مدل های ساختاری و درون زا در امور مالی شرکت ها: پیوند بین مالکیت مدیریتی و عملکرد شرکت

This paper presents a parsimonious, structural model that isolates primary economic determinants of the level and dispersion of managerial ownership, firm scale, and performance and the empirical associations among them. In particular, variation across firms and through time of estimated productivity parameters for physical assets and managerial input and corresponding variation in optimal compensation contract and firm size combine to deliver the well-known hump-shaped relation between Tobin's Q and managerial ownership. To assess the effectiveness of standard econometric approaches to the endogeneity problem, we apply those remedies to panel data generated from the model. The unfortunate conclusion is that, at least in the ownership–performance context, proxy variables, fixed effects, and instrumental variables do not generally provide reliable solutions to simultaneity bias.

This paper pursues two interrelated themes. First, we specify and estimate a structural model of the firm in which managerial contract design, firm size, and firm performance are jointly determined in equilibrium. We use numerical methods to calculate the productivity parameters for managerial input and investment that would give rise to the levels of chief executive officer (CEO) ownership and investment observed in the data as optimal choices in our model. The structural model is relatively successful in explaining both (a) the level and dispersion of managerial ownership, firm scale, and performance and (b) the character of the empirical associations among those variables. This suggests that our model captures some of the primary economic determinants of the endogenous equilibrium relation between firm performance and structure. Second, we use our model to evaluate a number of commonly applied econometric approaches to the endogeneity problem. Our unfortunate conclusion is that, in the ownership–performance context, the use of proxy variables, fixed effects, and instrumental variables does not generally provide a reliable solution to simultaneity bias. Overall, the construction of our model and its application to data illustrate how quantitative structural models are likely to be applicable to a spectrum of other empirical questions in corporate finance. For our analysis we focus on a substantial and consistently active segment of the empirical corporate finance literature, the relation between firm performance and managerial incentives. Important early contributions include Morck, Shleifer, and Vishny (1988) which documents a nonmonotonic relation between Tobin's Q and managerial stock ownership, and McConnell and Servaes (1990), which reports an “inverted-U” or “hump-shaped” relation between Q and managerial ownership. Numerous successors investigate the ownership–performance relation using different data, various measures of performance and ownership structure, and alternative empirical methods. 3 One common interpretation of the estimated hump shape is that the incentive alignment effects of ownership dominate at low ownership levels, but that high ownership levels facilitate managerial entrenchment.4 Under this view, shareholders maximize firm value if they can induce managers to own precisely the amount of stock associated with the peak of the performance–ownership relation. In our data the effective ownership from stock and options of the CEO varies from 0.01% to 57.6%, with a standard deviation of 5.7%, and the point at which the maximum of the estimated hump-shaped relationship between Q and effective CEO ownership arises is 20.0%. One obvious possibility is that large transaction costs prevent some firms from moving to the optimum. Based on our estimates of the Q-ownership relation, however, increasing CEO ownership by one standard deviation, from 14.3% to 20.0%, implies an increase in firm value equal to $662 million, on average. Supposing these calculations are representative for the average firm or even just some firms, it seems implausible that the transaction costs of realigning CEO ownership exceed that figure, much less the even greater amounts associated with larger departures of ownership from that which supports maximal Q. Based on this line of reasoning and plausible transaction costs, there is far more variation in observed ownership structure than one would expect. An alternative interpretation of the data is that the inverted-U pattern represents a value-maximizing relation between two endogenous variables. Under this view, if the empirical specification adequately captures the effects of all relevant exogenous variables, i.e., those structural parameters that jointly drive both ownership and performance, that specification would be unlikely to detect any remaining relation between the jointly determined endogenous variables (Demsetz and Lehn, 1985). One challenge for those who operate in the equilibrium paradigm, in this particular empirical context or any other, is to identify the underlying economic forces that drive what presumably is an equilibrium relation between organization structure and firm performance. We take up this challenge by specifying and estimating a structural model of the firm. Exogenous parameters specify managerial risk aversion, volatility of cash flow, profit margin, productivity of managerial input, productivity of investment, and how cash flow volatility depends on firm size. The shareholders choose investment (firm size) and ownership (the compensation scheme) of the manager, realizing that the manager chooses input, which cannot be observed by the shareholders. Of course, in the standard agency problem (Mirrlees, 1976 and Holmstrom, 1979; and successors) it is the slope of the compensation scheme (i.e., the ex ante sensitivity of managerial wealth to firm performance, or wealth-performance sensitivity (WPS)) that is the primary contractual characteristic that influences the manager's choice of unobservable input. We use data on firm size from Compustat and managerial stock and option ownership from Execucomp to solve for the two model parameters that describe the firm's production function. In particular, for each firm-year observation, we calculate the productivity parameters for managerial input and investment that would give rise to the observed levels of managerial ownership and total assets as optimal choices in our model. We then use these estimated productivity parameters as variables in the model to generate simulated firm-year data on Tobin's Q. To assess economic content, we confront the model with several classes of empirical tests. From least to most formal, first we find that the model is sufficiently flexible to accommodate what appears in the data. There always exist productivity parameters for investment and managerial input that support observed firm size and CEO ownership as optimal in the model. Second, relative productivity of managerial input versus investment appears to significantly differ across industries in patterns that might be expected. For example, the relative productivity of managerial input compared to capital is high in personal and business services (including educational services, software development, and networking services) and business equipment (including computers), and low in metal mining and utilities. In the cross-section of industries, CEO ownership is larger and firm size smaller when our measure of productivity of managerial input is high relative to measured productivity of capital. Third, we examine whether the productivity parameters and our estimate of Q based on the model (call it Q⁎) are correlated with actual Q and other operating characteristics of the firm. We find that the correlations between model-generated Q⁎ and research and development (R&D) intensity, sales, leverage, and advertising effort are statistically significant and have the same sign as the correlations that these variables have with actual Q. Additionally, Q⁎ has significant power to explain actual Q. Finally, we directly examine the performance–ownership relation. We find that the simulated data from the model produce the inverted-U relation when we regress model-generated Q⁎ on CEO ownership (t=9.49) and its square (t=−7.65). Based on the estimated coefficients, the maximal point of the performance–ownership relation occurs at 21.2%, which is quite similar to what we obtain (20.0%) when we estimate the McConnell and Servaes (1990) specification using Execucomp and Compustat data. Overall, the results demonstrate that a simple optimal-contracting model can provide a plausible equilibrium explanation for the nonlinear performance–ownership relation that is widely documented in the literature. While some readers will view the specification and estimation of the structural model as the chief contribution, others will have a stronger interest in our second research thrust. In particular, we employ the model to evaluate the statistical and economic relevance of the endogeneity problem and whether standard econometric remedies are therapeutic. To begin, we generate a panel of data supposing that our model is the true model and that our estimated exogenous productivity parameters are correct. These productivity parameters are unobservable by the econometrician and within our equilibrium framework, construing them as necessary control variables, their omission in a regression model of Q on ownership leads to a spurious relationship between ownership and firm performance. A standard solution to the omitted variable problem in the literature is to use a variety of control variables as proxies for the unobserved exogenous parameters. Using firm size (e.g., sales), leverage, R&D expense, advertising expense, and industry indicator variables to proxy for the structural productivity parameters, the spurious relation between Q and managerial ownership typically remains. By way of comparison, adding simple transformations of the actual productivity parameters to the regression specification yields instead an insignificant relationship between ownership and performance. Together, these results suggest that standard proxy variables are not sufficient to deal with the endogeneity problem in this context and potentially in others as well. Moreover, the model reveals that the relation between the unobserved productivity parameters and Q is nonlinear, which also leads to issues arising from misspecification of the functional form. A second solution to the endogeneity problem is to use panel data and include firm fixed effects. Fixed effects can accommodate unobserved heterogeneity in the contracting environment. The implicit assumption in the case of firm fixed effects is that the omitted variables that describe the contracting environment are time-invariant. In our simulated data the productivity parameters are time-varying and, in this case, we find that firm fixed effects are insufficient to eliminate the spurious relation between ownership and performance. A third remedy is to use instrumental variables (IV). In our empirical context, we present some evidence on the difficulties of employing the IV approach. Using plausible instruments does not displace the spurious relation between Q and managerial ownership. In the end, our results suggest that endogeneity can be a severe problem and that standard remedies used in the literature often fail, unfortunate conclusions which provide further impetus for application of a structural approach. In broad terms, our analysis makes three classes of contributions. First, we provide an equilibrium explanation for an important and oft-examined empirical finding. In our framework, the Q-ownership relation in the data represents the envelope of value-maximizing contract choice, firm size, and firm performance, all of which are jointly determined based on the exogenous firm-level parameters governing productivity of investment and managerial input. Though our model has a minimal number of elements, it appears to capture some of the essential economic factors that determine contract form, the boundaries of the firm, and firm value, all in a way that is consistent with an important empirical regularity. Second, the methodological implications of our analysis suggest the presence of significant research opportunities in empirical corporate finance. Our model is consistent with recent calls by Zingales (2000) and Himmelberg (2002), among others, for a quantitative theory of the firm that is empirically implementable and testable and that allows an assessment of the economic significance of various dimensions of the organization. To this end, our work is similar to several other recent papers, including Hennessy and Whited, 2005 and Hennessy and Whited, 2007 and Strebulaev (2007) on capital structure, Riddick and Whited (2009) on corporate cash holdings, and Coles, Lemmon, and Wang (2011) on the joint determinants of compensation policy and board structure. Finally, our approach can help to avoid the endogeneity and causation problems that commonly plague empirical corporate finance. Doing so is essential. By simulating data from the model, we illustrate the difficulty of controlling for endogeneity and assessing causation using standard methods. The remainder of the paper is organized as follows. Section 2 presents and analyzes a principal-agent model augmented by an investment (scale) choice. Section 3 describes our sample. Section 4 describes our empirical strategy. In Section 5, we solve the model. Using data on managerial ownership and total assets, we calculate the productivity parameters for managerial input and physical capital that would give rise to observed managerial ownership and firm size as optimal choices in the model. Using the results, we perform numerical comparative statics to characterize the economic importance of changes in the structural parameters for investment, ownership, and our proxy for Tobin's Q. Section 6 examines variation across industries in the productivity parameters and Q⁎. We also report the results of our analysis of the correlation between model parameters and firm characteristics. Section 7 shows that our model generates the hump-shaped relation between Tobin's Q and managerial ownership. We also clarify the economic intuition for how the model replicates this important empirical regularity. Section 8 examines the severity of the endogeneity problem and assesses the effectiveness of applying the standard econometric remedies. Section 9 concludes.

This paper specifies a structural model of the firm in which managerial contract design, firm size, and firm performance are jointly determined in equilibrium. We estimate the parameters of the model using data from Execucomp, CRSP, and Compustat. Our approach is to calculate the productivity parameters for managerial input and investment that would give rise to the observed levels of CEO ownership and investment as optimal choices in our model. In terms of the economic importance for firm design of the structural productivity parameters, increasing the productivity of managerial input has a strong positive effect on the optimal level of managerial ownership, but very little effect on firm scale and model-generated Q⁎. On the other hand, increasing investment productivity has a substantial positive effect on optimal firm scale and a strong negative effect on both the slope of the compensation contract and on Q⁎. We find that the estimated firm-level productivity parameters vary significantly and in an intuitive fashion across industries. In addition, we find that the estimates of Q obtained from the model (Q⁎) are significantly correlated with actual Q in the data. Model-generated Q⁎ is also correlated with scaled R&D expenditure, sales, leverage, and scaled advertising expenditure in the same way that these variables are correlated with actual Q. We directly examine the relation between managerial ownership and firm performance predicted by our model. The equilibrium relationships between the endogenous variables in our model produce the familiar inverted-U relation when we regress Q⁎ on CEO ownership and its square. While an established interpretation of the hump is based on a tradeoff between incentive alignment and entrenchment effects, our augmented principal-agent model lends credence to the idea that Q and δ (ownership) vary together endogenously, as their underlying determinants, marginal productivity of investment and input, vary in the cross-section and through time. Thus, our model provides an explanation of the empirical relationship between performance and managerial ownership as an envelope of optimal contract design and the level of Q⁎ arising from maximized firm value. Consistent with the equilibrium interpretation of our model, including simple transformations of the productivity parameters generated by our model on the right-hand side of the regression drives out the relation between ownership and Q⁎. These results suggest that we have isolated at least some of the joint economic determinants of contract design, firm size, and firm performance. Finally, we use our model to evaluate a number of commonly applied econometric approaches to the endogeneity problem. Our unfortunate conclusion is that, in the ownership–performance context, the use of proxy variables, fixed effects, and instrumental variables does not generally provide a reliable solution to the endogeneity problem. One prominent reason is that nonlinear regression specifications are likely to be appropriate. Another is that some remedies do not address endogeneity arising from the joint time-series (within-firm) variation of performance, size, and contract design. In addition to providing an explanation for a prominent empirical regularity, the construction of our model and its application to data provide one illustration of how quantitative structural models can be applied to a spectrum of empirical questions in corporate finance. Our procedure provides an example of how a structural model of the firm can isolate the important aspects of governance and quantify the economic significance of incentive mechanisms. Moreover, though we do not do so in this paper, this approach is more likely to permit well-specified tests of competing hypotheses and present the opportunity for conducting analysis of economic policies aimed at changing exogenous aspects of the underlying contracting environment. As Himmelberg (2002) points out, this is a line of attack that has been employed successfully in other branches of economics. Furthermore, our approach is consistent with recent calls by Zingales (2000) and Himmelberg (2002), among others, for a quantitative theory of the firm that is empirically implementable and testable and that allows an assessment of the economic significance of various dimensions of the organization. Finally, our analysis coincides with other recent interest in endogeneity concerns and solutions (e.g., Roberts and Whited, 2011).