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Matching Capital and Labor∗ Jonathan B. Berk Stanford University and NBER Jules H. van Binsbergen University of Pennsylvania and NBER Binying Liu Northwestern University September 26, 2016 Abstract We establish an important role for the firm by studying capital reallocation decisions of mutual fund firms. The firm’s decision to reallocate capital amongst its mutualfundmanagersaddsatleast$474,000amonth,whichamountsto30%ofthe total value added of the industry. We provide evidence that this additional value added results from the firm’s private information about the skill of its managers. Investors reward the firm following a capital reallocation decision by allocating additional capital to the firm’s funds. JEL classification: G30, J24, D22 ∗We thank Anat Admati, Peter DeMarzo, Daniel Ferreira, Francisco Perez-Gonzalez, Paul Pfleiderer, Anamaria Pieschacon, Jonathan Reuter, Michael Roberts, Paulo Volpin, and seminar participants at GeorgiaStateUniversity,theUniversityofChicago,StanfordUniversity,UCLA,theUniversityofMary- land,Wharton,UniversityofNewSouthWales,UniversityofSydney,UniversityofMelbourne,theAdam Smith Workshop, the SFS Cavalcade, and the NBER Corporate Finance Meetings, for helpful comments and suggestions. We demonstrate that an important role of a firm in the mutual fund sector is to effi- ciently match capital to skill. In a world with perfectly rational players, no information asymmetries and no other frictions, the role of a mutual fund firm would be irrelevant be- cause investors themselves would efficiently allocate their own capital amongst managers. In reality, what we find, is that mutual fund executives play a very important role in capital allocation. A decision to increase a portfolio manager’s assets under management (AUM) leads to an increase in the manager’s productivity as measured by value added. Similarly, we find that decisions to reduce managers’ responsibilities by taking away assets also lead to increases in subsequent value added. We find that at a minimum, the decision to reallocate capital to a manager adds, on average, $474,000 per manager per month, implying that the firm is responsible for at least 30% of the total value added of the average manager. Mutual fund firms appear to add substantial value by intermediating between investors and managers and thereby efficiently matching capital to skill. We further demonstate that investors are unable to match the firm’s capital realloca- tion decision themselves. We hypothesize that the reason why derives from the significant informational advantage mutual fund executives have relative to investors. For example, firm executives know every trade a manager makes, and in addition, trades that the man- ager chooses not to make. Executives use this information to direct capital away from overfunded managers towards underfunded managers. We provide supporting evidence in favor of the informational advantage hypothesis: (1) external hires that involve a change in AUM do not lead to a detectable change in future value added, (2) while past performance does explain investor flows, it does not have much power to explain firm capital reallocation decisions and (3) investors respond to these capital reallocation decisions by investing additional capital in the firm’s funds. We also find that the capital reallocation decision adds more value for young managers, supporting the hypothesis that the firm’s advantage derives from its access to better information about managerial ability. These facts are consistent with the hypothesis, first theorized by Alchian and Demsetz (1972), that firm executives use factors that are noteasilyobservabletopeopleoutsidethefirmtomakepersonneldecisions. Theyarealso consistent with the hypothesis in Gennaioli, Shleifer, and Vishny (2015) that investors trust mutual fund firms to make sound financial decisions on their behalf, and so when they see these firms making a managerial change they respond by investing additional capital. Although there is a large body of evidence demonstrating the importance of the firm’s 1 informational advantage in assigning workers to jobs and thereby determining compensa- tion, there is little evidence demonstrating that firms also use this knowledge to determine the job scope of the employee. Our results imply that by correctly determining how much responsibility to give an employee in a particular job, firms add considerable value. Con- sequently, the documented wage gains that result from internal job assignments likely not only result from the productivity gains from correctly matching jobs to workers, but also from correctly assigning worker responsibility within a job. Many of the questions pertaining to the economics of organizations are difficult to study because it is often hard to measure employee output directly. An advantage of our study is that because the performance of a mutual fund is public information, employee output is directly observable. That is, a mutual fund manager has one task — to invest capital on behalf of investors. The return he generates, as well as the amount of capital invested, is public information. The investor’s next best alternative investment opportu- nity, an investment in passively managed index funds, is also observable. By comparing the manager’s performance against this alternative, we can directly calculate an individ- ual manager’s productivity, that is, the value she adds. A second advantage of our study is that mutual fund firms own little physical capital.1 Consequently, ownership rights to capital cannot play an important role in why mutual fund companies exist or are valuable. What our results imply is that other factors, such as the informational role of the firm, are also important. Although we do not find strong evidence for a behavioral explanation of our findings, we cannot definitively rule out the possibility that at least part of our results derive from suboptimal investor behavior. For example, part of the value the firm adds could potentially result from investor inattention. Firms add value by paying attention on investors’ behalf. We leave it to future research to determine the possible importance of this explanation for our results. In the next section we describe how our paper fits into the existing literature. We develop a simple model that formalizes our hypothesis for why firms add value in Section 2. In Section 3 we define the value added of firms, funds and managers. The data set is described in Section 4 and provides summary statistics. In Section 5 we show that we can reject our Null hypothesis that firm capital reallocation decisions do not add value and, more importantly, provide a lower bound estimate of the value firms add. In the following 1Although the industry is capital intensive, firms do not own their own capital. Instead, the firms manage capital on behalf of outside investors. That is, capital providers retain full ownership rights to their capital and can call it back at any time. 2 section, Section 6, we show that investors respond to these capital allocation decisions by investing additional capital with the firm, indicating that investors are aware of the value these decisions add. In Section 7 we present a body of evidence that is consistent with the hypothesis that the value the firm adds by reallocating capital derives from the firm’s informational advantage from observing the quality of its own employees. 1 Background The literature on the economics of organizations has raised several important questions related to the role of firms. What makes a firm successful? Is it a characteristic of the firm itself, or is it simply that a successful firm is a collection of particularly talented employees? Why do people choose to work for firms rather than for themselves? Do personnel decisions within the firm add to overall firm value? There is now a large theoretical literature designed to answer these questions (see Hart and Moore (1990), Holmstrom and Tirole (1989), Hart (1995) and Rajan and Zingales (1998)). A key aspect of modern theories of the firm is the concept of ownership. In a world with incomplete contracting, incomplete information and bounded rationality, ex post bargaining power is affected by ownership. Asset owners, because they retain the rights of control, have inherently more bargaining power. An important insight of this literature is that firms exist to ensure that ex ante ownership is concentrated to allow for efficient ex post outcomes. Although these theories undoubtedly explain an important component of why modern firms exist, they cannot explain a particular, and increasingly important, type of firm — a firm that consists almost exclusively of human capital. These firms have little physical capital other than perhaps some intangible capital such as the firm’s brand name. Hence, a primary reason for the existence of these types of firms cannot be the assignment of ex post bargaining rights through asset ownership. Ourpaperrelatestoanexpandingliterature,pioneeredbyBertrandandSchoar(2003), that seeks to isolate the productive role of the worker (manager) from that of the firm. Bertrand and Schoar (2003) demonstrate the importance of firm managers by studying CEOs. More recently, Ewens and Rhodes-Kropf (2013) separate the value added in ven- ture capital projects into a manager component and a firm component and argue that human capital, rather than organizational capital, accounts for most of the skill in the venture capital world. This research relies on the fact that workers move between firms to identify the separate roles of workers and firms. However, because switching firms is an 3 endogenous decision, this methodology is generally unable to put a quantitative estimate on the contribution of the firm nor is it informative on what precisely the firm does to add value. Instead of focusing on external moves as the identification strategy, we rely on the firm’s internal decision to promote and demote its workers and thus we are able to both identify the source of the firm’s value added and derive a quantitative bound on the firm’s contribution to productivity. Our paper also relates to the labor literature studying personnel economics and the internal labor market of the firm pioneered by Doeringer and Piore (1971).2 That lit- erature focuses on how firms establish and end employment relationships and how firms provide incentives to workers through the wage contract. Our focus is different. We do not observe employee wages, but instead observe employee productivity (value added). That allows us to study how firm decisions regarding the scope of the managers’ job (the size of their AUM) affects their productivity rather than their wages. We argue that the firm uses its private information about employee skill to efficiently allocate capital and thereby determine the scope of responsibility of the employee. Finally,ourpaperisalsopartoftheliteraturethatstudieshowtheintra-firmallocation of capital and labor affects productivity and drives heterogeneity in the quality of firms. Gertner, Scharfstein, and Stein (1994) model the costs and benefits of internal capital allocation versus external capital allocation in the form of bank lending. Stein (1994) studies the comparative advantages of decentralized versus hierarchical firms in efficiently allocating capital to projects. Tate and Yang (2014) show that diversified firms have higher labor productivity and actively redeploy their human capital to business areas with better prospects. Giroud and Mueller (2014) find that firms take resources away from less productive plants and reallocate them to plants with better investment opportunities. Resource allocation (or misallocation) across firms and across industries has also been identified as a major determinant of economic productivity at the macroeconomic level.3 A key determinant of a firm’s productivity is its management. Bloom, Sadun, and van Reenen (2013) find significant differences in management quality across firms both in the U.S. and abroad. Bloom, Eifert, Mahajan, McKenzie, and Roberts (2013) show, 2In more recent work, Abowd, Kramarz, and Margolis (1999) find worker fixed effects to be more importantthanfirmfixedeffectsindrivingheterogeneityinworkers’wages. Graham,Li,andQiu(2011) decomposevariationinCEOcompensationandshowthatmostofthisdifferenceisexplainedbymanager heterogeneity rather than firm heterogeneity. Oyer and Schaefer (2011) and Waldman (2013) are recent surveys of this literature. 3For example, see Hsieh and Klenow (2009), Alfaro, Charlton, and Kanczuk (2009) and Bartelsman, Haltiwanger, and Scarpetta (2013). 4 based on randomized experiments in India, that management practices have a significant impact on firm productivity. Lazear, Shaw, and Stanton (2014) find that hiring better supervisors make workers more productive. Finally, most mutual funds are owned and marketed as part of a fund family, so a number of studies have looked into how the family structure affects the mutual fund industry.4 2 Theory Our underlying hypothesis in this paper is that internal firm decisions about how to allocate capital amongst employees add value, and that this value derives from the fact that firms have better information about their employees’ abilities than outside investors in the firm. With that in mind, in this section we will develop a simple model that formalizes this hypothesis. We assume that there are three types of agents. Outside investors, employees and a firm executive. Both employees and the firm executive have a skill in short supply and receive all the rents for this skill. A firm consists of an executive and I employees. The net present value (NPV) of the value created by each employee, i, using capital q is, i V ≡ q ψ (q ), i i i i where ψ (q) is the average excess return on capital employee i generates when given i responsibility for the amount of capital q. In the mutual fund literature, ψ (q) is referred i to as the gross alpha and V corresponds to what Berk and van Binsbergen (2015) refer i to as value added. We will maintain the realistic assumption throughout the paper that ψ(cid:48)(q) < 0. In words, there are decreasing returns to scale so that the excess return on i capital decreases in the amount of responsibility an employee is assigned.5 Employee i receives a wage (compensation) W . The firm executive determines the amount of capital i employees are given responsibility for. 4Massa (2003) argues that having fund families reduces investors’ cost of switching between funds. Gaspar,Massa,andMatos(2006)andBhattacharya,Lee,andPool(2013)findevidencethatmutualfund families transfer performance from one group of funds to another group of funds through coordinated trades. Kempf and Ruenzi (2008) show that intra-firm competition has important effects on managers’ appetite for risk. Chen, Hong, Jiang, and Kubik (2013) find that funds outsourced to advisory firms underperform funds managed in-house. Fang, Kempf, and Trapp (2014) show that a firm allocates its skilled managers to funds targeting inefficient markets. 5There is a growing body of empirical evidence documenting decreasing returns to scale in the mu- tual fund industry, see Chen, Hong, Huang, and Kubik (2004), Pollet and Wilson (2011), and Pastor, Stambaugh, and Taylor (2015). 5 2.1 Coasian Benchmark First we derive the equilibrium level of capital in a frictionless market with no asymmetric information (the null hypothesis in this paper). In such a world, there is no role for a firm executive because the executive does not add any value over the value added of individuals working for themselves. To see this formally, consider the case where each employee works for herself but needs to raise money from outside investors. The outside investors maximize the NPV of their investment, subject to the condition that the NPV is not negative: max[q ψ (q )−W , 0]. (1) i i i i qi The solution to this problem for each employee i = 1,...,I, is ψ (q∗)+q∗ψ(cid:48)(q∗) = 0. (2) i i i i i Each employee chooses his wage by maximizing his compensation taking into account the outside investor’s participation constraint, implying W = q∗ψ (q∗). (3) i i i i Now assume employees work for a firm. In this case the firm executive’s maximization problem, taking employees’ wages as given, is (cid:34) (cid:35) I (cid:88) max q ψ (q )−W , 0 . (4) i i i i {qi} i=1 The solution to this problem, {q∗,...,q∗}, uniquely satisfies the following I first order 1 I conditions: ψ (q∗)+q∗ψ(cid:48)(q∗) = 0, i = 1,...,I, (5) i i i i i which is identical to (2). The employees can always choose to work for themselves, which implies that, in equilibrium, the firm must pay at least (3). The investor participation constraint implies the firm cannot pay more, so we have W = q∗ψ (q∗). (6) i i i i At this wage the NPV of investing in the firm is zero, so we can assume that outside investors will be willing to provide capital (cid:80)I q∗ and so the two equilibria are identical. i=1 i 6 2.2 Asymmetric Information The alternative hypothesis in this paper is that the firm executive can better observe the quality of her employees than the providers of capital. We assume that employees cannot credibly communicate their ability and so the providers of capital cannot differen- tiate between employees.6 This model is observationally equivalent to a model in which investors can observe employee ability but nevertheless choose to ignore this information for behavioral reasons. Under these assumptions the providers of capital believe employee excess return on capital is ψ(q) ≡ E[ψ (q)]. (7) i If the employees work for themselves, the outside investors maximize the NPV of their investment subject to their participation constraint: max[E[V ]−W , 0] = max[q ψ(q )−W , 0], (8) i i i i i qi qi where we are assuming that employee productivity risk is idiosyncratic and so does not command a risk premium. The first order condition is: ψ(qˆ)+q ψ(cid:48)(qˆ) = 0, i = 1,...,I. (9) i As before, each employee maximizes his wage subject to the participation constraint: ¯ W = qˆψ(qˆ). (10) The solution does not depend on i and so all employees manage the same amount of ¯ capital, qˆ, and earn the same wage, W. The total amount of capital invested is therefore: ¯ Q ≡ Iqˆ. Next we turn to the firm’s optimization problem. The firm executive has a competitive advantage because she has private information that allows her to allocate capital better. 6That is, for ease of exposition, we normalize the information set of outside investors by assuming that the publicly available information for all employees is the same. This model is easily generalizable to the case where outside investors can partially differentiate between employees and we thus we allow outside investors to partially differentiate in the empirical work that follows. 7 For a given level of capital invested by outside investors, Q, they add value by efficiently allocating capital, and because this skill is in short supply, they are able to capture this value, ∆V. That is, the NPV of the additional value added by the firm is the solution to I I (cid:88) (cid:88) ¯ ∆V = max q ψ (q )−IW s.t. q = Q. (11) i i i i {qi} i=1 i=1 The employee wage is set subject to the constraint that employees can choose to work ¯ for themselves, implying that each employee earns W, and so total wage expenses are ¯ IW. As before, in equilibrium, the NPV of outside investors’ investment is zero, implying that they are indifferent to the choice of Q, so the firm executive can assume that outside investors will provide the level of Q that maximizes her value added, that is, I I (cid:88) (cid:88) ¯ ∆V = max q ψ (q )−IW s.t. q = Q. (12) i i i i {qi,Q} i=1 i=1 ˜ At the optimal allocation of capital, {q˜ ,...,q˜ ,Q}, 1 I I (cid:88) ¯ ∆V = q˜ψ (q˜)−IW ≥ 0, (13) i i i i=1 ¯ where the inequality follows because q = qˆ∀i and Q = Q is feasible. i For most firms neither q nor ψ (q ) are directly observable and so measuring ∆V is i i i challenging. The mutual fund industry is exceptional because both quantities are directly observable at the employee level. In the next subsection we illustrate this explicitly in the context of a simple example. 2.3 A Simple Mutual Fund Example Our objective is to measure the contribution of mutual fund firms, ∆V. In this regard, we are departing from the conventional approach in the mutual fund literature. In that literature researchers have used ψ, that is, alpha, to measure skill. Consequently, some readers have questioned our approach arguing that to correctly measure the contribution of the firm, we should be measuring ∆ψ rather than ∆V. For that reason, we will illustrate, in the context of a simple example, why ∆ψ does not measure the contribution 8 0.12 Gross Alpha ψ(·) V V*= a2/40b.1 ΔV VI = 3a2/160.0b8 0.06 Promotion 0.04 ψ(0) = a 0.02 ψ(qI) = 3a/4 ψ(q*) = a/2 -b 0 0161116212631364146qI51 =56a/614b667176818691q96*=01a06/211b16212631364146515661667176818691q=96a01/b 111111111111111111112 Figure 1: Value Added and Gross Alpha: The blue (solid) line plots gross alpha as a function of thesizeofthefund: ψ(q)=a−bq. Thegreen(dashed)curveisthevalueaddedofthefundasafunction of fund size, q ψ(q). of the firm.7 Suppose ψ(q) = a−bq, that is, a fund manager’s excess return on capital (gross alpha) on the first dollar she manages is a and it decreases at a rate b, plotted in blue in Figure 1. Assume that the parameters a and b are both known to firm executives. The optimal amount the manager shouldbemanagingisfoundbymaximizingthetotalvalueaddedoverq (thegreendashed line in the figure): maxqψ(q) = q(a−bq). q 7Berk and van Binsbergen (2015) prove (based on the arguments in Berk and Green (2004)), in a world that features competitive capital markets, that alpha measures do not measure skill. 9

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∗We thank Anat Admati, Peter DeMarzo, Daniel Ferreira, Francisco Perez-Gonzalez, Paul Pfleiderer,. Anamaria . Gaspar, Massa, and Matos (2006) and Bhattacharya, Lee, and Pool (2013) find evidence that mutual fund families
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Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.