A Reduced Form Coefficients Analysis of Executive Ownership, Corporate Value, and Executive Compensation

The Financial Review 38 (2003) 399--413 A Reduced Form Coefficients Analysis of Executive Ownership, Corporate Value, and Executive Compensation Marsha Weber Minnesota State University Moorhead Donna Dudney University of Nebraska-Lincoln Abstract Most simultaneous equations studies analyze the coefficients from the structural forms of the models, which provide estimates of the direct effects of independent variables on the dependent variables in each equation, but ignore the indirect effects these independent variables have on dependent variables in other equations. This paper modifies the work of Chung and Pruitt (1996) by extending the model to include board composition and institutional ownership variables and then estimating the structural and derived reduced form coefficients for the extended model. The signs and significance of the reduced form coefficients differ in several material respects from the results of the structural form coefficient analysis, which suggests that analysis of only the structural form coefficients is incorrect and potentially misleading. Keywords: executive ownership, Tobin s Q, executive compensation, simultaneous equations JEL Classifications: G30/G34/C30 Corresponding author: Department of Business Administration, Minnesota State University Moorhead, Moorhead MN 56563; Phone: (219) 299-5834; Fax: (218) 236-2238; E-mail: weberm@mnstate.edu We wish to thank Kathleen Farrell, James Schmidt, Tom Zorn, and the anonymous reviewers of The Financial Review for their helpful comments and suggestions. 399

400 M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 1. Introduction Numerous theoretical and empirical studies have examined the interactions between compensation, managerial ownership, and firm performance. Whereas early studies generally utilized ordinary least squares (OLS) regression techniques, more recent studies have focused on the simultaneous nature of the processes determining ownership structure and firm value (Jensen, Solberg, and Zorn, 1992; Bathala, Moon, and Rao, 1994; Agrawal and Knoeber, 1996; Chung and Pruitt, 1996). Most, if not all, of the simultaneous equations studies in the area of compensation and managerial ownership research analyze coefficients from the structural forms of the simultaneous equation models. Although structural coefficients provide estimates of the direct effects of independent variables on the dependent variables in each equation, these coefficients ignore the indirect effects these independent variables have on dependent variables in other equations. For a given equation, the structural coefficients give the change in the relevant dependent variable caused by a one-unit change in an explanatory variable assuming all other variables are held constant. However, as noted by Ford and Jackson (1998), jointly dependent variables are prevalent in simultaneous equations models (otherwise a single-equation model would have been appropriate), and jointly dependent variables are often included as explanatory variables in other equations in the system. When the relevant dependent variable changes in response to an initial change in an explanatory variable, the jointly dependent variable will also respond to this change, thus causing a further change in the relevant dependent variable and/or in dependent variables in other equations. Because structural coefficients assume that all other variables are held constant, these secondary changes are ignored. If we want to take into account the secondary effects that feed back through the system after an initial change, derived reduced form coefficients must be used. 1 The use of structural coefficients can misstate the magnitude of the effect of a change in an explanatory variable and can even misstate the direction of the effect. To illustrate the potential dangers of evaluating only structural form coefficients from a simultaneous equations model, we extend a model developed by Chung and Pruitt (1996) and then calculate both the structural form and derived reduced form 2 coefficients for the extended model. Chung and Pruitt investigate the factors that 1 Reduced form coefficients are generated by many econometric software packages; however, none of the popular econometrics software packages provide t-statistics for the reduced form coefficients. As a result, the significance of the structural form coefficients can often be incorrectly assumed to carry over to the reduced form coefficients. Theil (1971, pp. 537 538) provides a process for calculating the t-statistics for reduced form coefficients that can be accomplished using the published output from the statistical packages and the application of some linear algebra operations to the data. 2 Derived reduced form coefficients are those that recognize the restrictions in the simultaneous equations model and are provided by popular software packages for two stage least squares and three stage least squares estimations. For simplicity, we refer to these coefficients as reduced form coefficients in the remainder of the paper.

M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 401 affect executive ownership, the firm s market value of equity (MVE), and executive compensation using a simultaneous equations model estimated by three stage least squares. Our extension of Chung and Pruitt s model includes board composition and institutional ownership variables identified as significant in the determination of firm value, ownership, and compensation by previous researchers. 3 We show that the signs and statistical significance of the reduced form coefficients for this model differ in several material respects from the results of the structural form coefficient analysis. For example, in the equation for firm value (measured by Tobin s Q), the coefficients on five variables (tenure as CEO, company age, the percentage of institutional ownership, whether the CEO is a founder of the firm, and whether the CEO is a family member successor to the founder) were found to be significant in the structural form of the model, but insignificant in the reduced form. Firm size, as measured by total assets (TA), is not included in the structural equation for firm value, but its reduced form coefficient is highly significant. In addition, the use of reduced form estimation highlights a possible theoretical misspecification of the original model. These findings suggest that analysis of only the structural form coefficients in a simultaneous equations system is incorrect and potentially misleading. The remainder of the paper is organized as follows. Section 2 discusses the empirical model specification. Section 3 presents data sources and descriptive statistics for model variables. Section 4 compares and contrasts the structural and reduced form coefficient results, and summary and conclusions are presented in Section 5. 2. The model Chung and Pruitt (1996) use a three-equation simultaneous equations model to test the hypotheses that (1) executive ownership is a positive function of firm value (as measured by Tobin s Q), (2) Tobin s Q is a positive function of executive ownership, and (3) CEO compensation is a positive function of Tobin s Q. The first two hypotheses suggest that Tobin s Q and executive ownership can be jointly dependent. The third hypothesis suggests that firms with high Tobin s Q ratios are likely to provide higher levels of executive compensation or will offer higher compensation to attract managers with the ability to increase value or to maintain high Q ratios. We begin with Chung and Pruitt s original model and extend the model to include variables mentioned by Chung and Pruitt in their suggestions for further research. We 3 David, Kochhar, and Levitas (1998) examine the role of institutional investors in determining CEO compensation policy. Barnhart and Rosenstein (1998), Firstenberg and Malkiel (1994), and Yermack (1996) examine the relation between firm value and board size, and the relation between CEO compensation and the percentage of inside directors on the board is investigated by Sridharan (1996).

402 M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 also correct a theoretical misspecification error in the original model. The structural form of the revised model is stated below and explanation of revisions and variable descriptions follow. ln (CEO ownership) = α 0 + α 1 ln (Tobin sq)+ α 2 ln (CEO compensation) + α 3 ln (CEO years) + α 4 ln (CEO age) + α 5 ln (company age) + α 6 ln (MVE) + α 7 ln (board size) + α 8 ln (institutional own) + α 9 founder dummy + α 10 family dummy + ε 1 (1) ln (Tobin s Q)= β 0 + β 1 ln (CEO ownership) + β 2 ln (MVE) + β 3 ln (CEO years) + β 4 ln (company age) + β 5 ln (board size) + β 6 ln (inside directors) + β 7 ln (institutional own) + β 8 college dummy + β 9 graduate dummy + β 10 founder dummy + β 11 family dummy + ε 2 (2) ln (CEO compensation) = γ 0 + γ 1 ln (Tobin sq)+ γ 2 ln (TA) + γ 3 ln (CEO years) + γ 4 ln (CEO age) + γ 5 ln (company age) + γ 6 ln (board size) + γ 7 ln (inside directors) + γ 8 ln (institutional own) + γ 9 college dummy + γ 10 graduate dummy + ε 3 4 (3) As Chung and Pruitt (1996) note, a complete analysis of the impact of executive ownership on firm value should include variables dealing with board composition and institutional holdings. Therefore, we extended Chung and Pruitt s original model to include board size, board insider composition, and institutional ownership variables. 4 A two-digit SIC code industry dummy variable to control for the possibility of spurious correlations among variables operating through industry effects was included in Chung and Pruitt s (1996) original model. However, when the industry dummies were excluded from the model, the R 2 fell only slightly and the estimated coefficients were statistically identical. Therefore, Chung and Pruitt reported their results without the industry dummy variables. We also ran our extended model with and without the SIC code dummies, and found that regression results were very similar. Therefore, our results are reported without the industry dummies.

M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 403 Analysis of the reduced form coefficients generated from the original model highlighted a possible theoretical misspecification. 5 To cure this misspecification, we add CEO compensation to the ownership equation because CEO compensation in the form of salary and bonus can complement compensation in the form of stock ownership. Mehran (1995) finds a positive relation between compensation and ownership, and Murphy (1999) argues for a positive relation between compensation and ownership because most components of incentive compensation (including option grants, bonuses, and restricted stock grants) are determined by base salary levels, so increases in base salary lead to increases in other compensation components. 2.1. Exogenous variables 2.1.1. CEO tenure The length of time the CEO has been in his or her current position (CEO years) and CEO ownership are expected to be positively related because the value of stock options and other compensation incentives will be greater for executives with longer tenures. The relation between CEO years and Tobin s Q is not hypothesized. A positive relation could exist if more experienced CEOs are better at managing assets-in-place, but a negative relation would hold if more experienced CEOs are more conservative and less likely to search out risky projects. 2.1.2. CEO age The relation between CEO age and CEO ownership is also indeterminate. An argument for a positive relation suggests that older CEOs will tend to have accumulated more wealth, which would allow greater personal investment in the firm. The opposite could also be true if, as executives get older, they reduce their ownership levels to diversify their portfolios. We might expect CEO age and compensation to be positively related because older CEOs tend to have more experience, which can be expected to result in higher compensation. However, if salary compression occurs as a result of older CEOs not actively seeking positions in other firms, compensation and age can be inversely related (Chung and Pruitt, 1996). 5 In the original model, the total asset variable appeared only in the compensation equation and the endogenous compensation variable did not appear in either of the other equations. Therefore, total assets were not linked to equation (1) or equation (2) either directly or indirectly, so changes in total assets affected only the compensation equation. The reduced form coefficient on total assets was therefore identical to the structural coefficient and changes in total assets had no effect on CEO ownership or Tobin s Q. Furthermore, total assets was the only significant reduced form coefficient in the entire model. This result is counter to a number of papers that show a significant relation between firm size and both CEO ownership and Tobin s Q (see for example McConnell and Servaes, 1990; Bathala, Moon and Rao, 1994; Bathala, 1996; Murphy, 1999).

404 M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 2.1.3. Company age According to Chung and Pruitt (1996), the firm s growth potential, size, CEO age, probability of a founder-ceo, and experience variables may systematically vary according to the age of the firm (p. 1144). Therefore, the variable company age is included in the model to control for these differences. 2.1.4. Total assets Asset size and executive compensation are assumed to be positively related. Murphy (1999) notes that one of the most well-documented empirical regularities in executive compensation studies is the positive relation between executive compensation and firm size. Chung and Pruitt (1996) argue that the larger the firm, the more complex the CEO s job becomes, so it is logical to expect a positive relation between asset size and compensation. 2.1.5. Board size Board size is used as a measure of board cohesiveness by Barnhart and Rosenstein (1998), who suggest that firms with smaller boards tend to outperform those with larger boards because they are better able to make decisions that affect firm performance. There are several streams of research involving behavioral aspects of boards of directors that indicate smaller boards are associated with better performance (e.g., Firstenberg and Malkiel, 1994; Yermack, 1996). Board size is strongly related to firm size (e.g., Yermack, 1996); therefore, board size is anticipated to be positively related to CEO compensation and negatively related to CEO ownership. 2.1.6. Institutional holdings David, Kochhar, and Levitas (1998) argue that institutional shareholders typically seek a more active governance role in the corporation and exercise more scrutiny of top management incentives than do individual investors, to protect against erosion of their investment value. These groups of institutional owners can have the power to influence executive compensation, which can indicate a negative relation between institutional ownership and executive compensation. Barnhart and Rosenstein (1998) use the percentage of institutional investor ownership as a measure of institutional monitoring and found a positive relation between institutional holdings and firm value as measured by Tobin s Q (see also McConnell and Servaes, 1990; Agrawal and Knoeber, 1996). Their findings support the hypothesis that institutional investors have greater expertise than individual investors and can monitor management at a lower cost. Bathala, Moon, and Rao (1994) find that institutional ownership is negatively related to CEO ownership, as firms with greater monitoring by institutional

M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 405 investors find it optimal to use lower levels of managerial ownership to control agency conflicts in the firm. 2.1.7. Founder and family dummy variables Two dummy variables, founder dummy and family dummy, are also included in the model. The founder dummy is one if the current CEO was a founder of the company and zero otherwise. The family dummy is one if the current CEO is a descendant of a company founder and zero otherwise. Chung and Pruitt (1996) argue that the founding of a successful corporation indicates the entrepreneurial talents of the CEO and his or her descendents, so these firms tend to seek out greater growth opportunities than firms not managed by a founder or his or her descendents (implying a positive relation with Tobin s Q). Because a company founder and his or her descendents can own a substantial part of the firm, the founder and family dummies are expected to be positively related to CEO ownership. 2.1.8. Market value of equity Chung and Pruitt (1996) hypothesize a negative relation between the market value of equity and CEO ownership. Wealth constraints can keep a CEO from increasing ownership as the value of the firm becomes larger. The relation between MVE and Tobin s Q is hypothesized to be positive because of the strong correlation between Tobin s Q and the market-to-book value of the firm. Keim (1986) finds that the marketto-book value ratio tends to be higher for firms with higher market capitalizations. 2.1.9. Board composition Sridharan (1996) argues that board composition is an indicator of CEO influence over the board, so that the nature of board composition can influence CEO compensation. If the board consists of insiders who hold positions within the firm, the board is more likely to approve higher CEO compensation (i.e., CEO compensation is positively related to the percentage of insiders on the board of directors). Agrawal and Knoeber (1996) argue that firm performance is reduced when there are more outside directors on the board, and because CEO compensation is often directly related to shareholder returns, lower firm performance leads to lower CEO compensation. Baysinger and Hoskisson (1990) suggest that inside directors have the knowledge to objectively and accurately assess the strategic choices of the CEO (the board possesses strategic control), which enhances firm performance. However, inside directors can find themselves in uncomfortable positions when conducting CEO performance evaluations because of personal loyalties or fear of retaliation. Their loyalties can cause difficulties when determining executive compensation (Johnson, Daily, and Ellstrand, 1996).

406 M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 2.1.10. Education dummy variables Two additional dummy variables, college dummy and graduate dummy, are included as proxies for human capital. The college dummy is one if the current CEO has an undergraduate degree and zero otherwise. The graduate dummy is one if the current CEO has a postgraduate degree and zero otherwise. Education levels can signal management quality and, if managerial quality is rewarded, would be associated with higher compensation as well as higher firm value. Therefore, college dummy and graduate dummy are expected to be positively related to CEO compensation and Tobin s Q. 3. Data Compensation data and CEO stock ownership data were collected from Forbes magazine s annual compensation survey for the year 1990 (1990 data were used because later data do not explicitly identify successors to founders). CEO compensation includes salary and bonus, but does not include the value of stock options granted to the executive. CEO stock ownership is measured by the percentage of CEO ownership, which is found by dividing the number of shares owned by the CEO by the total shares outstanding, and includes shares of beneficial interest and shares held by an executive s spouse and minor children (shares held by family members active in the business or by foundations are not included). We use the method developed by Chung and Pruitt (1994) to approximate Tobin s Q. Under this method, the approximate Tobin s Q is calculated by adding the firm s market value of equity, the liquidating value of the firm s outstanding preferred stock, the value of the firm s short-term liabilities net of its short-term assets, and the book value of the firm s long-term debt. This sum is then divided by the book value of the firm s assets. 6 Business Week s Corporate Elite report for October 1990 and the Forbes compensation survey were used to identify founders of companies and family successors to company founders, and Ward s Business Directory of U.S. Private and Public Companies (1989) was used to determine company age (measured from the date of incorporation). Institutional ownership holdings (the percentage of a company s shares held by institutions) as of the fourth quarter of 1990 were hand-collected from Value Line Investment Survey, and board size (number of directors on the board) and the proportion of inside directors (percentage of directors listed as senior officers of the firm) were hand-collected from Standard and Poor s Register of Corporations, Directors, and Executives (1990). All other data were collected from Compustat. The final sample consists of 288 firms for which data on all variables were available. 6 We use this method because the Manufacturing Sector Master File data used to compute the traditional Tobin s Q is available only through 1987. Chung and Pruitt (1994) found no significant differences between the Tobin s Q using the traditional and the approximation methods. Barnhart and Rosenstein (1998) also used the Chung and Pruitt method for approximating Tobin s Q.

M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 407 3.1. Descriptive statistics Descriptive statistics for the variables in the model are found in Table 1. The average Tobin s Q is 1.189, and the average compensation using 1990 data is $1.04 million. The distribution of the CEO ownership percentage is skewed by the presence of large CEO ownership positions by some company founders; the median CEO ownership percentage is 0.22%, and the average ownership percentage is 2.556%. On average, the CEOs are approximately 59 years old and have an average tenure of slightly more than nine years. The average company in this sample has been in existence for 65.5 years. The average board size for firms in the sample is between 11 and 12 members, and inside directors make up an average of 28% of board membership. Institutions own approximately 53% of the stock of the firms included in the study. These averages are consistent with Agrawal and Knoeber s (1996) sample showing a mean institutional ownership percentage of 50.9% and with Sridharan s (1996) sample showing an average board size of 13.32, with a 28.27% mean of inside directors. 4. Model results The results of the structural and reduced form estimation of the extended model are shown in Table 2, Panels A and B. The structural results will only be discussed briefly. Discussion of the results will focus on the more accurate reduced form coefficients, and on how the significance and signs of some coefficients changed between the structural and reduced forms of the model. 4.1. Structural form results Structural form coefficients for our revised extended model were estimated using three stage least squares (3SLS) and are found in Panel A of Table 2. 7 Results of structural estimation indicate that higher firm value is associated with higher CEO compensation. Our results also indicate dual causality between CEO ownership and Tobin s Q. We find that the coefficient on the CEO ownership variable is significantly positive in the Tobin s Q equation, and the coefficient on Tobin s Q is positive and significant in the CEO ownership equation. The coefficients on the market value of equity and company age variables in the CEO ownership equation are negative and significant, consistent with expectations. The founder and family dummy variables, as well as CEO years, are positively related to percentage ownership, also as anticipated. 7 To validate our results, we estimated Chung and Pruitt s (1996) original model using our (1990) data. With the exception of the intercept coefficients, our structural form results for the original model are similar in sign and significance to Chung and Pruitt s results. The structural and reduced form coefficients from our replication of the original Chung and Pruitt model are available from the authors on request.

Table 1 Descriptive statistics The sample includes 288 firms for which data on all variables were available. Data for CEO Ownership and CEO Compensation are from Forbes Annual Compensation Survey, 1990. Institutional Ownership holdings were collected from Value Line Investment Survey, 1990. Board Size and the proportion of Inside Directors were gathered from Standard & Poor s Register of Corporations, Directors, and Executives, 1990. Ward s Business Directory of U.S. Private and Public Companies was used to find company age. Data for Tobin s Q, Market Value of Equity (MVE) and Total Assets (TA) are from Compustat. Variable Mean Deviation Minimum Maximum Median First quartile Third quartile Tobin s Q 1.189 1.016 0.076 7.612 0.88 0.598 1.439 CEO own (%) 2.5563 7.37 0.01 61.52 0.22 0.078 1.12 CEO comp (millions) 1.0396 0.9973 0.036 14.822 0.88 0.625 1.215 MVE (millions) 3,590.979 6,445.044 68.250 64,449.035 1,643.661 925.289 3365.273 TA (millions) 3,996.131 6,931.884 79.758 87,707.000 2,082.564 1,080.129 4385.2 CEO years 9.1188 8.1449 0.5 45.00 7.00 3.00 12.00 CEO age 57.0938 6.5049 34.00 78.00 57.00 53.00 61.00 Company age 65.5 34.7504 5.00 150.00 63.5 36.00 90.00 Board size 11.6875 3.1224 3.00 20.00 12.00 10.00 14.00 Institutional own (%) 53.3958 16.6768 3.472 95.247 57.241 42.821 66.186 Inside directors (%) 28.2718 14.8937 6.25 100.00 25.00 18.182 35.714 408 M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413

M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 409 Table 2 Model Estimation Results Estimation of a three-equation simultaneous system using three-stage least squares (3SLS). The dependent variables are the percentage of CEO ownership, Tobin s Q, and CEO compensation. MVE = market value of equity. The results of structural form estimation are found in Panel A and results for reduced form estimation are in Panel B. Panel A: Structural results Panel B: Reduced form results CEO Tobin s CEO CEO Tobin s CEO ownership Q compensation ownership Q compensation Intercept 9.291 9.018 1.915 5.783 0.615 1.993 (3.19 ) ( 4.29 ) ( 1.63) (2.81 ) ( 0.31) ( 1.74) Tobin s Q 1.003 0.127 (3.69 ) (2.54 ) CEO own. 1.453 (4.61 ) CEO comp. 1.450 (1.37) MVE 0.973 0.863 0.073 0.758 0.096 ( 3.39 ) (6.14 ) ( 0.77) (13.55 ) (2.56 ) Total assets 0.226 0.452 0.656 0.143 (6.73 ) ( 4.27 ) ( 10.55 ) (3.30 ) CEO years 0.388 0.808 0.113 0.562 0.008 0.114 (2.04 ) ( 3.74 ) (3.38 ) (6.02 ) (0.09) (3.29 ) CEO age 0.007 0.063 0.137 0.199 0.038 ( 0.02) ( 0.26) (0.57) (0.57) ( 0.14) Company age 0.309 0.409 0.036 0.315 0.048 0.029 ( 2.30 ) (2.10 ) (0.74) ( 2.39 ) (0.49) (0.60) College 0.354 0.184 0.212 0.047 0.178 (1.26) ( 1.77) ( 1.06) (0.31) ( 1.71) Graduate 0.151 0.065 0.116 0.018 0.068 (0.99) ( 1.10) ( 0.97) ( 0.06) ( 1.16) Founder 2.162 3.125 2.134 0.024 0.003 (4.73 ) ( 3.99 ) (3.85 ) ( 0.03) ( 0.03) Family 2.275 3.245 2.175 0.084 0.011 (6.19 ) ( 4.06 ) (6.08 ) ( 0.19) ( 0.20) Board size 0.531 0.437 0.144 0.271 0.043 0.149 ( 1.50) (1.04) (1.16) ( 0.92) (0.25) (1.22) Inst. own. 0.371 0.600 0.038 0.548 0.196 0.013 ( 1.79) (2.18 ) (0.52) ( 2.99 ) ( 1.72) (0.18) Inside dir. 0.247 1.072 0.190 0.029 0.111 (1.46) ( 1.80) ( 1.21) ( 0.29) ( 1.84) Indicates statistical significance at the 0.05 level. In the Tobin s Q equation, as anticipated, the coefficients on the market value of equity, company age, and institutional ownership variables are positive and significant. CEO years and the founder and family dummy variables are significantly negatively related to firm value. The negative relation between CEO years and firm

410 M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 value supports the hypothesis that more experienced CEOs can be more conservative and less likely to seek out risky projects. The negative relation between the founder and family dummies and firm value is not as hypothesized. Morck, Schleifer, and Vishny (1988) found that the presence of the founding family can adversely affect Tobin s Q in older firms, in which the entrepreneurial talent of the founder can be less valuable than in younger firms. The average company age in our sample is 65.5 years; therefore, our findings support Morck, Schleifer, and Vishny s (1988) hypothesis. Total assets and CEO years are significant in the CEO compensation equation; these coefficients are positive, as expected. 4.2. Reduced form estimation To determine the significance of the estimated reduced form coefficients, t-statistics for these coefficients must be calculated. T-statistics for reduced form coefficients are not automatically generated by popular statistical software packages, but can be calculated using a process suggested by Theil (1971). This process is briefly described below, followed by a discussion of the results of reduced form estimation. 4.2.1. Computing reduced form t-statistics The derived reduced form can be stated as Y = X where = BƔ 1. The matrix B contains the coefficient estimates on exogenous variables of the system and the matrix Ɣ contains the estimators of the coefficients on the endogenous variables of the system. The process for calculation of t-statistics for derived reduced form coefficients begins with augmenting the variance/covariance matrix from structural form estimation by adding rows and columns of zeros for the fixed coefficients (i.e., the endogenous and exogenous variables not appearing in each equation in the structural form). The final variance covariance matrix for the derived reduced form is calculated as J J where J = (Ɣ ) 1 [ I], I is the identity matrix of the appropriate dimensions, and is the supplemented variance/covariance matrix described above. T-statistics are calculated by dividing the roots of the elements of the diagonal of the J J matrix into the derived reduced form coefficients ( ). 4.2.2. Reduced form results Estimation of the reduced form of the extended model provides significantly different results than estimation of the structural form. When all exogenous variables are allowed to filter through the whole system, the implications of the estimation change. Reduced form results are found in Panel B of Table 2. In the CEO ownership equation, institutional ownership was not significant in the structural form of the ownership equation but is negative and significant in the reduced form equation, suggesting that higher institutional ownership leads to lower CEO ownership, as hypothesized. Structural results indicated that the market value

M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 411 of equity is negatively related to ownership, whereas the reduced form coefficient on market value of equity is not significant. Also, the total assets coefficient is negative and highly significant, which is an interesting result in part because it illustrates the importance of reduced form estimation. The total assets variable was not included in the structural form but is significant when changes in this exogenous variable filter through the entire system. This result is consistent with Bathala s (1996) hypothesis that firm size (i.e., TA) and CEO ownership are negatively correlated. Bathala (1996) and Demsetz and Lehn (1985) argue that total assets can capture the wealth constraint more completely than market value of equity. The reduced form coefficients for the Tobin s Q equation are substantially different from the structural form coefficients for this equation. CEO years, company age, institutional ownership, founder dummy, and family dummy coefficients were significant in the structural estimation but are not significant using the reduced form results. The coefficient on total assets, which was not included in the structural form, is negative and highly significant. The compensation equation reduced form results are similar to the structural form results. The only difference in the compensation equation is that market value of equity, which does not appear in the structural compensation equation, is positively related to CEO compensation in the reduced form results. If CEOs are compensated based on the firm s equity performance, it follows that CEOs of firms with higher market values would receive greater compensation. 4.3. Robustness tests Barnhart and Rosenstein (1998) show that simultaneous equations models can be very sensitive to changes in model specifications. To test the sensitivity of our results to model specification changes, several additional control variables used in previous research were added to the model. 8 Variable signs and significance levels were virtually unaffected by the inclusion of these additional variables. 9 5. Summary and conclusions The contribution of this study to the literature is twofold. First, the structural and reduced form coefficients are estimated for an extension of a simultaneous equations model of executive ownership, corporate value, and executive compensation determination originally developed by Chung and Pruitt (1996). Chung and Pruitt s model 8 These variables included ROA in the Tobin s Q and CEO compensation equations (Yermack, 1996), sales growth in the CEO compensation and Tobin s Q equations (Sridharan, 1996), earnings volatility (the standard deviation of EBIT/Assets over a five year period) in the CEO ownership and compensation equations (Bathala, 1996), and advertising expense and research and development expense in the CEO ownership and Tobin s Q equations (Barnhart and Rosenstein, 1998). 9 Results of these model are not presented here, but are available upon request from the authors.

412 M. Weber and D. Dudney/The Financial Review 38 (2003) 399 413 is extended to include variables that measure the roles of boards of directors and institutional investors on CEO ownership, firm performance, and CEO compensation structure. Our results indicate that higher firm value is associated with higher CEO compensation and that dual causality exists between CEO ownership and firm value. Analysis of the reduced form coefficients from the extended model shows significantly negative correlations between institutional ownership and CEO ownership and between company age and CEO ownership. CEO age is positively related to both CEO ownership and compensation, and the founder and family dummy variables are positively correlated with CEO ownership. Firm size is negatively related to CEO ownership and firm value and positively related to CEO compensation. Second, the structural and reduced form coefficients for the extended model are compared to illustrate the potential dangers of evaluating only structural form coefficients from a simultaneous equations model. The reduced form coefficients show the effects of all exogenous variables on each of the endogenous variables in the system, which provides a valuable interpretation of results as both the direct and indirect effects of changes in the exogenous variables are considered. Previous compensation literature utilizing simultaneous equations models analyzes only the structural form coefficients of the models. We find that the signs and significance of the reduced form coefficients differ in several material respects from the results of the structural form coefficient analysis, particularly in the CEO ownership equation and the firm value (Tobin s Q) equation. Our analysis suggests that interpretation of only the structural coefficients is incorrect and can be misleading. References Agrawal, A. and C.R. Knoeber, 1996. Firm performance and mechanisms to control agency problems between managers and shareholders, Journal of Financial and Quantitative Analysis 31, 377 398. Barnhart, S.W. and S. Rosenstein, 1998. Board composition, managerial ownership, and firm performance: An empirical analysis, The Financial Review 33, 1 16. Bathala, C.T., 1996. Determinants of managerial stock ownership: The case of CEOs, The Financial Review 31, 127 148. Bathala, C.T., K.P. Moon, and R.P. Rao, 1994. Managerial ownership, debt policy, and the impact of institutional holdings: An agency perspective, Financial Management 23, 38 50. Baysinger, B.D. and R.E. Hoskisson, 1990. The composition of boards of directors and strategic control, Academy of Management Review 15, 72 87. Chung, K.H. and S.W. Pruitt, 1994. A simple approximation of Tobin s Q, Financial Management 23, 70 74. Chung, K.H. and S.W. Pruitt, 1996. Executive ownership, corporate value, and executive compensation: A unifying framework, Journal of Banking and Finance 20, 1135 1159. David, P., R. Kochhar, and E. Levitas, 1998. The effect of institutional investors on the level and mix of CEO compensation, Academy of Management Journal 41, 200 209. Demsetz, H. and K. Lehn, 1985. The structure of corporate ownership: Cases and consequences, Journal of Political Economy 93, 1155 1177. Firstenberg, P.B. and B.G. Malkiel, 1994. The twenty-first century boardroom: Who will be in charge, Sloan Management Review 36, 27 35.

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