogenous flow output y. It uses this output to pay its workers an exogenous wage ␻,15 and to pay back to its 11 See, for instance, Roger Farmer (1985) or Ricardo J. financier a flow amount ␳ as long as the Caballero and Mohamad Hammour (1998). productive unit operates. 12 Dell’Ariccia and Garibaldi (2000) and den Haan et al. ● Destruction. In the final stage 3, the match (2003) also represent credit market frictions using a matching function, but they do not focus on the labor market. Den between firm and worker is destroyed. We Haan et al. (2003) investigate the average distance between assume that destruction is exogenous—i.e., borrowers and lenders, and justify credit matching functions that the transition from stage 2 to 3 occurs by the relevance of geographical considerations in financing with a probability s.16 decisions. Finally, Petersen and Rajan (2002) argue empirically that the IT revolution and the Internet have substantially affected the geography of financial relationships, a Throughout, we assume that their are no com- fact which again is consistent with the existence a credit mitment problems for financiers, firms, or market matching function. workers. All agents are risk neutral, with dis- 13 We impose m Ͼ 0, m Ͼ 0, m Ͻ 0, m Ͻ 0. 1 2 11 22 count rate r Ͼ 0. Output, as well as wages and 14 Our concept of liquidity is the willingness of financiers to part from their resources to lend them to firms. It is similar to the notion of liquidity used in stock markets. There are of course other (more aquatic ...) meanings of liquidity studied in the literature—such as the volume of 15 We study in subsection A what happens when the funds available for lending. For a leading analysis of liquid- wage is instead negotiated between entrepreneurs and ity as the availability of financial instruments able to trans- workers. fer wealth across periods, see Bengt Holmstrom and Jean 16 We introduce endogenous destruction in sub- Tirole (1998). section B. 948 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004

ϭ Ϫ ␻ Ϫ ␳ ϩ ͑ Ϫ ͒ all search costs, are assumed for simplicity to be (6) rE2 y s E3 E2 . constant through time.17 The entrepreneur expends a flow sweat cost c in ϭ The Value of a Bank.—Call Bi, i 0, 1, 2, the first stage, nothing during the recruitment 3, the value of a bank in the fund-raising, re- phase (the cost of posting a job vacancy is borne cruitment, creation, and destruction phases. Fo- by the financier), and receives a cash flow y Ϫ cusing for the moment on long-run equilibria ␻ Ϫ ␳ in the operating stage (output net of wage (we will discuss the short run below), the Bell- and financial costs). We again assume that de- man equations describing the evolution of the struction with probability s of the match be- steady-state values of the bank over these four tween firm and worker destroys all specificity, ϭ 19 stages are: so that E3 E0. ϭ Ϫ ϩ ␾ ͑␾͒͑ Ϫ ͒ (1) rB0 k p B1 B0 , C. Bargaining Between the Financier and the Entrepreneur ϭ Ϫ␥ ϩ ͑␪͒͑ Ϫ ͒ (2) rB1 q B2 B1 , The contract between financier and entrepre- ϭ ␳ ϩ ͑ Ϫ ͒ (3) rB2 s B3 B2 . neur is negotiated when they meet. The terms of the contract are (i) that the bank will finance the The financier suffers a cash outflow k in the recruitment cost of the entrepreneur (␥ per unit fund-raising stage while it is looking for a cli- of time) for as long as it takes to find a worker, ent. It pays out a flow ␥ in the recruitment stage, and that, in exchange, (ii) the entrepreneur will while it finances the entrepreneur’s posting of a repay the financier a constant amount ␳ per unit job vacancy. Once the firm is created, the bank of time as long as the firm operates.20 Note that enjoys a cash inflow ␳ that corresponds to the we refer to this financial contract as a “loan” repayment by the firm of its debt. We assume, although it has equity-like aspects. The return to for simplicity, that the destruction of the match the financier depends on how quickly the firm between firm and worker with probability s finds a worker and on how long the firm will entails a loss of the specificity of all matches, so operate. ϭ 18 that B3 B0. Financier and entrepreneur share the surplus of their relationship according to a generalized The Value of an Entrepreneur.—Let Ei, Nash bargaining rule i ϭ 0, 1, 2, 3, denote the steady-state value of an ␳ ϭ ͑ Ϫ ͒␤͑ Ϫ ͒1 Ϫ ␤ entrepreneurial unit in the fund-raising, recruit- arg max B1 B0 E1 E0 , ment, creation, and destruction phases. It evolves as follows: where ␤ ʦ (0, 1) measures the bargaining power of bankers in the credit relationship.21 It ϭ Ϫ ϩ ͑␾͒͑ Ϫ ͒ ␳ (4) rE0 c p E1 E0 , follows that the stipulated loan repayment must satisfy ϭ ͑␪͒͑ Ϫ ͒ (5) rE1 q E2 E1 , ␤͑ Ϫ ͒ ϭ ͑ Ϫ ␤͒͑ Ϫ ͒ (7) E1 E0 1 B1 B0 .

17 Were output and wages to grow exogenously at a 19 ϭ common rate, search costs (which represent the opportunity This assumption is symmetrical to the condition B3 cost of time) would have to grow at the same rate. It is thus B0 we imposed above, and is subject, mutatis mutandis, to straightforward to extend our model to allow for balanced the caveat of footnote 18. growth. 20 An alternative to this loan contract would be a loan 18 ϭ An alternative formulation would impose B3 B1,so schedule that would make repayment to the financier con- that the value of the bank remains positive after the disso- tingent on accumulated debt and on the time it took the lution of the match between firm and worker. This would entrepreneur to find a worker. This alternative contract substantially complicate the model without affecting its would force us to introduce ex post heterogeneity between main insights. This is similar to what happens in labor entrepreneurs—which we want to avoid. matching models when, in spite of free entry, the value of 21 In a Rubinstein game of alternating offers and coun- firms remains positive after the destruction of the match teroffers, the parameter ␤ reflects the relative impatience of when there is, say, a fixed capital stock. the negotiating parties. VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 949

II. Equilibrium the lower ␾* (i.e., the higher the number of available financiers relative to the number of Assume it is costless to set up a bank or a firm entrepreneurs raising funds). Moreover, the less in stage 0. Free entry of financiers and entre- profitable the sharing of the surplus of the credit preneurs on the credit and labor market then relationship is to the bank (low ␤), the tighter ensures that, in equilibrium:22 the credit market (higher ␾*). Remarkably, ␾*, and hence the equilibrium value of the financier ϭ ϭ (8) B0 0 and E0 0. and of the entrepreneur, is constant in equilibrium, and depends only on technological (c and A. Equilibrium Credit Market Tightness k) and institutional (␤) features of the credit market. This feature, which is built by design From the fund-raising stage value functions into the model by our assumptions, allows for a (1) and (4), it follows from reading period 0 convenient recursive solution. Bellman equations backwards in time that B. Equilibrium Financial Contract k (9) B ϭ , 1 ␾p͑␾͒ Banker and entrepreneur split the expected present discounted value of output, net of while wages, that the firm will generate once it starts operating. The stronger the bargaining power of c the bank relative to the firm, the larger the (10) E ϭ . 1 p͑␾͒ equilibrium repayment of the firm to the financier in the production stage: In a less liquid credit market (higher ␾), the equilibrium value of a (matched) financier is PROPOSITION 2: In equilibrium, the repay- lower, while the value of a (matched) firm is ment flow from entrepreneur to financier is higher—as financiers have to search less and firms more when there are more firms relative to ␳ ϭ ␤͑ y Ϫ ␻͒ ϩ ͑1 Ϫ ␤͒͑r ϩ s͒␥/q͑␪ ͒. banks. Since the surplus of the banking relationship PROOF: is split between financier and entrepreneur ac- The proof is by forward substitution of the cording to the sharing rule (7), we immediately Bellman equations. From equations (9) and have: (10), the Bellman equations in the recruitment stage, (2) and (5), imply that, in equilibrium, PROPOSITION 1: In equilibrium, the tight- Ϫ␥ ϩ ͑␪͒ ness of the credit market is q B2 (11) B ϭ , 1 r ϩ q͑␪͒ 1 Ϫ ␤ k ␾* ϭ . ␤ c and ͑␪ ͒ q E2 PROOF: (12) E ϭ . Substitute (9) and (10) into (7). 1 r ϩ q͑␪ ͒ ϭ ϭ The lower the flow cost k for financiers look- Similarly, the “exit” equations B3 B0 0 ϭ ϭ ing for a suitable lender, and the higher the flow and E3 E0 0 imply, from equations (3) cost c for entrepreneurs searching for a banker, and (6), that,

22 ␳ These free-entry conditions are very convenient to (13) B ϭ , obtain closed-form solutions. They are not necessarily real- 2 r ϩ s istic and may not hold if entry is associated to a ﬁxed cost, or if agents are heterogenous. In either case, the simplicity of the solutions we exhibit here would be lost. and, from equations (5) and (6), that 950 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004

y Ϫ ␻ Ϫ ␳ ket tightness ␪* are the solution to the pair of (14) E ϭ . 2 r ϩ s equations k q͑␪͒ y Ϫ ␻ ␥ (15) ϭ ␤ ͭ Ϫ ͮ, By forward substitution of (13) into (11), and ␾p͑␾͒ r ϩ q͑␪͒ r ϩ s q͑␪͒ of (14) into (12), we ﬁnd, using the (equilib- ␤ ϭ Ϫ rium) Nash bargaining condition E1 (1 ␤ ␳ c q͑␪͒ y Ϫ ␻ ␥ ) B1, that the value of must be the one (16) ϭ ͑1 Ϫ ␤͒ ͭ Ϫ ͮ. given in the proposition. p͑␾͒ r ϩ q͑␪͒ r ϩ s q͑␪͒

Once multiplied by the discount factor PROOF: q/[(r ϩ q)(r ϩ s)], the equilibrium Nash bar- Equations (9) and (10) provide us with back- gaining loan contract described in Proposition 2 ward-looking expressions for B1 and E1 that can be interpreted as stipulating that the ex- depend solely on ␾: it is these expressions that pected present discounted value of repay- we read on the left-hand side of equations (15) ments from the entrepreneur to the financier and (16). Now, forward substitutions of equa- is a weighted average of the expected present tion (13) into (11), and of equation (14) into discounted value of the firm’s output net of (12) give us two alternative formulas B1 and E1 wages, and of the expected present discounted that depend on the endogenous parameters ␳ value of the loan made by the financier to the and ␪. Substituting ␳ out of these formulas using entrepreneur, with weights given by the re- Proposition 2, we get alternative expressions for ␪ spective bargaining power of financier and B1 and E1 that depend only on :wefind these entrepreneur. expressions on the right-hand side of equations The stronger the bargaining power of the (15) and (16). Equilibrium requires that the financier in the credit contract negotiation (i.e., backward and forward expressions for B1 and ␤ the larger ), the larger the share of the ex- E1 coincide—whence Proposition 3. pected present discounted value of output net of wages that he can extract from the entrepreneur, To understand this proposition, note that the and the further away the value of the firm’s total surplus value of a job vacancy (to both the repayment from the expected present dis- banker and the entrepreneur) is expected present counted value of what it has borrowed. Finally, discounted value of output net of wages and note that, since qЈ(␪) Ͻ 0, the entrepreneur on search costs,23 i.e., average repays more when labor markets are tight—for it takes on average longer for the firm q͑␪͒ y Ϫ ␻ ␥ ͑␪͒ ϭ Ϫ to find a worker in a tight labor market. (17) V ϩ ͑␪͒ ͭ ϩ ͑␪͒ͮ. Should we conclude from Proposition 2 that r q r s q our model predicts that the equilibrium loan contract depends on the state of the labor market Using equations (9) and (10), the equilibrium condi- ␪ but not on the tightness of the credit market? tions (15) and (16) are just another way of writing ␪ ϭ ␤ ␪ ϭ Ϫ ␤ ␪ No, because, as we shall now see, equilibrium B1 V( ) and E1 (1 )V( ) or that, as itself depends on ␾*. described, the surplus V(␪) is split in proportions ␤ and 1 Ϫ ␤ between banker and entrepreneur. C. Equilibrium Labor Market Tightness As depicted in Figure 1, equation (15) defines ϭ an upward-sloping iso-value (B0 0) locus BB In a free-entry equilibrium, the expected in (␪, ␾) space with a vertical asymptote at ␪៮ search costs that financiers and entrepreneurs defined as the unique solution to the equation incur by entering the credit market must equal V(␪) ϭ 0. If the expected cost of entry for a the expected benefits that they will eventually bank is higher because the credit market is derive from forming a financial relationship. looser (i.e., there are many financiers chasing Therefore: few entrepreneurs), zero profits can only be

PROPOSITION 3: Equilibrium credit market tightness ␾* ϭ [(1 Ϫ ␤)/␤](k/c) and labor mar- 23 See Pissarides (2000). VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 951

FIGURE 1. EQUILIBRIUM CREDIT AND LABOR TIGHTNESS FIGURE 2. MORE EFFICIENT CREDIT MATCHING

maintained by more slack in the labor market free-entry condition for firms in the absence of (i.e., more vacancies relative to unemploy- credit frictions. Our framework thus nests the ment), which shortens the expected duration of Pissarides equilibrium without credit market the recruiting stage. Similarly, equation (16) frictions. How does ␪* compare with ␪៮? The ϭ defines a downward-sloping iso-value (E0 0) answer is provided by inspection of Figure 1, or locus EE in (␪, ␾) space, depicting the trade-off more formally by: for the entering firm between a tighter credit market (which raises the expected cost of COROLLARY 1: Credit market imperfections searching for a bank) and a looser labor market lower equilibrium labor market tightness: ␪* Ͻ ␪៮. (which lowers the expected cost of finding a worker). Consistent with Proposition 2, the BB PROOF: and EE loci intersect at ␾* ϭ [(1 Ϫ ␤)/␤]/[k/c]. From either equation (15) or (16), and using Moreover, Figure 1 shows that existence and Proposition 1, equilibrium labor market tight- uniqueness of equilibrium are easy to guarantee.24 ness satisfies As credit markets become more efficient in matching borrowers and lenders [this can be (18) ␥/q͑␪*͒ ϭ ␥/q͑␪៮ ͒ modeled as an increase in the matching proba- ␾ ␾ bility p( ) at all levels of ], the BB curve c 1 Ϫ ␤ k Ϫ1 shifts down and to the right. As a result, ␪* Ϫ Ͻ ␥ ͑␪៮͒ Ϫ ␤ ͫpͩ ␤ ͪͬ /q . rises, but equilibrium ␾* remains unchanged as 1 c long as c and k remain unchanged and positive. .Figure 2, which illustrates these features, there- Since qЈ٪ Ͻ 0, it follows that ␪* Ͻ ␪៮ fore suggests that policies that shift the EE curve to the right are more effective in raising These results about equilibrium labor market ␪* the stronger credit frictions are. We elaborate tightness translate directly into statements about on this remark in the next section. equilibrium unemployment and gross output, In the limit, as credit matching becomes in- since unemployment declines and gross output stantaneous [p(␾) ϭϩϱfor all ␾], equilibrium rises when ␪ rises.25 The EE/BB curves drawn labor market tightness tends to ␪៮, so that V(␪៮) ϭ in Figure 1 are thus reminiscent of IS/LM, al- 0. This is nothing but the Pissarides (2000) though they rest on very different theoretical foundations: on the horizontal axis, gross output rises with ␪, while on the vertical axis ␾ is a 24 ␾ ␾ ␾ ϭ ␤ Ϫ ␻ ϩ Let B be such that k/[ Bp( B)] (y )/(r s), and ␾ ␾ ϭ Ϫ ␤ Ϫ ␻ ϩ measure of the tightness of credit markets. E be such that c/[p( E)] (1 )(y )/(r s). Figure 1 shows that a necessary and sufficient condition for existence ␾ Ͻ ␾ and uniqueness of equilibrium is B E. We assume that this restriction on the parameters of the model is satisfied. 25 See subsection D for a proof. 952 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004

One might be tempted at this stage to argue that the result that credit frictions raise equilibrium unemployment relative to the Pissarides model is not surprising, and that all we have done is to prove that credit frictions shift the labor demand curve to the left, resulting in more equilibrium unemployment. But the mechanism at work in our model is much richer and subtler. Credit market frictions reduce the number of financiers. This discourages entry by firms, who find it harder to finance themselves. The reduced number of firms in turn discourages financiers from entering the credit market, as it is more difficult for banks to find an entrepreneur. This discourages entry by firms, which discourages entry by finan- FIGURE 3. BEVERIDGE CURVE ciers, and so on. Hence, rather than an inward shift in the labor demand curve, what is really Notes: P ϭ Pissarides equilibrium; W ϭ equilibrium with credit market imperfections. at work here is a financial accelerator stem- ming from general-equilibrium effects. As in Bernanke et al. (1999), credit markets frictions “amplify and propagate shocks to the macro- As a result, u is decreasing in ␪, and so is gross economy.” To be sure, the nature of the am- output (1 Ϫ u)y. Since ␪ ϭ ᐂ/u, the equation of plification mechanism in our double search the Beveridge curve is u ϭ s/[s ϩ (ᐂ/u)q(ᐂ/u)], model is different from the collateral/net worth which can be shown, given our assumptions, to effects at the heart of Kiyotaki and Moore be decreasing and convex. Now, we know that (1997) or Bernanke et al. (1999). Ours is based in the equilibrium with credit market imperfec- on the general-equilibrium interaction between tions ᐂ ϭ ␪*u while ᐂ ϭ ␪៮u in the Pissarides credit and labor markets, while theirs rests equilibrium without credit frictions. Equilib- on the equilibrium link between current and rium job vacancies and unemployment with and future credit markets. But both mechanisms without credit frictions are thus determined in point out that a general-equilibrium analysis Figure 3 by the intersections W and P of the of the impact of credit frictions, rather than Beveridge curve with these two rays from the the study of shifts in the labor demand curve, origin. is required to assess the effectiveness of economic policy. We return to this theme in III. A Financial Accelerator Section III. We have suggested above that credit market D. A Beveridge Curve Representation frictions amplify shocks in the economy. We now document in two ways the existence in our To characterize the effects of credit market model of a financial accelerator. First, we return imperfections on job vacancies and unemploy- to the long-run equilibrium described in the ment, we can represent equilibrium as the inter- previous section and describe, both qualitatively section of the Beveridge curve and of the ray and quantitatively, how this accelerator oper- representing equilibrium labor market tightness ates. Second, we establish that macroeconomic in the (ᐁ, ᐂ) plane. volatility is amplified even further in the short Let u denote the unemployment rate. run (i.e., before entry by banks takes place) by Normalize the mass of workers to 1, so that credit market frictions. u ϭ ᐁ. In steady state, flows in and out of the unemployment pool must equilibrate, so A. The Long Run that We first show that the amplitude of the re- (19) s͑1 Ϫ u͒ ϭ ␪q͑␪͒u. sponse of shocks to search costs and profits is VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 953 magnified by the existence of credit market frictions. We will exhibit this long-run financial accelerator graphically, and then quantify its magnitude.

Qualitative Comparative Statics.—Let us look first at the effect on equilibrium of higher search costs for banks, of lower search costs for firms, and of improved firms’ net output.

Higher Search Costs for Banks.—What happens if the banks’ search cost k rises? Inspection of equations (15) and (16) reveals that the BB curve shifts up and to the left (for any given level ␪, a higher k induces exit by financiers and FIGURE 4. INCREASE IN NET OUTPUT y Ϫ ␻ raises ␾), while the EE curve stays put (firms entry decisions are not directly affected by k). to search when y Ϫ ␻ is higher, so that the EE As a result, the credit market tightens and the curve shifts out and to the right. At the same labor market slackens. The economic mecha- time, for any given labor market tightness, more nism underlying this result is the following: financiers are willing to search when y Ϫ ␻ is higher search costs make some financiers exit high, so that the BB curve shifts down and to the credit market. This induces some firms to the right. Figure 4 depicts the equilibrium: exit, which lowers ␪ and mitigates the tighten- credit market tightness is ultimately un- ing of the credit market—through a move along changed,26 but the labor market tightens and the EE curve. If we think of higher search costs unemployment declines. for banks as being induced by tighter monetary Examination of Figure 2 shows that the effect policy or more restrictive credit conditions, of these cost or profit shocks on ␪ is amplified these comparative statics are quite similar qual- by credit market frictions as we move away itatively to that associated with contractionary from the Pissarides equilibrium. The magnitude monetary policy in the IS/LM model. of the financial accelerator thus depends on the strength of credit market frictions. Lower Credit Search Costs for Entrepre- neurs.—What happens if the firm’s fund-raising Measuring the Financial Accelerator.—To cost goes down? Lower credit search cost c for get a quantitative feeling for the size of the firms induces entry of new entrepreneurs at any effects we have been discussing, we now log- given level of credit market tightness: the EE linearize the main equations of the model around curves shifts out and to the right. The banks’ equilibrium. We proceed under the simplifying entry decisions are not directly affected by c,so assumption that the discount rate r is zero.27 that BB does not move. In equilibrium, entry of new firms tightens Labor Market Tightness.—Call both the credit and labor markets (a move along the BB curve), but the tightening of the credit ⌸ ϭ ͑y Ϫ ␻͒/͑r ϩ s͒ ϭ ͑y Ϫ ␻͒/s market is mitigated by the entry of new financiers trying to take advantage of the increase in the expected present discount value of output net the number of entrepreneurs looking for credit. of wages at the time the firm meets its worker. Denote by xˆ the proportional deviation of a vari- Improvement in the Firm’s Profits.—Imagine able x from its equilibrium value x*, i.e., xˆ ϭ output net of wages y Ϫ ␻ increases. This (x Ϫ x*)/x*. Call ␧ and ␩ the elasticities of the credit improved profitability directly affects the entry and labor matching functions at equilibrium: decisions of both firms and financiers by raising the size of the surplus that entering banks and firms will eventually split. As a result, for any 26 This is a result of Proposition 1. given credit tightness ␾, more firms are willing 27 The generalization to the case r Ͼ 0 is uninstructive. 954 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004

qЈ͑␪*͒␪* pЈ͑␾*͒␾* Unemployment.—Using equation (19), the ␩ ϵ Ϫ , ␧ ϵ Ϫ . ϭ q͑␪*͒ p͑␾*͒ unemployment rate and employment rate e 1 Ϫ u respond to changes in ␪ according to: Under the assumptions we have made on the Ϸ Ϫ͑ Ϫ ͒͑ Ϫ ␩͒␪ˆ matching functions, ␧ ʦ (0, 1) and ␩ ʦ (0, 1). (22) uˆ 1 u* 1 , Elementary algebraic manipulations of equation (15), using Proposition 1,28 tell us how equilib- (23) eˆ Ϸ ͑1 Ϫ e*͒͑1 Ϫ ␩͒␪ˆ . rium labor market tightness responds to changes in c, k, ␥, and ⌸ when r ϭ 0: As in the Pissarides model, the proportional effect of labor market tightness on the (un)em- 1 ployment rate thus depends on the level of em- ␪ˆ Ϸ ͑ ϩ ␮͒⌸ˆ (20) ␩ ͭ 1 ployment—areflection of the convexity of the Beveridge curve. A similar result of course holds for gross output per head, which is pro- Ϫ ␮͓␧kˆ ϩ ͑1 Ϫ␧͒cˆ͔ Ϫ ␥ˆ ͮ, portional to 1 Ϫ u. Now note that, for ␪៮ close to ␪*, a first-order ␪ where Taylor expansion of equation (21) around * yields ␮ Ϸ ␩␪ˆ*. Combining this approximation with equation (23) hence provides us with a way B q͑␪*͒ ␮ ϭ 1 ϭ Ϫ Ն to quickly gauge empirically the magnitude of (21) ␤⌸ Ϫ ៮ 1 0 B1 q͑␪͒ the financial accelerator close to the Pissarides equilibrium: is a measure of credit market tightness—i.e., a 1 Ϫ ␩ 1 measure of the departure of equilibrium labor (24) ␮ Ϸ eˆ. market tension from the Pissarides model. The ␩ 1 Ϫ e* coefficient ␮ ranges from 0 when ␪* ϭ ␪៮ (no credit frictions) to ϩϱ when credit frictions go Now eˆ is the percentage decline in the equilib- to infinity and ␪* goes to zero. We conclude rium employment rate (equivalently, in gross that: output per head) that is due to credit frictions. Call it the credit gap. For moderate credit fric- ● The elasticity of equilibrium labor market tions, the financial accelerator is thus propor- tightness with respect to the present dis- tional to the credit gap. The coefficient of counted value of net output is (1 ϩ ␮)/␩ Ͼ 1. proportionality equals 10, for instance, if the Credit market frictions thus amplify by a fac- elasticity of the labor matching function is ␩ ϭ tor 1 ϩ ␮ the effect of changes in profits on 0.5, and the employment rate is 90 percent. As labor market tightness relative to the Pissar- a result, if the credit gap is 7 percent, the finan- ides case (␮ ϭ 0). The coefficient ␮ is thus a cial accelerator ␮ equals 70 percent, implying measure of the financial accelerator. that the financial accelerator amplifies, say, the ● The elasticity of ␪* with respect to the search elasticity of equilibrium labor market tension cost of banks k is Ϫ␮␧/␩, while its elasticity with respect to profit shocks by 70 percent rel- with respect to the credit search cost of firms ative to the Pissarides equilibrium.29 is Ϫ␮(1 Ϫ ␧)/␩. Both elasticities are negative: credit frictions slacken the labor market. Excess Return.—Finally, define the internal These elasticities are larger in absolute value rate of return of loans to firms, as the interest the tighter the credit market. rate R that equalizes the expected present dis- ● The elasticity of ␪* with respect to the labor counted value of the loan ␥/[R ϩ q(␪*)] and the search cost ␥ is exactly the same, Ϫ1/␩,asin expected present discounted repayment on the the Pissarides model.

29 Formula (24) relates two obviously endogenous vari- ables, and is only provided for back-of-the-envelope calcu- lations. A proper equilibrium computation is performed in 28 Alternatively, we could use both (15) and (16). the next subsection. VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 955

TABLE 1—EQUILIBRIUM UNEMPLOYMENT native perspective: high unemployment might result from the combination of moderate labor Credit and moderate credit frictions. ϭϩϱ ϭ u (percent) p0 p0 1 This exercise confirms the macroeconomic Labor relevance of intermediation or financial costs, ϭ q0 1.5 5.6 9.3 already documented by Pierfederico Asdrubali ϭ q0 1.1 9.9 16.0 et al. (1996), and suggests that credit costs are a good way to improve the calibration of the matching model.31 loan {q(␪*)/[R ϩ q(␪*)]}{␳/(R ϩ s)}. Using Consistent with our earlier back-of-the- Proposition 2, we find that envelope computations based on equation (24), the financial accelerator ␮ equals 0.74, so that (25) R Ϫ r ϭ ␤͑r ϩ s͒␮. the elasticities of tightness to profits ⌸, search costs c or k, and ␥ are respectively, using (20), The excess return R Ϫ r on business loans is 3.4, Ϫ1.74, and Ϫ2. The internal rate of return increasing in ␤ (the share of the bank) and in ␮ on loans to the firms is 22.4 percent a year, i.e., (credit market imperfections). Credit market an excess return of 17.4 percent over the risk- imperfections affect the excess return on com- less rate r ϭ 5 percent. In other terms, the mercial paper by increasing the duration of the internal rate of return on loans is 17.4 percent (costly) first stage, and by increasing the cost of higher than it would be absent credit market credit (and therefore ␮). Furthermore, an in- imperfections—which we view again as an im- crease in the destruction probability s increases provement over standard calibrations. R by decreasing the expected length of the repayment period. B. The Short Run: Overshooting

Numerical Evaluation.—To get a feel for the We have so far only discussed equilibria in equilibrium levels predicted by our model, we which free entry of banks or firms drives down adopt the following parameterizations for match- to zero the value of yet inactive financiers or ing functions: entrepreneurs. In these equilibria, which can be viewed as describing long-run outcomes, fi- ͑␪͒ ϭ ␪Ϫ␩ q q0 nancial liberalization, modeled as a policy that lowers the search cost k of banks, always p͑␾͒ ϭ p ␾ Ϫ␧, has unambiguous expansionary effects: lower 0 search costs for banks attract more financiers into credit; this attracts more entrepreneurs, where q0 and p0 are (scale) measures of the which reduces equilibrium unemployment. intensity of the matches in labor and credit What if, by contrast, we lived in a short run in markets. which the total number of banks were fixed and Table 1 reports equilibrium unemployment did not respond to improved profit incentives? If rates in four different cases that correspond to the free entry of banks that is at the heart of the possible combinations of “high” and “low” expansionary long-run effects of a lower k is credit and labor market frictions.30 Traditional blocked, lowering k simply increases the value explanations (based solely on labor market im- of existing banks B0, instead of attracting more perfections) must rely on a high degree of mis- match on the labor market, as measured by q0, to explain high unemployment: they are cap- 31 See Monika Merz (1995), and Harold L. Cole and tured by the southwestern cell of Table 1. The Richard Rogerson (1999) for more on calibration issues. For northeastern cell of Table 1 suggests an alter- the parameters of the northeastern cell of the table, it takes about one year to find a credit line, and eight months to recruit a worker. Total pecuniary credit costs, excluding the sweat cost for the entrepreneur of finding a financier, rep- 30 We assume ␤ ϭ 0.5 and c ϭ k ϭ 0.35, so that ␾* ϭ resent 7 percent of total discounted output y/(r ϩ s). Equiv- 1. Furthermore, we specify ␥ ϭ 1.5, y ϭ 1, s ϭ 0.15, r ϭ alently, flow pecuniary costs Bk represent 5.3 percent of 0.05, ␩ ϭ ␧ ϭ 0.5, and ␻ ϭ 0.66. annual GDP. 956 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004 banks. This strengthens the bargaining power of trois” between workers, entrepreneurs, and existing banks in their negotiation with firms (as bankers. How the final output of the firm is split entrepreneurs are now facing a given number of between its three partners, and which institu- banks that have more favorable outside op- tional arrangements are put in place to organize tions). As a result, the equilibrium repayment their conflicting interests, is the central problem from firms to banks rises when k falls. This of capitalist economies. Our model provides a deterioration of the firms’financial condition simple framework in which to think about the leads some entrepreneurs to leave the credit macroeconomic impact of various arrangements— market. This in turn must result in higher un- a theme often associated with Marxian economics. employment in the short run. We show that the fact that entrepreneurs and It is easy to confirm formally that, as a result bankers meet before entrepreneurs and workers of financial liberalization, the unemployment does affect financial and wage bargaining. The rate overshoots its long-run value: a lower k first parties who bargain first (the financier and the raises, but then eventually lowers equilibrium entrepreneur) anticipate in their financial deal- unemployment.32 This rationalizes the belief ings the later arrival of workers in the firm. Debt that financial liberalization might generate thus becomes a strategic instrument that finan- short-run volatility, and reinforces the message ciers and entrepreneurs can use to reduce the that an understanding of the effects of financial wage that workers will eventually negotiate imperfections requires going beyond demand with their employer.33 However, we argue that and supply. The mechanism at play is straight- incentive compatibility considerations limit, in forward, and it is at the heart of the economics practice, the use of debt as a strategic variable.34 of imperfect markets: reducing the incumbents’ costs when, in the short run, all barriers to entry Sequential Bargaining.—There are now two have not yet been removed, only increases the types of contracts in our economy: loan contracts incumbents’ rents. Consequently, financial re- negotiated between financiers and entrepre- form raises short-run unemployment when there neurs, and wage contracts bargained between are still obstacles to entry in the banking sector. entrepreneurs and workers. Consistent with the necessity for an entrepreneur to find a banker IV. Extensions before she can look for a worker, these contracts are negotiated sequentially. The loan contract is We now demonstrate, by exploring possible struck in stage 1, when financier and entrepre- extensions and applications, that our basic neur meet. The wage contract is then negotiated framework is well-suited to study two macro- in stage 2 when entrepreneur and worker find economic questions at the junction of labor and each other. financial economics. What are the effects of Entrepreneurs and workers take as given the financial imperfections on bargained wages and loan contract which was written before they on the incentives of entrepreneurs to recruit met. Bankers and entrepreneurs know that the suitable workers? What happens when a firm result of their financial bargaining will influence experiences episodes of negative cash flows? the terms of the eventual labor contract.

A. Endogenous Wage 33 The use of debt as a device to decrease the share of We have assumed up to now that the wage workers has been studied empirically and formalized theo- paid to workers was exogenous. We now exam- retically by Bronars and Deere (1991) and Perotti and Spier ine what happens when, more generally and (1993). The existence of this problem is recognized by perhaps more realistically, the wage is negoti- Caballero and Hammour (1998) but assumed away by the assumption of block bargaining (workers against bankers ated between workers and entrepreneurs. and entrepreneurs). Endogenous wages gives rise to “me«nage a` 34 Another limit, which we do not explore here because it would take us too far into contract theory, is the possibility that workers might refuse to work in a highly levered 32 As long as there is free entry in the entrepreneurial ﬁrm paying too low wages. This might induce the ﬁrm’s sector, there is of course no such contrast between long-run bankers to accept ex post a debt reduction. The anticipation and short-run effects of decreasing the search cost c of of this renegotiation might constrain ex ante the use of debt entrepreneurs. as a strategic variable. VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 957

Wage Bargaining.—We proceed backwards, tions (6), (26), and (27) into this first-order con- and start with a description of wage bargain- dition yields the expression in the proposition. ing between entrepreneur and worker, given the terms of the financial contract ␳ struck The larger the firm’s output net of repayment earlier between the entrepreneur and his to the financier, the larger the wage. The more financier. pleasant the prospect of unemployment looks to Let W denote the value for a worker of being the worker (i.e., the larger U), the larger the employed, U the value of being unemployed, wage must be. If workers have all the bargain- and b unemployment benefits. Then W and ing power (␣ ϭ 1), they extract all the surplus U satisfy the following steady-state Bellman of the relationship by claiming what is left of equations: output once the financier has been repaid (␻ ϭ y Ϫ ␳). If workers have no bargaining power, they (26) rW ϭ ␻ ϩ s͑U Ϫ W͒, are just paid the annuity value of the utility they would get if they were unemployed (␻ ϭ rU). (27) rU ϭ b ϩ ␪q͑␪͒͑W Ϫ U͒, We will need below the following characterization of the effect of the repayment ␳ on the since ␪q(␪) is the probability that an unem- wage contract in the firm: ployed worker will get out of the unemployment pool by finding a job. Assume that COROLLARY 2: A unit increase in repay- entrepreneur and worker share the surplus ments to the firm’s financier decreases the wage Ϫ ϩ Ϫ ␣ Ѩ␻ Ѩ␳ ϭϪ␣ (E2 E0) (W U) generated by their rela- by (i.e., / ). tionship according a general Nash bargaining rule.35 Then The more the entrepreneur has promised to repay its financier, the smaller the total surplus ␻ ϭ ͑ Ϫ ͒1 Ϫ ␣͑ Ϫ ͒␣ arg max E2 E0 W U , that remains available to the firm and its worker. Since the workers get all the surplus when they where ␣ ʦ (0, 1) measures the bargaining have all the bargaining power (␣ ϭ 1), it is in power of workers in the labor relationship. This such a case that an increased repayment to the enables us to establish: banker affects them most. We obtain an alternative characterization of PROPOSITION 4: The wage schedule in any the optimal wage contract by using equations individual firm is given by (26) and (27) to compute U in Proposition 4. This yields: ␻ ϭ ␣͑ y Ϫ ␳͒ ϩ ͑1 Ϫ ␣͒rU. COROLLARY 3: The optimal wage contract is: PROOF: ϭ ␻ ϭ ␣ ͑ Ϫ ␳͒ ϩ ͑ Ϫ ␣ ͒ Using the free-entry condition E0 0, the (28) ␪ y 1 ␪ b, first-order condition for optimal surplus sharing ␣ ϭ Ϫ ␣ Ϫ ␣ ϵ ␣ ϩ ϩ ␪ ␪ ϩ ϩ is E2 (1 )(W U). Substituting equa- where ␪ [r s q( )]/[r s ␣␪q(␪ )].

The weight ␣␪ increases from ␣ to 1 when ␪ 35 As in the exogenous wage section (see footnote 18), rises from 0 to ϱ: increased labor market tight- we make the assumption that the relation between banker ness improves the workers’ outside options, and and entrepreneur is destroyed in case of a separation raises their share ␣␪ of output net of repayment between entrepreneur and worker. Alternative specifica- to the financier. In the limit, when ␪ ϭϩϱ, the tions are possible (e.g., an outside option of E instead of 1 workers’ outside option is the same as their E0), but they have the unappealing feature that the bank would continue to finance the firm’s job search beyond a current net value, and they capture all the sur- breakdown of the wage negotiation. It is thus in the plus (␣␪ ϭ 1). interest of the bank to commit ex ante to dissolve its relationship with the firm should the latter fail to hire a worker after a match—whence our assumption that the Loan Bargaining.—Since the loan contract between financier and entrepreneur is written fallback option of the firm is E0. In any case, both assumptions (E0 or E1) lead to similar qualitative results. before the entrepreneur meets his worker, 958 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004 banker and entrepreneur take into account the Equilibrium credit market tightness is de- effect of the bargain they strike now on the later noted ␾*␣ to emphasize its dependence, in the negotiation between entrepreneur and worker. endogenous wage case, on the parameter ␣ that ␳ ϭ Ϫ While it is still true that arg max(B1 governs the sharing of the surplus between en- ␤ Ϫ 1Ϫ␤ B0) (E1 E0) , the outcome of bargaining is trepreneurs and workers. now given by For any ␣, the credit market is less tight when the wage is endogenous than when it is exoge- PROPOSITION 5: The financial contract be- nous. A higher ␣ has two effects. First, a size- tween financier and entrepreneur is of-the-cake effect. When workers have more bargaining power, there is less remaining sur- (29) ␳ ϭ ␤␣ ͑y Ϫ ␻͒ ϩ ͑1 Ϫ ␤␣ ͒͑r ϩ s͒␥/q͑␪͒, plus to be shared by bankers and entrepreneurs. However, as in the case of exogenous wages, where ␤␣ ϵ ␤/[1 Ϫ ␣(1 Ϫ ␤)] Ͼ ␤. size-of-the-cake effects, which affect entry mar- gins for financiers and entrepreneurs equally, PROOF: are irrelevant for the determination of equilib- Using Corollary 2 to track the effect of ␳ on rium credit market tightness. Second, a distrib- the firm’s future wage, the first-order condition utive effect that tilts the allocation of output, net for optimal sharing of the surplus is, using the of wages, in favor of bankers to the detriment of ϭ ϭ exit conditions B0 E0 0: entrepreneurs (see Proposition 5). Proposition 6 shows that only the latter effect matters for ͑ Ϫ ␤ ͒ ϭ ␤ ␣ (30) 1 ␣ B1 ␣ E1 . equilibrium credit market tightness. Indeed, if were equal to zero, we would have ␤␣ ϭ ␤ and The expression in the proposition follows ␾*␣ ϭ ␾* as the distributive effect would then immediately, using equations (2), (3), (5), disappear. and (6). We now compute the equilibrium labor market tightness ␪*␣: The equilibrium Nash-bargaining loan contract is formally similar to the one described by PROPOSITION 7: Equilibrium labor market Proposition 5 in the exogenous wage case. tightness ␪*␣ and credit market tightness ␾*␣ ϭ However, it is now the higher effective bargain- [(1 Ϫ ␤␣)/␤␣][k/c] are the solution to the pair of ing power ␤␣ of the banker that matters for the equations: equilibrium outcome. For instance, when ␣ ϭ ␤ ϭ 0.5, ␤␣ equals 2/3, which represents a k q͑␪ ͒ ϭ ␤␣ ͑1 Ϫ ␴␪ ͒ nonnegligible increase in the effective bargain- ␾p͑␾͒ r ϩ q͑␪ ͒ ing power of financiers. y Ϫ b ␥ Equilibrium.—Since sequential financial and ϫ Ϫ ͩ ϩ ͑␪͒ͪ, wage bargaining effectively reinforces the hand r s q of the banker in financial negotiations, we c q͑␪ ͒ ϭ ͑1 Ϫ ␤␣ ͒͑1 Ϫ ␴␪ ͒ should expect the credit market to be less tight p͑␾͒ r ϩ q͑␪ ͒ in the equilibrium with endogenous wages. In- deed, we have: y Ϫ b ␥ ϫ ͩ Ϫ ͪ. r ϩ s q͑␪͒ PROPOSITION 6: When wages are endogenous, equilibrium credit market tightness is with ␴␪ ϵ [␣␪(1 Ϫ ␤␣)]/[1 Ϫ ␣␪␤␣].

1 Ϫ ␤␣ k 1 Ϫ ␤ k ␾ ϭ Ͻ ϭ ␾ (31) *␣ ␤ ␤ *. PROOF: ␣ c c Similar to the proof of Proposition 3.

PROOF: Using this proposition, equilibrium wage and By straightforward analogy with the proof of ﬁnancial contracts can in turn be computed from Proposition 1. Corollary 3 and Proposition 5. VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 959

Debt as a Strategic Variable?—We have so While we have assumed so far full commit- far assumed that entrepreneurs borrow exactly ␥ ment of all agents, we should however not for- per unit of time, and repay the corresponding ␳. get that debt usually has disincentive effects that However, since increasing the value of ␳ is a must be taken into consideration as soon as one way to decrease the share of workers in the starts analyzing strategic behavior. In that re- Ϫ Ͻ wage bargaining problem, it is in the interest of spect, a situation in which E2 E1 0 provides both bankers and firms to use debt as a strategic no incentive to the entrepreneur to ever actually variable to expropriate workers, and to stipulate hire a worker. In other words, if debt is so high ␥ a flow loan larger than and, accordingly, a that it reduces E2 to zero, the entrepreneur pre- repayment larger than the ␳ we have computed fers to remain in stage 1, and to forever pocket above. It is therefore natural to wonder whether the positive difference between what the entre- the cash flow from financier to entrepreneur preneur lends her, call it z, and the labor search might rise, beyond ␥, up to the point where cost ␥. wages have been reduced to their reservation To foreclose this temptation, we should im- level b.36 We now show, by contradiction, that pose the incentive compatibility constraint this is ruled out if we introduce incentive com- Ϫ Ն patibility considerations. E2 E1 0. Suppose that the debt of the firm is so high that the negotiated wage rate equals its reserva- Combining this constraint with the stage 1 Bell- tion level: ␻ ϭ b. From Corollary 3, this can man equation37 only occur, since ␣␪ Ͼ ␣ Ͼ 0, if y Ϫ ␳ ϭ b. But ϭ Ϫ ␥ ϩ ͑␪͒͑ Ϫ ͒ then equation (14) implies the value of the firm rE1 z q E2 E1 , in stage 2 is zero: and using equation (32), we conclude, not sur- y Ϫ ␻ Ϫ ␳ prisingly, that banks ration the credit they ex- E ϭ ϭ 0, 2 r ϩ s tend to firms: as the wage bargained between firms and work- z Յ ␥ ϩ rcp͑␾*͒. ers is indeed reduced to its reservation level b only if the surplus shared in stage 2 is zero. What do we learn from all this? First, that the Financier and entrepreneur can achieve this re- strategic use of debt by bankers and entrepre- duction by raising the payment the entrepreneur neurs to expropriate workers is a real possibil- receives from the financiers above the search ity: banks might indeed lend to firms more than cost ␥, so that output net of repayment to the what is required to finance a job search. In that financier, y Ϫ ␳, equals b. respect, it is both remarkable and reassuring that Notice, however, the value of the firm in our stylized model of credit and labor market stage 1 is strictly positive as, by equation (10), imperfections, once extended to include an endogenous wage, replicates the results of Perotti c and Spier (1993) on the strategic use of corpo- ϭ Ͼ rate debt. Second, that the possibility to expro- (32) E1 ͑␾ ͒ 0. p *␣ priate workers never reduces them to their reservation wage. We have indeed established Ϫ Ͻ We therefore conclude that E2 E1 0ifthe this would require so much debt that the firm financier and the entrepreneur use debt strategi- would lose any incentive to actually hire a cally to bring down the wage to zero: the firm worker, start producing, and repay its bank. suffers a capital loss when moving from stage 1 Finally, that the strategic use of corporate debt, to stage 2. while theoretically plausible, probably does not amount to much in practice, as the difference

36 This reasoning of course presupposes either that the entrepreneur has consumed right away the resources lent to him by the financier above and beyond what was needed to 37 This Bellman equation is the generalization of equa- search for a worker, or, if she has not, that he has protected tion (5) when the amount z lent by the financiers differs them to exclude them from the negotiation with the workers. from the labor search cost ␥. 960 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004 z Ϫ ␥ ϭ rcp(␾*) is very small relative to ␥ for source, which we must still characterize for- any sensible values of the parameters.38 mally, that captures the optimal dissolution of firms in “bad” states of nature.41 The novelty introduced by stochastic changes B. Endogenous Destruction in productivity is that there are now states of nature in which the firm operates in spite of We have assumed until now rather rudimen- negative output net of wages (y Ϫ ␻ Ͻ 0). tary production and destruction processes: out- These are states in which the financier has com- put y is constant, and destruction occurs mitted to inject new liquidity in the firm—to exogenously at rate s. Fortunately, our results help it ride out of a temporary negative cash readily generalize to a richer stochastic environ- flow period—because the value of the match ment that yields interesting insights into the between bank and firm is still positive. How- endogenous destruction of firms and their finan- ever, as we shall see below, some of these states cial fragility. with positive total surplus are financially frag- Maintain, for simplicity, the assumption that ile, in the sense that the banker would neverthe- wages ␻ are exogenous, but imagine that the less like ex post to close down the firm, but is output of a firm is governed by the following restrained by his prior commitment to keep it in random process:39 operation. We must therefore determine for which values of y the firm is closed down, when ● When a firm starts producing in stage 2, its it is refinanced, and when it is financially initial output is y0. All firms start with the fragile. same y0. ● With Poisson arrival rate ␭ Ͼ 0, the output Viability Cutoff Rule and Equilibrium.—The of a firm then idiosyncratically jumps to value functions of banks and entrepreneurs another level y, with y drawn randomly add up to the total surplus Si of their relation- from a distribution with cumulative distri- ship in stage i, with i ϭ 1, 2, 3. In stage 2 bution G٪.40 (which is crucial for destruction), the total surplus S2( y) depends on the state of nature y, Destruction or Refinancing?—If a firm were and satisfies operating in all states of nature until it gets ͑ ͒ ϭ Ϫ ␻ ϩ ͓ Ϫ ͑ ͔͒ destroyed exogenously at rate s, computing the (33) rS2 y y s S3 S2 y present discount value of its output, net of wages, would be as simple a matter as it was in Section II. However, the firm does not operate, ϩ ␭ ͵ͭmax͓S ͑yЈ͒, S ͔ Ϫ S ͑y͒ͮ dG͑yЈ͒. 2 3 2 when output is random, in all states of nature: the financier and the entrepreneur optimally agree to dissolve their match, and close down The relationship generates total flow profits y Ϫ the firm, if, and as soon as, the total surplus of ␻. The match is exogenously destroyed with the match between the bank and the firm be- intensity s, generating a capital gain (or loss, if Ϫ comes negative. Thus, there are two sources of negative) equal to S3 S2(y). In addition, with destruction of the firm. An exogenous source, at intensity ␭, output reaches a new level yЈ, and rate s, that represents outside forces impinging the match generates a capital gain which equals Ј Ϫ on the firm’s viability. Plus an endogenous max[S2(y ), S3] S2(y) since the match is endogenously destroyed in states of nature in Ј Ͻ which S2(y ) S3. 38 ϭ ␣ ϭ Assume, as in Section I, that the termination With p0 1, 0.5 and for the calibration parameters of footnote 30, rcp(␾*) is only equal to 0.8 percent of of the relationship leads to the loss of the spec- the search cost ␥—a negligible quantity. Assuming, as we ificity of the entrepreneur-banker relationship, ␥ ϭ ϭ have done earlier, that z equals , is thus not a drastic so that B3 B0 and E3 E0. Together with the oversimplification. 39 See Dale T. Mortensen and Pissarides (1994). 40 We can allow output to be negative if we think of y as output net of operating costs other than wages or financial 41 Destruction, whether exogenous or endogenous, is costs. thus always efficient in our scenario. VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 961

ϭ ϭ free-entry conditions B0 E0 0, this implies Financial Fragility.—We now show that a ϭ ϩ ϭ that S3 B3 E3 0. As a result, inspection salient feature of the equilibrium with endoge- of equation (33) reveals that S2(y) is linear in y, nous destruction we have just described is that and can be written as the financier would like ex post to renege on his commitment to refinance the firm in states of Ϫ d y y nature y ʦ [yd, ␻)ify ends up at the bottom of S ͑y͒ ϭ , 2 r ϩ s ϩ ␭ that range. Consider the stage 2 Bellman equation of the with the cutoff point yd solving the equation bank in states of nature where y Ͻ ␻: S (y) ϭ 0 or, from equation (33), 2 ͑ ͒ ϭ Ϫ ␻ ϩ ͓ Ϫ ͑ ͔͒ (35) rB2 y y s B3 B2 y ϱ (34) yd ϭ ␻ Ϫ ␭ ͵ S ͑yЈ͒ dG͑yЈ͒ Ͻ ␻. yd 2 ϩ ␭ ͵ ͕B Ϫ B ͑y͖͒ dG͑yЈ͒ yd 3 2 Ϫϱ This defines a viability rule: banker and entrepreneur agree to keep the firm in operation for ϱ values of y above yd for which output is suffi- ϩ ␭ ͵ ͕B ͑yЈ͒ Ϫ B ͑y͖͒ dG͑yЈ͒. 42 2 2 cient to generate a positive total surplus. In yd states where y ʦ [y d, ␻), the bank injects additional liquidity ␻ Ϫ y Ͼ 0inthefirm to keep The bank injects ␻ Ϫ y in the firm. The firm is it alive.43 As a result, the value of the firm in destroyed with exogenous intensity s. With in- ␭ Ј Ј stage 2, E2(y), is always positive, since the tensity , output changes to a new level y .Ify entrepreneur receives (as long as the firm oper- is below yd, the firm is closed down and the ates) additional liquidity in bad states of nature, bank is left with B3. Otherwise, it makes a Ј Ϫ and makes positive flow profits in good states. capital gain B2(y ) B2(y). ϭ In their financial negotiation in stage 1, fin- With our assumption that B3 B0 and free Ͻ anciers and entrepreneurs agree on how to share entry, equation (35) implies that B2 0 when the total surplus of their relationship, given the y Ͻ ␻ if, in addition, 0 total surplus S2(y ) that their relationship will generate at the very beginning of stage 2. ϱ Hence, the equations of the BB and EE curves (36) y Ͻ ␻ Ϫ ␭ ͵ B ͑yЈ͒ dG͑yЈ͒ ϵ yB. 2 of the economy with endogenous destruction yd are the same as in the economy with exogenous destruction [equations (15) and (16)], but with Now, comparing this expression with equation 0 Ϫ ␻ ϩ S2(y ) replacing the term (y )/(r s). The (34), we conclude that intersection of these modified BB and EE curves determines equilibrium credit market ϱ tightness—which remains, as before, equal to yB Ϫ yd ϭ ␭ ͵ ͓S ͑yЈ͒ Ϫ B ͑yЈ͔͒ dG͑yЈ͒ 2 2 ␾ ϭ Ϫ ␤ ␤ * [(1 )/ ](k/c)—and equilibrium labor yd market tightness ␪*. The latter depends on the 0 initial profitability y of firms, and on the re- ϱ d strictiveness of the viability cutoff rule y . The ϭ ␭ ͵ E ͑yЈ͒ dG͑yЈ͒ Ͼ 0. 2 larger y0 or the smaller yd, the larger ␪* and the yd lower equilibrium unemployment. The inequality follows from the remark above that the value of the firm in stage 2, E2(y), is positive 42 If y0 Ͻ yd, the economy is not viable ex ante: firms do in all states of nature, even when y Ͻ ␻.44 not get the funds required to proceed to the recruiting stage, This means that some of the states of nature and no output is ever produced. We henceforth rule out that case. 43 This feature is already present in Mortensen and Pis- sarides (1994), but it is irrelevant in their perfect capital 44 Note that this result does not depend on the shape of market setup. the financial contract. 962 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2004 in which the bank has contracted to refinance generate a mechanism for the propagation and the firm because the total surplus is positive transmission of shocks over time. (y Ͼ yd) can also be states in which the value of Second, endogenous growth could be intro- the bank is negative (y Ͻ yB). Were it not for its duced in our model by assuming that new en- prior commitment not to do so when y Ͼ yd, the trepreneurs, instead of using an existing bank would therefore prefer ex post to sever its technology, are the engine of technological in- relationship with the firm when y Ͻ yB.45 novation. Accordingly, finance would become In these states, firms are financially fragile, as an essential input into long-run growth. their survival hangs solely on the strength of the Finally, the search for additional cross- bank’s prior commitments (or on its reputa- sectional empirical evidence on credit frictions tion).46 Any weakening of these commitments figures prominently on our research agenda.48 would entail the destruction of some, or all, of Most importantly, we would like to understand these financially fragile firms. further the contribution of differences in the fluidity of regional credit markets to the some- V. Conclusion times persistently divergent unemployment experiences of areas that share, within the same This paper has built a simple macroeconomic country, identical labor market institutions. This model of credit and labor market imperfections might ultimately help to understand why dereg- based on matching frictions. Its main feature is ulation of labor markets at the margin has not the derivation of a financial accelerator that produced in Europe its expected effects on results from the general-equilibrium feedback employment. between credit and labor markets. Our paper leaves open a number of questions, REFERENCES both theoretical and empirical. First, what would happen if liquidity not only meant will- Aghion, Philippe; Bacchetta, Philippe and Baner- ingness to lend, but also existence of sufficient jee, Abhijit. “Capital Markets and the Insta- financial resources to finance economic activ- bility of Open Economies,” in Pierre-Richard ity? Second, can we build upon our model to Age«nor, Marcus Miller, David Vines, and generate a theory of growth and business cy- Axel Weber, eds., The Asian financial crisis: cles? Finally, what empirical evidence could be Causes, contagion and consequences. Cam- adduced to back up our claim that the combi- bridge: Cambridge University Press, 1999, nation of moderate credit frictions and moderate pp. 167Ð90. labor frictions is enough to explain high Asdrubali, Pierfederico; Sorensen, Bent E. and unemployment? Yosha, Oved. “Channels of Interstate Risk Answering the first question would require Sharing: United States 1963Ð1990.” Quar- us to close our model differently (liquidity terly Journal of Economics, November 1996, would need to assume a more traditional 111(4), pp. 1081Ð110. meaning of financial “water”flowing in and Bernanke, Ben S. and Gertler, Mark. “Agency out of the economy). Doing so, although no Costs, Net Worth, and Business Fluctua- simple matter, would enable us to study tions.” American Economic Review, March whether the economy generates enough li- 1989, 79(1), pp. 14Ð31. quidity in the face of shocks to finance itself Bernanke, Ben S.; Gertler, Mark and Gilchrist, without outside intervention,47 and would Simon. “The Financial Accelerator in a Quan- titative Business Cycle Framework,” in John B. Taylor and Michael Woodford, eds., Handbook of macroeconomics, Vol. 1C. Am- 45 To ensure that the bank initially signs a contract with sterdam: North-Holland, 1999, pp. 1341Ð93. the firm, we must thus reinforce our previous condition y0 Ͼ yd (which ensures a positive surplus) to require that, in addition, y0 Ͼ yB. 46 For an alternative view of financial fragility, see den 48 A cross-country extension of the data set compiled for Haan et al. (2003). the United States by Dell’Ariccia and Garibaldi (2003) on 47 This is one of the main question asked by Holmstrom gross credit flows would help us provide additional corrob- and Tirole (1998). oration of our results. VOL. 94 NO. 4 WASMER AND WEIL: MACROECONOMICS OF CREDIT AND LABOR MARKETS 963

Blanchﬂower, David G. and Oswald, Andrew J. in Colin Mayer and Xavier Vives, eds., Cap- “What Makes an Entrepreneur?” Journal of ital markets and ﬁnancial intermediation. Labor Economics, January 1998, 16(1), pp. Cambridge, MA: Cambridge University 26Ð60. Press, 1993, pp. 156Ð89. Bronars, Stephen G. and Deere, Donald R. “The Kiyotaki, Nobuhiro and Moore, John. “Credit Threat of Unionization, the Use of Debt, and Cycles.” Journal of Political Economy, April the Preservation of Shareholder Wealth.” 1997, 105(2), pp. 211Ð48. Quarterly Journal of Economics, February Levine, Ross. “Financial Development and Eco- 1991, 106(1), pp. 231Ð54. nomic Growth: Views and Agenda.” Journal Caballero, Ricardo J. and Hammour, Mohamad. of Economic Literature, June 1997, 35(2), pp. “Improper Churn: Social Costs and Macro- 688Ð726. economic Consequences.” National Bureau Merz, Monika. “Search in the Labor Market and of Economic Research (Cambridge, MA) the Real Business Cycle.” Journal of Mone- Working Paper No. 6717, September 1998. tary Economics, November 1995, 36(2), pp. Cole, Harold L. and Rogerson, Richard. “Can 269Ð300. the Mortensen-Pissarides Matching Model Mortensen, Dale T. and Pissarides, Christopher Match the Business-Cycle Facts?” Interna- A. “Job Creation and Job Destruction in the tional Economic Review, 1999, 40(4), pp. Theory of Unemployment.” Review of Eco- 933Ð59. nomic Studies, July 1994, 61(3), pp. 397Ð Dell’Ariccia, Giovanni and Garibaldi, Pietro. 415. “Gross Credit Flows.” Centre for Economic OECD. “Job Study.” Paris, OECD, 1994. Policy Research (London) Discussion Paper Perotti, Enrico C. and Spier, Kathryn E. “Capital No. 2569, 2000. Structure as a Bargaining Tool: The Role of . “Gross Credit Flows.” Mimeo, IGIER, Leverage in Contract Renegotiation.” Amer- Milano, 2003. ican Economic Review, December 1993, den Haan, Wouter J.; Ramey, Garey and Watson, 83(5), pp. 1131Ð41. Joel. “Liquidity Flows and Fragility of Busi- Petersen, Mitchell A. and Rajan, Raghuram G. ness Enterprises.” Journal of Monetary Eco- “Does Distance Still Matter? The Informa- nomics, September 2003, 50(6), pp. 1215Ð tion Revolution in Small Business Lending.” 41. Journal of Finance, December 2002, 57(6), Diamond, Peter. “Pairwise Credit in Search pp. 2533Ð70. Equilibrium.” Quarterly Journal of Econom- Pissarides, Christopher A. Equilibrium unem- ics, May 1990, 105(2), pp. 285Ð319. ployment theory, 2nd Ed. Cambridge, MA: Farmer, Roger. “Implicit Contracts with Asym- MIT Press, 2000. metric Information and Bankruptcy: the Effect Rajan, Raghuram G. and Zingales, Luigi. “Finan- of Interest Rates on Layoffs.” Review of Eco- cial Dependence and Growth.” American nomic Studies, July 1985, 52(3), pp. 427Ð42. Economic Review, June 1998, 88(3), pp. Gertler, Mark and Gilchrist, Simon. “Monetary 559Ð86. Policy, Business Cycles, and the Behavior of Robinson, Joan. The rate of interest, and other Small Manufacturing Firms.” Quarterly essays. New York: Macmillan, 1952. Journal of Economics, May 1994, 109(2), pp. Shapiro, Carl and Stiglitz, Joseph E. “Equilibi- 309Ð40. rum Unemployment as a Worker Discipline Holmstrom, Bengt and Tirole, Jean. “Private and Device.” American Economic Review, June Public Supply of Liquidity.” Journal of Po- 1984, 74(3), pp. 433Ð44. litical Economy, February 1998, 106(1), pp. Stiglitz, Joseph E. and Weiss, Andrew. “Credit 1Ð40. Rationing in Markets with Imperfect Infor- King, Robert G. and Levine, Ross. “Financial mation.” American Economic Review, June Intermediation and Economic Development,” 1981, 71(3), pp. 393Ð410.