12. Internal Capital Market
Part IV 主题：内部与外部资本市场。 企业经营项目，为何不简单地把企业拆成单个项目？因为摩擦（如信息不对称）使单个项目极难融资。故需要企业以某种方式组织多个项目，使整体价值大于各项目价值之和——这正定义了企业的边界。本部分讨论融资资源，并将看到内、外部融资都可能带来无效率。本章 (Ch 12) 内部资本市场。§12.1 何时需要企业：Coase (1937)——摩擦使企业必要（企业有内部权威、信息优势、非正式协议以降低摩擦）；Alchian-Demsetz (1972)——当生产需多方联合投入、存在一个可独立重谈所有合约且持剩余索取权的中心方时，企业出现，并通过持续重谈与廉价侦测偷懒提升效率。§12.2 Stein (1997) 过度上报与总部资源再配置：项目经理因帝国构建（私人收益正比于现金流）总向市场谎报「好状态」，市场不信→只投 1→投资不足。单项目时总部纯属浪费（有运营成本）；多项目时总部能在内部高效再配置（好状态投 2、坏状态投 0 优于各投 1），市场预期到此而愿投更多（Remark 12.1：企业通过再配置资源提升效率）。§12.3 Rajan et al. (2000) 部门间窃取：实证上多元化组合常折价交易（与 Stein 表面相反）。两部门可选高效技术（回报不减但可被对方按比例 \(\theta\) 窃取）或防御技术（回报减 \(\gamma\) 但免遭窃取）。维持「双方都用高效技术」的均衡需 IC：任一部门禀赋须低于 \(\frac{c}{\pi\theta-\gamma}\)；否则有部门偏离去窃取，迫使对方转向防御技术——这解释了多元化部门的无效率（折价）来源。
Part IV theme: internal and external capital markets. Firms run projects — why not simply split firms into individual projects? Because frictions (e.g. information asymmetry) make an individual project very hard to finance. So we need firms to organize multiple projects in some way that the total value exceeds the sum of the individual project values — which is exactly what defines the boundary of the firm. This part is about financing resources, and we will see that both internal and external financing can lead to inefficiencies. This chapter (Ch 12): the internal capital market. §12.1 When do we need firms: Coase (1937) — friction makes the firm necessary (a firm has internal authority, informational advantage, informal agreements to reduce frictions); Alchian-Demsetz (1972) — a firm arises when production requires joint inputs from several owners and there is a central party who can independently renegotiate every contract and holds the residual claim, enhancing efficiency through continuous renegotiation and cheap detection of shirking. §12.2 Stein (1997) over-reporting and resource relocation by headquarters: project managers, driven by empire building (private benefit proportional to cash flow), always misreport a "good state" to the market, which disbelieves them → invests only 1 → under-investment. With one project the headquarters is pure waste (it has an operating cost); with multiple projects the headquarters can efficiently relocate resources internally (invest 2 in the good-state project, 0 in the bad, beating 1-1), and the market, anticipating this, will invest more (Remark 12.1: firms improve efficiency by relocating resources). §12.3 Rajan et al. (2000) inter-division stealing: empirically, diversified portfolios often trade at a discount (seemingly opposite to Stein). Each division chooses an efficient technology (returns not reduced but stealable by the other at proportion \(\theta\)) or a defensive technology (returns reduced by \(\gamma\) but protected). Sustaining the "both efficient" equilibrium requires the IC that any division's endowment be below \(\frac{c}{\pi\theta-\gamma}\); otherwise some division deviates to steal, forcing the other into the defensive technology — explaining the inefficiency (discount) of diversified divisions.
Part IV — Internal and External Capital Market (preamble)
企业经营项目。为何不简单地把企业拆分成一个个单独的项目？因为摩擦（例如信息不对称）使单个项目很难被融资。所以我们需要企业以某种方式组织多个项目，使得整体价值大于这些项目各自价值之和。对这个问题的解答，正定义了企业的边界。
本部分讨论融资资源。我们将看到，内部融资与外部融资都可能导致某些无效率。
Firms run projects. Why don't we simply split firms into individual projects? Because frictions (e.g. information asymmetry) make an individual project very hard to be financed. So we need firms to organize multiple projects in some way that the total value is greater than the sum of the individual values of those projects. The solution to this problem defines the boundary of firms.
This part is about financing resources. We will see that both internal and external financing could lead to some inefficiencies.
12.1 When Do We Need Firms: Coase (1937) and Alchian and Demsetz (1972)
- Coase (1937) 论证摩擦使企业成为必要：
- 没有任何摩擦时，市场价格就能高效配置资源；
- 企业的存在与稳定，恰恰意味着存在摩擦；
- 企业拥有内部的权威、秩序、信息优势与非正式协议，可降低摩擦的影响。
- Alchian and Demsetz (1972) 为企业的存在假设了另一些条件：
- 设企业内不存在威权式控制；
- 在下列情形会出现企业：
- 生产需要来自多个投入所有者的联合投入；
- 有一个中心方 (central party) 为所有合约所共有，且有权独立地重新谈判任一合约；
- 该中心方持有剩余索取权，并有权出售此索取权。
- 企业提升效率：
- 对投入合约进行持续的重新谈判；
- 更好（且更便宜）地侦测偷懒、约束投入所有者。
- Coase (1937) 与 Alchian-Demsetz (1972) 强调拥有企业的不同好处，但总体思想相同：当整合的结果优于各单独项目之和时，我们就需要企业。
- Coase (1937) argues that friction makes the firm necessary:
- without any friction, prices in the market can allocate resources efficiently;
- the existence and stability of firms imply that there are frictions;
- a firm has internal authority, order, informational advantage and informal agreement, which can reduce the impact of frictions.
- Alchian and Demsetz (1972) assume other conditions for the existence of firms:
- let there be no authoritarian control of the firm;
- we will have a firm when:
- production requires joint inputs from several input owners;
- one party (the central party) is common to all the contracts and has the rights to renegotiate any contract independently;
- the central party holds the residual claim and has the right to sell that claim.
- the firm enhances efficiency:
- continuous renegotiation of input contracts;
- better (cheaply) detecting shirking and disciplining input owners.
- Coase (1937) and Alchian-Demsetz (1972) emphasize different benefits of having firms. But the overall idea is the same: we need firms when the integrated outcome is better than the sum of the individual projects.
12.2 Over-Reporting and Resource Relocation by Headquarters: Stein (1997)
Stein (1997) 讨论一个设定：项目经理总是过度上报自身状态，而企业（总部）的存在使项目能被更好地融资。
12.2.1 设定.
- 有两个项目，每个项目可独立地处于好状态（\(s=g\)）或坏状态（\(s=b\)）。
- 投资 \(I\) 可为 1 或 2：
- 对每个项目：若 \(s=g\)，投资者最优应投 2；若 \(s=b\)，仍应投资但只投 1；
- 假设「\(s=g\) 投 2、\(s=b\) 投 0」严格优于「两者都投 1」。
- 市场投资者无法弄清每个项目的真实状态。
- 这两个项目有一个总部 (headquarter)：
- 总部经理相对市场有信息优势，即总部确知每个项目的状态；
- 总部可在两个项目之间再分配资源（投资）；
- 总部运营有额外成本。
12.2.2 帝国构建与过度上报.
- 设各项目经理与总部经理都有帝国构建 (empire building) 的欲望，因为他们享有正比于现金流的私人收益。
- 过度上报导致投资不足：
- 项目经理总会告诉市场自己处于好状态（\(s=g\)）；
- 市场无法弄清真相，故从不相信项目经理，任何情况下都只投 1——这就是投资不足问题。
12.2.3 结果.
- 若只有一个项目，总部（企业）严格地减损价值：
- 因我们假设总部有严格为正的运营成本；
- 单项目时总部毫无作用，只是以其运营成本浪费资源。
- 若有多个项目，总部（企业）增加价值：
- 尽管总部经理也有为私人收益过度上报的动机，但他们也想把蛋糕做大，即会在企业内部高效地再配置资源；
- 当有一个坏状态项目和一个好状态项目时，两项目各自分立只能各在 \(I=1\) 下运作；
- 按假设，好状态项目 \(I=2\)、坏状态项目 \(I=0\) 严格优于各投 1；
- 故企业会再配置投资资源（两项目合计仍假设为 2）。
- 市场知道这种高效再配置会发生，故或许愿对每个项目投资多于 1；
- 例如随着效率提升，市场可能愿向总部合计投 3。
Remark 12.1 这一结果简单地说：企业通过再配置资源提升效率。
Stein (1997) discusses a setup where project managers always over-report their states, and the existence of a firm (headquarters) enables projects to be better financed.
12.2.1 Setup.
- There are two projects, each could independently be in either a good state (\(s=g\)) or a bad state (\(s=b\)).
- An investment \(I\) could be either 1 or 2:
- for each project: if \(s=g\), investors should optimally invest 2; if \(s=b\), they should still invest but only invest 1;
- assume that "invest 2 for \(s=g\) and 0 for \(s=b\)" is strictly better than "invest 1 in both."
- Market investors cannot figure out the true state of each project.
- There is a headquarters for these two projects:
- the headquarters manager has an information advantage over the market, i.e. headquarters knows the exact state of each project;
- the headquarters could redistribute resources (investment) between the two projects;
- the headquarters operates at an additional cost.
12.2.2 Empire building and over-reporting.
- Suppose each project manager and the headquarters manager all have a desire for empire building, because they enjoy a private benefit proportional to the cash flow.
- Over-reporting leads to under-investment:
- project managers would always tell the market they are in the good state (\(s=g\));
- the market has no way to figure out the truth, so it never believes the project managers and only invests 1 in any case — the under-investment problem.
12.2.3 Results.
- If there is only one project, the headquarters (firm) is strictly value-reducing:
- this holds since we assumed a strictly positive operating cost of the headquarters;
- with one project the headquarters makes no difference but just wastes resources via its operating cost.
- If there are multiple projects, the headquarters (firm) is value-increasing:
- although headquarters managers also have an incentive to over-report for private benefit, they also want to make the pie bigger, i.e. they relocate resources within the firm efficiently;
- with one bad-state and one good-state project, the two separately could only work at \(I=1\) each;
- by assumption, the good-state project at \(I=2\) and the bad-state project at \(I=0\) is strictly better than 1-1;
- so the firm relocates investment resources (still assumed to be 2 in total for both projects).
- the market knows such efficient relocation would take place, so they would invest more than 1 for each project;
- for example, the market might invest 3 in total to the headquarters as efficiency improves.
Remark 12.1 This result simply says that firms improve efficiency by relocating resources.
12.3 Internal Stealing Among Units: Rajan et al. (2000)
由 §12.2，我们本应得出「不同项目的组合价值高于各项目之和」。然而实证证据恰恰相反：项目组合（多元化集团）总是以折价 (discount) 交易。这类实证发现并不必然与 Stein (1997) 矛盾，但需要引入企业集团更多维度的弊端。Rajan et al. (2000) 讨论了一个部门间窃取 (inter-division stealing) 的模型。
12.3.1 设定.
- 有两个部门 \(A\) 与 \(B\)：
- 部门 \(A\) 禀赋 \(\lambda^A\)、投资回报 \(\alpha^A\times\lambda^A\)；
- 部门 \(B\) 禀赋 \(\lambda^B\)、投资回报 \(\alpha^B\times\lambda^B\)。
- 两个部门都可采用两种技术：
- 高效技术 (efficient)：回报不减（\(A\) 仍 \(\alpha^A\)、\(B\) 仍 \(\alpha^B\)），但可被对方按比例 \(\theta\) 窃取；
- 防御技术 (defensive)：回报减少 \(\gamma\)（\(A\) 为 \(\alpha^A-\gamma\)、\(B\) 为 \(\alpha^B-\gamma\)），但该部门免遭任何窃取。
- 成功窃取的一方（如 \(A\)）可从部门 \(B\) 取得 \(\pi\theta\lambda^B\)（\(\pi\in(0,1)\)），窃取成本为 \(c\)。
12.3.2 机制.
- 若两部门都采用防御技术：均无法窃取。\(A\) 的收益为 \((\alpha^A-\gamma)\lambda^A\)，\(B\) 的收益为 \((\alpha^B-\gamma)\lambda^B\)。
- 若一方（如 \(A\)）防御、另一方（如 \(B\)）高效：\(A\) 的收益为 \((\alpha^A-\gamma)\lambda^A+\pi\theta\lambda^B-c\)（\(A\) 从高效的 \(B\) 处窃取），\(B\) 的收益为 \((\alpha^B-\theta)\lambda^B\)。
- 若两部门都采用高效技术：\(A\) 收益 \(\alpha^A\lambda^A\)、\(B\) 收益 \(\alpha^B\lambda^B\)。
- 为使「双方都用高效技术」成为均衡，需两部门的 IC 约束成立。对部门 \(i\in\{A,B\}\)（偏离即转防御并窃取）：
$$\alpha^i\lambda^i>(\alpha^i-\gamma)\lambda^i+\pi\theta\lambda^i-c$$
$$\Rightarrow\pi\theta\lambda^i<\gamma\lambda^i+c$$
$$\Rightarrow\lambda^i<\frac{c}{\pi\theta-\gamma}$$
- 为维持高效均衡，两部门的 IC 必须满足，即要求任一部门的禀赋低于 \(\frac{c}{\pi\theta-\gamma}\)。若不然，则某部门会偏离去窃取其他部门，进而迫使可能被窃取的部门转向防御技术。这种效应解释了多元化部门所带来的无效率（折价）。
From §12.2, we should be able to conclude that a portfolio of different projects has a higher value than the sum of the projects. However, empirical evidence suggests exactly the opposite: a portfolio of projects (a conglomerate) is always traded at a discount. Such empirical findings are not necessarily contradicting Stein (1997), but do require more dimensions of drawbacks of conglomerates. Rajan et al. (2000) discuss a model for inter-division stealing.
12.3.1 Setup.
- There are two divisions \(A\) and \(B\):
- division \(A\) has an endowment \(\lambda^A\) and investment payoff \(\alpha^A\times\lambda^A\);
- division \(B\) has an endowment \(\lambda^B\) and investment payoff \(\alpha^B\times\lambda^B\).
- Two technologies are possible for both divisions:
- efficient technology: returns are not reduced (still \(\alpha^A\) for \(A\) and \(\alpha^B\) for \(B\)), but could be stolen by the other division at a proportion \(\theta\);
- defensive technology: returns are reduced by \(\gamma\) (\(\alpha^A-\gamma\) for \(A\) and \(\alpha^B-\gamma\) for \(B\)), but the division is protected against any stealth.
- The division that successfully steals, say \(A\), can get \(\pi\theta\lambda^B\) from division \(B\) (\(\pi\in(0,1)\)) at a cost \(c\) of stealing.
12.3.2 Mechanism.
- If both divisions take the defensive technology: neither could steal. Payoff to \(A\) is \((\alpha^A-\gamma)\lambda^A\), payoff to \(B\) is \((\alpha^B-\gamma)\lambda^B\).
- If one (e.g. \(A\)) takes defensive and the other (e.g. \(B\)) takes efficient: payoff to \(A\) is \((\alpha^A-\gamma)\lambda^A+\pi\theta\lambda^B-c\) (\(A\) steals from the efficient \(B\)), payoff to \(B\) is \((\alpha^B-\theta)\lambda^B\).
- If both take the efficient technology: payoff is \(\alpha^A\lambda^A\) to \(A\) and \(\alpha^B\lambda^B\) to \(B\).
- To make "both efficient" an equilibrium, we need the IC constraints for both divisions. For division \(i\in\{A,B\}\) (deviation = switch to defensive and steal):
$$\alpha^i\lambda^i>(\alpha^i-\gamma)\lambda^i+\pi\theta\lambda^i-c$$
$$\Rightarrow\pi\theta\lambda^i<\gamma\lambda^i+c$$
$$\Rightarrow\lambda^i<\frac{c}{\pi\theta-\gamma}$$
- To maintain the efficient equilibrium, the IC of both divisions must be satisfied, requiring that the endowment to any division is below \(\frac{c}{\pi\theta-\gamma}\). If this is not true, then some division will deviate and steal from the others, which in turn leads the potentially stolen firm to invest in the defensive technology. Such effects explain the inefficiency (discount) coming out of diversified divisions.
References
- Alchian, A. A. and H. Demsetz (1972). Production, information costs, and economic organization. American Economic Review 62(5), 777–795.
- Coase, R. H. (1937). The nature of the firm. Economica 4(16), 386–405.
- Rajan, R., H. Servaes, and L. Zingales (2000). The cost of diversity: The diversification discount and inefficient investment. The Journal of Finance 55(1), 35–80.
- Stein, J. C. (1997). Internal capital markets and the competition for corporate resources. The Journal of Finance 52(1), 111–133.