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«Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Executive ...»

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4.2 Potential explanations for the changing role of aggregate market size These preliminary results suggest that the dynamics of compensation arrangements have changed over time. One reason for this change could be that the level of pay is currently tied to contemporaneous fluctuations in firm size, whereas it was more responsive to lagged firm size in These results also cannot be explained by an asymmetric response of pay to increases and decreases in firm size.

When we interact average market size with a dummy variable indicating years of decline in aggregate market size, the estimated coefficient on the interaction term is zero in both sample periods and the coefficients on average firm size are unchanged.

These results are based on an ANOVA decomposition for each sample period. The fraction of the variance explained by each independent variable is the sum of squared residuals explained by that variable relative to the total sum of squared residuals of ln(compensation).

In Appendix Table A7, we show that the strong correlation between compensation and aggregate firm size was limited to the 1980s and 1990s. For all other decades in our sample, average market value accounts for less than 1 percent of the variation in executive pay.

the past. For example, this difference in timing would result from switching from accountingbased to market-based measures of firm performance when determining incentive pay.

However, panel 3 of Table 4 shows little support for this conjecture. Although the average market value in the previous year had a larger effect on compensation than the current value during the earlier sample period, the sum of these two coefficients is still considerably smaller than the corresponding sum in recent years.

Alternatively, our estimated coefficients in the earlier period may be biased downwards if firms responded to the high personal income tax rates during this period by increasing components of pay that we do not observe, such as pensions and perks. However, an exercise similar to our back-of-the envelope calculation in Section 3.3 suggests that it is unlikely that these components alone can explain the significant change in the correlation between aggregate market size and the level of pay.28 If the growth rate of total compensation has a one-to-one correlation with aggregate firm size (as we find for the recent period), the level of compensation should have increased by a factor of 3.3 from 1950 to 1968. In this case, unobserved forms of pay would need to have amounted to $1.6 million by 1968, an improbably high level of perks and other benefits.

A third potential explanation is that the relevant measure of firm size has changed over time. However, our results are robust to using the value of sales instead of market value (see cols. 3 and 4 of Table 4).29 Although the coefficients are two to three times larger for aggregate sales than aggregate market capitalization, the distribution of sales is far more dispersed (as indicated by the standard errors) and the fraction of the variance of compensation explained by To further study the implications of tax policy for the correlation of the level of pay and firm size, we have also analyzed the relationship between after-tax compensation and size. While the after-tax correlation of pay with average market size is stronger for the 1945-1975 period than the correlation with pre-tax compensation, it is still markedly weaker than the relationship between pay and firm size in later decades.

We could also consider firm earnings as a size proxy, but we lack data on this variable prior to the 1950s.

each of these variables is about the same. Thus, using the value of sales as an alternative measure of firm size still suggests that the importance of the aggregate market was much smaller earlier in the century.

It is tempting to conclude that aggregate firm size has become a key determinant of executive pay during the past 30 years. However, these coefficients are only correlations and may be biased by spurious upward trends in firm size and the level of compensation. Indeed, adding a quadratic time trend to the regression reduces the coefficient on average market value a bit (panel 4 of Table 4). Moreover, tests for non-stationarity cannot reject the null hypothesis that there is a unit root in the residuals of equation 1 in either period.30 To address this concern, we estimate the relationship between changes in compensation and changes in firm size (panel 5 of Table 4). The estimated effects of both the average size of the market and the idiosyncratic component of firm size are notably smaller in this specification, and they both explain a much smaller fraction of the variance in changes in pay than the corresponding specification in levels.31 Thus, the seemingly-strong correlation between average firm size and the level of pay of the past several decades may be driven by spurious correlation between the two variables.

In sum, a firm’s relative position in the distribution of firm size has accounted for about 20 percent of the variation in the level of compensation for our entire sample period. By contrast, aggregate market size has become more strongly correlated with the level of executive pay since the 1970s, although this relationship may be spurious.

Using Pesaran's (2007) panel unit root test, the null hypothesis of non-stationarity in the residuals of the second period has a p-value of 0.59. Therefore the presence of a unit root in the residuals cannot be ruled out. The p-value for the residuals in the early period is 0.03, suggesting that there may be a unit root in those residuals as well.

Evidence from both Hall and Liebman’s 1980-1994 and ExecuComp’s 1992-2005 datasets confirms this result.

Using the Hall-Liebman data, we find an elasticity of CEO pay with respect to average market value of 0.85 and the elasticity with respect to the idiosyncratic component of firm size of 0.32. The coefficients are -0.10 and 0.28 respectively for the specification in changes. Using all of the executives in ExecuComp, we find that the effect of average market value falls by half when the regression is estimated in changes instead of in levels.

5. The evolution of pay-performance sensitivities over time Sparked by the rise in stock option use and a concurrent surge in the level of executive pay, a marked increase in the correlation between managerial wealth and firm performance during the past 20 years has brought agency problems to the forefront of research in executive compensation (Murphy 1985, Jensen and Murphy 1990, Gibbons and Murphy 1990, Aggarwall and Samwick 1999, Bertrand and Mullainathan 2001, Bebchuk and Fried 2004). Although the recent surge in attention may lead to an impression that the conflict between managers and shareholders was not important in earlier times, this topic has been a concern ever since the separation of corporate ownership from corporate control in the early twentieth century (Baker and Crum 1935, Berle and Means 1932, Chandler 1977). However, a scarcity of data from earlier time periods has limited empirical studies of the long-run evolution of managerial incentives.32 The availability of detailed information is particularly important for the case of options, because changes in the value of stock option holdings account for a considerable portion of the increase in pay-to-performance during recent decades (Hall and Liebman 1998). Studies of option use prior to the 1970s used different methods to value options, and most estimates of managerial incentives did not include stock option revaluations. Because our dataset allows us to construct the portfolio holdings of stock and stock options for each executive, we are able to calculate consistent estimates of the sensitivity of managerial wealth to firm performance over the longer run.

5.1 Defining the appropriate measure of executive pay We are only aware of one study that measures pay-to-performance using a long-term series. Boschen and Smith (1995) provide estimates from 1948 to 1990, but their sample may not show the entire picture because it is based on only 16 firms and does not include executives’ holdings of stock and stock options.

Managerial decisions are influenced not only by the remuneration awarded in a given year but also by any other change in wealth that is tied to the performance of the firm (Jensen and Murphy 1990, Hall and Liebman 1998). Since the value of equity and stock options in the firm depends on firm value, a comprehensive analysis of pay-to-performance should include revaluations of an executive’s stock and stock option holdings.33 By depicting the long-run evolution of option awards and holdings, Figure 3 shows that stock options were already a major component of wealth by the 1960s. Although the fraction of executives receiving stock options prior to the 1980s was relatively modest, the fraction of individuals holding options was large. For example, 28 percent of the executives were granted an option in any given year in the 1960s, but more than 64 percent held options during this period. This difference arises because options had a long duration and vested slowly over time.

Options are now a regular part of the compensation package, so almost all executives receive and hold options in a given year.

Equity holdings of top executives have declined over the century relative to the firm’s total number of shares outstanding, with a more pronounced contraction among individuals who hold a larger fraction of the firm (see Table 5).34 By 2005, median fractional stock holdings were about one third of their pre-war level.35 Even though we consider a broader measure of changes in wealth than executive pay, we keep in line with the literature by referring to this correlation as pay-to-performance.

We collect information on equity holdings after 1942 from proxy statements. From 1935 to 1941, we construct stock holdings from an initial SEC report on holdings in 1935 and bi-monthly reports on the equity transactions of each officer The use of transactions data introduces noise in our measure of stock holdings, but we do not find evidence of a large bias. See the Appendix Section 2.4 for further details.

These results differ from Holderness, Kroszner and Sheehan (1999), who find higher stock ownership in 1995 than in 1935. There are two main explanations for this discrepancy. First, the increase in fractional holdings does not occur among the largest publicly-held firms in their sample, which are more comparable to our sample of firms.

In addition, they focus on the holdings of all top officers and directors. When they restrict the sample to the top of the hierarchy, they find a similar decline in ownership: the holdings of the median CEO in their sample fell from

0.09 percent of shares outstanding in 1935 to 0.06 percent in 1995.

Table 6 compares the level of total compensation to changes in an executive’s wealth

–  –  –

revaluations based on the number of shares held at the end of the previous year and firm’s stock market return during the fiscal year (adjusted for stock splits and dividends). The dollar value of these changes in wealth increased in the past 25 years as the number of shares held by corporate officers rose. For most of the post-war period, the median change in wealth—including all forms of remuneration and revaluations of stock and option holdings—was 12 to 45 percent higher than the median level of total compensation. Revaluations of stock and option holdings were larger in the 1990s, as they amounted to 68 percent of total pay.

5.2 Defining measures of pay-to-performance The empirical literature on executive compensation has used a wide range of specifications to measure the correlation between pay and firm performance.37 Two common alternatives are the dollar change in executive wealth per dollar change in firm value (or the Jensen-Murphy statistic), and the dollar amount of wealth that an executive has at risk for a one percent change in the firm’s value (or the value of equity at stake). The Jensen-Murphy statistic and the value of equity at stake are each an appropriate measure of incentives for a specific type of managerial decision.38 In a simple agency model that allows the marginal product of managerial effort to vary with the value (or size) of the firm, the optimal level of effort (or strength of managerial A limitation of our data is the lack of information on forms of wealth and earnings that are not related to compensation, such as dividends, capital gains, and non-firm related wealth. Unless otherwise specified, we use the term “wealth” throughout the paper to refer to firm-related wealth.

For a discussion of the statistics, see Jensen and Murphy (1990), Joskow and Rose (1994), Garen (1994), Hall and Liebman (1998), Murphy (1999), Aggarwall and Samwick (1999), and Baker and Hall (2004).

Both these statistics give an empirical measure of the correlation between pay and firm performance. While a higher pay-to-performance correlation will likely influence managerial actions, it is not clear that this correlation is caused by firms’ desire to provide incentives. Pay-to-performance correlations can also be the result of a bargaining or fairness model (Blanchflower, Oswald, and Sanfey 1996, Benjamin 2005). Although we cast our findings as incentives, we want to stress that we are only calculating a correlation.

incentives) depends on the type of CEO activity being considered (Baker and Hall 2004). The Jensen-Murphy statistic is the correct measure of incentives for activities whose dollar impact is the same regardless of the size of the firm, like buying a corporate jet, and the value of equity at stake is appropriate for actions whose value scales with firm size, like restructuring the firm.

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