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This PDF is a selection from a published volume from the National Bureau of Economic Research Volume Title: NBER Macroeconomics Annual 2007, Volume 22 Volume Author/Editor: Daron Acemoglu, Kenneth Rogoff and Michael Woodford, editors Volume Publisher: University of Chicago Press Volume ISBN: 978-0-226-00202-6 Volume URL: http://www.nber.org/books/acem07-1 Conference Date: March 30-31, 2007 Publication Date: June 2008 Chapter Title: Aggregate Implications of Credit Market Imperfections Chapter Author: Kiminori Matsuyama Chapter URL: http://www.nber.org/chapters/c4078 Chapter pages in book: (p. 1 - 60) 1_ Implications Aggregate Market Imperfections Kiminori Matsuyama, University families resemble one another. Each unhappy "All happy its own Northwestern of Credit way/' Leo 1 in family is unhappy Tolstoy, Anna Karenina Introduction that the market It is widely recognized investment credit to the most productive economy fails to allocate because credit the trans projects are subject to agency problems. In the presence of such imper as net worth?also known the balance sheet the borrower's fections, across in crucial roles the credit entrepre condition?plays allocating level of neurs, firms, industries, and nations. A change in the aggregate actions and a change in the distribution of wealth thus affect the equi Fur of the credit and hence patterns of investments. allocation causes a in the investments the resulting further thermore, change wealth librium in the level and distribution of wealth, which leads to a further in investments. the of patterns change equilibrium in part by the advances made in the microeconomics Stimulated of fi change nancial markets of credit market business and corporate finance over the last 30 years, the problems in have recently found many applications imperfections and development, and international economics. has left in its wake a bewildering array of indi with seemingly conflicting results. For example, do the im cycles, growth this progress However, vidual models as sug to the macroeconomic add persistence dynamics, and Bernanke Gertler and Moore (1989), Kiyotaki (1997), and gested by as suggested by Azariadis others? Or, do they add volatility, and Smith and Banerjee (2005), and Matsuyama (1998), Aghion (2004b)? If they are perfections 2 Matsuyama is it because for causing fluctuations, the misallocation of responsible or creates it creates boom-and-bust credit recessions because cycles? Does credit markets make fluctuations more or less volatile? Does improving the credit market financial globalization alleviate or exacerbate imperfec tions? Do the rich and the poor help households? credit transactions between or magnify to reduce the inequality among that credit market This paper comes out of my conviction imperfec a wide issues. tions offer the key to understanding range of important are so rich of credit market Yet, aggregate imperfections implications and diverse that one should not expect to find a simple answer of any of come as no surprise that they manner inwhich dif they depend on the investments with each other, different interact ferent agents and/or and propagation mechanisms. which consequently affects amplification a particular fam This suggests that the intuition gained from studying the above "either-or" are so rich and diverse questions. because It should can be misleading the results may be driven by the because made about the set of agents and investment proj specific assumptions ects that are competing for credit. ily of models for understanding This paper offers a road map aggregate implica a diverse set tions of credit market By bringing together imperfections. a unified framework, it of results (many existing and some new) within aims to draw nections a coherent picture so that one is able to see some close con across many topics that as unre viewed sometimes results between seemingly conflicting or even are ordinarily treated separately a simple, highly of abstract model lated.1 To this end, I first develop to capture all sorts of is meant which credit market imperfections, this single model transactions. affect credit that Using agency problems in se I examine the effects of credit market imperfections throughout, or will be The discussion ries of relatively simple equilibrium models. manners in which different models "close the system"; ganized by the about the sets of agents and of proj that is, based on the assumptions in for the credit and about the price effects of different ects competing vestment mechanisms and propagation the amplification be shown how a wide range of ag cause. They in to the common be attributed projects, which determine Itwill in these models. may gregate phenomena clude, among other things, changes,2 development cessions, recurrent technical investment-specific of inefficient re traps, leapfrogging, persistence endogenous boom-and-bust flows, the rise and fall of inequality trade. The framework international cycles, reverse across nations, is also used international and capital the patterns of some to investigate Aggregate Implications of Credit Market and distributional equilibrium credit markets. One spond recurring finding impacts of improving is that the properties to non-monotonically parameter 3 Imperfections changes. the efficiency of equilibrium For example, often of re increas net worth first leads to a higher equilibrium rate of return ing borrower's a to rate of return; improving and then lower equilibrium credit market first leads to increased volatility and then to reduced volatility; produc first lead to greater inequality and then to reduced improvements Such inequality. suggests some cautions for studying non-monotonicity a narrow class or a particular their effects within For family of models. in to their understand the effects of im credit market attempts example, tivity with no credit market. Yet, study models that the effects of an imperfect credit mar to those of no credit market. In their attempts to under many perfections, there is no reason ket are similar authors to believe stand the effects of improving the credit market, many authors compare with credit market and models with the perfect imperfections credit market. Yet, there is no reason to believe the effects of (partially) are to markets similar credit of those credit mar improving eliminating ket imperfections completely.3 models 2 A Simple Model of Credit Market A Single Agent's Perspective Imperfections: Let us start with a simple and im highly abstract model of credit market perfections, which will be used as a building block in all the equilibrium models below. Here, we will look at the problem discussed faced by a a or in its environ isolation, taking firm) single agent (an entrepreneur ment as exogenous. The world lasts for two periods: 0 and 1. The agent is endowed with o> 1 units of the input in period 0 and consumes only in period 1. There are two ways of converting the period-0 con input into the period-1 can run a the non-divisible investment First, sumption. agent project, converts one unit of the input in which period 0 into R units in con in period 1 by 1 - a>at the gross market rate of re sumption borrowing turn equal to r. Second, the agent can lend x <w units of the input in pe riod 0 for rx units of consumption in period 1. < The is to maximize the period-1 agent's objective consumption. By - co to run 1 the the borrowing project, agent could produce R units of the r(l co)units need to be repaid, so that consumption good, from which = R the period-1 the (and consumption r(l utility) would be equal to U 4Matsuyama = = rco, the amount that co) R r + rco.This is greater than or equal to U rate r, if and the agent could consume by lending at the gross market - only if > R r. (PC)(1) the project return needs to be higher than (or equal to) the oppor the agent eager (or tunity cost of running the project in order to make as the analogous to borrow and invest. constraint well This (as willing) Thus, in all the models constraints Profitability Even when later) shall be called developed (PC) for Constraint. (PC) holds with strict inequality and hence the agent is ea to invest, credit market ger imperfections might keep the agent from to the somehow To obtain credit, the agent must generate investing. is determined How the market. lenders the rate of return, r,which by ever, for a variety of reasons, the entire project output, R, may not be used it is assumed To capture this in the simplest manner, for the purpose. to that no more than a fraction, X, of the project revenue can be pledged for the repayment. Thus, the agent the lenders, if and only if required by the lenders return can generate the rate of XR> r(l co).(BC)(2) and the agent is capable of borrowing as in all the the constraints analogous investing. Constraint.4 for models later) shall be called (BC) Borrowing developed is to is b = 1 - co<XR/r, which Another way of looking at this constraint Only when this constraint This constraint ismet, (as well value of the is limited by the present discounted say that that borrowing can also be revenue of the project, XR/r. This constraint pledgeable a states that which rewritten as co>1 XR/r, sufficiently high net worth overcome the credit market would imperfection.5 and to take place, the agent must be both willing are satisfied. when and both to that borrow, is, only (PC) (BC) capable on X + co. If X + co> Which of the two is a relevant constraint depends 1, (PC) ismore stringent than (BC). That is, the agent can borrow when do not ever he wants to borrow. In this case, credit market imperfections For the investment the investment In this simple, decision. highly If X + co< 1, on the other hand, (BC) is more stringent than (PC). That is, credit market imperfections may affect investment. A, Indeed, if 1 <R/r < (1 co) (PC) holds but (BC) does not, investment project that the agent cannot initiate the profitable meaning constraint. due to the borrowing affect abstract model of credit market imperfections, Aggregate Implications of Credit Market Imperfections to capture the pledgeability, X, ismeant restrict the agent's ability to finance the The severity of these agency problems factors industry, or the institutional 5 all sorts of agency problems that investment profitable externally. could depend that determine on the project, the the general effi en such as the quality of legal or contractual ciency of credit markets, or more state of the financial forcement, corporate governance, broadly I will of For later allow the the this reason, economy. development X, to vary across projects, across industries, parameter, pledgeability across countries in equilibrium models with many projects, many dustries, or or in countries. many In this simple, highly abstract model of credit market imperfections, to capture the entrepreneur's net the input endowment, co, is meant more the firm's balance sheet bor the or, condition, worth, broadly, For this reason, I will rower's credit-worthiness. later allow the net worth parameter, heterogeneous vestment when co, to vary across agents in equilibrium models with to depend on the past in agents. Itwill also be allowed the of credit market dynamic implications considering imperfections. Remark 1: The microeconomics of credit markets offers many different to the that the bor agency assumption justify rowers cannot the project revenue.6 The simplest fully pledge story would be that they strategically obli the repayment default, whenever cost. each exceeds the default is gation Alternatively, project specific to the agent and requires his services to generate revenue. the maximum stories that could be used the services, the revenue would be reduced. Then the borrower, towithdraw his services, can renegotiate the repayment; by threatening see Hart and Moore Hart Moore and and (1994), (1995), (1997). Kiyotaki There is also the costly-state-verification of Townsend (1979), approach used by Bernanke and Gertler (1989), Boyd and Smith (1997), and oth ers. See also the moral hazard and Tirole approach used by Holmstrom and are A others. to the is number of studies devoted (1997,1998) large sues of the relative merit of different and/or (conceptual empirical) Hart and stories; see, for example, agency (1995, ch. 5, appendix) Without and Karaivanov I Paulsen, Townsend, (2006). In this paper, however, will not be concerned with of which the question stories offer most or causes of for the microeconomic plausible compelling explanations credit market Instead, Iwill simply treat credit market imperfections. as a fact of and proceed with their ag life, imperfections investigating or the reduced abstract, gregate equilibrium consequences, using highly 6 Matsuyama form approach, lems discussed ismeant which Remark 2: The careful "loan and reader must have undoubtedly noticed the use of the terms such as "debt capacity," avoid liberately rate," to encompass all sorts of agency literature.7 prob in the microeconomic and market," instead use "borrowing of return," and "credit market." This is because with of credit market aggregate implications from broad external financing difficulties. Note that I de "interest constraint," this paper "rate is concerned imperfections, arising con that the borrowing to pledge the entire of the borrowers to the inability to the higher rate for the lenders, not because generate project of any arbitrary restriction on the menus of the financial claims that they can issue. The main issues addressed that they here are general enough straint arises due revenue are independent is too ab of the financial structure. Indeed, the model stract tomake ameaningful distinction between the equity, the debt, the should be viewed bonds, or any other forms of financial claims, which as an advantage of the model.8 3 Partial Equilibrium We have so far looked holding actions through 3.1 Models at only the single agent's problem in isolation, as exogenous, about inter and without worrying interact agents agents. Let us now start letting many all the prices among equilibrium Homogeneous Let us now consider prices. Agents: The Net Worth a continuum (Balance Sheet) Effect of homogenous agents with unit mass. with co< 1 units of the input at period to the presence 1. In addition of many As before, each agent is endowed 0 and consumes only at period is that the projects run by the agents convert the the difference agents, key the consumption good input into capital. Capital is then used to produce in period 1,with the constant returns to scale (CRS) technology, F(k, Q, in equi where k is the total supply of capital (which will be determined a in fixed supply. Let/(fc) librium), and ? is vector of "the hidden factors" = ?>.The = > 0 factor F(k, Q, which satisfies/' competitive >/" and/'(0) reward each unit of capital by/'(fc) and the residual,/(fc) markets kf'(k) > 0, goes to the owners of the "hidden factors" in fixed supply.9 the input endowments of converting The agents have two means a investment into consumption. First, each agent can run non-divisible Implications of Credit Market Aggregate Imperfections 7 converts one unit of the input in period 0 into R units of project, which con 1 - coat the market in rate, r,which capital period 1 by borrowing as exogenous.10 Since each unit of capital earns/'(A:) in consumption, each project generates Rf'{k) units of the consumption can lend the input endowment in period 0 at good. Second, each agent as to rate return total of the before. Finally, the r, equal supply of capi n is the number tal is given by k = Rn, where (or the fraction) of the = Rn are determined in agents who borrow and invest. Both n and k tinues to be treated equilibrium. 1 - co to run the project, the agent can consume 17 = By borrowing rate, r, the agent can consume r(l co). By lending at the market Rf'(k) U = rco. By comparing the two, (PC) now becomes Rf'(k) On > r. (BC) is now the other hand, XRf'(k)>r(l-(o). (PC)(3) given by (BC)(4) in this model, that the two constraints (3) and (4), differ from those in the single agent's problem, and (1) (2), only in that the project revenue, now is hence become endogenous. and R, replaced by Rf'(k), In equilibrium the investment takes place until one of the (BC) and so that (PC) becomes binding, Note = Rf'(k) Max 1, This determines -^^ \r the equilibrium + (BC)(5) (PC) value of fc.11 When X + co< 1, (5) be comes Rf\k) = (~^-\r>r. (6) Thus, (BC) is binding but (PC) is not; the project than the opportunity cost of the project. All the no more but vest, agents can borrow and invest, In olate (BC). short, there is too little investment. return is strictly higher agents are eager to in vi because that would In this case, improving an increase in X, the credit market, to a higher leads invest obviously ment. A higher co also leads to a higher investment. This is the net worth the agents (or balance sheet) effect. As the borrower net worth improves, need to borrow more investment (5) becomes eases the borrowing and hence less, which constraint, will be financed. When X + co> 1, on the other hand, 8 Matsuyama Rf\k)= (7) r>(^^y Thus, (PC) is binding there is no net worth and the level of investment effect; a higher cowould is optimal. In this case, not affect the investment. Remark 3: In this model, only the fraction n of the agents invests in equi that the fraction 1 - n of them becomes the lenders. librium, which means This obviously "How can the credit be allocated only raises the question, to a fraction of homogeneous agents?" When X + co> 1, this is not a prob = r. lem, because Thus, the agents are indifferent (PC) is binding; Rf'{k) and lending. However, when X + co< 1, (PC) is not borrowing > r, so that the to lend agents strictly prefer borrowing binding, Rf'{k) are we two There resolutions for this. think that First, may ing. possible between the equilibrium allocation case. The credit is allocated in this involves credit rationing n of the agents, while to the fraction randomly are denied credit.12 The latter have no choice but to necessarily the rest of the agents the lenders; they would not be able to entice others to switch and a become lenders by promising higher return because that would violate we as the limit the view Second, (BC). may agent model homogeneous case of some heterogeneous models. For the agent agents may example, become in their endowment, to G(co). Then, the equi distributed according librium is given by the threshold level of the endowment, coc, such that are lower (higher) than cocbecome the agents whose endowments the a we at will with lenders (borrowers). look such model Indeed, shortly as the endowments. The above model may be obtained heterogeneous to a single mass point. limit when G(co) converges differ Remark 4: Just in case one might suspect that the results here may be driven by the indivisibility of the projects, not by credit market imper here ismore subtle than fections, the role of the indivisibility assumption one might think. In the literature, it is often argued that the equilibrium is fundamentally difficult be imperfections analysis of credit market cause it is necessary to model in for credit order agents heterogeneous transac to take place. This is not true; credit market market transactions are some if there tions can take place even among homogeneous agents In what follows, I find it useful to assume the the effects of within each economy when exploring homogeneous agents across countries. The in across projects or heterogeneity heterogeneity to is active even among the market assumed credit keep divisibility only indivisibility constraints. Aggregate Implications of Credit Market Imperfections 9 the homogeneous agents. To ensure that the results are not driven by the of the projects per se, it is assumed that a continuum of the indivisibility access to have the identical This (indivisible) agents projects. helps to the said this, how aggregate production convexify technologies. Having ever, let us now 3.2 Heterogeneous look at some examples Agents: with Distributional heterogeneous agents. Implications Let us first allow or the net the agents to differ in the input endowment, co is distributed to model the worth, where Otherwise, G(co). according is the same as above. In particular, the agents share the same R, that is, as entrepreneurs. they are equally productive With different face different endowments, heterogeneous agents co> coc= 1 can (BC). For a given level of k, only those with XRf'(k)/r, borrow. If (PC) holds strictly, Rf'(k) > r, all of these agents invest. Hence, the total supply of capital is equal to R times the fraction of the agents so that (BC), satisfying T / . k = R 1 - Gil-LX1XRf'(k)Y(8) As the RHS of (8) is decreasing in k, this equation determines k uniquely. > r holds at this solution, as it is indeed the long Rf'(k) equilibrium value of k. If not, the equilibrium is given by Rf'(k) = r. Inwhat follows, As let us assume are such that the that the parameters is char equilibrium by (8)with Rf'(k) > r. Both a lower r and a higher X increase the RHS for a given k. Hence, both lead to a higher k. The reason is These simple. changes increase the discounted value of the raises the revenue, which present pledgeable acterized limit. Hence, more agents can finance the project. One can that k goes up, when the distribution of the net worth shifts to the right in the First-Order-Stochastic-Dominant manner. This is a gen eralized version of the net worth effect discussed earlier. Let us now see the distributional of the credit implications improving "-" denotes market. Let X go up from X~ and X+. the value (Superscript " " the change + before and superscript, denotes the value after the change.) As noted above, an increase in X leads to an increase in k from k~ to k+. This increase in k occurs because a larger fraction of the agents are now able to finance their means which that the projects, threshold level of the net worth has declined from co;= 1 - X Rf'{k~)/r to = three classes of Therefore, we need to distinguish coc+ 1 X+ Rf'(k+)/r. borrowing also show 10 Matsuyama u(co)yf * ' ' Rf\K)-r' s ' Rf{k+)~r S\ \ T ' \S\ O coc+ Figure 1.1 Distributional s o)c Impacts co < co/ invest neither before nor after the their before and after the change. Hence, utility (period-1 consumption) = = rco. < co< are those with Second, (i+(co) co/ given by U~(co) change co~ invest only after the change. Hence, their utility increases from U~(co) = rco to = > IT(co) co). r(l Rf'{k+) Finally, those with co co~invest both their utility declines from U~(co) = before and after the change. Hence, = declines from r(l co), before/'(fc) co) to IT(co) r(l Rf'(k-) Rf'{k+) agents. First, those with effects.13 f'(k~) to/'(/c+). Figure 1.1 illustrates these welfare from the credit market The Thus, not everyone gains improvement. middle class gains (as well as the owner of the hidden factors, which are of the consumption inputs to capital in the production complementary reason the rich lose. The is that credit market imperfections good), while like barriers. The should be operate entry political economy implications clear. If the political power is in the hands of the rich who have easy access to credit, the government has an incentive not to improve the credit market. 33 Heterogeneous Let us now Agents: Replacement the case where Effects the agents differ also in their pro each agent is identified by (co,R) distributed ductivity. More specifically, to G(co, R). Figure 1.2 illustrates the two constraints according consider Aggregate Implications of Credit Market Imperfections 11 i 1 V a| B i-r.:v...i ^X . X i-r.i.w X \ _I_i_V* 0 ^X N > r r/f{lf) r/f{k+) r/l+f(k+) r/X~f{k~) 1.2 Figure Effects Replacement Bf'(k)/r>l (PC)(9) = 1co> coc(fc, R) XRf{k)/r. (BC)(10) The agents (PC), while XRf'(k)/r, satisfy aggregate supply lowing = line, R r/f'(k), satisfy = = 1line, co coc(fc,R) satisfying both invest. Thus, the to the right of the vertical the agents above the negative-sloped located (BC). Only of capital the agents is given by the unique solution to the fol equation: 00 k= \ R \ r/[f'(k)) 00 ?(co,R)dcodR(11) lJG>c(k,R) it is straightforward to show that k goes up in response to a lower Again, a a First-Order Stochastic-Dominant shift of the net r, higher X, and to the right. worth distribution Let us look at the effects An increase hence of an improved credit market more closely. in X from X" to A,+ leads to an increase in k from k~ to k+, and to a decline the in/'(fc) from/r(fc~) to f'(k+). These changes move line to the right, and the negative-sloped line to the left, as shown by arrows in figure 1.2. This means that four classes of the agents in A be Those in may distinguished. stop investing. Those in B continue vertical vesting. Those in C start investing. The rest never invest. This means the rich but less pro that, as a result of a credit market improvement, 12Matsuyama inA are replaced by the poor but more productive agents now able to bor are in C.14 Clearly, those in C are better off because they row and invest in the profitable those in A and in B are project, while ductive worse agents off because their projects become less profitable due to the entry by the agents in C. To explore further let us now look at amore specific ex implications, are only two types of agents. Their relative that there ample. Imagine < > co2, so that and net worth R2, coa type-1 satisfy R: productivity are than Let 6 denote the richer but less agents type-2 agents. productive and that 1 - coa< (R1/R2)(l furthermore share of type-1. Suppose co2) 1 - co1< X' < consider the effects of an increase in X from X~ to X+, where < < 1 - co2. Then, for co2) X+ type-1, (PC) ismore stringent (RJRJil than (BC) both before and after the change, and, for type-2, (BC) ismore than (PC) both before and after the change. Furthermore, stringent when 0 and r are chosen to satisfy the inequalities, 1 - co2 f'(Rfl) ^ ^ X~R2 one can show r 1 ^ /'(R2(l R1 that the equilibrium r 0)) ^ 1 co2 ' X+R2 takes the following form: the change (X = X~), RJ'{k~) = r,where k~ < Rfi. That is, (PC) for type-2. Some type-1 in is binding for type-1 and (BC) is violated vest, but no type-2 invest. < After the change (X = X+), X+R2f,(k+) = r(l 0). co2),where k+ R2(l for type-1. Some for type-2. (PC) is violated That is, (BC) is binding no type-1 invest. type-2 invests, but Before = but rich agents invest, none of X~, only the unproductive Thus, with X = but poor With X is credit-constrained. whom X+, only the productive are all credit-constrained. whom of Furthermore, aggre agents invest, (the total amount of the inputs going into the projects) gate investment in the credit market. This is may decline as a result of an improvement as the credit investment improve endogenously, technologies more to the from the less productive agents. productive agents a feature of the above example. More This is by no means peculiar a better credit market does not necessarily mean that there are generally, the two ex the active firms. Consider less credit-constrained among is perfect so that no firms are treme cases. If X = 1, the credit market shuts If X = 0, on the other hand, the credit market credit-constrained. down completely. Hence, only the firms that can self-finance entirely op because shifts Implications of Credit Market Aggregate erate so that no active diate cases should we Imperfections 13 firms are credit-constrained. expect some active Only in the interme firms to be credit-constrained. so far have been in partial equilibrium in that the market the models rate of return required by the lenders, r, is treated as exogenous. It is now in general equilibrium. endogenized All 4 General Deepening with Equilibrium versus Net Worth Endogenous Effects Saving: Capital Let us go back to the homogeneous case, where all (investing) agents have the same R and co. In this section, we call them "entrepreneurs," because we also add some agents, "savers," who have no access to the investment co?units of the input. In addition projects. The savers are endowed with to the period-1 consumption, they also consume some of the inputs in pe riod 0.More specifically, U? = V(C?0) + C?, subject to the they maximize = r(co? Co0),where Vis an increasing, concave func budget constraint, C? tion. Then they choose their saving, S? = co? C?Q,such that V (co?- S?) = r, which defines their saving function, S?(r) = w?- (V'y\r). Since the entre the aggregate preneurs save all of their endowment, saving of this econ or to in the total used the available be omy, inputs projects, is given by S(r) = co+ co?= co+ into cap S?(r) (V)_1(r). Since these inputs are converted ital at the rate equal to R, the aggregate of is supply capital given by k = RS(r) = R[co + co?- {V')-\r)l (RQ(12) where (RC) stands for the Resource Constraint of the economy. are given and (PC) (BC) of the entrepreneurs by = Rf'(k) Max 1, i^ r ~ co+ co? (W(r) - S(r)= I(r)- I(/')-if Max 1, 1.3 depicts + (BC)(5) (PC) k and r. These (5) and (12) jointly determine Equations as ditions may be rewritten more compactly As before, equilibrium Jj\ con (13) of the upward (13) by the intersection equation and the sloping aggregate saving schedule, S(r), ag downward-sloping on the aggre schedule, l(r).15Note that S(r) depends gregate investment co + co?,while on the entrepreneur's en I(r) depends gate endowment, Figure dowment, co. 14Matsuyama J RKJ { V X \R) r ^V /S(r) = co+a)?-(Vyl(r) _ k/R O Figure General 1.3 Equilibrium with Endogenous Saving the effect of a higher endowment of the savers, Figure 1.4 shows to the right, while keeping the invest which shifts the saving schedule An in fi ment intact. schedule increase the aggregate saving, which nances the aggregate that more capital is produced. investment, means to diminishing of capital de returns, the marginal productivity a rate In to return. of this is the standard leads low which essence, clines, Due neoclassical capital deepening effect. The effect of a higher X,when (BC) is binding (X + co< 1), is shown in to the right, while the saving 1.5. schedule investment shifts The figure intact. By easing the borrowing constraint, more en could borrow to finance their investment. With the upward trepreneurs rate of return. Re sloping supply of saving, this raises the equilibrium = savers to the entrepreneurs the the wealth from (Aco -Aco? distributing > 0) would have the same effect, through the pure net worth effect. schedule remains The effect of a higher net worth of the entrepreneurs (Aco > 0), when the offsetting (X + co< 1), without (BC) is binding change in the saver's a as two effects discussed combination the be viewed of wealth, may above: the capital deepening effect, due to an increase in the aggregate Aggregate Implications of Credit Market Imperfections .r S(r) = 15 co+co?-(V)-\r) "?]-"m Figure 1.4 Capital Deepening Effect: Aco0 > 0 - k/R O I Figure 1.5 Net Worth Effect: Aco = -Aco0 > 0 (and AX > 0) for X + co < 1. increases the aggregate in saving, and the pure net worth effect, which vestment. When the latter dominates the former, as shown in figure 1.6, rate of return goes up.16 However, once the entrepre the equilibrium neur's net worth becomes high enough to make (BC) irrelevant (X + co > 1), a further increase in co reduces the rate of return, because only the capital deepening In short, the equilibrium effect is at work. rate of return may to the borrower net worth. respond non-monotonically a rate return in a sign of low of be could generally, equilibrium either good or bad economic In section 6, we will explore conditions. More 16Matsuyama ?- Figure 1.6 Combined Effects: further Aco> implications 0, for X + "* co< 1. of this feature of the model in the context of a global economy.17 5 General It has been Equilibrium assumed Let us now project. ect to invest. with Heterogeneous Projects so far that each agent has access to one type of only where agents can choose which proj look at amodel with the world with homogenous entrepreneurs Again, we consider unit mass, each of whom is endowed with counits of the input at period 0 and consumes only at period 1. To keep it simple, we assume that there are no outside agents, "savers." Despite that this makes the aggregate and the net worth saving inelastic, credit market imperfections the composition affect the equilibrium allocations by changing can still of credit flows. can choose one (and Entrepreneurs = A 1,2,...,/). projects (; Type-j project puts in period 0 into m;R; units in capital tion good. Thus, the projects may differ as well as the types of the goods produced only one) of / non-divisible converts m. > counits of the in and units in the consump m]B] in the set-up cost, productivity, (and their compositions). By = + can consume a the co) agent running project-/, B;] r(m; m.[JR;./'(fc) + rco in + can always consume period 1. Since the agent B; r] mj[Rjf'(k) rco by lending, the Profitability Constraint for a Type-j Project (PC-;) is given by Aggregate Implications of Credit Market Imperfections (BC-j) / n(co) Rjf'{k)+Bj-/ i i ^/ 4 17 (PC-j) / I | **^ XiRjfW+MjBj \ __? I ? CO o Figure 1.7 ?,./'(*:)+ B;>r. (PC-;)(14) the credit market that only a imperfections by assuming X. of capital and a fraction of of the consumption good are jul; to a the lenders. the Constraint Then, pledgeable Borrowing for Type-] Proj ect (BC-j) is given by We introduce fraction mfcRf'ik) Both + > Mj-B,] r(mj co).(BC-/)(15) (PC-;) and (BC-/) need type-/ projects. Figure 1.7 shows = Min r(co) 1 the graph u.B. 'JLR,/'(*) ' >J + ^> II ? co/m to be satisfied for the credit to flow into of . + B,' (16) ',Rf'(k) J < In other words, (PC-j) and (BC-/) are satisfied if and only if r /^(co). this graph shows the maximal rate of return that a type-; project can gen erate to the lenders without (PC-/) nor (BC-;). As shown, the violating co is in when is the relevant constraint. The rea graph increasing (BC-;) son is that a eases net worth the constraint as the en higher borrowing need to borrow less. This makes it possible for them to trepreneurs a rate return to of the lenders. The promise higher graph is flat when is the relevant constraint. (PC-;) Both the equilibrium let n. denote the measure of formally, initiated of the who in invest (and type-; projects agents type-; projects). Since each type-; project requires m. units of the sav input, the aggregate the if investment and if ing equals aggregate only To describe 18Matsuyama <0= 5>;"> (17) j Since each type-; project of capital is given by k= produces m;R; units of capital, the total supply (18) 5>,R,*,.). can compete with one another for credit and they to the credit all the goes only projects projects, freely among rate of re the highest and hence generate which have the highest jj(co) as can be expressed turn to the lenders, which Finally, choose as the agents r = Max = > (j;.(co)} r.(co) Min ; ] \X.RJ'(k) _ + u.B. ^ 1 ],R.f'(k) + Bj ; (19) = l,2,.../), n,=>0(; the two where conditions. inequalities The equilibrium slackness in (19) are the complementarity is fully characterized of this economy by (17)-(19). Let us now 5.1 A Model look at some with Investment-Specific Suppose projects special cases. Pure Capital Projects: Technical Change Endogenous = = 0 for as inMatsuyama 1,2,...,/, all; B;. of the output; do not differ in the compositions homogeneous capital. In this case, (16) is simplified (2007). Thus, the they all produce to 4^ =Mini?^?,lk (20)> f'(k) J [l-co/m/ to the RHS of (20), which that the projects can be ranked according of the of the allocation is independent of fc, and hence independent has a credit allocation of the means that the equilibrium credit. This Note all the credit goes to only feature. That is to say, generically, bang-bang a and when one type of project at each given level of the net worth is the effect credit net in affects the the worth composition, change from one type to an the switches credit drastic: and completely abrupt to say, this is neither realistic nor robust feature of the other. Needless the exposition.18 it but model, greatly helps to simplify 5.1.1 where the case Let us begin with Change Productivity Procyclical = 2 and are > be trade-offs In there words, / X2R2. R2> R1> Xftx Aggregate Implications of Credit Market tween productivity hence and agency problems. Project 2 ismore productive, to the borrowers, while Project 1 offers more pledge unit of investment, which makes them potentially appealing return per "safer" or a "more able can be important 19 Imperfections secure" when alternatives some for the lenders. advanced technologies may be subject to bigger dane projects that use well-established projects agency Such tradeoffs that use problems leading edge than some mun technologies. inwhich the graphs of (20) for; = Figures 1.8 and 1.9 show two ways 1 and 2 could intersect with each other. In both cases, there is a critical net worth all the credit flows to type-1 projects level, coc,below which = 1= and above which all the credit flows to type-2 projects n2 1) (nx r2{(o)lf\k) R2-_ R/ hRi- Figure 7 n((o)/f'(k) A / j ^^ hRi \ o -7\-* Wc 1.8 r2(co)/f'(k) R; R' T^ hRi-y\ ^ hRi Figure 1.9 \ n(co)/f'(k) e> 20Matsuyama Rico / / R\co *<? -TT" Figure 1/ O coc 1.10 Procyclical Productivity Change = = 0). Then, l-n2 (n1 rium supply of capital from (17) and (18), we can show that the equilib is fl ifco<coc, (21) [2 ifco>coc, as shown in figure 1.10. Thus, a higher net worth can raise the productiv used from Rx to R2. In short, the invest ity of the investment technologies ment productivity changes procyclically through the credit channel. The k= where Rm<o, /(co) = a low net worth, the agents have to rely the into flows heavily borrowing. saving type-1 projects, which rate net worth im the higher return.19 When of pledgeable generate the borrowers need to borrow enables the entrepre less, which proves, neurs to offer the higher return to the lenders with type-2 projects, despite intuition should on that they generate The equilibrium = r(co) be clear. With Thus return per unit of investment. the lower pledgeable rate of return is now given by RRJ'(Rma>) (22) Mini?-^f-, [ 1 co/m/(co)1}J rate of return that a higher net worth affects the equilibrium to pledge it three allows the borrowers channels. First, separate through more to the lenders per unit of lending. Second, the credit composition Note may shift toward more productive projects. These two channels work in this is the usual capi the direction of a higher rate of return. Offsetting in the direction of a lower return. The tal deepening effect, which works overall effect can go either way. Implications of Credit Market Aggregate Imperfections 21 Let us briefly consider the implications of an increase in One may Xr or that a better corporate contractual enforcement governance cause more to into would the credit flow the invest always productive think ment raises X2. But projects. That is certainly the case, if the improvement if it raises Xxl Look at figure 1.9. In this case, a higher X1 leads to a higher coc.This offers some cautions. If an attempt to improve corporate what ismore effective for the well-established industries, where governance are the nature of the agency problems well understood relatively (type-1 itwould end up preventing the saving from flowing into new, projects), but more productive technologies, the nature of the agency problems Dynamic run by small venture capital, where are less understood (type-2 projects).20 Implications: Credit Traps so far treated coas exogenous. Let us now explore the dynamic of implications procyclical investment-specific technological changes by some positive feedback from k to co.To keep it simple, we fol allowing low Bernanke and Gertler (1989) and consider the world where the econ We have a la Diamond of a sequence of overlapping generations = zero Time is to discrete and extends from (1965). 0,1,2,...). infinity (t In each period, a new generation of the homogenous agents arrives and (those "born" in period t), stays active for two periods. For generation-f omy consists their "period 0" is period t and their "period 1" is period t + 1. They dif fer from the two-period in discussed above instead of that, agents only a are endowed with fixed endowed with the "hidden co, they being ?, factors" in fixed supply, which are used with the capital stock produced of the final good, F(kt, Q, (where -1), kt, in the production by generation-(f the final good may be used both as the consumption good and the input = for the investment earn save thus and co, f(kt) project). They kj'(kt) = t. Then, at the end of period t, they enter the W(kt) during period credit relationship and produce among themselves kt+1,which will be come available in period t + 1, and used to the final good with produce + 1). The factors" in fixed supply supplied by generation-^ of this overlapping dynamics economy are described generations simply co and k in (21), which becomes by replacing by W(kt) by kt+1 equation the "hidden = = K+i V<jy>W(fc*)'where /(?>) fl if co< coc, (23) [2 if co> coc. For any initial condition, k0, the entire equilibrium tained simply by iterating (23) forward.21 trajectory can be ob 22Matsuyama y\RiW(k) R\W(kt)/j Figure Credit | 1.11 Traps = ismonotonically follows, let us assume that W(0) 0, W(k)/k ? = o? and is the with 0, which \ivcvk_^JN(k)/k limjt_>0W(fc)//c decreasing, case iff(k) ? ka, with 0 < a < 1. Under the dynamics these assumptions, are characterized of the form, kt+1 = convergence by monotone R;W(A:,), In to the unique positive with other for fixed state, words, any /. steady or out heterogeneous credit market the without projects, imperfections, Inwhat one-sector of the economy look like the standard neoclassical dynamics case a with (23), because credit mar la Solow. This may not be the model cause endogenous in invest ket imperfections productivity changes ment technologies. one of three generic cases. It shows the case Figure 1.11 illustrates < < where fc* kc fc**,where fc*, fc**, and kc are defined by fc*= R1W(fc*), fc** = = coc.There are two stable steady states, fc* and R2W(fc**), and W(kc) as a credit trap. In this steady fc**. The lower one, k*, may be interpreted so net low that worth is the the state, saving flows into the projects that return per unit of investment, the higher pledgeable although of The lower less capital leads to supply resulting capital. they produce a lower price of the endowment of entre held by the next generation a state the net worth. Which low and hence economy preneurs, steady generate on the initial condition. If the econ to depends converge entirely to fc*. If the economy omy starts below kc, it converges monotonically to A;**. Thus, kc may be starts above kc, it converges monotonically as the critical threshold level for economic development.22 viewed will 5.1.2 where now the case Consider Productivity Change Countercyclical = 2 with < > and (1 ^2R2/R1)/(1 / mjm2 R2>RX> X2R2 XXRV Aggregate Implications of Credit Market Imperfections 23 r2(co)/f\k) R,--y hlR2 **.^f AiRi \ \ \ -':-:Wc O Figure co COcc 1.12 are less productive and generate less XJ < 1. Thus, type-1 projects rate return of than set cost the However, up pledgeable type-2 projects. ismuch smaller for type-1 projects, so the agents need to borrow much less to invest into these projects, which may give type-1 projects advan type-2 projects. For example, type-1 projects could represent or other farms small while businesses, family operated type-2 projects in sector. the investments the Or, type-1 projects represent corporate traditional such as textile and furniture, represent light industries, tage over which a small initial expenditure, while relatively type-2 proj as ects represent modern such industrial equip industries, steel, heavy ments, require and petrochemical, pharmaceutical industries that require a rel atively large initial expenditure. = 1 and 2 intersect twice Figure 1.12 shows that the graphs of (20) for; an with each other. For intermediate value of coc< co< cocc,all the credit = 1= 1. all the credit goes to Otherwise, goes to type-1 projects, nx n2 = 1= 0. the Therefore, n2 type-2 projects, nx equilibrium supply of cap ital is now given by r2 k= Rm<o, as shown neurs must where /(co) = if co< coc <1 if coc< co< cocc, [2 ifco>cocc, in figure 1.13. When the net worth almost rely entirely on external (24) is very finance, into type-2 projects that generate more pledgeable of investment. As the net worth rises, the entrepreneurs attractive rate of return with type-1 projects than with flows low, the entrepre so that the saving return per unit can offer amore type-2 projects, 24Matsuyama i / // ' -??--;-1-+C0 O coc because net worth s cocc they need to borrow little for type-1 projects. Hence, leads to a shift of the credit toward less productive enough rises even type-2 projects. In this case, a higher which the savings flow a caution when offers fections a rise in the projects. If need becomes small further, then the borrowing for type-2 projects that the credit shifts back tomore productive the net worth targeted cocand hence X1 reduces into the more productive thinking about alleviating the range in type-2 projects, which credit market imper expands to small businesses. Implications: Leapfrogging Let us explore the dynamic by kt+1 in (24) to obtain implications Dynamic '2 = / 1.13 Figure K+i Rico Rj(W(kt))W(K)>where K?) = ' 1 ,2 and Credit Cycles as a Trap by replacing coby W(kt) and k if co< coc if coc< co< cocc, (25) if co> cocc, In figure among many. Figures 1.14 and 1.15 illustrate two possibilities = < < < are defined and A:* where 1.14, kc cocand kc kcc kcc fc**, by W(kc) = are fc* and A;**, cocc,and the two stable steady states, again de W(kcc) = = fined by fc* RaW(fc*) and fc** R2W(fc**). If kc<k0< kcc, the economy > to fc*. If converges mo converges monotonically k0 kcc, the economy as as we focus our attention to the range to fc**.Hence, long notonically to it can be look similar above kc, the dynamics figure 1.11. However, more complicated starts below kc. After the initial phase if the economy Aggregate Implications of Credit Market 25 Imperfections 45? kt+\ s ulL-1?L_i-u+K m Figure 1.14 Leapfrogging kt+\ 0| Figure Credit 45? k* kc kcck** 1.15 Cycles as a Trap to k*, if it falls into the intermedi of growth, the economy will converge ate interval, (kc, kcc).However, if R2W(kc) > kcc, the economy could bypass as arrows to in figure 1.14. this stage and converge indicated by the fc**, In this case, the long run performance of the economy sensi depends it suggests the possibility tively on the initial condition.23 Furthermore, of leapfrogging. That is, an economy that starts at a lower level may take over another economy that starts at a higher level.24 In figure 1.15, A:*< kc < < fc** and R2W(kc) < kcc. For kQ< kcc, the economy these credit cycles, an improvement nitely.25 Along causes a shift in the credit towards the less worth kcc that contribute net worth causes less to the future net worth. the credit to shift back fluctuates indefi in the current net productive projects in the The resulting decline towards the projects that help 26Matsuyama more in the following the net worth period. For k0 > kcc, on the the economy to the unique stable converges monotonically as another example of steady state, A:**.Thus, this may also be viewed credit traps except that the traps here take the form of cycles around kc, instead of the lower steady state, k*. to build other hand, 5.2 A Model A higher with Private Benefits net worth might also shift the composition of credit toward less are the agents attracted to running "socially productive" projects, when more some "socially unproductive" because projects, they generate or some satisfaction" other consumption "private benefits," "personal little to the lenders. To capture this idea, let R1 < R2, values, which mean and Bx > B2 = 0 with X1 = X2 = 1 and |i1 = \i2 = 0. Thus, capital is fully at all. type-1 but the consumption good is not pledgeable pledgeable, than type-2, but it is a lot of fun to projects are less "socially productive" run type-1 projects. Let AR = R2-Rl>0. From (17)-(19), one can show = = = > < that k Rx(o if co coc R2co if co coc (AR/R2)m1 or AR/'(R2co) >B1;k > B1 > and AR/'(Raa)) < Br If co > coc and AR/'^co) AR/'(R2g>), then = means RjCO< k < R2co. Inwords, all the credit goes to which Bv ARf'(k) cannot borrow for when the type-1 projects agents type-2 projects either or the private benefits of type-1 projects are not big enough to compen in capital when everybody else invests in type sate its low productivity for the agents can borrow 2; all the credit goes to type-1 projects when are of and the benefits big enough type-1 projects private type-1 projects the credit goes to else invests in type-1. Otherwise, everybody the private ben both types so that the total productivity (i.e., including are and between efit) type-2. type-1 equalized case where B1 > ARf,((R1/R2)ARm1). Then, Figure 1.16 illustrates the when [2 ifco<coc, k = Rma>,where /(co)= \ (26)if [1 co>coc. that they In this case, the agents enjoy running type-1 projects so much are rich enough to borrow, that is, co > coc= will do so whenever they (AR/R2)rar Dynamic Implications: Credit Cycles Again, we can look at the dynamic k = kt+1 in equation (26). Figure implications 1.17 shows co= W(kt) and by setting of credit the possibility Aggregate Implications of Credit Market Imperfections 27 k I R2CO {fT\Bi/AR) ./- \ / ' \ / s * \/' / M ' ! j \i ?co O(AR/R2)ml Figure 1.16 kt+\ . O I Figure Credit 45? k* kc k** 1.17 Cycles cycles. During booms, a high net worth allows the agents to pursue proj ects that generate but less capital, which satisfaction slows personal the agents cannot pursue down the economy. During such recessions, to credit more hence the that goes projects, generate projects capital, which leads to the next boom. Note that the welfare of these implications are credit cycles very different from those shown in figure 1.15. Here the booms occur as a result of the misallocation of credit, and they end when a sufficiently high net worth eventually corrects the misallocation. If the credit markets were perfect, and the agents could fully pledge their 28Matsuyama to the lenders, the booms would not occur and with "private benefits" out the booms the economy would never experience In con slowdowns. occur as a re in the recessions the shown trast, along cycles figure 1.15 sult of the misallocation of credit. 53 A Model with Pure Capital and Consumption Projects let us look at the case where / = 2 with R1 = R > R2 = 0 and Bx = 0 = B. Thus, type-1 projects produce <B2 type-2 proj only capital, while ects produce only the consumption good. The equilibrium conditions, (17) through (19), now become Now co= m1n1 + m2n2 (27) k = m^Rnx (28) Mini-?-, [1-co/V 1 \Rf'(k) - \JKf r> Mini-^-, [l-co/m2 that (29) contains the complementary type-2. Since only type-1 projects produce Note 1 B; n22> 0. V (29); J slackness condition only = <*> ensures capital,/'(0) in (29). the first equality in the absence of credit market Figure 1.18 shows the equilibrium = = which is 1, 1), jll2 given by (Xx perfection for nx > 0, hence Rd) ifco<cor, k R(Oc, = (30) ifco>coc, k Rcoc _.^^^^__^_ co -L-:- O COc Figure Perfect 1.18 Credit Case im Aggregate Implications of Credit Market Imperfections 29 = B. Thus, all the credit goes to the by Rf'(R(dc) return until its becomes project equal to the return capital generating which absorbs all additional of the consumption project, generating credit. where cocis now 5.3.1 Persistence defined of Recessions: Inefficient Starting from this benchmark, fection to the capital-generating a small Xv there sufficiently Financial Accelerator let us introduce the credit market imper < 1 and \i2 = 1).With type-1 projects (X1 some of the is an interval of co, in which a that type-1 generates into type-2 projects (k < Rco), despite > B, as shown in figure 1.19. higher return than type-2 projects, Rf'(k) to type-1 projects occurs because This under-investment (BC-1) is bind = B. The > over is (D/mJ ing: Rf (k) XxRf (fc)/(l graph upward-sloping a this interval, because shifts the credit flows from the higher net worth credit flows consumption-generating type-2 to the capital-generating type-1 proj ects by easing (BC-1). = = kt+1, one can easily see how a credit mar By setting co W(A:,) and k ket imperfection of this kind introduces persistence into the dynamics. 1.20 1.22 show three Figure 1.20 repli Figures possibilities.26 through and Gertler the key result of Bernanke (1989). There is a unique is characterized Now steady state, k*, which by the under-investment. a is that the hit which one-time-shock, economy imagine by temporarily the productivity of the final goods production. reduces the Without cates credit market state, RW(kc), the economy would go back to its steady imperfection, after one period. With the credit market imperfection, k hRf(k) Rcoc = B(\-(o/mfi ,.?\....A_ -i-!-:- O 1.19 Figure Under-investment of Type-1 <?' co mx{\-M) 30Matsuyama ki+\ RW(k,) ^'''/45? RW{kc) .mX~"^*\ h ~o[ **W\mi(\-M)) ' 1.20 Figure Financial Accelerator i 45? r w(kc).7 ?I y/ Vr\m\(\-Xx)) 1.21 Figure Slow Recovery its steady towards the economy goes back only gradually state, fc*, as indicated by the arrow. Even though the shock itself is tem porary, it reduces the current net worth, which tightens the borrowing however, the future investment. This in turn reduces future reducing or financial acceler so on. In short, the credit multiplier and ator mechanism creates an echo effect, transforming the i.i.d. shocks into = In serial the correlations. 1.21, unique steady state is fc* positive figure constraint, net worth, Aggregate Implications of Credit Market 31 Imperfections kt+\ R Figure Multiple _, 45? W(kc).i--7* 1.22 Steady States across projects the marginal is equalized RW(kc), in which productivity and there is no under-investment. the financial accelerator is However, at work at lower ranges. Thus, when the economy starts with a low cap ital stock, the credit market slows down the recovery pro imperfection the inefficient recessions. In figure 1.22, this mecha cess, prolonging nism is so strong that it creates two stable steady states, the lower of is characterized which and the economy may by the under-investment, a be permanently into All cases imply per recession. of these trapped sistence because the type of investment that helps to enhance the future borrower net worth is subject to credit market imperfections. 5.3.2 and Volatility Let us now introduce the = 1 and to < instead imperfection type-2 projects jli2 l).27 (A,a With a sufficiently small |i2, there is an interval of co for which the credit continues to flow into the capital-generating type-1 projects, even after the return of type-1 projects becomes lower than type-2 projects (k > as in shown 1.23. This over-investment to Rcoc), figure type-1 projects oc curs because ^ is that is, |i2B/(l (BC-2) binding, co/m2) Rf(k) < B. Note that the graph is non-monotonic. It is initially because upward-sloping, all the additional credit go to type-1 projects because net worth is too low for type-2 projects < to be financed: < B. |H2B/(1 co/m2) Rf'(R(ri) net worth so becomes some that credit Eventually, sufficiently high = flows into type-2 projects: < In B. this |li2B/(1 co/m2) Rf'{k) range, the Inefficient Booms credit market graph is downward-sloping because further increase in net worth shifts 32 k Matsuyama = {\-co/m2)Rf{k) Bn2 AY -L-1-i-+co coc 0 1.23 Figure Over-Investment m\(l-ju2) to Type-1 and credit flow from the capital-generating type-1 to the consumption type-2 projects by easing (BC-2). generating In The non-monotonicity of the graph carries over to the dynamics. a credit market into the dynamics, stead of putting persistence imper into the dynamics. It may generate or In fluctuations. convergence, oscillatory over-shooting, endogenous state is unstable and the fluctu its 1.24, economy unique steady figure ates indefinitely within the interval I.One can show that the two condi fection of this kind puts volatility tions are necessary for endogenous fluctuations (as well as oscillatory occur. to B to be sufficiently and needs First, convergence over-shooting) never flow into the type-2 projects. Sec credit would high; otherwise, too high nor too low. The intuition is simple. If |i2 can be neither small suffer from (a jn2),they are major agency problems type-2 projects = case never financed. which shuts the 0, (Just think of \i2 completely ond, credit always goes only to type-1 for type-2.) Hence, are If (a large projects. subject tominor agency problems type-2 projects are as soon as they become more productive than financed |i2), they = us back to the type-1 projects. (Just think of the case (i2 1,which brings occur only for in fluctuations credit market case.) Endogenous perfect termediate values of |i2. That is, the condition requires that the agency with the associated type-2 projects consumption-generating problems down the credit are too big to be financed when is low, but small enough the net worth is high.28 Again, the welfare to be financed when the net worth implica are similar to the case of figure 1.17 and op tions of these fluctuations Aggregate Implications of Credit Market Imperfections 33 45? kt+{ i^y^x\ RW(kc) f. J "}*--j-\?-J i ; , -l?_J-i-1-LJ-L> U I /Co v ^ ?** / Figure 1.24 Booms Inefficient and Volatility 1.15. That is, the misallocation of credit causes booms, a net worth corrects the borrower when collapse sufficiently high misallocation of the credit. posite which of figure sources of fluctu is to add some exogenous interesting extension ations to this model. For example, suppose that B may change over time. Recall that B needs to be big enough for the graph to look as in figure 1.24. If it is not big enough, the downward-sloping part of the graph is An far to the right so that the RW(A;,) intersects with the 45? line at fc**. If B permanently to fc**. converges stays small, then the economy once a in B that while to becomes However, every imagine big enough located the graph look as in figure 1.24. With occasional arrivals of alter investment which divert the credit away from the opportunities, the economy fluctuates around k*, below projects, capital-generating small again. fc**, at least until B becomes make native 5.3.3 Cases: Asymmetric and Intermittent Hybrid Cycles Volatility cases The two previous mar offer seemingly views credit of conflicting one ket imperfections, the other persistence, suggesting suggesting Indeed, each might volatility. However, they are not actually conflicting. of business capture different phases cycles as the following hybrid model illustrates. Let / = 3 with Rx = R > R2 = R3 = 0, B1 = 0, B2 > B3 > 0, and Xlf \i2 < 1, 34 Matsuyama = there jli3 1. Thus, type-1 is the only capital-generating projects, while are now two different of types consumption-generating (type-2 and the two, type-2 is more productive than type-3, but type-3). Between to not is the constraint. One could show, under type-3 subject borrowing certain values, parameter irrelevant type-2 projects become constraints) satisfy the borrowing with compete type-3. type-3 projects become ductive type-2 projects compete with type-2. In other words, cessions" model within volatility" The dynamics can be co (because they cannot so that type-1 projects effectively for a large co (because more pro so that type-1 effectively financed) re like the "persistence of inefficient the lower range, and the "inefficient booms and the model model irrelevant for a small within now looks the higher range. look like figure the features 1.25, combining 1.24. In this case, there is no stable steady state. of figure is characterized The equilibrium by asymmetric cycles, along which path the economy goes through a slow recovery from recessions, and, once in a into re and then, plunges booms, experiences period of high volatility, look like figure 1.26, com the dynamics may cessions.29 Alternatively, may 1.21 and figure kt+\ .y-p?r- ?o Figure 1.25 y Implications of Credit Market Aggregate Imperfections 35 kt+\ 45o k* 1.26 Figure of figure 1.22 and figure stable steady state, fc*. 1.24. In this case, the features bining unique Now there is a consider that the the following Imagine thought experiment. some is hit i.i.d. the shocks, shaking economy regularly by graph up and down. Figure 1.26 represents the situation when the size of a shock is be low a certain threshold the situation level, while figure 1.25 represents the size of a shock slightly exceeds the threshold level. Then, for most fluctuates of the time, the economy around k*, exhibiting the a la Bernanke financial accelerator mechanism and Gertler (1989). when encounters the economy bubble like asymmet However, intermittently ric boom-and-bust it which cycles, during experiences volatility much than that it. the shock larger triggers 6 General and Capital: We have now with Heterogeneous Equilibrium Patterns of International Capital so far assumed look at amodel different produce arises naturally is homogeneous. Let us with heterogeneous capital, where different agents in which context of One this problem types capital. is the case where the agents differ in their countries of and capital Imagine the world residence that capital produced Agents Flows they produce economy, are nontradable.30 consisting of two countries: North and 36 Matsuyama South. The structure of each country is given by the model with endoge in section 4. The two countries share the identical discussed saving and but they may differ in X, co,and co?.To avoid technologies preferences, a taxonomical us assume 1 > XN > Xs > 0,1 > coN> cos> 0, and 1 let analysis, > co^> co?> 0. Both the and the consumption input endowment good can nous the two countries. be traded between across borrow the borders. On (aswell as the hidden factors) in the North the entrepreneurs This allows the agents to lend and the other hand, it is assumed that capital us assume is nontradable. Let also that only (South) know how to produce capital used in the production of the consumption (South).31 We use good in the North on to explore the implications this model of credit market imperfections the patterns of international capital flows and economic development.32 The autarky equilibrium of each country is obtained = N or the S, as follows: / by adding subscripts, from (5) and (12) = = + (RC-;)(31) k, R[Sffl] R[co; co; (V'y1^)]. = Rf'(k,) Max\ 1, Or, from (PC-/) -r, ^-^ + (RC-/)(32) (13), = = <33) SAr/> | W + a>?and co; (V')_1(J)) = where Sfa) = Iff) = Nor S). ^{fV\Max\l, now -^UjO' that the two countries become fully financially integrated Suppose so that the agents from both countries can lend and borrow their input en across the borders and repay in the consumption dowments good with costs. By "without additional costs," ismeant, among other in of the lo each that the country, Xjf is independent pledgeability things, that the cation of the lenders. Of course, one could think more generally < < can from the fraction cpA,.(0 borrowers cp 1), when borrowing pledge the analysis is restricted to the two extreme cases abroad. Here, however, = of the autarky cp= 0 and the full financial integration, cp l.33 leads to a Rate of Return Equalization Full financial integration (RRE) out additional across the Min\-^?, two [1-(BN countries, 1W (U = r= Mini -^?, J [l-<os 1U/' (ks), J (RRE)(34) Aggregate = The world rewritten kN, ks = + R[aN + co?N cos+ co?s R[SN(r) + Ss(r)] is determined equilibrium as = SN(r)+ Ss(r) = ^^ 37 Imperfections = o?ensures the interior solution, (0) is constraint (WRC) given by where/' resource kN + ks Implications of Credit Market by > 0. The world-wide (V)~1(r)]. (34)-(35), which (WRCH35) can also be IN(r)+ Is(r). (36) > 1, which > also implies ^N/(l coN) 1, (RRE) be = = r= comes or kN (kN) f (ks), equivalently, ks. In this case, simply/' in either country, so that the movement of interna (BC) is not binding inmarginal tional capital flows is entirely dictated by the difference pro a result of financial integration, in South is the investment ductivity. As When - Xs/(1 cos) and capital flows until the differ by the lending from North, inmarginal eliminated. is productivity in South, the lend Even when Xs/(1 - cos) < 1, so that (BC) is binding to two if the differ countries in the flows from North South ing mostly saver's wealth. This is illustrated by figure 1.27, which assumes XN = XS, = share the same investment coN cos, co^ > (0?s.Then, the two countries financed ence investment is located to the right of schedule schedule, while North's South's. Hence, the autarky rate of return is lower inNorth than in South < are rates return With financial of the The (rN rs). integration, equalized. = = now + rate return is of given by [SN(r) Ss(r)]/2 IN(r) Is(r), equilibrium Ss(r) i View | ~ 1 Figure 1.27 Neoclassical a^^^^i of Financial Integration 1m B^?a " * h/R (XN = Xs, coN = cos, co^ >co?) 38Matsuyama as shown by the intersection the average saving schedule of the (common) investment schedule and dotted (depicted by the upward-sloping a rise in its rate of return, which increases its curve). North experiences and hence run a current account sur saving and reduces its investment, a fall in its rate of return, which plus, while South experiences its saving and increases its investment, and hence run a current deficit. ment. reduces account In short, North's to South to finance its develop saving flows This captures the standard neoclassical view of the global finan cial integration. The reverse flows than South's. higher ing schedule, while ifNorth's occur, however, autarky rate of return is In figure 1.28, the two countries share the same sav North's investment schedule is located to the right of financial the rate of return is hence, rN > rs.With integration, at the level the the intersection of (common) given by saving equalized schedule and the average investment schedule (depicted by the down South's, its rate of return to dotted curve). North (South) witnesses ward-sloping to rise (fall), and hence fall (rise), its saving to fall (rise), and its investment its current account to turn into a deficit (surplus). In short, the capital investment. One way inwhich the sit flight from South finances North's = = > in figure 1.28 can occur is XN Xs, coN cos, co^ uation depicted co^.This case captures stitutional the view factors that weak contribute and governance corporate to financial any in South in other and hence insecurity capital flight from South toNorth. Another way inwhich the situation de can occur is XN = Xs, coN- cos= co^- co^> 0. In this case, picted in figure 1.28 lr t S^r) =Ss(r) \ \ Mr] ~: : : : %Ur) ? ks/R kN/R Figure 1.28 Capital Flight -co?N>0. = (I): XN > Xs, coN cos, co^ = co?;OR Capital Flight (II); XN = Xs, coN - cos = co" Implications of Credit Market Aggregate Imperfections 39 a larger share of the wealth is in the hand of the savers in the South than in the North. Then, even though the two countries do not differ in the the "capital flight" occurs from South toNorth. This is other dimensions, the firms in the South have weaker because the firms in the North. balance sheet conditions the former more This makes than on exter dependent in turn makes nal finance, which them less credit-worthy. A financial in tegration forces the firms in the South to compete with those in the North when financing their investments, which put the former in disadvantage. As a result, South's saving flows to finance North's investment. = = Figure 1.29 illustrates the case where XN Xs, coN> cos, co^ co^. In this case, North's saving and investment If the pure net worth of South's. right we have rN> rs.35Again, ening effect, schedules are both located to the effect dominates the capital deep that, with financial in this implies the toNorth, because from South flows the firms in the tegration, saving South have the weaker financial position than those in the North.36 Note that, inmany of these cases, kN> ks continues to hold after the full so that the marginal financial integration, re of investment productivity the assumption higher in the South: Rf (kN) < Rf (ks). Obviously, that only the local firms can produce the capital stock used in the pro duction of the final good in each country, plays an important role in the mains If any firm from any country could operate at the analysis. anywhere same in the difference would be productivity, marginal productivity some eliminated in which FDI to flows from North by two-way flows, South (some agents inNorth produce capital in South), and at the same ''' *W* mmm >jK b^b ^kf* ?-i-: Figure Capital *A* ^W* u ks/R kN/R 1.29 Flight = = (III): A,N Xs, coN > cosco^ 1 "^^ co?. 40Matsuyama time, the saving flows from South to North. Even if their productivity declines when operating abroad, the two-way flows may occur, as long as their financial to offset the produc is more than enough advantage of abroad.37 tivity disadvantage operating So far, it has been assumed that the two countries share the identical ifNorth ismore productive than South, the re technologies. Obviously, verse could occur.38 For if flows RN> Rs, the capital capital example, even without flows from South to North credit market imperfections. it is difficult to draw a sharp distinction between the two the However, one on tech and based ories, one based on credit market imperfections because the differences differences, may be nological technological caused by credit market Recall that credit market imper imperfections. fections may often prevent the credit from flowing into the most pro of section 3.3) or the most productive agents (in the model proj some models of section (in 5). To the extent that credit market cause in investing it technologies, imperfections endogenous changes to tell the two theories apart empirically. would be a challenge ductive ects Implications: Dynamic Symmetry-Breaking and Endogenous In the above it is shown how the cross-country analysis, distribution (coN, cos) affects the cross-country Inequality net worth dis of the capital now us Let feedback from introduce (kN, ks) to (coN, (kN, ks). positive remove savers us it from model. the the To let By re cos). simple, keep we in obtain the k. and (31), dy by kjt+1 equation placing co;by Wj(kjt) namics of each country in autarky, as follows: tribution stock = = kjt+1 RW(kjt) (;' NorS), (37) which fc* = implies that each country converges RW(lfc*). From equations (34)-(35), the dynamics financial integration are given by: monotonically of the world to A:*,where economy under (rre)(38) Ht^'+^-Mt^'1^^ = KM + *sm *[W(U + W(kst)]r (WRC)(39) a function of (kNt, kst). Hence, (kNt+1, kst+1) as jointly determine can be the from any initial condition, trajectory (kNQ,kso), equilibrium solved for by iterating (38) and (39) forward. which Aggregate Implications of Credit Market Imperfections 41 Let us look at the steady states. In what let us restrict our follows, to the case where XN = XS = X,which means that the only possible source of across countries is in the initial capital stocks.39 heterogeneity selves are binding in both countries are given by constraints If the borrowing the steady state conditions //(M in steady nK) = state, (RRE)(40) l-W(kN) 1-W(ks) = kN+ ks R[W(kN)+ W(ks)] (WRC)(41) 1.30 illustrates these conditions for an intermediate value of R. It that there are three steady states. One of them, (SS), is symmetric, = (A:*, A:*).The other two are asymmetric, given by (kN, ks) (ASN) and = = (ASS), given by (kN, ks) (kH, kL) and (kN, ks) (kL,kH),where kH > fc* > kL. Furthermore, (SS) is unstable because Xf(k)/[1 W(k)], is increasing at = so k rate the return that in of each k*, pledgeable country is increasing in the steady state capital stock. The instability of (SS) seems to suggest Figure shows (ASS) are stable, if this is the case, the two-country world under financial integration. Thus, this cap economy develops unevenly tures the structuralist view that poor countries are unable to compete in that (ASN) and integrated capital markets cial security to the lenders can offer finan against rich countries, which and that the global capital market contributes ks . , (WRC) kL Figure I dpS f\\) y k*kH = kN ks VT\\) 1.30 Symmetry-Breaking and the Emergence of Core-Periphery Patterns 42Matsuyama to uneven of the world the core economy, creating development or and the International Economic Order, or the patterns periphery of the Rich and the Poor.40 World-System is suggestive, the two While the above analysis analytically verifying "ifs" above is difficult.41 Instead of the two-country case, Matsuyama a of countries and with continuum the above model studied (2004a) showed analytically, as a whole In autarky, the world economy converges of the initial distribution ric steady state, regardless across to the symmet of capital stocks countries. small X, and for an intermediate For a sufficiently range of R, financial a symmetry-breaking.42 causes That is, the symmetric integration stable steady asymmetric steady state loses its stability and many states richer In any stable steady state, to emerge. other countries than in autarky, while some countries become poorer become than in autarky. into the rich and divided is endogenously Thus, the world economy of these results deserve emphasis. the poor. Two implications First, this a partial improvement in market credit the how demonstrates example = 0 to = could have move X less than while from cp 1, one) 9 (a keeping are to that dramatic distributional consequences surprising perhaps in the credit market financial integration alleviates imperfections many; in other some countries and exacerbates the credit market imperfections Second, the instability of the symmetric steady state and the an intermediate occur states of asymmetric only for steady across nations. That the rise and fall of inequality value of R. This suggests R improves over time, the world is, as productivity economy may first as some countries start taking off, and then fol divergence, experience as other countries start catching up, thereby gener low by convergence, across nations. patterns of inequality ating the inverted U-curve above is that "hidden factors" are nontradable. One key assumption the fu in one country would means investment the This that improve not same else in the ture net worth of the entrepreneurs country, but in one If these factors were where. freely tradable, then the investment in any country, on the net worth same effect the have would country across countries. of inequality the persistence eliminate which would some of these factors are tradable at The interesting case would be when countries. existence some positive costs. Then, the investment demand would have bigger Implications of Credit Market Aggregate Imperfections 43 in the neighboring lead to some countries, which might as as at well the global scale. effects contagion divergence spillovers gional 7 General Equilibrium Heterogeneous Projects: re with Heterogeneous Agents with Patterns of International Trade In all the models with heterogeneous agents above, it has been assumed that each agent has access to only one type of projects. Let us now discuss amodel with agents, where each agent has access to a di heterogeneous verse set of projects, in the context of international trade. a variation of the Ricardian model with a continuum Consider of trad able goods, indexed by z e [0,1], a laDornbusch, and Samuelson Fischer, a continuum is populated of homogeneous (1977). The economy by < co 1 whom is with each of endowed units of the input. Let us agents, now call this input labor, the tradition of the trade literature. following are given by symmetric so that demand The preferences Cobb-Douglas, = for good z is D(z) E/p{z), where p(z) is the price of good z and E is the in this economy. To produce aggregate any tradable good, expenditure the agents must run a project. Each project in sector z requires one unit of labor and generates R units of good z. Each agent may run one proj ect or may simply become aworker, by the labor endowment supplying to other agents. Since any project requires one unit of labor, and the labor endowment of any agent is co< 1, each agent who runs the project must employ 1 - co units of labor supplied by those who do not run the project. Let w be the can which the to after rate, wage pay to the workers employers pledge the project has been completed and the output has been sold. By running a project in sector z the earns p(z)R, out of which entrepreneur they pay the wage bill, w(l - co), so that they consume p(z)R - w(l - co). run By not labor, they consume wen. Hence, ning the project and supplying any to run the project in sector z if and agent is willing w(l only if p(z)R > co) wco, and equivalently, p(z)R>w, where (PC-z)(42) (PC-z) stands for the Profitability Constraint for Sector z. This con straint may not be binding, can because the employers a pledge only fraction of the project revenue for the wage payment. The employers in sector z can pledge where is continuous and X(z) only X(z)p(z)R, strictly the range from zero to one. Because of the partial increasing with the projects in sector z take place if and only if pledgeability, they satisfy 44Matsuyama > co),(BC-z)(43) X(z)p(z)R w(l where (BC-z) stands for the Borrowing Constraint for Sector the pledgeable fraction of the project revenue, X(z), is The that it is assumption specific. strictly increasing means are tors indexed such that the agency problems underlying ing constraint are bigger in lower-indexed ensure The Cobb-Douglas preferences z. Note now that sector that the sec the borrow sectors. that, in autarky, the economy in sectors. all both the Thus, (PC-z) and (BC-z) must be satis produces z. one fied for all for each z, of them must be binding; oth Furthermore, erwise, p(z)/w no agent would = max{l, (1 - become workers. co) A(z)}/R. Therefore, (44) in X(z) < 1 - coand constant for X(z) > 1 - co.Note that, for It is decreasing X(z) < 1 co, (BC-z) is binding and p(z)R > w. In the sectors plagued by big in order to as each project must earn higher revenues agency problems, sure the workers for their wage payment. The higher prices and higher are to sectors in the these due the difficulty of obtaining project see in restricts let which the these sectors.43 To de this, credit, n(z) entry note the number of projects run in sector z. Then, the total output in sec tor z is n(z)R, which must be equal to D(z) in autarky. Thus, E = p(z)D(z) = (44)becomes p(z)n(z)R. Hence, revenues = co))EM(45) n(z) min{l, X(z)/(1 in X(z) < 1 - coand constant for X(z) > 1 - co.Since each is increasing is labor endowment project requires one unit of labor, and the aggregate resource in is to constraint this the co, economy given by equal i which [ n(z)dz = co. (46) Summing up (45) for all z and using (46)yields n(Z) min{l,Mz)/(l-co)} ^( } \lmin{l, X(s)/(1 co)}ds < co for low z and n(z) > co for high z.44 This restricted implies n(z) excess firms to sat entry and the resulting profits enable the incumbent sectors. in low-indexed constraints isfy their borrowing which consists of two countries of the Now, suppose that the world economy and South. North kind analyzed above, They have identical parameters co. it is that XN(z) = XNA(z) and assumed Furthermore, except X(z) and = in z with the and increasing XsA(z), where A(z) is continuous Xs(z) Implications of Credit Market Aggregate \ 1pu{z)lwA Imperfections 45 ps(z)/ws . \/Rvx .^-^ ?-l-[- O 1.31 Figure of Absolute Patterns A(z) {\-coN)/XN (\-cos)as Advantage to one, and 0 < A,N, A,s < 1. This means that the agency two the constraint have components; problems underlying borrowing on the and other sector-specific factors, and A(z) depends technologies on corporate and governance, XN and Xs depend legal enforcement, from zero range other factors that determine country-specific in these economies. In what cial development -coN)AN<(l-cos)As. From (44), the autarky now given by prices = P/(z)/u;. max{l,(l-co;.)A7A(z)}/R in North (j the overall follows, and South, = level of finan let us assume (1 pN(z) and ps(z) are N, S). (48) - < < (1 -cos) (48) implies that pN(z)/wN coN) AN equation As, < ps(z)/ws for all z and pN(z)/wN ps(z)/ws for z such that A(z) < (1 cos)/ as means in 1.31. shown This that the credit market Xs, figure imperfec tions effectively over become the source of North's absolute advantage Since (1 South. Hence, when North and South trade with each other, the equilibrium so that South relative wage must satisfy wN>ws, ad gains comparative in sectors. indexed com 1.32 shows the of vantage Figure high patterns credit market functions better and North, whose parative advantage. are more whose and richer hence entrepreneurs credit-worthy, special izes and exports in the lower indexed sectors that suffer from bigger South specializes and exports in higher indexed sec agency problems. are subject to smaller agency The relative wage tors, which problems. = rate and the marginal are determined sector, A(zc) Ac, by the balanced trade condition.45 46Matsuyama i \ _pn(z) wN/R\.\ ws/R.j.|.^-ps(z) A(z) ?\-j-'-!- OJ (\-a>N)IXNAc (\-cos)lh 1.32 Figure Patterns of Comparative 8 Advantage with Pure Price Equilibrium A Model of Polarization General Effects: In all the models distort we the allocation have at so far, credit market In the following model, of resources, the allocation looked of resources. imperfections credit market and yet, they do not distort imperfections their effects of prices. The have distributional through implications is clearly very special, but it helps to highlight how the net worth model effect could operate through prices rather than quantities. a continuum of agents with unit mass, whose Consider input endow In to lending to addition ment in period 0 is distributed G(co). according < in period x counits of the input in period 0 for rx units of consumption the with variable 1, each agent now has access to an investment project converts I units of the input into RI units in consump scale I>m, which tion in period 1. To operate this project at the scale equal to I, the agent rate equal to r.Here, m is the mini needs to borrow I co at the market mum investment that is, investing I<m generates nothing. requirement, the period-1 consumption. As before, each agent maximizes By running = = RI at the this project the scale, I>m, r(I co) agent can consume U = rco. if R Therefore, (R r)I + rco. By lending, the agent can consume U = < r, the agent prefers lending; if R r, the agent is indifferent; and if R > r, the agent wants to borrow and invest as much as possible. the agent can pledge only the fraction X of the project However, constraint: enue, hence facing the following borrowing XRI>r(I-a). (BC)(49) rev Implications of Credit Market Aggregate Imperfections 47 If r < XR, the agent would borrow and invest by infinite amount, which never occur in equilibrium. would for XR<r <R, the agent However, would borrow and invest up to its borrowing limit, as long as it also sat investment isfies the minimum that, for XR requirement, m. This means the investment <r<R, 1 ? = schedule by an agent with the input en co, is given by dowment, I((d) demand co if co> coc= m and zero otherwise. Aggregate Saving Therefore, = 1 -? the credit market = F( -? XR\-i codG(co) J0 1 r / \ = , Aggregate equilibrium r?? is given by corfG(co) m(l-XR/r) (50) Investment for XR<r<R. Figure 1.33 illustrates this condition. The vertical line rep curve represents the LHS of (50), while the downward-sloping the RHS of (50). For a sufficiently small X, that is, if X< J0m(1-^codG(co)/Jo line intersects with the corfG(co), the vertical part of downward-sloping < <r the aggregate investment that in R XR holds schedule, ensuring In this the rich become the borrow equilibrium. equilibrium, relatively from the relatively poor, who have ers; they borrow as much as possible no choice but to lend to the rich. In this model, what the rich separates resents from the poor is their relative position in the wealth distribution. They do not have to be rich by any absolute standard, because the equilibrium r R V \ V r ( 1-?ART1 ^ I r)axlG(a>) r J Ml-AR XR ? ? O ^codG(co) Figure 1.33 48 Matsuyama rate of return always adjusts tomake sure that some agents would to become become borrowers. lenders, while others would have Now suppose that X is reduced further. This shifts down the aggregate investment schedule. the aggregate investment does not However, change, due to the inelastic aggregate saving. The overall effect is hence a reduction in r such cocremains resources, intact. Thus, as rmoves that XIr remains constant, which that also means a no effects on the allocation of in X has change to offset any effect that X might endogenously have. it has However, as seen effects, for each agent as follows: distributional consumption period-1 ' (\-X)R I calculating the XR\ ifco>coc^l--j ^r-W7co U(co)=| by / if co< co = m rco 1 \ I XR\ rJ return of hav is illustrated by figure 1.34. Note that the marginal an across additional unit of the input differs the agents. For the poor, ing it is equal to r,which is strictly lower than the project return, R, because to in the credit market the poor from borrowing prevents imperfection vest. For the rich, on the other hand, it is equal to (1 - X)R/(1 - XR/r), is strictly higher than R, because of the leverage effect. That is, the which rate enable them to borrow at the market credit market imperfections which 1/ UUo) \-XRIr Rco J / /f / / / / * yr ? _?-!O Figure 1.34 rco m(\-XR/r) Aggregate Implications of Credit Market Imperfections 49 due to the lever strictly lower than the project return, R. It is precisely as as possible, to borrow much the rich wanting age effect that makes that is, equation is precisely the reason why their (BC) is binding, which arrows rich. The with for the holds (49) depict the effects of a equality the terms of trade against reduces r. By moving lower X,which this further magnifies lenders and in favor of the rich borrowers, parity of the marginal returns on wealth Long-Run What Implications between the poor the dis the rich and the poor. on Wealth Distribution if we allow for some to the wealth distribution happen and Newman from (J(co) to co?Following (1993) and Banerjee to that each agent has an offspring, and Zeira (1993), imagine would feedback Galor is an increasing he leaves the bequest, which function of (i(co). the threshold level of wealth, the shape of IT(co), including coc, is a the dynamic evolution of wealth dis function of G(co), this determines = can be iterated to solve for the long tribution, Gt+1(-) <E>(G,(-)),which run wealth distribution In some cases, the from any initial distribution. whom Since run distribution converges long initial distribution. This occurs to a single mass point, regardless of the if a fast wealth accumulation by the rich rate of and their strong investment demand drives up the equilibrium return so much that the poor lenders could also accumulate their wealth by lending, which helps This is the case where the credit market. them to cross over the threshold level of wealth. to the poor "trickles down" con the long run distribution of the initial distribution. regardless the rich's wealth In other cases, through verges to a two-point distribution, causes an endogenous The credit market of the society be polarization a high level of wealth the rich and the poor. The rich maintain in part because of the cheap credit offered by the poor, who have no choice but to lend their small saving to the rich. In some other cases, the long run distribution on the initial distribution, the his depends exhibiting tween tory dependence.46 9 Concluding Credit market Remarks the key to understanding im imperfections many provide and and interna portant issues in business cycles, growth development, tional economics. in these areas, however, has left in its Recent progress wake a bewildering conflict array of individual models with seemingly same the of credit market ing results. Using single model imperfections 50Matsuyama this paper brought throughout, In so doing, unified framework. be attributed may phenomena clude, among other together it showed a diverse set of results within a how awide to credit market range of aggregate imperfections. They in technical investment-specific recur recessions, traps, leapfrogging, persistent cycles, reverse international capital flows, the rise things, changes, development ring boom-and-bust endogenous across nations, and the patterns of international some equilibrium to is also used and investigate distributional of the of credit markets. One impacts improving efficiency of equilibrium often respond non recurring finding is that the properties and fall of inequality trade. The framework some cautions for suggests changes, which a of credit market studying aggregate implications imperfections within narrow class or a particular of models. family monotonically Although cuss many it is highly to parameter the simple framework used in this paper enabled me to dis issues within the limited space, it has some limitations. First, in the dynamic restrictive For ex feedback mechanisms. it rules out endogenous agents, and savings by the investing ample, in antici the net worth hence the possibility that they may accumulate the issue addressed pation of their future financing needs, by Green and Jovanovic also (1990), Buera (2006), and others. The model net worth might depend on that the borrower's rules out the possibility determination of the future allocation of credit through the equilibrium issue Shleifer assets the the addressed owned by durable borrowers, by and Moore and Vishny (1997), and Kiyotaki (1998). The (1992), Kiyotaki wood in one period. that all the projects are completed also assumes such as rules out any issues associated with multistage financing, as and Clementi and addressed terminations refinancing, by project and Fishman (1992). (2006), and Gertler (2006), DeMarzo Hopenhayn model This is essential for such multi-period projects allowing importantly, of credit market the liquidity implications for understanding imperfec and and Kiyotaki and Tirole (1997,1998) tions, as shown by Holmstrom the pledgeability Moore X, which mea (2002, 2005a, 2005b). Second, sures (inversely) the severity of agency problems behind the credit mar To the extent that it re has been treated as exogenous. ket imperfections, we like to introduce would flects the state of financial development, More some feedback mechanisms from the investments to the credit market economic the two-way causality between efficiency issue the addressed and financial by Acemoglu development, growth and Rey and Smith and Zilibotti (1997), Martin (1997), Greenwood (1992). To the extent that it reflects the quality of (2004), and Saint-Paul in order to address Aggregate or contractual legal would enforcement Imperfections and Finally, aggregate implications in the otherwise been examined work. While other 51 institutional factors, we some political economy of credit market imperfections neoclassical frame competitive to address it in order like to endogenize issues. have Implications of Credit Market im for isolating the effects of credit market to examine how credit market im be interesting interact with other departures from the neoclassical this is useful itwould perfections, perfections might For example, credit market framework. into introducing imperfections the monopolistic also rich and diverse in its ag framework, competitive as gregate implications, pointed out by Matsuyama be essential for understanding how credit market the process of product economies. glomeration Ibelieve innovation, (1995,1997), imperfections as well firm entry dynamics, would affect as ag that incorporating these additional into the present elements would the basic message framework of the paper. only strengthen are Credit market in and im rich diverse the imperfections aggregate plications important a wide and they provide the key to understanding range of issues. What has been discussed here ismerely the tip of the iceberg. Acknowledgment site: http://faculty.wcas.northwestern.edu/~kmatsu/; This paper is prepared [email protected]. on Macroeconomics, Annual Conference March Web Email: k-matsu for the NBER 2007. 22nd It is a 30-31, highly condensed version of lecture series given at various places (Kyoto, LSE, Northwestern, Toulouse, UCL, and Zurich) over the years, which has slowly evolved into its current form. (Most recent lecture slides are available on my web site.) My special thanks go to the graduate students who attended ments these by the editors, ference. I thank also lectures. This paper benefits greatly from the com the discussants, and other participants at the con those who attended the seminars at Chicago Fed, Paris-I, and Washington University of this paper was presented. in St. Louis, where a broad outline Endnotes 1. The existing focus on a few specific areas of See Bernanke, surveys Gertler, applications. and Gilchrist (1999) for business mechanisms; cycle propagation (2005) in Banerjee-Duflo Zweimueller economics; Bertola, Foellmi, (2006, chapter 7) for income dis development 52Matsuyama tributions. it does teresting in spirit to this paper, but 13) is closest (2005, part VI, particularly chapter in Gertler international economics. (1988) offers an in any applications Tirole not cover on the state of the field before glimpse a major it became research topic. fluctuations of TFP to the ex market could endogenous imperfections on I to have tent they affect financing chosen of working focus investment-specific capital. tech that investment-specific of some recent studies technical change because suggesting see neutral better nical changes than the traditional, (TFP) technical changes; perform and Fisher Krusell Hercowitz, Greenwood, (2006). (1997,2000), also cause 2. Credit at least seriously in the credit market In my view, anyone who believes imperfections, to do research the impacts of any policy under in this area, should never examine enough one could that such a policy the imperfections. The most the assumption could eradicate the credit market. is to improve hope for in any policy 3. to refer to the Profitability of agency theory may want prefer the language as the Borrower's and to Constraint Incentive Compatibility (or Participation) as the Lenders' Constraint Incentive Compatibility Constraint the Borrowing (or Partici pation) Constraint. 4. Those who Constraint to co > 1 - XR/r "the collateral call the inequality constraint/' analogous or "the In do constraint." call it "the cash flow constraint/' while other authors liquidity assets or net worth held only in collateralizable that the borrower's ing so, they assume the use of I deliberately avoid to satisfy the constraint. only in liquid assets could be used with the question or "liquidity" I am primarily because concerned the terms "collateral" net worth, abstract is affected by the (level of) borrower constraint of how the borrowing to say, this is or liquidity Needless holdings. portfolio ing from the role of the borrower's 5. Some authors an important the one used 6. See, issue, but its careful in this paper. for example, Tirole treatment (2005; chapter would require 3, supplementary richer framework than sections). for this. First, 7. Broadly there are three reasons speaking, even ifwe could identify them in certain ket imperfections, across amuch the major causes of credit mar are likely to vary specific cases, at least qualitatively and times. Second, of credit market imperfec implications investment countries, industries, types, and equilibrium of the aggregate speaking, much the imperfec on the specific nature of the agency problems behind tions do not depend reason one. This reduced is a practical the most tions. The last, and perhaps important, this as the time and effort of the reader. For example, saves space, as well form approach and of and Gertler me to reproduce the key results of Bernanke enables (1989) approach to explain the devoted many pages and appendices Boyd and Smith (1997), each of which one I needed In contrast, state verification. under contract only costly problem optimal constraint. to describe the borrowing short paragraph 8. See Tirole (2005, p. 119) who of credit market imperfections the general of separating also argues for the benefits structure. the questions of the financial issues from other than sup factors" play no active role in the economy factors income. The hidden the residual and absorbing inelastically plying "hid these returns to to generate are introduced here merely Later, capital. diminishing is embedded role when this model den factors" in fixed supply will be given an additional net worth. to endogenize the borrower in a dynamic setting 9. The owners these of the "hidden factors think that the agents have 10. One may as amodel be viewed this may natively, access to a storage of a small open of return, r.Alter technology or of an industry. economy Aggregate of Credit Market Implications 11. Equation assumes (5) implicitly 53 Imperfections the interior can be ensured which solution, by impos ing thatRf (R)< r.Then, (5)holds with 0 < k < R, which implies that 0 < n < 1. 12. For proves cations the following imagine sequential example, n credits on the first-come, first-serve basis, and are be denied. delayed 13. A change (for some in rwould are straightforward: tent with the evidence facturing random have more a rise in r leads reasons) constraint: those agents the market whose credit ap appli effects, but its effects on k and coc in k by raising consis coc. This is roughly and Gilchrist that small manu (1994) and others complicated to a decline found firms are more will service by Gertler to the tightening sensitive welfare of monetary policy. 14. Aghion, some evidence liber that, after a financial (2007) shows Fally, and Scarpetta the entry of small firms force larger firms to scale down or to exit alization, completely. as a 15. The partial equilibrium of the previous section may be viewed model special case, = are given the saver's preferences is pC? + C?, so that the aggregate by U? saving the case without elastic. One may also analyze the savers by looking at the spe infinitely the aggregate cial case where is inelastic at S(r) = co. saving where so that the total the case without the savers, is equal to saving = can show that this is (5), r co). Simple XRf (Rco)/(l algebra = = in co in the range, t\/(1 + r\) < co< 1 - X,where is t\ increasing )/log(/c) log(/' -kf'/f the elasticity of of the marginal capital. productivity 16. For example, consider k = Rco and from co. Then, in coand co? (as well as X) on k are studied. What changes from k to co and co?? Imagine net that the entrepreneur's in period and the saver's net worth t, co, and co?, jointly determined kt+1, as described which in turn determines that co,+1 = W(kt+1) and co?+1 = W?(kt+1). (This can be jus our for example, into the overlapping by embedding two-period agents agents 17. Here, the effects of exogenous ifwe also allow for some feedback worth above, tified, as discussed on how a of this economy then depends framework, later.) The dynamics in k affects the distribution of the wealth the entrepreneurs between and the savers. change and Piketty (1999) conducted Banerjee, Aghion, analysis along this line in a similar setting, and found the case of endogenous of low investment, cycles, where periods during which the wealth is shifted distribution towards the savers, alternate with of high in periods the wealth distribution is shifted toward the entrepreneurs. vestment, during which 18. One could remove this feature the effects G(co) and by studying limit case where G(co) converges by letting the endowment of shifts in G(co). The analysis to a single mass. 19. One may call this effect "flight (2003), who also developed Barlevy lower productivity projects during to safety" amodel 20. Recall when 21. This that figure 1.9 is applied be distributed here may to according as the be viewed to "flight to (as opposed quality"), following inwhich the credit composition shifts toward recessions. m2/m1 < (1 ^/(l X^/RJ < 1. to the dynamic framework is simple in part because the "hidden fac durable such as the land. Otherwise, the borrower net worth assets, in period twould on the asset in period on the future tra t,which depend prices depends on the investment which in turn depends and the borrower's net jectory of the economy, in period worth t. Kiyotaki and Moore that such asset (1997) and Kiyotaki (1998) argued make This conjecture has been price movements amplification quantitatively significant. studied by Kocherlakota and Quadrini (2000), Krishnamurthy (2003), Cooley, Marimon, and Ripoll (2004), and Cordoba (2004). conversion tors" do not include 54Matsuyama 22. The associated (2005b) space constraint with poverty on these issues. me prevents broad methodological from discussing issues many see Azariadis and Stachurski (2005) and Matsuyama trap models; 23. Mathematically, for any e > 0, there exist open intervals, e I* and as t?> oo, kt?> k* for kt?> k** for k0 e I**. k0 24. I** c I* and (0, e), such that, For that only textile and other industries that imagine type-1 projects, example, are available at some coun the time of the first revolution industrial and emerged initially, in reaching the steady state, k*. Then, the second indus tries, say Britain, have succeeded some new trial revolution arrives and type-2 projects, like chemi including technologies are born. Britain, cal and steel industries, in k*, is unable to switch to the new located while some, but not technologies, take over the technology leadership all, 25. Although these form. period-2 figures depict latecomers, come say Germany, by successfully the new adopting and can take a more the fluctuations cycles, from behind technologies. com plicated 26 As than in all these shown twice. This the graph intersects with figures, can be same way as the in the proved proof line no more the 45? degree inMatsuyama (2004, p. 865; lemma). 27. This cases the next and are based on Matsuyama (2004b). and Piketty that endogenous 28. Aghion, (1999) also showed cycles occur when Banerjee, an intermediate credit market has the parameter the of imperfection representing degree at an intermediate level of financial de value. They interpreted it as saying that countries are in the con This may be an appropriate interpretation velopment subject to volatility. text of their model, but not here. access to many investment have the capital-generating nancing that affect the imperfections credit market credit 29. flow away from be more might flow For agents the empirical have specialized 31. Or, opportunities and projects, the capital-producing to financing at situations where constraint borrowing (1993), projects. such alternative might projects, thereby evidence for the business and Acemoglu and Scott cycle asymmetry, see, for example, when R, declines operating substantially productivity, investment. rules out the foreign direct Later, some effectively will be discussed. this assumption 32. Prasad, Rajan, ing) offer overviews section 2) by adding 33. Of course, and Subramanian of the empirical the savers. (2006) and Kose, Prasad, here The model patterns. Falk (1997). the entrepreneur's assumption tions of relaxing into account the diverting is the case where in which arises naturally context this problem and capital in different industries and/or technologies expertise or in a specific industry technology. This the following intermediate the agents when fi we change happen when which divert the could projects, One could argue that a better credit seeing what of alternative the financing prone are looking face no and away. (1986), Sichel 30. Another that we Recall Rogoff, extends and Wei Matsuyama different are highly abroad. implica (forthcom (2005a, in cp, so that a priori, there is no reason to believe that the effect ismonotone the with great caution. However, results should be interpreted dealing with one would as to have take cases would the analysis, substantially complicate one for the domestic and one for the in two separate borrowing constraints, Implications of Credit Market Aggregate Kiyotaki It is assumed even 55 and Krishnamurthy Caballero (2001) and Aoki, borrowings. in issue models. small this both studied economy (2006) open ternational 34. Imperfections though here for the case without 35. Again, (2005a, Matsuyama are of the equal size tominimize is straightforward. that the two countries for different allowing section and the notation, sizes country the saver, Benigno, rN> rs if r\/{l + = vi)<(Ds<(0N<l-XN l-Xs. See 2). and Rogoff that capital Gertler hazard model, (1990) demonstrated in the imperfect to the information the rich to the poor ismuted case, compared case. It is not clear whether in their the reverse information flows occur capital In their moral 36. flows from perfect In the present model, the reverse cap of the poor is negative. unless the net worth model, is slightly of the Southern less than ital flows occurs even if the net worth entrepreneurs that of the Northern entrepreneurs. See Ju and Wei for some related analysis of the two-way flows of FDI and (2006,2007) a country. Sav at at within be work levels the lending. Similar mechanisms regional might the local businesses, flow into big city finan may ings in rural areas, instead of financing into the rural areas by big businesses the investment whose cial centers, which finance 37. headquarters are located 38. Lucas (1990), for example, the saving does not flow why areas. inmetropolitan that human argued capital externalities to the South. from the North and Hamada the case where (2001) studied Sakuragawa in a similar model. fers from the credit market imperfections 39. 40. The intellectual can be of this view origin traced back only might one be the reason country to the structuralism (South) suf of Nurske (1953),Myrdal (1957), and Lewis (1977). 41. Boyd and Incidentally, their two-country model of cation problem. They found and two stable asymmetric same the exactly (1997) obtained dynamics, on the the credit market based imperfection costly numerical symmetry examples with one unstable Smith in (38)-(39), state verifi steady state considered the case (2006), who of two countries with unequal sizes. His simulation shows that, if the country population sizes are similar, the asymmetric he also found endoge steady states are stable. However, nous fluctuations around the asymmetric the countries sizes are suffi steady states, when ciently (2005c) discusses the notion This means that the entrepreneurs in lower-indexed the running project when the agents are not indifferent. 44. Note that the binding borrowing The total profit in sector for X(z) > 1 - co. Summing the aggregate profit n is given by n = wco + n = e. tive profits. co and zero 45. This See also Kikuchi different. 42. Matsuyama economics. 43. states. steady section credit-based is taken explanations of symmetry-breaking are not indifferent sectors. See Remark between and its applications the sectors. 3 for how to allocate to They prefer the credit in low-indexed constraints sectors give rise to posi z is is positive for X(z) < 1 equal to E wn(z), which it up across all the sectors and that verifies (46) using = E - wco. the aggregate income Y satisfies Y Hence, from Matsuyama of the patterns (2005a, section of trade include that looked at 3). Earlier studies Kletzer and Bardhan (1987) and 56 Matsuyama recent examples. This (2006a, 2006b) and Wynne (2005) for more (2002). See Manova that seeks the institutional is a part of the growing ad of comparative literature origins as and Helpman such Costinot Antras, (2006), vantage, Acemoglu, (forthcoming), and Vogel Levchenko Nunn (forthcoming), (forthcoming), (forthcoming). Beck 46. In essence, (2000). The literature on the evolution by Matsuyama under credit market is vast. In addition imperfections see and Bolton mentioned, (1997), Freeman (1996), Aghion this iswhat wealth of household is shown distributions to the three studies already and Ray (2002), and Piketty (1997). Just as in the macro dy (2006), Mookherjee Matsuyama on the distri of the credit market the implications namics, long run wealth imperfections on the assumptions inter about the way different households bution sensitively depend A proper act with cannot be explained each other, which here due to the space constraint. a whole new paper. of this literature would require exposition References and E. Helpman. D., P. 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