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The Hong Kong University of Science and Technology
香港科技大学
January 2025  2025 年 1 月

The Hong Kong Reprographic Rights Licensing Society Limited
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Twenty-five years of corporate governance research. . . and counting, 2001
二十五年的公司治理研究……还在继续，2001
Understanding the determinants of managerial ownership and the link between ownership and performance, 1999
理解管理层持股的决定因素以及持股与绩效之间的联系，1999
Wealth and Executive Compensation?, 2006
财富与高管薪酬?, 2006
Do CEOs Matter? Evidence from Hospitalization Events, 2020
首席执行官重要吗？来自 2020 年住院事件的证据

You are not permitted to make any further copy of this work, or to make it available to others. No re-sale is permitted
您不被允许对本作品进行任何进一步的复制或将其提供给他人。禁止转售。

Received 9 March 1998; received in revised form 19 October 1998; accepted 2 March 1999
收到日期：1998 年 3 月 9 日；修订版收到日期：1998 年 10 月 19 日；接受日期：1999 年 3 月 2 日

controlling both for observed firm characteristics and firm fixed effects, we cannot conclude (econometrically) that changes in managerial ownership affect firm performance. © 1999 Elsevier Science S.A. All rights reserved.
在控制了观察到的公司特征和公司固定效应后，我们无法得出（计量经济学上）管理层持股的变化会影响公司绩效的结论。© 1999 Elsevier Science S.A. 保留所有权利。

JEL classification: G14; G32; D23; L14; L22
JEL 分类：G14；G32；D23；L14；L22
Keywords: Managerial ownership; Corporate governance
关键词：管理层持股；公司治理

Since Berle and Means (1932), the conflict between managers and shareholders has been studied extensively by researchers seeking to understand the nature of the firm. When shareholders are too diffuse to monitor managers, corporate assets can be used for the benefit of managers rather than for maximizing shareholder wealth. It is well known that a solution to this problem is to give managers an equity stake in the firm. Doing so helps to resolve the moral hazard problem by aligning managerial interests with shareholders’ interests. Therefore, Jensen and Meckling (1976) suggest that managers with small levels of ownership fail to maximize shareholder wealth because they have an incentive to consume perquisites. In a similar fashion, some commentators have decried low levels of managerial ownership in U.S. corporations, and the theme has even appeared in discussions by compensation specialists and boards of directors.
自从 Berle 和 Means（1932）以来，研究人员广泛研究了管理者与股东之间的冲突，以理解公司的本质。当股东过于分散以至于无法监控管理者时，企业资产可能会被用于管理者的利益，而不是为了最大化股东财富。众所周知，解决这个问题的一种方法是让管理者在公司中拥有股权。这样做有助于通过将管理者的利益与股东的利益对齐来解决道德风险问题。因此，Jensen 和 Meckling（1976）建议，拥有少量股份的管理者未能最大化股东财富，因为他们有动机消费特权。以类似的方式，一些评论者对美国公司中管理层持股比例低表示谴责，这一主题甚至出现在薪酬专家和董事会的讨论中。

In this paper, we propose an equilibrium interpretation of the observed differences in ownership structures across firms. Rather than interpret low ownership levels as per se evidence of suboptimal compensation design, we argue that the compensation contracts observed in the data are endogenously determined by the contracting environment, which differs across firms in both observable and unobservable ways. In particular, low levels of managerial ownership might well be the optimal incentive arrangement for the firm if the scope for perquisite consumption (or more generally, the severity of the moral hazard problem for managers) happens to be low for that firm. We do not deny the importance of agency problems between stockholders and managers, but rather emphasize the importance of unobserved heterogeneity in the contracting environment across firms.
在本文中，我们提出了对公司间所有权结构差异的平衡解释。我们认为，低所有权水平不应被视为补偿设计不理想的直接证据，而是认为数据中观察到的补偿合同是由合同环境内生决定的，而这一环境在可观察和不可观察的方面在不同公司之间存在差异。特别是，如果某公司的特权消费范围（或更一般地说，管理者的道德风险问题的严重性）恰好较低，那么低水平的管理者所有权可能是该公司的最佳激励安排。我们并不否认股东与管理者之间代理问题的重要性，而是强调不同公司之间合同环境中未观察到的异质性的重要性。

We begin by examining the observable determinants of managerial ownership. This investigation builds upon Demsetz and Lehn (1985), who use crosssectional data to show that the level of managerial ownership is determined by the riskiness of the firm, measured by the volatility of the stock price. They argue that the scope for moral hazard is greater for managers of riskier firms, which therefore means that those managers must have greater ownership stakes to align incentives. They also point out that riskiness makes it costlier for managers
我们首先考察管理层持股的可观察决定因素。这项研究基于 Demsetz 和 Lehn（1985）的工作，他们使用横截面数据表明，管理层持股的水平由公司的风险性决定，风险性通过股票价格的波动性来衡量。他们认为，风险较高的公司的管理者面临的道德风险更大，因此这些管理者必须拥有更大的持股比例以对齐激励。他们还指出，风险性使得管理者的成本更高。
to hold nondiversified portfolios (assuming that equity holdings in the firm are not easily hedged), so the relation between managerial ownership and nondiversifiable stock price risk is not necessarily monotonic.
持有非多样化投资组合（假设公司股权不易对冲），因此管理层持股与不可多样化股票价格风险之间的关系不一定是单调的。

To document the extent to which managerial ownership is endogenously determined by the contracting environment, we extend the empirical specification used by Demsetz and Lehn by including a number of additional explanatory variables other than stock price variability (see also Kole, 1996). Most importantly, we include variables (such as firm size, capital intensity, R&D intensity, advertising intensity, cash flow, and investment rate) designed to control for the scope for moral hazard. To the extent that our additional explanatory variables proxy for moral hazard, our specification clarifies the role of stock price variance as an explanatory variable for managerial ownership. We also use panel data that allow us to estimate the importance of unobserved (time-invariant) firm effects. These results show that a large fraction of the cross-sectional variation in managerial ownership is ‘explained’ by unobserved firm heterogeneity. In our subsequent analysis of the determinants of firm value, we argue that this unobserved heterogeneity generates a spurious correlation between ownership and performance.
为了记录管理层持股在多大程度上是由契约环境内生决定的，我们通过包括除股票价格波动之外的一些额外解释变量，扩展了 Demsetz 和 Lehn 使用的实证规范（参见 Kole，1996）。最重要的是，我们包括了旨在控制道德风险范围的变量（如公司规模、资本密集度、研发密集度、广告密集度、现金流和投资率）。在我们的额外解释变量代理道德风险的程度上，我们的规范阐明了股票价格波动作为管理层持股解释变量的作用。我们还使用了面板数据，使我们能够估计未观察到的（时间不变的）公司效应的重要性。这些结果表明，管理层持股的横截面变异中有很大一部分是由未观察到的公司异质性“解释”的。在我们后续对公司价值决定因素的分析中，我们认为这种未观察到的异质性产生了持股与绩效之间的虚假相关性。

The second goal of this paper is to reexamine theoretical explanations of the empirical link between managerial ownership and firm performance. Mørck et al. (1988) estimate a piecewise-linear relation between board ownership and Tobin’s $Q$$Q$QQ and find that Tobin’s $Q$$Q$QQ increases and then decreases with managerial ownership. McConnell and Servaes (1990) examine a larger data set than the Fortune 500 firms examined by Mørck et al. and find an inverted U-shaped relation between $Q$$Q$QQ and managerial ownership, with an inflection point between $40\mathrm{\%}$$40\mathrm{\%}$40%40 \% and $50\mathrm{\%}$$50\mathrm{\%}$50%50 \% ownership. Hermalin and Weisbach (1991) analyze 142 NYSE firms and find that $Q$$Q$QQ rises with ownership up to a stake of $1\mathrm{\%}$$1\mathrm{\%}$1%1 \%; the relation is negative in the ownership range of $1-5\mathrm{\%}$$1-5\mathrm{\%}$1-5%1-5 \%, becomes positive again in the ownership range of $5-20\mathrm{\%}$$5-20\mathrm{\%}$5-20%5-20 \%, and turns negative for ownership levels exceeding $20\mathrm{\%}$$20\mathrm{\%}$20%20 \%. The pattern identified by Mørck et al. has been corroborated for a cross-section of U.S. firms from 1935 by Holderness et al. (1999). Kole (1995) examines the differences in data sources used in several recent studies and concludes that differences in firm size can account for the reported differences between those studies. These studies generally interpret the positive relation at low levels of managerial ownership as evidence of incentive alignment, and the negative relation at high levels of managerial ownership as evidence that managers become ‘entrenched’ and can indulge in non-value-maximizing activities without being disciplined by shareholders. However, these studies do not address the endogeneity problem that confronts the use of managerial ownership as an explanatory variable, a problem noted early by Jensen and Warner (1988, p. 13).
本文的第二个目标是重新审视管理层持股与公司绩效之间经验联系的理论解释。Mørck 等人（1988）估计了董事会持股与托宾的 $Q$$Q$QQ 之间的分段线性关系，并发现托宾的 $Q$$Q$QQ 随着管理层持股的增加而先上升后下降。McConnell 和 Servaes（1990）研究了一个比 Mørck 等人研究的财富 500 强公司更大的数据集，发现 $Q$$Q$QQ 与管理层持股之间存在倒 U 形关系，拐点位于 $40\mathrm{\%}$$40\mathrm{\%}$40%40 \% 和 $50\mathrm{\%}$$50\mathrm{\%}$50%50 \% 的持股之间。Hermalin 和 Weisbach（1991）分析了 142 家纽约证券交易所公司，发现 $Q$$Q$QQ 随着持股上升至 $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 的股份而上升；在 $1-5\mathrm{\%}$$1-5\mathrm{\%}$1-5%1-5 \% 的持股范围内关系为负，在 $5-20\mathrm{\%}$$5-20\mathrm{\%}$5-20%5-20 \% 的持股范围内再次变为正，并且在超过 $20\mathrm{\%}$$20\mathrm{\%}$20%20 \% 的持股水平时变为负。Mørck 等人识别的模式得到了 Holderness 等人（1999）对 1935 年以来美国公司横截面的证实。Kole（1995）研究了几项近期研究中使用的数据来源的差异，并得出结论认为公司规模的差异可以解释这些研究之间报告的差异。 这些研究通常将低水平的管理层持股与激励一致性之间的正相关关系解释为证据，而将高水平的管理层持股与管理者变得“固守”并可以沉迷于不追求价值最大化的活动而不受股东约束的负相关关系解释为证据。然而，这些研究并没有解决将管理层持股作为解释变量所面临的内生性问题，这一问题早在 Jensen 和 Warner（1988 年，第 13 页）就已被提及。

We investigate the degree to which this heterogeneity makes managerial ownership an endogenous variable in models of firm performance. Following in the tradition of Demsetz and Lehn, we describe the contracting problem faced
我们研究这种异质性在多大程度上使管理层持股成为公司绩效模型中的内生变量。沿袭 Demsetz 和 Lehn 的传统，我们描述了面临的契约问题。
by the firm and develop a simple empirical model to illustrate the econometric issues that are encountered when estimating the relation among managerial ownership, its determinants, and its effect on firm performance. Distinct from Demsetz and Lehn, and in contrast to previous papers that attempt to measure the impact of managerial ownership on firm performance, we use panel data to test for the endogeneity of managerial ownership in models linking ownership to performance (measured by Tobin’s $Q$$Q$QQ ). In particular, we use panel data to investigate the hypothesis that managerial ownership is related to observable and unobservable (to the econometrician) firm characteristics influencing contracts. If the unobserved sources of firm heterogeneity are relatively constant over time, we can treat these unobserved variables as fixed effects, and use panel data techniques to obtain consistent estimates of the parameter coefficients. This approach provides consistent estimates of the residuals in the $Q$$Q$QQ regression, which we use to construct a test for correlation between managerial ownership and unobserved firm heterogeneity.
由公司提出并开发一个简单的实证模型，以说明在估计管理层持股、其决定因素及其对公司绩效影响之间的关系时遇到的计量经济学问题。与 Demsetz 和 Lehn 不同，并且与之前试图衡量管理层持股对公司绩效影响的论文相对，我们使用面板数据来检验管理层持股在将持股与绩效（以 Tobin’s $Q$$Q$QQ 衡量）联系起来的模型中的内生性。特别是，我们使用面板数据来研究管理层持股与影响合同的可观察和不可观察（对计量经济学家而言）公司特征相关的假设。如果公司异质性的未观察来源在时间上相对恒定，我们可以将这些未观察变量视为固定效应，并使用面板数据技术获得参数系数的一致估计。这种方法提供了 $Q$$Q$QQ 回归中残差的一致估计，我们用它来构建管理层持股与未观察公司异质性之间相关性的检验。

Our principal findings are threefold. First, proxies for the contracting environment faced by the firm (i.e., observable firm characteristics) strongly predict the structure of managerial ownership. We substantially extend the set of explanatory variables examined by Demsetz and Lehn, and we show that many of our results are robust to the inclusion of observed determinants of managerial ownership, industry fixed effects, or firm fixed effects. Second, we show that the coefficient on managerial ownership is not robust to the inclusion of fixed effects in the regression for Tobin’s $Q$$Q$QQ. Our formal statistical test rejects the null hypothesis of a zero correlation between managerial ownership and the unobserved determinants of Tobin’s $Q$$Q$QQ, thus supporting our conjecture that managerial ownership is endogenous in $Q$$Q$QQ regressions. That is, managerial ownership and firm performance are determined by common characteristics, some of which are unobservable to the econometrician. Third, we explore the use of instrumental variables as an alternative to fixed effects to control for the endogeneity of managerial ownership in the $Q$$Q$QQ regression. We find some evidence to support a causal link from ownership to performance, but this evidence is tentative because of the weakness of our instruments. We argue that future progress will require a more structural approach to the model.
我们的主要发现有三点。首先，企业面临的合同环境的代理变量（即可观察的企业特征）强烈预测管理层持股的结构。我们大幅扩展了 Demsetz 和 Lehn 所研究的解释变量集，并且我们表明，许多结果在包括管理层持股的观察决定因素、行业固定效应或企业固定效应时仍然稳健。其次，我们表明，在 Tobin’s $Q$$Q$QQ 的回归中，管理层持股的系数对固定效应的包含并不稳健。我们的正式统计检验拒绝了管理层持股与 Tobin’s $Q$$Q$QQ 的未观察决定因素之间零相关的原假设，从而支持了我们关于管理层持股在 $Q$$Q$QQ 回归中是内生的猜想。也就是说，管理层持股和企业绩效是由共同特征决定的，其中一些特征对计量经济学家是不可观察的。第三，我们探讨了使用工具变量作为固定效应的替代方案，以控制 $Q$$Q$QQ 回归中管理层持股的内生性。 我们发现了一些证据支持所有权与绩效之间的因果关系，但由于我们工具的弱点，这些证据是初步的。我们认为，未来的进展将需要对模型采取更结构化的方法。

Kole (1996) also argues that managerial ownership is endogenous; she further argues that causality operates in the opposite direction, from performance to ownership. Using a panel-data vector autoregression, we corroborate Kole’s reverse causality evidence (results available upon request). Our research, however, supports the idea that both ownership and performance are determined by similar (observed and unobserved) variables in the firm’s contracting environment. Thus, our interpretation is different from Kole’s interpretation. That is, we find evidence endogeneity caused by unobserved heterogeneity as opposed to reverse causality.
Kole (1996) 还认为管理层持股是内生的；她进一步认为因果关系是相反的，从绩效到所有权。通过使用面板数据向量自回归，我们证实了 Kole 的逆向因果关系证据（结果可根据请求提供）。然而，我们的研究支持这样一种观点，即所有权和绩效都是由公司合同环境中相似的（可观察和不可观察的）变量决定的。因此，我们的解释与 Kole 的解释不同。也就是说，我们发现证据表明内生性是由不可观察的异质性引起的，而不是逆向因果关系。

The paper is organized as follows. In Section 2, we outline a simple model of managerial ownership and explain why it is difficult to estimate the relation between managerial ownership levels and firm performance, particularly in the context of cross-sectional data. Section 3 describes the sample selection criteria and the data we use in our empirical analysis of managerial ownership and firm performance. In Sections 4 and 5, respectively, we present empirical evidence on the determinants of managerial ownership and on the relation between managerial ownership and firm performance. Section 6 concludes.
本文的组织结构如下。在第二节中，我们概述了一个简单的管理层持股模型，并解释了为什么在横截面数据的背景下，估计管理层持股水平与公司绩效之间的关系是困难的。第三节描述了样本选择标准以及我们在管理层持股与公司绩效的实证分析中使用的数据。在第四节和第五节中，我们分别提供了关于管理层持股决定因素的实证证据以及管理层持股与公司绩效之间关系的实证证据。第六节为结论。

A common approach for estimating the impact of managerial ownership on firm value is to regress Tobin’s $Q$$Q$QQ on such variables as the percentage of equity held by managers. In this section, we argue that this regression is potentially misspecified because of the presence of unobserved heterogeneity. Specifically, if some of the unobserved determinants of Tobin’s $Q$$Q$QQ are also determinants of managerial ownership, then managerial ownership might spuriously appear to be a determinant of firm performance. To motivate our focus on the endogeneity of managerial ownership, we provide three examples of likely sources of unobservable heterogeneity, and in each case, we discuss their econometric consequences for cross-sectional regressions. We follow this discussion with a more formal exposition, in which we assume that the unobserved heterogeneity is a ‘firm fixed effect’, and we show how, under this assumption, panel data can be used to mitigate the endogeneity problem. In Section 5, we return to this model to describe a test for the endogeneity of ownership in regressions for Tobin’s $Q$$Q$QQ.
估计管理层持股对公司价值影响的一个常见方法是将托宾的 $Q$$Q$QQ 对管理者持股比例等变量进行回归。在本节中，我们认为这种回归可能存在模型设定错误，因为存在未观察到的异质性。具体而言，如果一些未观察到的托宾的 $Q$$Q$QQ 决定因素也是管理层持股的决定因素，那么管理层持股可能会虚假地显现为公司绩效的决定因素。为了引导我们关注管理层持股的内生性，我们提供了三个可能的未观察到的异质性来源的例子，并在每种情况下讨论它们对横截面回归的计量经济学影响。我们在此讨论之后进行了更正式的阐述，在此我们假设未观察到的异质性是“公司固定效应”，并展示在这一假设下，如何使用面板数据来减轻内生性问题。在第 5 节中，我们回到这个模型，描述一个关于托宾的 $Q$$Q$QQ 回归中所有权内生性的检验。

For our first example of unobserved heterogeneity, consider two firms that are identical except that the owner of one of the firms has access to a superior monitoring technology. Under the optimal contracting regime, the owners with access to the superior monitoring technology will choose a lower level of managerial ownership to align incentives, and this firm will have a higher valuation because fewer resources will be diverted to managerial perquisites. If measures of the quality of the monitoring technology are omitted from the specification, a regression of firm value on managerial ownership will spuriously (and falsely) indicate a negative relation, because ownership is a negative proxy for the quality of monitoring technology.
在我们未观察到的异质性的第一个例子中，考虑两家完全相同的公司，除了其中一家公司的所有者拥有更优越的监控技术。在最佳契约制度下，拥有更优越监控技术的所有者将选择较低的管理层持股比例以对齐激励，而这家公司将具有更高的估值，因为更少的资源会被转移到管理特权上。如果在规范中省略了监控技术质量的衡量指标，对公司价值与管理层持股比例的回归分析将错误地（并且虚假地）表明存在负相关关系，因为持股比例是监控技术质量的负代理。

Intangible assets provide a second example of unobserved firm heterogeneity. Suppose two firms are identical except that one of the firms operates with a higher fraction of its assets in the form of intangibles. Under the optimal contracting regime, the owners of this firm will require a higher level of managerial ownership to align incentives because the intangible assets are
无形资产提供了未观察到的公司异质性的第二个例子。假设两家公司是相同的，只是其中一家公司以更高比例的无形资产运营。在最佳契约制度下，这家公司的所有者将需要更高水平的管理层持股以对齐激励，因为无形资产是
harder to monitor and therefore subject to managerial discretion. This firm will also have a higher $Q$$Q$QQ value because the market will value intangibles in the numerator (market value), but the book value of assets in the denominator will understate the value of intangibles (because Tobin’s $Q$$Q$QQ is measured as the ratio of the market value of the firm’s outstanding debt and equity divided by the book value of assets). In this example, the unobserved level of intangibles induces a positive correlation between managerial ownership and Tobin’s $Q$$Q$QQ, but this relation is spurious, not causal.
更难以监控，因此受到管理层的自由裁量权。这家公司也会有更高的 $Q$$Q$QQ 值，因为市场会在分子中评估无形资产（市场价值），但资产的账面价值在分母中会低估无形资产的价值（因为托宾的 $Q$$Q$QQ 是通过公司的流通债务和股本的市场价值与资产的账面价值的比率来衡量的）。在这个例子中，无形资产的未观察水平导致管理层持股与托宾的 {{2 }} 之间存在正相关关系，但这种关系是虚假的，而不是因果关系。
A third example of unobserved heterogeneity is variation in the degree of market power. Suppose there are two firms competing in a market with differentiated products and that one firm enjoys a competitive advantage because (for some historical reason) it has been able to locate its products in such a way that confers more market power. If this market power insulates managerial decision-making from the discipline of competitive product markets, then the optimal contract for managers will call for higher levels of managerial ownership. Hence, unobserved heterogeneity in the form of unobserved differences in market power will (spuriously) induce a positive relation between ownership and performance. Alternatively, causation could run the other way; stockholders might design the manager’s compensation to implicitly encourage collusive outcomes in the product market (Fershtman and Judd, 1987). Attempting to test this proposition using regressions of Tobin’s $Q$$Q$QQ on managerial ownership suffers from the same econometric problems we study here. The ownership decision is endogenous because of unobserved firm heterogeneity.
未观察到的异质性的第三个例子是市场力量程度的变化。假设有两家公司在一个具有差异化产品的市场中竞争，其中一家公司由于某种历史原因享有竞争优势，能够以一种赋予更多市场力量的方式定位其产品。如果这种市场力量使管理决策免受竞争产品市场的约束，那么对管理者的最佳合同将要求更高的管理者持股比例。因此，未观察到的异质性以未观察到的市场力量差异的形式将（虚假地）引发所有权与绩效之间的正相关关系。或者，因果关系也可能反向运行；股东可能会设计管理者的薪酬，以隐含地鼓励产品市场中的共谋结果（Fershtman 和 Judd，1987）。尝试使用对管理者持股比例的 Tobin’s $Q$$Q$QQ 回归来检验这一命题，面临着我们在这里研究的相同计量经济学问题。由于未观察到的公司异质性，所有权决策是内生的。

It is possible to generalize these examples in a simple analytical framework. We assume that within the general set of contracts agreed to by the firm, the owners of the firm choose a simple management compensation contract that includes a share of the firm’s equity. This equity share (or ‘managerial stake’) is chosen to maximize the owners’ equity return subject to incentive compatibility and participation constraints. For this purpose, we assume that gains from other means for reducing agency costs have been maximized, so that we examine the residual agency cost to be addressed by managerial ownership (we revisit this assumption in Section 5 below). Let $x_{it}$$x_{it}$x_(it)x_{i t} and $u_{it}$$u_{it}$u_(it)u_{i t}, respectively, denote observable and unobservable characteristics for firm $i$$i$ii at time $t$$t$tt related to the firm’s contracting environment (including, e.g., proxies for the potential for moral hazard). In addition to unobserved firm characteristics, we implicitly assume a profitability shock that is observable to the manager, but not to outside shareholders. This shock cannot be contracted upon, giving rise to moral hazard.
可以在一个简单的分析框架中对这些例子进行概括。我们假设在公司达成的一般合同集中，公司的所有者选择一个简单的管理薪酬合同，其中包括公司股权的一部分。这个股权份额（或称“管理者股份”）的选择是为了在激励兼容性和参与约束的条件下最大化所有者的股权回报。为此，我们假设通过其他手段降低代理成本的收益已经最大化，因此我们考察由管理层持股所需解决的剩余代理成本（我们将在下面的第 5 节中重新审视这一假设）。设 $x_{it}$$x_{it}$x_(it)x_{i t} 和 $u_{it}$$u_{it}$u_(it)u_{i t} 分别表示与公司 $i$$i$ii 在时间 $t$$t$tt 相关的可观察和不可观察特征，这些特征与公司的合同环境有关（包括例如道德风险潜在的代理）。除了未观察到的公司特征外，我们还隐含假设存在一个对管理者可观察但对外部股东不可观察的盈利冲击。这个冲击无法通过合同进行约定，从而产生道德风险。

The firm’s owners must decide how much equity to give to managers in order to align incentives for value maximization. This equity share $m_{it}$$m_{it}$m_(it)m_{i t} depends on such factors as the potential for moral hazard and managers’ exposure to risk, which we assume are partly measured by $x_{it}$$x_{it}$x_(it)x_{i t}, but are otherwise unobserved and
公司的所有者必须决定给予管理者多少股权，以便使激励与价值最大化保持一致。这部分股权 $m_{it}$$m_{it}$m_(it)m_{i t} 取决于道德风险的潜在性和管理者的风险暴露等因素，我们假设这些因素部分通过 $x_{it}$$x_{it}$x_(it)x_{i t} 来衡量，但其他方面则是不可观察的。
included in $u_{it}$$u_{it}$u_(it)u_{i t}. We assume that the functional relation is linear, and that $u_{it}=u_i$$u_{it}=u_i$u_(it)=u_(i)u_{i t}=u_{i} is time-invariant for the firm, so that
包含在 $u_{it}$$u_{it}$u_(it)u_{i t} 中。我们假设功能关系是线性的，并且 $u_{it}=u_i$$u_{it}=u_i$u_(it)=u_(i)u_{i t}=u_{i} 对于公司是时间不变的，因此

where $e_{it}$$e_{it}$e_(it)e_{i t} represents independent measurement error.
其中 $e_{it}$$e_{it}$e_(it)e_{i t} 代表独立测量误差。
Faced with this contract, managers choose an optimal ‘effort level’, $y_{it}$$y_{it}$y_(it)y_{i t}, which could include a range of participation in non-value-maximizing activities. This effort choice depends on the managerial ownership stake, $m_{it}$$m_{it}$m_(it)m_{i t}, and, like the optimal contract itself, depends on both observed and unobserved characteristics of the firm, $x_{it}$$x_{it}$x_(it)x_{i t} and $u_i$$u_i$u_(i)u_{i}. Assuming a linear functional form, we can represent the manager’s effort choice by the following relation:
面对这一合同，管理者选择一个最佳的“努力水平”， $y_{it}$$y_{it}$y_(it)y_{i t} ，这可能包括参与一系列非价值最大化活动。这个努力选择取决于管理者的所有权份额， $m_{it}$$m_{it}$m_(it)m_{i t} ，并且像最佳合同本身一样，取决于公司的观察到的和未观察到的特征， $x_{it}$$x_{it}$x_(it)x_{i t} 和 $u_i$$u_i$u_(i)u_{i} 。假设线性函数形式，我们可以通过以下关系表示管理者的努力选择：

Using firm value as a summary measure of expected firm performance, we assume that firm value depends on managerial effort plus the vector of observed and unobserved firm characteristics. Denoting the value of firm $i$$i$ii at time $t$$t$tt by $Q_{it}$$Q_{it}$Q_(it)Q_{i t}, we assume that
将公司价值作为预期公司绩效的总结指标，我们假设公司价值依赖于管理努力加上观察到的和未观察到的公司特征向量。我们用 $Q_{it}$$Q_{it}$Q_(it)Q_{i t} 表示时间 $t$$t$tt 时公司 $i$$i$ii 的价值，我们假设

We can now combine Eqs. (2) and (3) to derive the following relation among firm managerial ownership, firm characteristics, and firm performance:
我们现在可以将方程（2）和（3）结合起来，推导出公司管理层持股、公司特征和公司绩效之间的以下关系：

Simplifying the notation reveals the regression specification commonly used in the empirical literature:
简化符号揭示了实证文献中常用的回归规范：

In a cross-section of firms, as long as the error term, ${\epsilon }_{it}=(\delta {\gamma }_2+{\gamma }_3)u_i+$${\epsilon }_{it}=\left(\delta {\gamma }_2+{\gamma }_3\right)u_i+$epsi_(it)=(deltagamma_(2)+gamma_(3))u_(i)+\varepsilon_{i t}=\left(\delta \gamma_{2}+\gamma_{3}\right) u_{i}+ $\delta v_{it}+w_{it}$$\delta v_{it}+w_{it}$deltav_(it)+w_(it)\delta v_{i t}+w_{i t} - is uncorrelated with both $m_{it}$$m_{it}$m_(it)m_{i t} and $x_{it}$$x_{it}$x_(it)x_{i t}, one can consistently estimate the reduced-form coefficient on managerial ownership in the regression for firm value. However, because the choice of managerial ownership depends on unobserved firm characteristics, $m_{it}$$m_{it}$m_(it)m_{i t} depends on $u_i$$u_i$u_(i)u_{i}, and is therefore correlated with ${\epsilon }_i$${\epsilon }_i$epsi_(i)\varepsilon_{i}. Specifically,
在一组公司的横截面中，只要误差项 ${\epsilon }_{it}=(\delta {\gamma }_2+{\gamma }_3)u_i+$${\epsilon }_{it}=\left(\delta {\gamma }_2+{\gamma }_3\right)u_i+$epsi_(it)=(deltagamma_(2)+gamma_(3))u_(i)+\varepsilon_{i t}=\left(\delta \gamma_{2}+\gamma_{3}\right) u_{i}+ $\delta v_{it}+w_{it}$$\delta v_{it}+w_{it}$deltav_(it)+w_(it)\delta v_{i t}+w_{i t} 与 $m_{it}$$m_{it}$m_(it)m_{i t} 和 $x_{it}$$x_{it}$x_(it)x_{i t} 都不相关，就可以在公司价值的回归中一致地估计管理层持股的简化形式系数。然而，由于管理层持股的选择依赖于未观察到的公司特征， $m_{it}$$m_{it}$m_(it)m_{i t} 依赖于 $u_i$$u_i$u_(i)u_{i} ，因此与 ${\epsilon }_i$${\epsilon }_i$epsi_(i)\varepsilon_{i} 相关。具体来说，

In general, the expectation in Eq. (6) will be zero only in the unlikely event that the optimal contract does not depend on observed firm characteristics ( ${\gamma }_1=0$${\gamma }_1=0$gamma_(1)=0\gamma_{1}=0 ), or in the event that neither effort nor $Q_{it}$$Q_{it}$Q_(it)Q_{i t} do $({\gamma }_2={\gamma }_3=0)$$\left({\gamma }_2={\gamma }_3=0\right)$(gamma_(2)=gamma_(3)=0)\left(\gamma_{2}=\gamma_{3}=0\right). Hence one cannot estimate Eq. (5) using ordinary least squares. A natural solution to this problem would be to use instrumental variables for ownership, but this approach is difficult in practice because the natural instruments - the observed firm characteristics $x_{it}$$x_{it}$x_(it)x_{i t} - are already included on the right-hand side of the equation for firm valuation in Eq. (5). Hence it is difficult to identify instrumental variables that
一般来说，方程（6）中的期望值仅在不太可能的情况下为零，即最优合同不依赖于观察到的公司特征（ ${\gamma }_1=0$${\gamma }_1=0$gamma_(1)=0\gamma_{1}=0 ），或者在努力和 $Q_{it}$$Q_{it}$Q_(it)Q_{i t} 都不做 $({\gamma }_2={\gamma }_3=0)$$\left({\gamma }_2={\gamma }_3=0\right)$(gamma_(2)=gamma_(3)=0)\left(\gamma_{2}=\gamma_{3}=0\right) 的情况下。因此，无法使用普通最小二乘法估计方程（5）。解决这个问题的一个自然方法是使用所有权的工具变量，但在实践中这种方法是困难的，因为自然工具 - 观察到的公司特征 $x_{it}$$x_{it}$x_(it)x_{i t} - 已经包含在方程（5）中公司估值的右侧。因此，很难识别出可以用作工具变量的内容。
would permit identification of $a_1$$a_1$a_(1)a_{1}. With panel data, however, one can use a fixed-effects estimator, assuming that the unobserved heterogeneity is constant over time.
将允许识别 $a_1$$a_1$a_(1)a_{1} 。然而，使用面板数据时，可以使用固定效应估计量，假设未观察到的异质性在时间上是恒定的。

In contrast to the model for Tobin’s $Q$$Q$QQ, the model for the optimal choice of managerial ownership levels in Eq. (1) is more easily identified because it requires only the much weaker assumption that the unobserved firm characteristics are uncorrelated with observed characteristics. Hence the focus of our results in Section 4 is on Eq. (1).
与 Tobin 的 $Q$$Q$QQ 模型相比，方程(1)中关于最佳管理所有权水平选择的模型更容易识别，因为它仅需要一个更弱的假设，即未观察到的公司特征与观察到的特征不相关。因此，我们在第 4 节中的结果重点关注方程(1)。

The above discussion suggests four lines of empirical inquiry. First, we explore whether the observed firm characteristics (proxies for the potential for moral hazard and risk) influence managerial ownership in ways that are consistent with theoretical predictions. Second, we investigate the importance of unobserved characteristics as determinants of managerial ownership. Third, we investigate the extent to which the empirical relation between managerial ownership and firm performance (measured by Tobin’s $Q$$Q$QQ ) can be explained by the omission of observed and unobserved firm characteristics (i.e., by uncontrol-led-for or unobserved heterogeneity). Fourth, we explore the possibility of using instrumental variables to recover the parameter values in Eq. (5). We describe these results in Sections 4 and 5 after describing our sample and data in Section 3.
上述讨论提出了四条实证研究的思路。首先，我们探讨观察到的公司特征（道德风险和风险潜力的代理变量）是否以与理论预测一致的方式影响管理层持股。其次，我们研究未观察到的特征作为管理层持股决定因素的重要性。第三，我们调查管理层持股与公司绩效（通过托宾的 $Q$$Q$QQ 测量）之间的实证关系在多大程度上可以通过遗漏观察到的和未观察到的公司特征（即，未控制或未观察的异质性）来解释。第四，我们探讨使用工具变量来恢复方程 (5) 中参数值的可能性。在描述我们的样本和数据后，我们将在第 3 节中在第 4 节和第 5 节中描述这些结果。

Our sample consists of firms from the Compustat universe. We restrict ourselves to firms that have no missing data (on sales, the book value of capital, and the stock price) over the three-year period 1982-1984. (We cannot avoid this conditioning because we cannot use firms with missing data or fewer than three years of data for the variables of interest.) We then select 600 firms by random sampling, and we collect data for all subsequent periods. Our panel is therefore balanced at 600 firms from 1982 through 1984, but the number of firms declines to 551 by 1985 , and falls to a low of 330 by 1992, the last year in the sample. Because of this attrition from Compustat (principally due to mergers and acquisitions), our panel is systematically less random over time. However, we avoid exacerbating the scope for sampling bias by not requiring a balanced panel.
我们的样本由来自 Compustat 宇宙的公司组成。我们限制在 1982 年至 1984 年的三年期间内没有缺失数据（关于销售、资本的账面价值和股票价格）的公司。（我们无法避免这种条件限制，因为我们不能使用缺失数据或少于三年数据的公司进行感兴趣变量的分析。）然后，我们通过随机抽样选择 600 家公司，并收集所有后续时期的数据。因此，我们的面板在 1982 年至 1984 年期间是平衡的 600 家公司，但到 1985 年公司数量减少到 551，到 1992 年样本的最后一年降至 330。由于 Compustat 的这种流失（主要是由于合并和收购），我们的面板随着时间的推移系统性地减少了随机性。然而，我们通过不要求平衡面板来避免加剧抽样偏差的范围。

For this unbalanced panel of firms, we attempt to collect the following additional data for each firm-year observation: the number of top managers and directors (as reported in the proxy statement), the percentage of the firm’s shares owned by those managers and directors, and the date of the proxy statement from which these two numbers are collected. For those observations for which we can locate proxy statements, we collect the managerial ownership variables and merge this information with the Compustat data. Because smaller firms (in
对于这个不平衡的公司面板，我们试图为每个公司-年份观察收集以下额外数据：高管和董事的数量（如代理声明中所报告），这些高管和董事所持有的公司股份的百分比，以及收集这两个数字的代理声明的日期。对于我们能够找到代理声明的观察，我们收集管理层持股变量，并将这些信息与 Compustat 数据合并。因为较小的公司（在

Table 1  表 1
Sample of Compustat firms by year
按年份的 Compustat 公司样本
We start out with 600 firms randomly sampled from the universe of Compustat firms with data available over the period 1982-1984 on sales, book value of capital, and stock price. The number of firms declines after 1984, principally due to mergers and acquisitions. The number of available ownership observations represents firms for which we are able to obtain proxy statements with the number of top managers and directors and their collective percentage share ownership.
我们从随机抽取的 600 家 Compustat 公司开始，这些公司在 1982-1984 年期间有销售额、资本账面价值和股票价格的数据。1984 年后，公司的数量减少，主要是由于合并和收购。可用的所有权观察数量代表了我们能够获得代理声明的公司，这些声明中包含高管和董事的数量及其集体持股比例。

terms of the number of shareholders) are not required to file proxies with the Securities and Exchange Commission, we are unable to obtain proxy information for all firms. We end up with managerial ownership information for about $70\mathrm{\%}$$70\mathrm{\%}$70%70 \% of the Compustat firms. Table 1 summarizes the number of firms in our sample as a result of the sample selection process.
（股东人数的条款）不需要向证券交易委员会提交代理文件，因此我们无法获得所有公司的代理信息。我们最终获得了大约 $70\mathrm{\%}$$70\mathrm{\%}$70%70 \% 家 Compustat 公司的管理层持股信息。表 1 总结了由于样本选择过程而导致的我们样本中公司的数量。

Despite the problems of attrition and proxy availability (which are not unique to our study), our sample provides several distinct advantages over datasets used in previous studies. First, in contrast to studies that focus on the Fortune 1000, our sample includes a much larger number of small firms and is more representative of the typical firm in Compustat. Second, we have a panel of firms rather than a single cross-section. This allows us to control for firm-level fixed effects. Third, we deliberately construct our panel in such a way that we can control for sample selection bias because of lack of data (for ownership) and attrition. In fact, it is possible to describe the significance of the bias imposed on the level of managerial ownership by a requirement that the panel be balanced; looking over the 1982-1992 period, the average ownership share varies from $16.2\mathrm{\%}$$16.2\mathrm{\%}$16.2%16.2 \% to $19.4\mathrm{\%}$$19.4\mathrm{\%}$19.4%19.4 \%, and for the balanced panel, for the firms removed by the balancing criterion, the ownership share varies between $22.4\mathrm{\%}$$22.4\mathrm{\%}$22.4%22.4 \% and $25.3\mathrm{\%}$$25.3\mathrm{\%}$25.3%25.3 \%. The availability of data on managerial ownership is well predicted by variables such as firm size and fixed
尽管存在流失和代理可用性的问题（这些问题并非我们研究所独有），但我们的样本相较于以往研究中使用的数据集提供了几个明显的优势。首先，与专注于财富 1000 强的研究相比，我们的样本包含了更多的小型企业，更能代表 Compustat 中的典型企业。其次，我们拥有一组企业的面板数据，而不是单一的横截面数据。这使我们能够控制企业层面的固定效应。第三，我们故意构建我们的面板，以便能够控制由于缺乏数据（关于所有权）和流失造成的样本选择偏差。事实上，可以描述由于要求面板平衡而对管理层所有权水平施加的偏差的重要性；在 1982-1992 年期间，平均所有权份额从 $16.2\mathrm{\%}$$16.2\mathrm{\%}$16.2%16.2 \% 变化到 $19.4\mathrm{\%}$$19.4\mathrm{\%}$19.4%19.4 \% ，而对于平衡面板，被平衡标准移除的企业，所有权份额在 $22.4\mathrm{\%}$$22.4\mathrm{\%}$22.4%22.4 \% 和 $25.3\mathrm{\%}$$25.3\mathrm{\%}$25.3%25.3 \% 之间变化。管理层所有权的数据可用性可以通过企业规模和固定等变量很好地预测。

Table 2  表 2
Managerial ownership stakes by firm size, 1982
1982 年按公司规模划分的管理层持股比例
For the 398 Compustat firms for which we have data on sales, book value of capital, stock price, number of top managers and directors, and collective equity ownership of top managers and directors, we report the average number of managers and their average collective ownership stake by firm size.
对于 398 家我们拥有销售额、资本账面价值、股票价格、顶级管理者和董事人数以及顶级管理者和董事的集体股权所有权数据的 Compustat 公司，我们报告了按公司规模划分的管理者平均人数及其平均集体所有权股份。

capital intensity, but as we explain in our discussion of empirical results, controlling for this ‘missing data bias’ does not qualitatively affect our results. While our sample design allows us to estimate and control for the effects of attrition bias, exit from Compustat due to mergers and acquisitions or bankruptcies is, in practice, difficult to predict using observable firm characteristics. A simple probit model for exit reveals that size is the principal explanatory variable; many more firms exit because of mergers than because of failure. When we include the inverse Mills ratio in our $Q$$Q$QQ regressions, we find no statistically significant effect of selection bias. We therefore decide not to correct formally for attrition bias.
资本密集度，但正如我们在对实证结果的讨论中所解释的，控制这种“缺失数据偏差”并不会对我们的结果产生质的影响。虽然我们的样本设计使我们能够估计和控制流失偏差的影响，但由于并购或破产而退出 Compustat 在实践中很难通过可观察的公司特征进行预测。一个简单的退出概率模型显示，规模是主要的解释变量；由于并购而退出的公司远多于因失败而退出的公司。当我们在我们的 $Q$$Q$QQ 回归中包含逆米尔斯比率时，我们发现选择偏差没有统计学上显著的影响。因此，我们决定不正式纠正流失偏差。

To illustrate differences between small and large firms, Table 2 shows, by size class, the average number of managers per firm and the percentage of shares outstanding owned collectively by those managers in 1982. The frequency distributions of managerial ownership and the number of managers are reported in Fig. 1. Note that the percentage of shares owned by insiders is much higher for small firms, measuring $32\mathrm{\%}$$32\mathrm{\%}$32%32 \% on average for firms in (roughly) the bottom third of the size distribution of firms. By contrast, existing studies typically oversample large firms, and report average ownership shares of approximately $10\mathrm{\%}$$10\mathrm{\%}$10%10 \%. This figure is consistent with the ownership stakes in firms in the top third of our size distribution (for comparison, the sales cutoff for Fortune 1000 firms is approximately $\mathrm{\$}1$$\mathrm{\$}1$$1\$ 1 billion).
为了说明小型企业和大型企业之间的差异，表 2 按规模类别显示了 1982 年每家企业的平均经理人数和这些经理共同拥有的流通股份百分比。管理层所有权和经理人数的频率分布在图 1 中报告。请注意，小型企业内部人士所拥有的股份百分比要高得多，对于（大致上）规模分布底部三分之一的企业，平均为 $32\mathrm{\%}$$32\mathrm{\%}$32%32 \% 。相比之下，现有研究通常对大型企业进行过度抽样，并报告平均所有权股份约为 $10\mathrm{\%}$$10\mathrm{\%}$10%10 \% 。这一数字与我们规模分布顶部三分之一企业的所有权份额一致（作为比较，财富 1000 强企业的销售门槛约为 $\mathrm{\$}1$$\mathrm{\$}1$$1\$ 1 十亿）。

The simple model outlined in Section 2 indicates the need to identify observable variables that relate to potential moral hazard and influence optimal
第二节中概述的简单模型表明，需要识别与潜在道德风险相关并影响最优的可观察变量

Fig. 1. Frequency distribution of managerial ownership and number of managers, 1982.
图 1. 管理层持股和经理人数的频率分布，1982 年。
managerial stakes. If the scope for managerial discretion differs across firms according to observable differences in the composition of assets, then a prediction of the theory is that firms with assets that are difficult to monitor will have higher levels of managerial ownership. The specification used by Demsetz and Lehn (1985) to explain ownership concentration includes stock price volatility and industry dummies, but does not include proxies for the scope for managerial discretion (though managerial discretion is one interpretation offered for stock price volatility). We extend their specification by adding a large number of explanatory variables designed to proxy for the scope for managerial discretion, namely, size, capital intensity, cash flow, R&D intensity, advertising intensity, and gross investment rates. As we show below, this expanded variable set dramatically improves the $R^2$$R^2$R^(2)R^{2} statistic, and the coefficient estimates are all statistically different from zero with the predicted signs.
管理层的利益。如果管理层的自由裁量权在不同公司之间因可观察到的资产组成差异而有所不同，那么理论的一个预测是，拥有难以监控资产的公司将拥有更高水平的管理层持股。Demsetz 和 Lehn（1985）用于解释所有权集中度的规范包括股票价格波动和行业虚拟变量，但不包括管理层自由裁量权的代理变量（尽管管理层自由裁量权是对股票价格波动的一种解释）。我们通过添加大量旨在代理管理层自由裁量权的解释变量来扩展他们的规范，即规模、资本密集度、现金流、研发强度、广告强度和总投资率。正如我们下面所示，这一扩展的变量集显著改善了 $R^2$$R^2$R^(2)R^{2} 统计量，且系数估计值均在统计上显著不同于零，并具有预测的符号。

Size. Firm size has an ambiguous effect a priori on the scope for moral hazard. On the one hand, monitoring and agency costs can be greater in large firms, increasing desired managerial ownership. In addition, large firms are likely to employ more skilled managers, who are consequently wealthier, suggesting a higher level of managerial ownership. On the other hand, large firms might enjoy economies of scale in monitoring by top management and by rating agencies, leading to a lower optimal level of managerial ownership. We use the $\log$$\log$log\log of firm sales, $LN(S)$$LN(S)$LN(S)L N(S), and its square, $(LN(S){)}^2$$(LN(S){)}^2$(LN(S))^(2)(L N(S))^{2}, to measure size.
规模。公司规模对道德风险的范围有模糊的影响。一方面，大型公司的监控和代理成本可能更高，从而增加所需的管理层持股比例。此外，大型公司可能会雇佣更多技术熟练的管理者，他们因此更富有，这表明管理层持股比例更高。另一方面，大型公司可能在高层管理和评级机构的监控中享有规模经济，从而导致管理层持股的最佳水平较低。我们使用公司销售的 $\log$$\log$log\log 、 $LN(S)$$LN(S)$LN(S)L N(S) 及其平方 $(LN(S){)}^2$$(LN(S){)}^2$(LN(S))^(2)(L N(S))^{2} 来衡量规模。
Scope for discretionary spending. To the extent that investments in fixed capital are observable and more easily monitored, firms with a greater concentration of fixed or ‘hard’ capital in their inputs will generally have a lower optimal level of managerial ownership (Gertler and Hubbard, 1988). We use the firm’s capital-to-sales ratio, $K/S$$K/S$K//SK / S, and its square, $(K/S{)}^2$$(K/S{)}^2$(K//S)^(2)(K / S)^{2}, as measures of the relative importance of hard capital in the firm’s technology.
可自由支配支出的范围。在固定资本的投资可观察且更易于监控的情况下，投入中固定或“硬”资本集中度较高的公司通常会有较低的最佳管理层持股比例（Gertler 和 Hubbard，1988）。我们使用公司的资本与销售比率 $K/S$$K/S$K//SK / S 及其平方 $(K/S{)}^2$$(K/S{)}^2$(K//S)^(2)(K / S)^{2} 作为公司技术中硬资本相对重要性的衡量标准。

Beyond hard capital, other firm spending is more discretionary and less easily monitored. The greater the role of these ‘soft capital’ inputs in the firm’s technology, all else being equal, the higher is the desired level of managerial ownership. By including the capital-to-sales ratio, we have controlled (inversely) for soft capital, but some soft capital is ‘softer’ than others and hence more vulnerable to managerial discretion. To refine our proxies for the scope for discretionary spending, we use the ratio of $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} spending to capital, $(R\mathrm{\&}D)/K$$(R\mathrm{\&}D)/K$(R&D)//K(R \& D) / K, the ratio of advertising spending to capital, $A/K$$A/K$A//KA / K, and dummy variables for whether the firm reports $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} spending ( $RDUM$$RDUM$RDUMR D U M ) and advertising spending $(ADUM)$$(ADUM)$(ADUM)(A D U M) in that year. We include dummy variables when $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} and advertising are missing to control for the possibility that nonreporting firms are discretely different from reporting firms. By far the most common reason for not complying with the disclosure requirement is that the level of $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} or advertising expenditure is negligible. Simply eliminating observations with missing values for these variables is undesirable because it significantly reduces the sample size and biases the sample in favor of R&D-intensive and advertising firms.
除了硬资本，其他公司的支出更具选择性且不易监控。这些“软资本”投入在公司技术中所占的比重越大，其他条件相同，所需的管理层持股水平就越高。通过包括资本与销售比率，我们已经控制了（反向）软资本，但某些软资本比其他软资本“更软”，因此更容易受到管理层的自由裁量影响。为了细化我们对选择性支出范围的代理，我们使用了 $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} 支出与资本的比率， $(R\mathrm{\&}D)/K$$(R\mathrm{\&}D)/K$(R&D)//K(R \& D) / K ，广告支出与资本的比率， $A/K$$A/K$A//KA / K ，以及虚拟变量来表示公司是否在该年报告了 $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} 支出（ $RDUM$$RDUM$RDUMR D U M ）和广告支出 $(ADUM)$$(ADUM)$(ADUM)(A D U M) 。当 $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} 和广告缺失时，我们包括虚拟变量，以控制未报告公司与报告公司可能存在的离散差异。未遵守披露要求的最常见原因是 $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} 或广告支出的水平微不足道。 简单地消除这些变量缺失值的观察是不理想的，因为这会显著减少样本大小，并使样本偏向于研发密集型和广告公司。

As a proxy for the link between high growth and opportunities for discretionary projects, we use the firm’s investment rate measured by the ratio of capital expenditures to the capital stock, $I/K$$I/K$I//KI / K. Finally, we use the ratio of operating income to sales $Y/S$$Y/S$Y//SY / S to measure market power or a firm’s ‘free cash flow’ (the difference between cash flow and spending on value-enhancing investment projects). As suggested by Jensen (1986), the higher is a firm’s free cash flow, all else being equal, the higher is the desired level of managerial ownership. While free cash flow is itself unobservable, it is presumably correlated with operating income.
作为高增长与自由支出项目机会之间联系的代理，我们使用公司的投资率，该投资率通过资本支出与资本存量的比率来衡量， $I/K$$I/K$I//KI / K 。最后，我们使用营业收入与销售额的比率 $Y/S$$Y/S$Y//SY / S 来衡量市场力量或公司的“自由现金流”（现金流与价值提升投资项目支出之间的差额）。正如詹森（1986）所建议的，其他条件不变的情况下，公司的自由现金流越高，所期望的管理层持股水平就越高。虽然自由现金流本身是不可观察的，但它与营业收入可能是相关的。
Managerial risk aversion. Because higher managerial ownership levels, all else being equal, imply less portfolio diversification for managers, the optimal contract involves a tradeoff between diversification and incentives for performance. The higher is the firm’s idiosyncratic risk, the lower is optimal managerial ownership. Demsetz and Lehn (1985) offer a second interpretation of this relation, suggesting that higher volatility indicates more scope for managerial discretion and thereby increases equilibrium managerial ownership levels. Unlike their specification, ours includes measures of intangible capital to control for managerial discretion. We therefore focus on the first interpretation of risk. As an empirical proxy for volatility, we use the standard deviation of the idiosyncratic component of daily stock prices (constructed from residuals from a standard CAPM regression), denoted by SIGMA, although our results are not qualitatively changed by the substitution of total stock return variance for our definition of SIGMA. Analogous to our treatment of missing values of $(R\mathrm{\&}D)/K$$(R\mathrm{\&}D)/K$(R&D)//K(R \& D) / K and $A/K$$A/K$A//KA / K, we set missing values of SIGMA equal to zero, and then also include in the regression a dummy variable SIGDUM equal to unity when SIGMA is not missing, and zero otherwise.
管理层风险厌恶。因为在其他条件相同的情况下，较高的管理层持股比例意味着管理者的投资组合多样化程度较低，最佳合同涉及多样化与绩效激励之间的权衡。公司的特有风险越高，最佳的管理层持股比例就越低。Demsetz 和 Lehn (1985) 提出了这种关系的第二种解释，认为更高的波动性表明管理者的自由裁量权更大，从而增加了均衡的管理层持股水平。与他们的模型不同，我们的模型包括无形资本的衡量，以控制管理者的自由裁量权。因此，我们专注于风险的第一种解释。作为波动性的实证代理，我们使用每日股票价格特有成分的标准差（由标准资本资产定价模型回归的残差构建），记作 SIGMA，尽管我们的结果在用总股票收益方差替代我们对 SIGMA 的定义时并没有发生质的变化。 类似于我们对 $(R\mathrm{\&}D)/K$$(R\mathrm{\&}D)/K$(R&D)//K(R \& D) / K 和 $A/K$$A/K$A//KA / K 缺失值的处理，我们将 SIGMA 的缺失值设为零，然后在回归中还包括一个虚拟变量 SIGDUM，当 SIGMA 不缺失时等于 1，否则等于 0。

To deal with zero-volume trading days in the daily data, we construct $n$$n$nn-day returns by summing the Center for Research in Security Prices (CRSP) daily returns over the days in the period to create an approximate $n$$n$nn-day return. We then divide this return (as well as $n$$n$nn-day returns created by weekends and holidays) by the number of days in the period to obtain an average daily return. The variance of this average return will equal the variance of the daily return, and the same will be true for the idiosyncratic variance in a CAPM regression. Converting $n$$n$nn-day returns to average daily returns thus removes the heteroskedasticity introduced by combining $n$$n$nn-day-return observations with daily returns. Out of our initial universe of 600 firms for the 1984 period, the CRSP NYSE/AMEX and NASDAQ daily files contains 525 firms reporting returns in 1984. Of these, there are 502 firms with enough data to construct at least 20 observations on daily returns using only days for which trading volume is positive.
为了处理日数据中的零交易量交易日，我们通过对该期间内的 Center for Research in Security Prices (CRSP)日收益进行求和，构建 $n$$n$nn 天收益，以创建一个近似的 $n$$n$nn 天收益。然后，我们将该收益（以及由周末和假期产生的 $n$$n$nn 天收益）除以该期间的天数，以获得平均日收益。该平均收益的方差将等于日收益的方差，在 CAPM 回归中，特有方差也是如此。因此，将 $n$$n$nn 天收益转换为平均日收益可以消除通过将 $n$$n$nn 天收益观测值与日收益结合而引入的异方差性。在我们 1984 年初始的 600 家公司中，CRSP NYSE/AMEX 和 NASDAQ 日文件包含 525 家在 1984 年报告收益的公司。其中，有 502 家公司有足够的数据，仅使用交易量为正的日子构建至少 20 个日收益观测值。
In addition to the problem of days with zero trading volume, there are days for which closing prices are not available, or days for which CRSP uses the average of the closing bid-ask spread instead of the closing price. This introduces
除了零交易量的天数问题，还有一些天的收盘价不可用，或者 CRSP 使用收盘买卖差价的平均值而不是收盘价。这引入了
nonclassical measurement error into the return calculation, which could bias our ordinary least squares (OLS) estimates of beta, return variance, and residual variance. To check the robustness of our results, we experiment with smaller samples that include only firms for which we can construct at least 20 observations based on (i) positive trading volume and (ii) transactions prices rather than the average of bid-ask prices. This substantially reduces the sample in 1984 to 328 firms (from 502). In practice, however, the results do not differ qualitatively from the larger sample. Hence, we report results in the paper using the larger sample, which, for many firms, relies on the closing average of the bid-ask spread rather than an actual closing price.
将非经典测量误差纳入收益计算，这可能会偏倚我们对 beta、收益方差和残差方差的普通最小二乘法 (OLS) 估计。为了检查我们结果的稳健性，我们尝试使用较小的样本，仅包括我们可以基于 (i) 正的交易量和 (ii) 交易价格而不是买卖价差的平均值构建至少 20 个观察值的公司。这大大减少了 1984 年的样本，从 502 家减少到 328 家。然而，在实践中，结果与较大样本的定性并没有差异。因此，我们在论文中报告使用较大样本的结果，对于许多公司，这依赖于买卖价差的收盘平均值，而不是实际的收盘价。

While we have addressed the most obvious examples of nonsynchronous trading (namely, days on which no trading occurs or on which CRSP cannot obtain a valid transaction price), there remain days on which CRSP calculates returns using the last price transacted rather than the closing price. As Scholes and Williams (1976), among others, point out, the inclusion of nonsynchronous trading days produces biased OLS estimates of beta. To check the robustness of our results against the possibility of biased beta estimates due to nonsynchronous trading days, we follow the approach recommended by Dimson (1979) by including leads and lags of the market return in the beta regression. These additional regressors are occasionally significant for some firms in some years, but using the alternative estimates of the idiosyncratic variance does not materially affect our results.
虽然我们已经解决了最明显的非同步交易示例（即没有交易发生的日子或 CRSP 无法获得有效交易价格的日子），但仍然存在一些日子，CRSP 使用最后成交价格而不是收盘价来计算收益。正如 Scholes 和 Williams（1976）等人指出的，包含非同步交易日会导致 OLS 的 beta 估计偏差。为了检验我们的结果在非同步交易日导致的 beta 估计偏差下的稳健性，我们遵循 Dimson（1979）推荐的方法，在 beta 回归中包含市场收益的滞后和领先项。这些额外的回归变量在某些年份对某些公司偶尔是显著的，但使用替代的特异方差估计并不会实质性影响我们的结果。
Summary. Combining these observable variables associated with moral hazard yields the following reduced-form expression for managerial ownership:
摘要。将与道德风险相关的这些可观察变量结合起来，得出以下关于管理层持股的简化形式表达：

where $i$$i$ii and $t$$t$tt represent the firm and time, respectively, $u_i$$u_i$u_(i)u_{i} is a firm-specific effect, and ${\eta }_{it}$${\eta }_{it}$eta_(it)\eta_{i t} is a white-noise error term. Our list of variables is summarized in Table 3.
其中 $i$$i$ii 和 $t$$t$tt 分别代表公司和时间， $u_i$$u_i$u_(i)u_{i} 是公司特定效应， ${\eta }_{it}$${\eta }_{it}$eta_(it)\eta_{i t} 是白噪声误差项。我们的变量列表在表 3 中总结。

Table 4A reports our estimates of the determinants of managerial stakes. The dependent variable in each case is $LN(m/(1-m))$$LN(m/(1-m))$LN(m//(1-m))L N(m /(1-m)). Each of the specifications includes year dummies (not reported). In specifications including fixed firm effects, we control for the unobserved firm heterogeneity represented by $u_i$$u_i$u_(i)u_{i} in Eq. (6).
表 4A 报告了我们对管理层股份决定因素的估计。在每种情况下，因变量为 $LN(m/(1-m))$$LN(m/(1-m))$LN(m//(1-m))L N(m /(1-m)) 。每个规格都包括年份虚拟变量（未报告）。在包括固定公司效应的规格中，我们控制了在公式(6)中由 $u_i$$u_i$u_(i)u_{i} 表示的未观察到的公司异质性。

The first column reports results from a baseline specification using pooled data for all firm-years. Increases in firm size, all else being equal, are associated with a reduction in managerial stakes. Increases in fixed capital intensity (which
第一列报告了使用所有公司年份的合并数据的基线规范结果。在其他条件相同的情况下，企业规模的增加与管理层持股的减少相关联。固定资本密集度的增加（这

Table 3  表 3
Variable descriptions  变量描述

we associate with lower monitoring costs) also lead to a decline in managerial stakes. Among our proxies for discretionary spending (R&D, advertising, investment rates, and operating income relative to capital), $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} intensity appears to have a negative effect on ownership stakes, while advertising intensity, operating
我们与较低的监控成本相关联）也导致管理层持股的下降。在我们对自由支出的代理指标（研发、广告、投资率以及相对于资本的营业收入）中， $\mathrm{R}\mathrm{\&}\mathrm{D}$$\mathrm{R}\mathrm{\&}\mathrm{D}$R&D\mathrm{R} \& \mathrm{D} 强度似乎对所有权股份产生负面影响，而广告强度、营业
income, and the investment rate appear to have positive effects on ownership stakes. Increases in idiosyncratic risk, as measured by SIGMA, raise the cost of managerial ownership in terms of reduced portfolio diversification and also reduce managerial ownership.
收入和投资率似乎对所有权份额有积极影响。特有风险的增加（以 SIGMA 衡量）提高了管理层所有权的成本，表现为投资组合多样化的减少，同时也减少了管理层所有权。

Table 4  表 4
(A) Determinants of total equity ownership by top managers
(A) 高管总股权拥有的决定因素

The specifications reported in this table all model the fraction of common equity held by top managers, $m$$m$mm, by regressing the transformed dependent variable $LN(m/(1-m))$$LN(m/(1-m))$LN(m//(1-m))L N(m /(1-m)) on the explanatory variables indicated below. Intercept terms and year dummies are included for all regressions, but not reported. Fixed effects at the industry or firm level are included where indicated, but not reported. Variable definitions for the acronyms are given in Table 3.
本表中报告的规格均建模了高管持有的普通股比例 $m$$m$mm ，通过对转化后的因变量 $LN(m/(1-m))$$LN(m/(1-m))$LN(m//(1-m))L N(m /(1-m)) 进行回归，使用下面所示的解释变量。所有回归均包含截距项和年份虚拟变量，但未报告。行业或公司层面的固定效应在指示的地方包含，但未报告。缩略语的变量定义见表 3。