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THE JOURNAL OF FINANCE • VOL. LVII, NO. 5 • OCTOBER 2002 Information Production and Capital Allocation:
Decentralized versus Hierarchical Firms
This paper asks how well different organizational structures perform in terms ofgenerating information about investment projects and allocating capital to theseprojects. A decentralized approach—with small, single-manager firms—is most likelyto be attractive when information about projects is “soft” and cannot be crediblytransmitted. In contrast, large hierarchies perform better when information can becostlessly “hardened” and passed along inside the firm. The model can be used tothink about the consequences of consolidation in the banking industry, particularlythe documented tendency for mergers to lead to declines in small-business lending.
IN THIS PAPER, I TAKE UP the following question: How does organization designinf luence the process by which capital is allocated to competing investmentprojects? I contrast two basic organizational forms. The first is “decentral-ization,” in which small, single-manager firms choose between relatively fewprojects. The second is “hierarchy,” in which large firms with multiple layersof management evaluate many projects. The goal is to understand what project-level characteristics lead either decentralization or hierarchy to be the pre-ferred design.
This question can be given a concrete motivation. Over the last several years, there has been enormous consolidation in the banking industry, bothin the United States and worldwide. This consolidation has been accompa-nied by widely voiced concerns that the resulting larger banks will lend lessto small businesses, which are especially dependent on intermediaries forfinancing. And indeed, a number of researchers have documented that, whentwo banks merge, the resulting larger entity tends to cut back significantlyon its small-business lending. Moreover, the evidence suggests that the loansthat are cut are, at least on average, positive-NPV.1 Why would a newly enlarged bank ever turn its back on a profitable line of business in this way? An informal argument is given by Berger, Demsetz,and Strahan ~1999, pp. 165–166!: *Stein is with the Department of Economics, Harvard University and NBER. I am grateful to the National Science Foundation for research support, as well as to Ulf Axelson; AntoineFaure-Grimaud; Luis Garicano; Rob Gertner; Rick Green; Bengt Holmstrom; Anil Kashyap;Raghu Rajan; Julio Rotemberg; an anonymous referee; and seminar participants at HarvardBusiness School, the NBER, and the University of Chicago for their input.
1 The literature on this topic is surveyed in Berger, Demsetz, and Strahan ~1999!. I discuss The larger institutions created by consolidation may also choose to pro-vide fewer retail services to small customers because of Williamson ~1967,1988! type organizational diseconomies. . . . it may be scope inefficientfor one institution to produce outputs which may require implementa-tion of quite different policies and procedures. These diseconomies maybe most likely to arise in providing services to informationally opaquesmall businesses for whom intimate knowledge of the small business, itsowner and its local market gained over time through a relationship withthe financial institution is important . . . these arguments do not sug-gest that large complex financial institutions created by consolidationwould reduce services to all small customers, rather just to those cus-tomers who rely on relationships.
On the one hand, this informal argument is quite clear in asserting that there exist “organizational diseconomies” that somehow prevent big banksfrom being the most efficient providers of certain information-intensive ser-vices, such as relationship-based small business lending. On the other hand,it is vague as to what the root cause of these diseconomies might be. Forexample, the suggestion that big banks simply have trouble engaging inmultiple activities that require different technologies ~“different policies andprocedures”! seems less than compelling. After all, most big banks are in-volved in a wide range of technologically distinct activities, from check pro-cessing to credit cards to foreign-exchange trading.
So what is it about small-business lending—as opposed to other banking activities—that might lead it to be a particularly poor fit for a large bankingfirm? In what follows, I argue that the key distinguishing characteristic ofsmall-business lending is that it relies heavily on information that is “soft”—that is, information that cannot be directly verified by anyone other thanthe agent who produces it. For example, a loan officer who has worked witha small-company president may come to believe that the president is honestand hardworking—in other words, the classic candidate for an unsecured“character loan.” Unfortunately, these attributes cannot be unambiguouslydocumented in a report that the loan officer can pass on to his superiors.
This situation contrasts sharply with, for example, an application for a homemortgage loan. Here the decision of whether or not to extend credit is likelyto be made primarily based on “hard,” verifiable information, such as theincome shown on the borrower’s last several tax returns.2 With soft information, the advantage of decentralization is that it strength- ens the research incentives of line managers. Under full decentralization, aline manager is also the CEO of his firm and, as such, has the authority toallocate the firm’s funds as he sees fit. Given that he can count on havingsome capital to work with, he knows that his research efforts will not bewasted, and, hence, his incentives to do research are relatively strong. Said 2 The accounting literature has long drawn a similar distinction between hard and soft in- formation. See, for example, Ijiri ~1975! and Demski ~1994! for discussions and further references.
Information Production and Capital Allocation differently, decentralization rewards an agent who develops expertise byensuring that he will also have access to some capital that he can use tolever that expertise.
In contrast, if a line manager works inside a large hierarchy, he faces the risk that somebody higher up in the organization will decide that invest-ment opportunities are better elsewhere in the firm and will sharply cut hiscapital allocation. In this case, because he does not get a chance to act on theinformation that he has produced ~and because he is unable to credibly passit on!, the line manager’s research effort goes to waste. Ex ante, this impliesthat he does less research in a hierarchical setting. Here the authority toallocate capital is separated from expertise, which tends to dilute the incen-tives to become an expert.
Thus, with soft information, the advantage of decentralization relative to hierarchy is higher-powered research incentives and better capital allocationwithin operating units. However, there is also a countervailing cost: Underdecentralization, reallocations across operating units have to be mediated bythe external capital market, while under a hierarchical design, they are im-plemented by the integrated firm’s CEO. And there can be circumstances inwhich a CEO is able to bring higher-quality information to bear on suchacross-unit reallocation decisions than the external market does. Indeed, acentral assumption throughout the analysis is that the CEO of an integratedfirm has an advantage over the capital market in learning about the pros-pects of the units that she oversees. As I argue in detail below, this assump-tion can be rationalized in a number of ways, perhaps most convincingly byappealing to a complementarity between the CEO’s strong control rights andher incentives to produce information.
In sum, when information is soft, decentralization has both advantages and disadvantages. Balancing the two, decentralization will on net tend tobe a good design under soft information to the extent that line-managerresearch—and the accompanying potential for efficient within-unit reallo-cations—is relatively valuable.
Things work very differently when the information produced by line man- agers can be hardened and passed on to their superiors. Now, not only doesa hierarchy do better than the external capital market in terms of movingmoney across operating units, it can also generate more research on the partof line managers, and, hence, better within-unit allocations. This is becausewith hard information, line managers become advocates for their units; ifthey can produce verifiable positive information and pass it on to their su-periors, they can increase their capital budgets. Here, paradoxically, sepa-rating authority from expertise actually improves research incentives, asline managers struggle to produce enough information to convince their bossesthat they should get more of the firm’s resources.
Beyond just saying that soft information favors small firms, the model also produces several other conclusions. First, suppose that for some otherexogenous reason, it becomes optimal to have a relatively large integratedfirm operating in a setting where information is soft—say, because there are significant synergies across the firm’s different projects. In such a case, hold-ing the firm’s size and scope fixed, the softness of information will tend toimply that a f latter organizational structure, with fewer layers of manage-ment, is more attractive.
Another implication is that hierarchies tend to be characterized by inef- ficient levels of bureaucracy. This follows if one extends the model so thatthe hardness of information is made endogenous. Suppose that by devotingeffort to documentation, a line manager can harden information that wouldotherwise be soft. Because hard information is so privately valuable to linemanagers in a hierarchy, they will devote excessive efforts to such documen-tation. Thus, in this modified setting, the costs of a hierarchy do not take theform of line managers simply slacking off; rather, they work hard to gener-ate the wrong kind of information. In particular, there will be too muchreport writing and not enough soft-information production.
The ideas in this paper build on several earlier works. I defer a full dis- cussion of the related literature until Section IV and only note here the mostdirect linkages. The capital-allocation model itself is a direct extension ofthat in Stein ~1997!, with the new twist being the explicit consideration ofline-manager research incentives. In Stein ~1997!, line managers are treatedas passive robots who do not need to be motivated. Rather, the focus is morenarrowly on the CEO’s incentives to shift resources across the firm’s differ-ent operating units—an approach that naturally leads to a more favorableview of large organizations.
In arguing that line managers’ incentives may be blunted when they are in a hierarchy and do not have ultimate authority, I am following Aghion andTirole ~1997!. However, a key distinction is that in the model of this paper,a hierarchical structure need not weaken line-manager incentives—indeed,it only does so when information is soft. In contrast, in Aghion and Tirole, itis a more general proposition that line managers are discouraged when theydo not have full authority. Thus, the models have different empirical impli-cations, as the example of the banking industry suggests: The Aghion–Tirolemodel does not explain why large banks might be particularly unsuited tosmall-business lending, as opposed to credit-card or mortgage lending.
The remainder of the paper proceeds as follows. The basic model is devel- oped in Section I. Section II considers several extensions and variations. InSection III, I return to the banking industry and review the relevant empir-ical evidence more fully in light of the theory. Section IV discusses the re-lated theoretical literature on organizational design. Section V concludes.
I. The Model
The model considers two operating units, i and j, which may be organized either as two separate stand-alone firms or as subsidiaries under the sameroof of a single integrated firm. Abusing terminology slightly, I will refer to Information Production and Capital Allocation these operating units as “divisions” in both the decentralized and hierar-chical cases. Within each division, there are two potential investment projects.
Each of the projects can be allocated either zero, one, or two units of capital,and each can be in either a G ~good! or B ~bad! state. The probability ofeither state is 102, and the outcomes are independent across all projects,both within and across divisions.
A project that is in the G state yields a verifiable net output of g~1! . 0 if it gets one unit of capital and g~2! . 0 if it gets two units. A project that isin the B state yields a net output of b~1! with one unit of capital and b~2!with two units. I assume throughout that g~2! Ͻ 2g~1!; that is, there aredecreasing returns in the good state. In addition, g~2! Ͼ g~1! ϩ b~1!, whichmeans that if one has two units of capital along with a G project and a Bproject, it is better to give the G project both units, as opposed to dividingthe capital up equally across the projects.
An innocent normalization that reduces notational clutter, which I adopt from this point on, is to set b~1! ϭ 0. Finally, I assume that Ϫ1 , b~2! , 0,as well as that b~2! ϩ g~2! , 0. That is, the net return to investing two unitsin a bad project is so negative that it offsets the gains from investing twounits in a good project. As will become clear below, this assumption ensuresthat there will be credit constraints in equilibrium, since an uninformedprovider of external finance will never want to give each division four unitsof capital to work with. And financing frictions are necessary in this modelif one is to pose questions of internal capital allocation; without such fric-tions, all projects would get fully funded in all states of the world.3 Each of the two divisions has its own division manager. The division man- agers are, by virtue of research effort, able to obtain signals about the projectsthat they oversee. If manager i makes an effort e , he has a probability p of observing signals on both of his projects, where the function p~ ! is in-creasing, concave, and takes on values on the interval @0, 1!. I assume thatthe division managers have reservation utilities of zero, so that there isnever any issue of satisfying their participation constraints. In the hierar-chical setting, when the two divisions are integrated into a single firm, thefirm also has a CEO, who may also undertake her own research. The CEO’sresearch technology is described in detail below. For the time being, it suf-fices to say that, because the CEO is overseeing a total of four projects, sheis unable to learn as much about each one individually as are the divisionmanagers.
To model the incentives of the divisions managers, as well as the CEO ~when there is one!, I assume that any agent k has a utility function of the form: 3 In my model, the firm invests everything it raises from the outside market, due to the CEO’s empire-building tendencies. By contrast, in papers such as Antle and Eppen ~1985! andHarris and Raviv ~1996!, there can be internal capital rationing even absent external con-straints, as the CEO, acting as a principal, seeks to curb the information rents of her subordinates.
where y is the expected net output of agent k’s division firm, if k is the CEO!, I is the amount initially invested in the division in the whole firm, if k is the CEO!, and g is a measure of the degree of effortaversion. Thus, each agent seeks to maximize the expected gross outputfrom the assets under his or her control, as given by ~ y ϩ I of effort. This assumption can be motivated based on: ~a! private benefits ofcontrol that are proportional to gross output, and ~b! nonresponsiveness ofagents to monetary incentives.4 It has the following behavioral implication:Each agent prefers more capital to less, but conditional on being granted acertain budget, tries to allocate it efficiently. Or said differently, the agentsin the model are empire builders, but holding the size of their empires fixed,they prefer them to be profitable.
The goal of the subsections that follow is to establish two principal results.
First, when information is soft, decentralization may for some ~though notall! parameter values be the more efficient mode of organization. Second,when information is hard, hierarchy always dominates decentralization. Toproceed, I begin by analyzing the case of decentralization and evaluating thenet surplus created by investment. Next, I turn to the case of a hierarchywith soft information and again do a similar evaluation, which then allowsme to compare the two regimes. Finally, I take on the case of a hierarchywith hard information and again compare the net surplus created by invest-ment in this setting to that under decentralization.
B.1. External Financing Constraints Under Decentralization The analysis of the decentralized case can be broken into two parts. First, one has to determine how much a decentralized firm is able to raise fromthe external capital market. And second, one has to figure out how effi-ciently this capital will be allocated internally. I assume that investors inthe external capital market cannot directly observe the signals ~if any! re-ceived by division managers.5 And given that division managers always pre-fer more capital to less, and are not responsive to monetary incentives, thereis no incentive-compatible way for outside investors to get them to revealtheir private information—division managers will always want to claim thatboth of their projects are in the G state, so as to get more financing. Thus,the best that outside investors can do is to give each division a fixed, un-contingent allocation of capital. Depending on parameter values, this allo- 4 Nonresponsiveness to monetary incentives is a common—albeit extreme—modeling short- cut. It can be generated by assuming that agents are infinitely averse to risk in their monetaryincome, though not to variations in private benefits. See Aghion and Tirole ~1997!.
5 This assumption is a natural one when division managers’ signals are soft information. It requires more careful elaboration when division managers’ signals are hard information. Thisissue is taken up in detail in Section I.D below.
Information Production and Capital Allocation cation will be set at either two or three units per division; an allocation offour units per division can never be optimal given the assumption that b~2! ϩg~2! , 0.
I start by simply assuming that each division gets an allocation of two units from the external market. I then solve for expected output, given di-vision managers’ endogenously determined incentives in this case. Next, Irepeat the analysis, assuming instead that each division is able to raisethree units of external capital. Then it is a simple matter of comparing netoutput across the two cases and checking which leads to higher ex antereturns for investors.
B.2. Incentives and Output with Two Units of Capital per Division If a division manager with two units of capital is successful in his research efforts and observes $G, B% for his two projects, he will behave efficiently expost and give both units to the G project. The only question is how mucheffort he will put into research ex ante. To answer this question, note that ifa division manager knows the states and allocates the two units based onthis knowledge, expected net output is ~ g~2! ϩ g~1!!02. ~Again, recall thatb~1! is normalized to zero.! If, on the other hand, the manager is un-informed, each project always gets one unit of funding, and expected netoutput is simply g~1!. Thus, with a budget of two units, the manager ’s utilitygain from being informed under decentralization, denoted by ⌬d2, is Given equations ~1! and ~2!, the manager’s first-order conditions imply that, with two units of financing, the level of research effort under decen-tralization, ed With two independent divisions each behaving this way, the total expected net return on four units of capital under decentralization, denoted Y d~4!, isgiven by 2 !~ g~2! ϩ g~1!! ϩ ~1 Ϫ p ~e2 !! ~2g~1!!.
B.3. Incentives and Output with Three Units of Capital per Division The analysis of the case where each division has three units of capital is sim- ilar. If a division manager knows the states and can allocate the three unitsconditional on this knowledge, expected net output is ~3g~2! ϩ g~1! ϩ b~2!!04.
Note that in this case, even if the manager is informed, there are some states—that is, those with two B projects—where it is impossible for outside inves-tors to avoid the negative b~2! outcome.
If the manager is uninformed, he must randomly allocate two units to one of the projects, and one to the other, which leads to expected net outputof ~ g~2! ϩ g~1! ϩ b~2!!02. Thus, with three units of financing per division, theutility gain to being informed under decentralization, denoted by ⌬d3, isgiven by ~ g~2! Ϫ g~1! Ϫ b~2!!04.
The level of research effort with three units of financing, ed With two independent divisions each behaving this way, the total net re- turn on six units of capital under invested under decentralization, Y d~6!, isgiven by 3 !~3g~2! ϩ g~1! ϩ b ~2!!02 ϩ ~1 Ϫ p ~e3 !! ~ g~2! ϩ g~1! ϩ b ~2!!.
A comparison of equations ~2! and ~5! implies that research incentives will be stronger when a division is allocated three, rather than two units of cap-ital, if b~2! ϩ g~2! Ϫ g~1! , 0. This condition is always satisfied given theinitial assumptions that b~2! ϩ g~2! , 0 and g~1! . 0. Intuitively, beinginformed is more valuable when there are three units of capital to allocate,because now it helps avoid the very adverse outcome where two units areput in a bad project.
Of course, it does not follow that allocating three units to each division is the ex ante optimal policy for outside investors. Indeed, as can be seen bycomparing equations ~4! and ~7!, if b~2! is sufficiently negative, investorswill prefer to only give two units to each division. Although the exact cutoffvalue of b~2! for which this is the case depends on the shape of the p~ !function, it is easy to establish the following sufficient condition ~see theAppendix for details! LEMMA 1: If 3~ g~2! Ϫ g~1!! ϩ b~2! Ͻ 0, outside investors will always choose toallocate two units of capital to each division, regardless of the shape of thep~ ! function. In much of what follows, I assume that the sufficient condition in Lemma 1 holds, thereby focusing on regions of the parameter space for which equa-tion ~4! summarizes the output effects of decentralization. This is done solelyfor expositional purposes—it cuts down on the number of different cases tobe considered, without changing the important conclusions.
Information Production and Capital Allocation C. Hierarchy: The Case of Soft Information C.1. The CEO’s Research Technology The next regime to be considered is one in which there is soft information and the firm is organized as an integrated hierarchy, with the two divisionmanagers ceding formal authority to the CEO. To make this case interest-ing, one needs to assume that the CEO can gather some information on herown. If not, she can do no better than to always grant each division twounits of funding, thereby reproducing the decentralized outcome.
But allowing the CEO to gather information raises an important question: Why is it that the CEO is able to become better informed than externalproviders of capital, who are assumed to be incapable of learning anythingabout the projects? There are two possible answers to this question. First, ifthere are multiple outside investors ~e.g., dispersed shareholders!, free-riding problems will naturally reduce their incentives to acquire informa-tion. Second, and more subtly, even a single outside investor with the sameresearch capabilities as the CEO may endogenously choose to do less infor-mation gathering, to the extent that this outside investor has weaker controlrights than the CEO. That is, there is a complementarity between authority~either formal or informal! and research incentives.6 As an example, consider the differing incentives of a bank lender versus a CEO when both contemplate investing effort in learning about a specificdivision. The bank can use any information it acquires to guide its sub-sequent decision of how much to lend to the division. But suppose that in thecourse of its investigation, the bank also learns that the division would bemore valuable if its manager were replaced, or if some of its other existingphysical assets were reconfigured. Outside of default, the bank does nothave the authority to impose such outcomes on a reluctant division manager.
In contrast, a CEO overseeing the division can. As a result, the CEO hasmore to gain from acquiring information about the division in the first place,and hence does more research, even if her research technology is no differentfrom that of the banker.
Nevertheless, even if it is plausible that the CEO learns more about in- vestment prospects than outside investors, it would be unreasonable to positthat she can learn as much in total as the two division managers. Instead, Iassume that the CEO only gets coarse information about the aggregate pros-pects of each division. Specifically, there is a probability q that the CEO’sresearch efforts will be successful. Successful research means that, if one orboth divisions are “stars”—in the sense of having both of their projects inthe G state simultaneously—this star status is revealed to the CEO. Thecoarseness of the CEO’s research technology is captured in the fact that,even if her research is successful, she can never differentiate between a 6 This point is modeled by Gertner, Scharfstein, and Stein ~1994!.
division that is “average” ~has one G and one B project! and a division thatis a “dog” ~has two B projects!.
A few points about this formulation deserve comment. First, the CEO’s research-success probability q is, for the time being, an exogenous param-eter. In Section II.B, I discuss what happens when q is made an endogenousfunction of the CEO’s effort. In either case, I do not allow the CEO to pre-commit to not doing research ~i.e., to setting q ϭ 0!, even if this precommit-ment might raise ex ante expected net output.7 Second, the exact way thatI have modeled the coarseness of the CEO’s information is not critical. Icould equivalently assume that successful research allows the CEO only toidentify dog divisions and that she can never distinguish between averagedivisions and stars; this leads to the same results. Finally, I am assumingthat the outcome of the CEO’s research effort is independent of the outcomeof the division managers’ efforts. This simplifies the exposition slightly, butis not necessary. Similar conclusions emerge if, for example, the CEO ismore likely to succeed in learning something conditional on the division man-agers having also been successful in their research.
C.2. External Financing Constraints in the Hierarchical Case As before, a complete analysis of the hierarchical case involves solving for both the optimal amount of funding given to the hierarchy by the externalcapital market as well as the incentives which govern how these funds areallocated internally.8 And things are more complex now, because withoutfurther restrictions on parameters, there are four possible funding levels tobe considered: four, five, six, or seven units. Even if the condition in Lemma 1is satisfied, so that the two divisions can each raise only two units in thedecentralized case, it is possible that when they are integrated, the hierar-chy will be able to raise five or more units. This is due to the “ease-the-credit-constraint” effect identified by Stein ~1997!. Intuitively, because of thediversification inherent in a larger internal capital market, there is a lowerprobability that an extra unit of financing will be invested in a bad project,leading to the negative b~2! outcome.
Tackling all the scenarios corresponding to the various possible funding levels is, as before, straightforward. However, such a detailed treatment ofexternal credit constraints does not serve to advance the main goal here,which is to show that—in spite of hierarchy ’s potential for beneficial across-division reallocations—with soft information, it is possible for some param-eter values to have decentralization be the preferred organizational form. Toillustrate this point in the most transparent way, I impose another restric- 7 This no-precommitment assumption is discussed further in Section II.A. Cremer ~1995! is another paper in which a supervisor’s inability to commit to staying uninformed can weakenthe incentives of the agent she supervises.
8 The feature that no information can be credibly revealed to the external capital market still remains. Since the CEO also derives private benefits that increase with total investment, shewill have the same incentive to misrepresent investment prospects as the division managers.
Information Production and Capital Allocation tion on the parameters that is sufficient to ensure that a hierarchy willnever be able to raise more than four units of funding. This restriction putsaside the ease-the-credit-constraint effect, thereby isolating the trade-offbetween giving a CEO the ability to make transfers across divisions, versusdiluting the research incentives of the division managers. In the Appendix,I prove the following lemma.
LEMMA 2: If 25~ g~2! Ϫ g~1!! ϩ b~2! Ͻ 0, outside investors will only give fourunits of capital to a hierarchy, regardless of how efficiently the hierarchyallocates this capital internally.9 Again, the point is not that the condition required in the lemma— effectively, that the negative b~2! outcome is very bad—should be thought ofas representing the most likely case. Rather, it enables one to focus on thesimplest example of the costs and benefits of hierarchy, without worryingthat this example is inconsistent with optimization on the part of investors.
C.3. Incentives and Output When the Hierarchy Given that it is able to raise four units of external finance, capital allo- cation in a hierarchy works as follows. When the CEO’s research is unsuc-cessful ~which happens with probability ~1 Ϫ q!!, the best she can do is tojust give each division manager two units of funding and we are back to thecorresponding decentralized outcome.10 When the CEO’s research is success-ful ~which happens with probability q!, she may choose to deviate from equalfunding and give one division more than the other. This will only happen ifone division is identified as a star, and the other is not. In such a “lone-star ”scenario, the CEO has three options: ~a! still give each division two units,~b! give the star division three units and the other division one unit, or~c! give the star division all four units. It is easy to show that the CEO willchoose the most extreme tilting of the capital budget—giving all four unitsof funding to the star division—if the following sufficient condition is met: 9 In proving the lemma, I implicitly rule out schemes where the CEO raises four units of financing, irrevocably sinks it all in division i, and then later returns to the capital marketagain, asking for two more units for the as-yet-unfunded division j. One way to rationalize thisrestriction is to assume that outsiders cannot verify whether investment expenditures “belong”to one division of an integrated firm versus another; such an assumption is a common one inthe literature on internal capital allocation. See Scharfstein and Stein ~2000! for a discussion.
10 I do not consider mechanisms that the CEO might use to induce division managers to reveal their signals. One could imagine that if the CEO catches a manager lying about hissignal, he would be punished with a reduced capital allocation, as in Harris and Raviv ~1996!.
In my setup, such a scheme suffers from two distinct commitment problems. First, punishmentinvolves ex post inefficient allocations. And second, if in equilibrium the division managers dotruthfully reveal their signals, the CEO will no longer have any incentive to do her own research.
This condition simply requires that decreasing returns to scale are not too pronounced in the good state. The analysis that follows is most intuitivewhen this star-gets-everything condition is satisfied, so I will begin by assum-ing that it is. Later, I will come back to the case where returns decreasemore sharply with scale, so that the CEO gives just three, rather than fourunits of funding to a division that is identified as a lone star.
If division managers’ ex ante research incentives in a hierarchy were the same as under decentralization, it would follow that hierarchy is the strictlydominant organizational form. This is because ex post, hierarchy allows fora form of selective intervention. When the CEO knows nothing about divi-sional prospects, she does not interfere, and the outcome is the same as withdecentralization. When the CEO does know something, her ability to shiftfunds towards a star division leads to an improved across-division allocation.
The problem, however, is that division managers’ ex ante research incen- tives are weaker in a hierarchy when information is soft. To see why, sup-pose that the CEO’s research has been successful and that she has identifieddivision j as a star. Division i, meanwhile, has one G and one B project. Ina hierarchy, division j gets all four units of funding, and division i gets noth-ing. Hence, any information that manager i has acquired is not put to use.
In contrast, if the divisions were decentralized, and manager i had two unitsof funding to work with, he would find his information valuable—it wouldlead him to shift both units to his single G project. Thus, the downside to ahierarchy is that because the CEO sometimes takes away manager i ’s cap-ital budget, the marginal return to his research effort is reduced, and heproduces less information.11 It is important to recognize that the negative incentive effects of hierarchy arise not simply because the CEO sometimes has her own independent in-formation about divisional investment opportunities. It is also crucial to theargument that the CEO have the authority to take away all funding fromdivision i—even though i would be able to raise two units if it were a stand-alone entity—when her research indicates that division j is a star.12 As em-phasized by Stein ~1997!, this authority distinguishes the CEO from an equallywell-informed outside provider of finance, such as a banker.
11 This discouragement effect is not offset by the fact that the manager also sometimes gets two extra units in a hierarchy. When he receives four units, the only thing he can do is investtwo in each project, and information is again not of any value. Moreover, the feature that astable capital budget creates stronger research incentives than a variable one is actually moregeneral than the simple setup here suggests. Suppose instead that investment is continuous,that an amount I yields f ~I ! in state G, 0 in state B, and that a manager has one project ofeach type. If he is uninformed and has a budget of K, he will invest K02 in each project, yield-ing f ~K02!. If he is informed, he will get f ~K !. Hence, the value of being informed is V~K ! ϭf ~K ! Ϫ f ~K02!. A stable capital budget will lead to more research if V~K ! is concave, or if4f ''~K ! Ϫ f ''~K02! Ͻ 0. This mild condition is satisfied, for example, for any f ~I ! of the powerform f ~I ! ϭ I a0a, for 0 , a , 1.
12 Indeed, the discouragement effect occurs precisely because an “average” division ~i.e., one with one G and one B project! can lose all its funding based not on its own prospects, but ratherbecause the prospects of its counterpart division within the firm are so strong.
Information Production and Capital Allocation Assume that the timing of the game is such that a division manager must choose his level of research effort before he knows whether the CEO’s re-search has been successful. Denote by ⌬hs individual division manager obtains when, in a hierarchy with soft informa-tion and four units of capital, his own research efforts succeed. It is straight-forward to show that ~1 Ϫ q!~ g~2! Ϫ g~1!!02 ϩ 3q~ g~2! Ϫ g~1!!08 ϭ ~1 Ϫ q!⌬2 The corresponding level of research effort, ehs e2 . By working through all the possible outcomes, it can then be established that expected net output in a hierarchywith soft information and four units of capital is given by Y hs ~4! ϭ ~1 Ϫ q!$ p~ehs 4 !~ g~2! ϩ g~1!! ϩ ~1 Ϫ p ~e4 !! ~2g~1!!% 4 !~6g~2! ϩ g~1!!04 ϩ ~1 Ϫ p ~e4 !! ~3g~2! ϩ 4g~1!!04%.
By comparing equations ~11! and ~4!, one can evaluate the relative effi- ciency of decentralization versus hierarchy, conditional on there being a to-tal external capital constraint of four units in either case. The results to thispoint can be summarized in the following proposition.
PROPOSITION 1: Assume that the condition in Lemma 2 holds, so that the ex-ternal credit constraint is four units. Assume further that inequality (8) holds,so that in a hierarchy, a lone-star division gets all four units of funding.
Then decentralization always leads to more research effort than hierarchy:ed
Ͼ hs e4 . In addition, it is possible ~though not necessary! that decentraliza- tion leads to higher expected output; that is, that Y d~4! Ͼ Y hs~4!. To see why decentralization can generate higher expected output, consider a simple limiting case where q ϭ 1, p~ed 4 ! ϭ 1, and p ~e4 ! ϭ 0. ~The latter two conditions can always be generated by picking the proper form for the p~ !function.! In this case, equation ~4! simplifies to Y d~4! ϭ g~2! ϩ g~1!, whileequation ~11! simplifies to Y hs~4! ϭ ~3g~2! ϩ 4g~1!!04, implying that Y d~4! ϾY hs~4!. In this example, when the firm is organized as a hierarchy, only theCEO does any research, and division managers are totally discouraged. Con-versely, under decentralization, the division managers are highly motivatedand become perfectly informed. Given that the two division managers takentogether are able to gather more accurate information than the CEO, thislatter effect is more than enough to outweigh any improved across-divisionallocation that can be obtained in a hierarchy. As a result, decentralizationis the better mode of organization.
Of course, this example relies on p~ed 4 ! and p ~e4 ! being relatively far apart—that is, on division-manager effort being both important and respon-sive to incentives. If p~ed 4 ! and p ~e4 ! are suff iciently close to one another, it is easy to see that hierarchy becomes more efficient than decentralization:Y hs~4! Ͼ Y d~4!.
Although I have derived the results in Proposition 1 under the assumption that the star-gets-everything condition in ~8! holds, they are, in fact, moregeneral. Even when returns to scale are more sharply decreasing in the goodstate —so that a lone-star division gets three, rather than four units offunding—the basic intuition can carry over. That is, when manager i gener-ates information and gets allocated only one unit of financing ~because man-ager j has been deemed a star by the CEO!, manager i ’s information is notworthless, but it may still be less valuable than if he had been allocated twounits of financing. Thus, the threat of losing some—if not all—of their fund-ing can continue to exert a negative effect on division managers’ researchincentives.
To make this idea precise, in the Appendix I prove the following proposition.
PROPOSITION 2: Assume that the condition in Lemma 2 holds, so that the ex-ternal credit constraint is four units. Assume further that g~2!02 Ͼ 3g~1!04.
In this case, the CEO in a hierarchy will still tilt the capital budget towarda lone-star division, but the tilt may be less extreme, with the lone star re-ceiving three, rather than four units of funding. Nevertheless, decentraliza-tion continues to lead to more research effort than hierarchy: ed
Ͼ hs addition, it is possible ~though not necessary! that decentralization leads tohigher expected output than hierarchy, that is, that Y d~4! Ͼ Y hs~4!. D. Hierarchy: The Case of Hard Information The next task is to show that the relative merits of a hierarchy increase when the information generated by division managers can be hardened andpassed along to the CEO. I begin by assuming that the sufficient conditionin Lemma 2 continues to hold. This allows for a simple comparison of hier-archy relative to decentralization in a situation where the total amount ofavailable external finance is four units in either case. But once I have es-tablished that a hierarchy with hard information dominates decentralizationfor these parameter values, it is easy to extend the argument to show that itmust dominate for all parameter values—that is, regardless of how manyunits of financing can be raised under either decentralization or hierarchy.
To introduce hard information, I assume that the division managers have the same research technology as before—that is, if manager i makes aneffort e , he has a probability p ~ei! of observing the signals on both of his projects. Now, however, the CEO does no separate research of her own. In-stead, if a division manager learns something, there is a chance that he maybe able to credibly communicate it to the CEO. Specifically, conditional on adivision manager ’s research being successful and yielding information about Information Production and Capital Allocation his two projects, there is a probability z that this information is verifiableand can be shown directly to the CEO. With probability ~1 Ϫ z!, the infor-mation is nonverifiable and can be used by the division manager, but notcredibly transmitted to the CEO.
A critical assumption is that while hard information can be credibly trans- mitted from division managers to the CEO, it cannot be revealed to outsideinvestors. Otherwise, the hierarchy would no longer face a fixed externalcredit constraint. What is the economic interpretation of such an assump-tion? Think of division managers as providing the CEO with a variety of raw,albeit well-documented data about a project.13 For example, if the projectinvolves drilling for oil in a new location, the raw data might be a set ofgeological studies. These studies do not literally say what the project ’s dollarpayoff will be. Instead, they must be combined with the CEO’s specific ex-pertise ~e.g., her knowledge of geology, her assessment of the costs of doingthe drilling and extraction! to generate a final judgment about dollar value.
As before, the complementarity of the CEO’s authority and research in- centives imply that she will in equilibrium be better able to assess such rawdata than would an outside banker. Continuing with the example, becausethe CEO has the authority to decide how to deploy the firm’s drilling equip-ment, she will have more incentive to become informed about the costs ofdrilling in different locales, which in turn makes her better able to assessthe value implications of the geological studies. The CEO’s final judgment—what she concludes after studying the raw data—is itself soft informationthat cannot be credibly communicated to outside investors.
Under this interpretation, the parameter z can be thought of as ref lecting either the ability or effort of the CEO—a higher value of z means that theCEO can better evaluate the raw data produced by the division managers.
Moreover, the idea that the CEO needs to spend time evaluating raw datahelps to motivate the assumption that, when information is hard, she nolonger does her own separate research into divisional prospects: She is toobusy trying to process her subordinates’ output.14 As will be made clear be-low, the consequence of this assumption is that when information is hard,CEO and division-manager effort become strategic complements, as opposedto substitutes.
Another crucial assumption is that the CEO does not observe whether division-manager research has been successful. Consequently, when a divi-sion manager has hard information, he can choose whether or not to report it 13 Internal accounting or auditing mechanisms may have a role to play in making such raw data sufficiently well documented as to be credible.
14 Clearly, this aspect of the model could be more fully endogenized. For example, the CEO could face a trade-off between time spent gathering her own independent information and timespent interpreting division managers’ reports, and one could establish the conditions underwhich she tended to find the latter optimal. This line of thinking expands on Aghion and Tirole’s~1997! idea of keeping the CEO too busy to do her own separate project evaluation. Here, theCEO is kept busy not because she is overloaded with make-work, but rather because she choosesto engage in another more productive activity.
to the CEO.15 In particular, a division manager who gets hard informationthat his projects are $B, B% may opt to simply keep quiet. Importantly, thiswill not lead to an “unraveling” situation where the CEO can infer that thestate must be $B, B% simply because the division manager is quiet. This isbecause the division manager may also be quiet as a result of not havingobtained any hard information in the first place.
The option to keep quiet makes research very attractive to the division manager. To see why, assume that the CEO has a fixed conjecture eci aboutthe level of effort that manager i exerts, and a corresponding conjecture pc ϭp~eci! about the probability that his research is successful. Now suppose thatthe division manager’s reporting strategy is to reveal his hard informationto the CEO when it is either $G, G % or $G, B%, but to keep quiet when it is$B, B%. ~As will be seen below, this strategy can constitute equilibrium be-havior.! Bayes’ rule implies that, given his conjecture of pc, the CEO willinterpret quiet as follows: prob~$B, B%0quiet ! ϭ 10~4 Ϫ 3zpc ! prob~$G, G %0quiet ! ϭ ~1 Ϫ zpc !0~4 Ϫ 3zpc ! prob~$G, B%0quiet ! ϭ 2~1 Ϫ zpc !0~4 Ϫ 3zpc !.
Taking the CEO’s conjecture of pc as fixed, a division manager reasons as follows. If he does no research, he will certainly be quiet, and the CEO willupdate on him according to equations ~12!–~14!. However, if he does devotesome effort to research, he gains pure option value. If the research produceshard information that his division is $G, G %, he can speak up and therebyimpress the CEO. If the research produces hard information that his divi-sion is $B, B%, he just keeps quiet and is no worse off than if he had done noresearch.
The bottom line is that, from the perspective of the division manager, there is now an added benefit to doing research: If the information he gen-erates is hard and positive, it can help increase his capital budget and hencehis private benefits. This contrasts with both of the previous scenarios—decentralization and hierarchy with soft information—where division man-agers’ research efforts had no impact on the capital they were allocated.
In the Appendix, I provide a detailed characterization of the case when information can be hardened. The key results can be summarized as follows.
PROPOSITION 3: Assume that the condition in Lemma 2 holds, so that the ex-ternal credit constraint is four units. Assume further that g~2!02 Ͼ 3g~1!04.
Then in a hierarchy with hard information, there is an equilibrium with thefollowing properties:
15 A similar assumption has been made in accounting research that addresses the topic of discretionary disclosure to the capital market. See, for example, Verrecchia ~1983! and Dye~1985!.
Information Production and Capital Allocation (a) Division manager reporting strategies: Division managers reveal their hard information if it is either $G, G % or $G, B% and keep quiet if it is$B, B%. (b) CEO capital-allocation policy: If the CEO is facing one division that reveals itself to be $G, G % and one that is quiet, the $G, G % division getsat least three (and possibly four) units of capital. In all other cases, theCEO allocates each division two units of capital. (c) Division manager benefit from being informed: Denote by hh ity benefit to a division manager from being informed in a hierarchywith hard information. This benefit exceeds that under decentraliza-tion: hh Ͼ ⌬d ϩ z04. Consequently, division-manager research effort is greater than under decentralization: ehh Ͼ d (d) Output: Expected net output is greater than under decentralization: The intuition behind parts ~a! and ~b! of the proposition has already been discussed.16 Part ~c! gives a sense for how much stronger division managers’research incentives are when information can be hardened. The utility gainto being informed, ⌬hh 4 , is now not just larger than that under decentraliza- tion ⌬d4; it exceeds it by at least z04. This can be a substantial difference,since ⌬hh is denominated in units of net returns, while z04 is in units of gross capital. The difference arises because in a hierarchy with hard information,research effort can actually inf luence a division manager ’s gross capital bud-get. In contrast, under decentralization ~or in a hierarchy with soft informa-tion! research effort only enables a division manager to get a higher returnfrom a given capital budget. To the extent that the division manager ’s utilityis tied to gross output, the former effect is naturally much stronger than thelatter. Part ~d! of the proposition follows from part ~c!. Now a hierarchy doesbetter than decentralization on both dimensions of importance. Not only doesit generate more information at the division-manager level, and thereby leadto better within-division allocations, but it also allows for reallocations acrossdivisions when the CEO learns that such reallocations are value-increasing.
Although Proposition 3 deals with the case where the condition in Lemma 2 holds, so that the hierarchy faces an external credit constraint of fourunits, the result can easily be generalized. In the appendix, I prove the fol-lowing proposition.
PROPOSITION 4: Consider the more general case where the only restriction onb~2! is that g~2! ϩ b~2! Ͻ 0, while keeping the assumption that g~2!02 Ͼ3g~1!04. Under decentralization, each division may now be able to raise ei-ther two or three units of capital, and, under hierarchy, the aggregate credit 16 There are other equilibria that differ insignificantly from that in Proposition 3. When one division reveals $G, G % and the other reveals $G, B%, the CEO is actually indifferent betweenallocating two units to each, or three to the former and one to the latter. I focus on the two-twoallocation in the proposition, which implies that a manager with a $G, B% signal strictly prefersto reveal it. However, parts ~c! and ~d! of the proposition apply in either case.
constraint may be anywhere from four to seven units. Still, if information ishard, expected net output is always strictly greater in a hierarchy than underdecentralization. One might argue that the results in Propositions 3 and 4 in favor of hier- archy relative to decentralization are now “too strong”—once informationcan be hardened, hierarchy dominates decentralization for all parameter val-ues, which seems patently unrealistic. Certainly, the model omits a numberof other factors that might tip the balance back towards decentralization.
For example, other than research effort, the model assumes that divisionmanagers do not need to take any other actions. If one were to introduceanother dimension of noncontractible firm-specific investment, this might~following the logic of Grossman and Hart ~1986!, Hart and Moore ~1990!,and Hart ~1995!! be expected to make hierarchy less attractive. But it isimportant to emphasize that I am less interested in making absolute state-ments about the virtues of hierarchy compared to decentralization, and moreinterested in making comparative-statics statements about the circum-stances under which hierarchy is likely to be attractive. And the key resultin this regard—that hierarchy looks better when information is hard, asopposed to soft—seems like it should be robust to the inclusion of variousother factors into the model.
II. Further Issues
A. Does Decentralization Require Dis-Integration? I have been treating the concept of decentralization as synonymous with formal dis-integration, that is, with the two divisions being operated as in-dependent stand-alone firms. The key assumption has been that it is impos-sible for a single firm to replicate the decentralized outcome, because theCEO cannot commit to either remaining uninformed or to not using herinformation to reallocate capital across divisions. Given that the model hasno operating synergies across the two divisions, not much hangs on the dis-tinction between decentralization and dis-integration. But what if there aresignificant synergies? Then one must ask if it is possible to capture thebenefits of decentralization—that is, to commit to division managers thatthey will always receive two units of funding—without resorting to a costlybreakup.
On the one hand, it is hard to argue that a CEO can definitively alienate her right to get involved in capital-allocation decisions. Indeed, several au-thors ~Williamson ~1975!, Donaldson ~1984!, Stein ~1997!, and Scharfsteinand Stein ~2000!! have argued that the CEO’s authority to move capitalacross divisions is the single most defining characteristic of an integratedfirm.17 On the other hand, as Aghion and Tirole ~1997! point out, there are 17 Baker, Gibbons, and Murphy ~1999! go a step further, claiming that formal authority over all decisions necessarily resides at the top of an organization.
Information Production and Capital Allocation other devices short of a breakup that can reduce—albeit not fully eliminate—the CEO’s ex post incentive to meddle in the capital-allocation process; theysuggest keeping the CEO very busy, so she cannot do much research on herown. In a banking context, a relevant example of such a device might be thecreation of a multibank holding company. By making each of the divisions alegally distinct entity, such a structure could create some impediments tomoving capital freely among them.18 This logic leads to the following qualitative conclusions. Suppose that based purely on division-manager research incentives, an analysis such as that inSection I.C cuts in favor of decentralization. Suppose further that the other,non-capital-allocation-related synergies from integration are given by X. WhenX is relatively small, it will make sense to decentralize “to the max ” bybreaking up the firm. However, when X is large, it may be better to keep thefirm integrated, but at the same time to do as much as possible with variousinternal devices ~e.g., the multibank holding-company structure! to mimic—even if one cannot fully replicate—the decentralized outcome in terms ofdivision-manager incentives.
B. CEO Research Incentives: Why Soft Information FavorsFlatter Organizations In modeling a hierarchy with soft information, I have thus far taken as exogenous q, the probability that the CEO’s research will be successful. NowI ask what happens in the soft-information case when the CEO’s incentivesare also taken into account—that is, when q ϭ q~e CEO !, where e CEO is theresearch effort exerted by the CEO, and where q~ !, like p~ !, is an increas-ing concave function. For simplicity, I stick to the case where the externalcredit constraint is four units—that is, where the sufficient condition inLemma 2 is satisfied—and where the star-gets-everything inequality ~8! alsoholds.
The outcome~s! in this setting are the Nash equilibria of the game where the CEO and the division managers choose their research efforts simulta-neously. Denote by ⌬CEO the utility gain to the CEO when, in a hierarchywith soft information, her research effort is successful. This quantity is eas-ily calculated by evaluating Y hs~4! in equation ~11! for both q ϭ 1 and q ϭ 0,and taking the difference: 4 !~2g~2! Ϫ 3g~1!!04 ϩ ~1 Ϫ p ~e4 !! ~3g~2! Ϫ 4g~1!!04.
An immediate consequence of equation ~15! is that the CEO’s research is more valuable when division managers do less research—that is, whenp~ehs 4 ! is low. Specif ically, differentiation of ~15! yields 0dp ~e4 ! ϭ ~ g~1! Ϫ g~2!!04 Ͻ 0.
18 I am grateful to Raghu Rajan for suggesting this example.
It then follows from the CEO’s first-order conditions that de CEO also: The CEO’s research effort is reduced when the division managers areworking hard.19 The intuition behind this result is straightforward. Recallthat the CEO, even when her research is successful, has at best coarse in-formation. Thus, while her tilting of the capital budget adds value on aver-age, it does have a cost in some states of the world. In particular, when facedwith one division that is a star ~i.e., that is $G, G %! and one that is not, theCEO gives the star all four units of funding. This full tilting of the capitalbudget toward the star is optimal if it turns out that the nonstar division is$B, B%. However, the tilt is too extreme if the nonstar division turns out to be$G, B%—ideally, it would be better to leave a $G, B% division with at least oneunit of funding.
In other words, because of her coarse information, an activist CEO some- times takes away too much from a $G, B% division. And what is the cost oftaking capital away from a $G, B% division? It depends on how profitable thisdivision can be expected to be. If its division manager is informed, the $G, B%division generates a greater expected return from a given allocation of cap-ital, as this capital is always steered to the better project within the division.
Thus, the opportunity cost of the CEO’s activism is greater when she runsthe risk of taking resources away from informed division managers.
Note the symmetry that is at work here: the CEO’s research incentives are blunted by the possibility that the division managers will become informed,much as the division managers’ incentives are blunted by the possibility thatthe CEO will become informed. That is, the more senior agent in the orga-nization can be discouraged by the hard work of her subordinates, as well asvice versa. This symmetry has a couple of consequences. First, since theCEO’s effort e CEO is a decreasing function of division managers’ efforts ehs and conversely, this game—without further restrictions on the p~ ! and q~ !functions—admits the possibility of multiple Nash equilibria.20 For example,one might have either a “control-freak” equilibrium where the CEO is highlyinformed and intervenes often, and where the division managers are verydiscouraged, or a “laissez-faire” outcome where the reverse occurs. Depend-ing on parameter values, one equilibrium will be ex ante more efficient thanthe other, and there is no guarantee that a firm will end up in the betterone. Thus, for example, the negative consequences of the hierarchical formof organization may be more pronounced for a firm that has gotten stuck ina control-freak culture, as opposed to one that has somehow managed tomaintain a laissez-faire environment.
A further implication of the model with endogenous CEO effort is that it suggests another organizational form that may be optimal in some circum-stances. In the same way that decentralization can be valuable as a precom- 19 The model of Aghion and Tirole ~1997! produces a similar result.
20 In other words, Nash equilibrium involves the intersection of two downwards-sloping curves 4 ! space. Without any further restrictions on functional forms, it is possible that these two curves may cross more than once.
Information Production and Capital Allocation mitment to get the CEO out of the picture—and thereby increase division-manager incentives—it might sometimes make sense to remove the divisionmanagers, so as to increase CEO incentives. It is easy enough to constructnumerical examples that have this feature. The key is to make CEO effortboth valuable and highly elastic, while making division-manager effort lessso. In such cases, we are left with just the CEO overseeing all four invest-ment projects, which can be interpreted as an integrated ~i.e., large! firmwith a f lat management structure.
Thus, when we compare hard versus soft information in terms of their implications for organizational form, we now have a new conclusion. Notonly does soft information tend to favor decentralization ~i.e., smaller firmswith fewer projects!, but holding fixed a firm’s size and scope, soft informa-tion also favors a f latter, more streamlined management structure. This isbecause the efforts of higher-ups and subordinates are strategic substituteswhen information is soft, but strategic complements when information ishard.
C. Hardness of Information Is Endogenous:Excess Bureaucracy in Hierarchies I have been assuming throughout that the hardness of information is exogenous—either a division manager’s information can or cannot be cred-ibly transmitted to the CEO, but there is nothing that the division managercan do to inf luence this. An alternative approach is to posit that the degreeof hardness is endogenous, and, that by expending additional effort on doc-umentation, a division manager can harden information that would other-wise be soft.21 To capture this idea formally, I return to the version of the model in Sec- tion I.D, where the CEO does no research of her own, and make one modi-fication. Now each division manager can choose between one of two researchtechnologies: He can either put one unit of effort into acquiring soft infor-mation, or he can put one unit of effort into acquiring hard information. Ifhe opts for soft information, there is a probability ps that his research issuccessful. If instead he chooses to go after hard information, there is aprobability ph that his research is successful, and conditional on success, aprobability z that the information actually turns out to be verifiable. I as-sume that ph ϭ bps and b , 1. Thus, effort devoted to acquiring hard in-formation is less productive. A high value of b means that information aboutthe project in question is by its nature relatively easy to document, so thatnot too much of a price is paid to make it hard; one can think of the previous 21 An example would be an academic department chair, who, having already decided that he wants to make a tenure offer to somebody, undertakes the process of writing for outside letters.
The letters may provide no new information to the department chair, but they can help him tocredibly sell the case to a less well-informed dean.
cases of absolutely “hard” and “soft ” information in Section I as correspond-ing to the polar extremes where b ϭ 1 and b ϭ 0, respectively.
It is easy to see that even when b is much less than one, the only equi- librium may be one in which both division managers opt to go after hardinformation. If both managers go after soft information, the CEO never learnsanything, and we are effectively in a decentralized outcome, with each divi-sion manager ’s effort yielding him a utility gain of psd4 ~assuming the ex-ternal credit constraint is four units!. In contrast, if one division managerdeviates and goes after hard information, we know from part ~c! of Propo-sition 3 that this manager’s utility gain will exceed ph ~⌬d ϩ when ph is much smaller than ps, hard information can yield higher privatebenefits. This is just an application of the logic developed above: Hard in-formation is more attractive to division managers, because it can help themget larger capital budgets.
Moreover, while hard information is, all else equal, more valuable to the firm as a whole—it enables the CEO to make value-enhancing reallocations—division managers’ preference for it is far too strong. That is, there are lowvalues of b for which the firm would be better off if the division managerspursued soft information, but division managers’ private incentives are suchthat they pursue hard information instead. This is because of an externality.
Manager i ’s utility goes up by one when he generates hard information thatlands his division one additional unit of capital. However, manager j loses anequal amount, and the gain to the firm as a whole is only proportional to theimproved net return on this one unit.
This logic implies that, when project information is innately hard to doc- ument ~i.e., when b is small but nonzero!, the costs of a hierarchical form oforganization may manifest themselves not just as division managers slack-ing off and doing no research, as in Section I.C. Rather, one may observedivision managers working extremely hard at creating the wrong kind ofinformation. In other words, a hierarchy may be characterized by a greatdeal of bureaucracy, in the sense of division managers generating lots ofreports that are very well documented, but ultimately not terribly informa-tive. And conversely, if a hierarchical firm is broken up, the excessive bu-reaucracy vanishes, and division managers instead produce only sof tinformation.
III. Empirical Implications: A Closer Look at Banks’
Small-Business Lending Practices
The most basic implication of the theory developed above is that large, hierarchical firms are at a comparative disadvantage when information aboutindividual investment projects is innately soft. Moreover, if one takes themodel seriously, the hardness or softness that is most relevant for organi-zational form has to do with information about those “small” projects thatare overseen by line managers. In other words, what matters is the nature Information Production and Capital Allocation of information that, in a hierarchical setting, would be produced far from theultimate decisionmaker, the CEO.
While these ideas would seem to have significant empirical content, there are challenges in mapping the theory into a set of precise, differentiatingpredictions that can be readily tested. For example, one interesting impli-cation of the theory is that small firms might be better able than large onesto engage in certain types of new product development, since the prospectsof many new products must often be assessed based on soft information.
However, any test of this proposition would have to control for a variety ofother mechanisms that could lead to a similar outcome—for example, thewell-known “replacement effect,” whereby large firms are discouraged frominnovating for fear of cannibalizing their existing product lines.22 Imple-menting such a control would most likely require a careful case-by-case analy-sis of the new products in question.
These sorts of complications underscore why it can be particularly infor- mative to look at small-business lending by banks. Here we have a well-defined “industry” where: ~a! it is easy to identify the primary “projects” thatline managers must choose among—namely, individual loan applications; and,moreover, ~b! it seems quite plausible that information about these partic-ular projects is likely to be innately soft.
The following findings emerge from the empirical literature on small- business lending. First, small banks invest a much greater share of theirassets in small-business loans than do large banks ~Nakamura ~1994!, Berger,Kashyap, and Scalise ~1995!, Berger and Udell ~1996!, Peek and Rosengren~1996!, and Strahan and Weston ~1996!!.23 Perhaps more strikingly, whenlarge banks acquire small banks, the small-business lending of the combinedorganization tends to fall sharply ~Peek and Rosengren ~1998!, Berger et al.
~1998!, Sapienza ~2002!!. Moreover, it appears that the loans that are cutas a result of consolidation are not cut simply because they are negative-NPV—that is, because the acquiring bank is cleaning out the bad loans ofthe target. Two pieces of evidence support this view. Berger et al. ~1998!establish that many of the loans that are cut in the process of consolidationare picked up by other banks in the same local market. And Sapienza findsthat there is no relationship between a borrowing firm’s credit quality andthe likelihood that it will have its lending relationship severed following amerger.
Although these patterns are broadly consistent with the theory developed above, they do not pinpoint the exact mechanism at work. That is, they donot explain why large banks might be disadvantaged at small-business lend-ing. However, other findings are beginning to emerge that speak more di-rectly to the central idea of this paper, namely that large organizations are 22 See Tirole ~1988, Chapter 10! for a discussion of the replacement effect.
23 Relatedly, Brickley, Linck, and Smith ~2000! document that large banks are the dominant players in densely populated metropolitan areas ~where presumably borrowers are more likelyto be big firms!, while small banks have a greater role in suburban and rural regions.
not well suited to handling soft information. Three types of studies are es-pecially worth noting.
First, it appears that it is not just bank size per se that discourages small- business lending, but rather organizational complexity. For example, De-Young, Goldberg, and White ~1997! show that controlling for a bank’s sizeand age, its proclivity for making small-business loans is also negativelyrelated to the number of branches it has, as well as to its being part of amultibank holding company.24 Keeton ~1995! finds similar results, with aparticularly negative effect on small-business lending for banks that areowned by out-of-state holding companies.
Second, there is some evidence that in making small-business loans, large banks tend to shy away from those “difficult credits” where soft informationis likely to be most important in assessing whether or not the loan is positive-NPV. Berger and Udell ~1996! find that large banks charge about 100 basispoints less on small-business loans than do small banks and require collat-eral about 25 percent less often. One interpretation is that large banks onlylend to those small customers whose financial position is so strong thatdetailed further investigation is not needed.
Finally, Cole, Goldberg, and White ~1997! use a new survey of small- business finance to look at differences in the loan approval process acrosslarge and small banks. They show that large banks ~over $1 billion in assets!tend to base loan approvals primarily on standard criteria obtained fromfinancial statements. In contrast, “small banks deviate from these criteriamore and appear to rely on their impression of the character of the borrowerto a larger extent” ~p. 1!.25 This evidence fits very nicely with the spirit ofthe model developed above.
While much of the foregoing discussion has implicitly treated the softness of information in small-bank lending as an exogenously fixed parameter,there is evidence that this parameter is changing over time, with improve-ments in information technology, widespread adoption of credit scoringmodels, and the growth of “infomediaries” such as Dun and Bradstreet.
Petersen and Rajan ~2002! document that the distance between small firmsand their bankers has been growing—from an average of 16 miles in the1970s to 68 miles in the 1990s—a pattern which they interpret as evidencethat an increasing amount of hard information is being brought to bear oncredit decisions. If they are correct, and if this trend continues, then themodel suggests that the comparative advantage of small banks in small-business lending may diminish in the future.
24 It should be noted that the implications of the theory for the multibank-holding-company variable are ambiguous. Perhaps it proxies for complexity and the number of layers of man-agement, which would tend to discourage small-business lending. But as argued in Section II.A,a holding-company structure may also make it harder to move capital across divisions, whichwould help soft-information research incentives and small-business lending.
25 More precisely, standard measures of borrower credit quality do a better job of explaining ~in an R2 sense! the loan approval decisions of large banks.
Information Production and Capital Allocation IV. Related Theoretical Work
The ideas in this paper are related to several strands of earlier theoretical work. Rather than attempting a comprehensive survey, I will just brief lydiscuss a few of the most direct linkages. One branch of the literature takesthe perspective that firms are organized so as to be maximally efficient atthe processing and communication of various types of information ~see,e.g., Sah and Stiglitz ~1986!, Radner ~1993!, Bolton and Dewatripont ~1994!,Harris and Raviv ~1999!!. Although information production and transmis-sion are central to my story as well, I differ from these other works in acouple of ways. First, I focus on managers’ incentives to create and pass onvarious types of information, whereas the above-mentioned papers abstractfrom agency problems within the firm. Second, the notion of authority ismore prominent in my model. In particular, the CEO does more than justlisten to and act on reports from her subordinates; she actually controls theresources that these subordinates work with.
The soft-information variant of the model—which emphasizes how the CEO’s capital-allocation authority can discourage division managers from doingresearch—is, as has already been noted, closely related to Aghion and Tirole~1997!. On a similar note, Rotemberg and Saloner ~1994! argue that firmsmay wish to avoid being too broad in scope. For if there are credit con-straints at the firm level, such narrowness can help the CEO commit toemployees that she will adopt any good ideas that they generate, therebystrengthening ex ante research incentives. More generally, the idea that agents’incentives are weaker when they do not have control over asset-allocationdecisions is familiar from the work of Grossman and Hart ~1986!, Hart andMoore ~1990!, and Hart ~1995!.
However, a sharp distinction between my model and these “costs-of-a boss” theories arises when information is hard, rather than soft. With completelyhard information, there is no downside to integration in my model. To thecontrary, the fact that division managers do not have control actually servesto heighten their incentives, as they struggle to produce enough positiveinformation to convince the CEO to give them a larger share of the capitalbudget. Thus, the model not only paints a generally more favorable pictureof the incentive effects of integration than much of the recent literature, itscomparative statics with respect to the hardness0softness of information alsoimply more nuanced empirical implications. The empirical distinctions amongthe theories are underscored by the facts from the banking industry: Theother costs-of-a-boss stories cannot easily explain why large banks might beat more of a disadvantage in small-business lending than in, say, credit-cardor mortgage lending.
In some ways, the hard-information version of the model—with managers trying to convince the CEO to give them more capital—is also reminiscent ofthe inf luence-cost literature ~Milgrom ~1988!, Milgrom and Roberts ~1988!,Meyer, Milgrom, and Roberts ~1992!!. However, when information is in-nately hard ~i.e., when b ϭ 1!, the welfare implications are reversed. Unlike in the inf luence-cost models, division managers’ efforts to sway the CEO areproductive here, rather than wasteful.26 But this positive result is sensitiveto the details of the information structure. When the hardness of informationis endogenous and b is low ~as in Section II.C!, division managers’ efforts toattract more capital can lead to inefficient levels of bureaucracy, a resultvery much in the spirit of the inf luence-cost theories.27 Finally, it is worth touching on the connection between my model and Hart and Moore ~1999!. In their model, some agents ~specialists! have ideasabout individual assets, while other agents ~coordinators! have ideas abouthow to use multiple assets together. These ideas are mutually exclusive, sothat only one agent ’s idea can be implemented with a given asset. Moreover,there is no ex post renegotiation. In this setting, the problem is to allocatedecision rights ex ante in such a way as to make sure that the best ideas getimplemented ex post. In contrast, in my model, the “ideas” of the CEO andthe division managers can be ex post complementary. Specifically, the CEO’sresearch can help her decide to allocate a certain amount of capital to agiven division manager, who then draws on his own knowledge to make theright suballocations to individual projects within the division. Thus, there isno ex post inefficiency when both the CEO and the division managers haveideas. Rather, the issue is the ex ante one of creating incentives for them togenerate these ideas in the first place.
V. Conclusions
By way of conclusion, it is useful to point out a limitation of the model developed above. At a fundamental level, the question being asked is: “Whatorganizational form—decentralization or hierarchy—does the best job of al-locating capital to competing investment projects?” But in addressing thequestion, the focus has been on information production and transmissioninside firms. The notion that valuable information might also be generatedby outside investors—for example, by traders in the stock market—has beendownplayed.28 In particular, I have been assuming that, because their re-search incentives are weaker than those of a CEO, outside investors acquireno information about investment prospects and base their decisions simplyon their initial priors.
Clearly, it would be nice to incorporate a richer and more fully endogenous view of stock-market information production into the model. There are sev-eral further issues that this sort of extension might allow one to address. Inparticular, the quality of stock-market information may—like the quality ofinternally generated information—depend on firm size and scope. On the 26 The positive, information-creating effects of self-interested advocacy have also been em- phasized by Rotemberg and Saloner ~1995! and Dewatripont and Tirole ~1999!.
27 Other papers that stress the negative aspects of intrafirm struggles for capital include Rajan, Servaes, and Zingales ~2000! and Scharfstein and Stein ~2000!.
28 This idea is stressed by Holmstrom and Tirole ~1993!, among others.
Information Production and Capital Allocation one hand, a potential advantage of decentralization is that it leads to stockprices that are specific to narrow, “pure-play ” sets of assets, thereby pro-viding more precise guidance for investment decisions. On the other hand,pushed too far, decentralization may dampen the overall amount of stock-market information that is produced: Given fixed costs of information ac-quisition, tiny firms may not attract much interest from either sophisticatedinvestors or stock analysts. By taking such factors into consideration, onemight hope to develop a more complete understanding of the link betweenorganizational form and the efficiency of capital allocation.
Proof of Lemma 1: An upper bound on the surplus created by a division with a three-unit allocation can be obtained by assuming that the divisionmanager’s research succeeds with certainty, yielding expected net outputequal to ~3g~2! ϩ g~1! ϩ b~2!!04. Conversely, a lower bound for a division witha two-unit allocation can be obtained by assuming that the division manag-er ’s research never succeeds, in which case expected net output is simplyg~1!. Comparing these two, it must be that two units is preferred if3~g~2! Ϫ g~1!! ϩ b~2! , 0, which is the sufficient condition given in thelemma.
Proof of Lemma 2: An upper bound on the surplus created by a hierarchy with a five-unit allocation can be obtained by assuming that information isperfect throughout the hierarchy, so that the five units are always allocatedefficiently. In this case, expected net output is ~7g~1! ϩ 25g~2! ϩ b~2!!016.
Conversely, a lower bound for a hierarchy with a four-unit allocation can beobtained by assuming that all agents are uninformed, so that each projectalways gets one unit of capital, leading to expected net output of 2g~1!. Com-paring these two, it must be that four units is preferred if 25~g~2! Ϫ g~1!! ϩb~2! , 0, which is the sufficient condition given in the lemma. Similar logicalso implies that four units are preferred to six or seven, given the samecondition.
Proof of Proposition 2: First, straightforward calculation establishes that a sufficient condition for the CEO to prefer an allocation of at least threeunits to a lone-star division ~rather than just giving two units to each divi-sion! is g~2!02 Ͼ 2g~1!03. This condition is satisfied if, as the propositionrequires, g~2!02 Ͼ 3g~1!04. So it must be that a lone-star division will get atleast three units of funding.
Now suppose that a lone-star division does in fact get exactly three units of funding. It is easy to show that equation ~9! in the text is modified sothat the utility gain ⌬hs when a division manager’s research is successful is q~2g~2! Ϫ 3g~1!!016.
But given the condition in the proposition, we know that ~2g~2! Ϫ 3g~1!! is 4 , which, in turn, implies that e4 the tilt in the capital budget is less extreme, a hierarchy induces less re-search effort than under decentralization. That a hierarchy also may lead tolower output—that is, that we may have Y hs~4! Ͻ Y d~4!—follows from thesame reasoning as in the example that was used to illustrate Proposition 1in the text.
Proof of Proposition 3: I begin by assuming that division-manager report- ing strategies are as described in part ~a! of the proposition; I will verifymomentarily that these strategies are optimal for the division managers.
With these reporting strategies, the CEO updates on a quiet division man-ager using equations ~12!–~14! in the text. Given these updating rules, let usask what the CEO does when she faces one division manager that reports$G, G % and another one that is quiet. It is not hard to show that, for anyvalue of zpc, it will be optimal for the CEO to give at least three units ofcapital to the $G, G % division if the following sufficient condition ~which isthe one required in the statement of the proposition! holds: g~2!02 Ͼ 3g~1!04.
Conversely, it is easy to see that there is no advantage to deviating from theequal-funding allocation under any other circumstances.
If the CEO follows these capital-allocation rules, then it must in fact be optimal for a division manager to speak up when his information is either$G, G % or $G, B%. In the former case, he may get a third or fourth unit ofcapital by speaking up, and, in the latter case, he ensures that he will notbe reduced down to one or zero units ~which could happen if he were quietand the other division reported $G, G %!. It is also at least weakly better forthe division manager to remain silent when his information is $B, B%. In-deed, for many parameter values, it is strictly better, since a division thatreports $B, B% will get allocated zero units of capital in circumstances whena quiet division would get one unit.
These arguments establish parts ~a! and ~b! of the proposition. To prove part ~c!, assume that when a $G, G % division manager is paired with a quietone, the former is allocated exactly three units of capital. This will establisha lower bound on the gains to being informed, as being informed would bestrictly more attractive if a $G, G % division were to get four units of capitalin this situation. Now take the perspective of manager i, assuming thatmanager j exerts effort of e and therefore has a probability of research success of p~ej!. ~This implies that there is a probability zp~ej! that man-ager j will uncover hard information, and a probability zp~ej!04 that man-ager j will be able to document to the CEO that his division is $G, G %.!A little algebra yields the following expression for the utility gain ⌬hh manager i if his research is successful: z04 ϩ z~4g~2! Ϫ 4g~1!!016 ϩ zp~ej !~2g~1! Ϫ 2g~2!!016 ϩ z2p~ej!~2g~1!!016.
Information Production and Capital Allocation z04 ϩ zp~ej !~2g~2! Ϫ 2g~1!!016 ϩ z 2p~ej !~2g~1!!016.
It then follows immediately from ~A3! that ⌬hh Ͼ ⌬d ϩ p~ej!, which establishes part ~c! of the proposition. Part ~d! is then obvious,since in a hierarchy with hard information, there is both more informationproduced than under decentralization, plus the added advantage that theCEO reallocates funds across divisions according to a value-maximizingcriterion.
Proof of Proposition 4 (Sketch): There are two cases to consider. In the first, the credit constraint facing a decentralized division remains at twounits, but that for a hierarchy is relaxed, and exceeds four units. In thiscase, revealed preference on the part of outside investors implies that thehierarchy must do at least as well as it did with four units under the con-ditions of Proposition 3, so it continues to dominate decentralization.
In the second case, suppose that each decentralized division can raise three units. In this case, a hierarchy must be able to raise at least six units, andmaybe more. One can thus put a lower bound on the value created by ahierarchy by assuming that it raises exactly six units. In a hierarchy withsix units, it is easy to verify that the following constitutes an equilibrium,for any parameter values: ~a! a division manager speaks up if his informa-tion is $G, G % and keeps quiet otherwise; ~b! when just a single divisionreports $G, G %, the CEO gives it four units of financing; and ~c! in all othercases, both divisions get three units of financing. It then follows from argu-ments analogous to those in the proof of Proposition 3 that research incen-tives are stronger in a hierarchy, and, that as a result, net output is alsogreater in a hierarchy.
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