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

One potential worry is that our trends are biased by reflecting the compensation in firms that will become successful around 1940, 1960 and 1990. However, we do not find differential patterns when we split the firms into subsamples based on the year of selection into the sample, or when we restrict the data for each firm to the period after the year for which it was selected into the sample.

Hall and Liebman (1998) expanded on a sample of 792 firms constructed by Yermack (1995).

This difference can be partly explained by the larger size of the firms in our sample, but a small differential between the samples (about 10 to 15 percent) remains even after controlling for firm size in a regression framework.

Using ExecuComp we find that the trend in salaries and bonuses in our sample is similar to a broader set of publicly-traded firms not just for CEOs but also for the three highest-paid executives.

Results are similar when we use weights inversely proportional to a firm’s market share.

For example, in 1950 we have 38 firms ranked among the largest 50, so any firm in this category is given a weight of 50/38.

3.2 Stock Options We are only able to evaluate the representativeness of stock option grants in our sample from 1980 to 2005 because the Forbes survey does not report information on option grants. Appendix Figure A6 compares the median value of stock option grants in our sample to the Hall-Liebman and ExecuComp datasets. Our data line up well with the other samples for firms ranked among the 100 largest, but our estimates of grants in smaller firms are somewhat larger than the HallLiebman sample in the 1980s. For the smallest group of firms, our estimates are also noisy due to the small sample size.

The discrepancy in the use of stock options can be partly attributed to our imputation of option grants from the multi-year totals reported in the proxy statements (see Section 2.3 above).

This imputation smooths out grants over a period of several years, raising the frequency of stock option grants. In the Hall-Liebman sample, firms that reported multi-year totals were contacted by mail to provide annual information. Due to a high response rate to this inquiry, the HallLiebman sample has few cases where annual option grants are unknown.72 Although option grants were probably lumpier than our data suggest, the total value of options granted to each individual in our sample should be accurate. Among the 45 firms that appear in both our sample and the Hall-Liebman datasets, the average value of options granted from 1980 to 1989 was $0.42 million in our data, compared with $0.40 million in the Hall-Liebman data.

A second reason why we find a greater extent of option use in the 1980s may be that the use of stock options in the smaller firms in our sample may not be representative of a typical publicly-traded firm of a similar size. Since our sample consists of firms that were successful in at least one point in time, some of the smaller firms in our sample may be experiencing a temporary negative shock. Because stock option policies typically last for several years, option grants in these firms may look more similar to larger firms than to firms that have always been small. Indeed, the Hall-Liebman sample shows a more pronounced positive correlation of option grants with firm size (see Appendix Table A4). Thus, the composition of pay in firms smaller than the top 100 in our data may be more heavily weighted towards options than the typical publicly-traded firm in the economy.

Although no nationally-representative data on stock option grants exist prior to the 1980s, Lewellen (1968) calculates the value of options in a sample of 50 large manufacturing firms from 1940 to 1963. He finds a much higher value of stock options than we find in our sample.

This disparity can be explained by differences in the methodologies of valuing options. Whereas we use the Black-Scholes formula to value options in the year they are granted, Lewellen calculates the difference between an option’s exercise price and the market price of the company’s stock at the end of each fiscal year, and then spreads these potential gains from stock appreciation over the duration of the option.73 Gains from exercising options were significantly higher than the value of grants during this period, so this ex-post valuation method overstates the value of option grants. More importantly, Lewellen’s statistics greatly overstate the value of options because he reports a “before-tax equivalent value,” which he defines as the before-tax value of salaries that an executive would need to receive in order to achieve an after-tax level of pay equivalent to the potential gains from exercising his stock options. Because options were We thank David Yermack for providing information on this topic.

A potential concern is that investors did not have access to the Black-Scholes formula prior to 1973. However, this does not imply that investors did not have an understanding of derivative pricing. For example, Moore and Juh (2006) find that investors were able to determine the fair value of warrants traded in the Johannesburg Stock Exchange in the early twentieth century.

taxed at a much lower rate than cash salaries, this valuation is substantially larger than the simple (before-tax) value of option grants that we use in our analysis.

3.3 Total Compensation To assess the effect that the possible overestimation of stock option grants in small firms may have on our measure of total compensation, we calculate an alternative value of grants using the relationship between option grants, total pay, and firm size in the Hall-Liebman sample. For all firms ranked lower than 100, we assume the share of option grants in total compensation to be proportional to the average share of grants in firms ranked in the top 100 in that year. This proportion is based on the Hall-Liebman sample, which we calculate separately for the periods 1980-84 and 1985-89. By splitting the data into these two periods, we smooth through the noise in annual grants while still accounting for the spread of options to smaller firms over time.

Because we have no other evidence on option grants prior to 1980, we apply the 1980-84 shares in the Hall-Liebman data to all years prior to 1980. For example, for a firm ranked 150th in 1984 or in any prior year, we assume that the share of options in total pay is 0.101/0.164=62 percent of the share of option grants in the largest 100 firms in that year (see Appendix Table A4). For 1990 onwards we use actual option grants because our data are similar to the Hall-Liebman and ExecuComp data in that period. We also use actual option grants for firms ranked in the top 100 because our data are not biased in large firms.

Appendix Figure A7 compares median compensation of the three highest-paid officers in each firm in our unweighted sample to total pay using this alternative assumption for stock option grants. The alternative assumption reduces the level of pay a bit in the 1950s through the 1980s, but the effect is minor. The figure also shows the alternative compensation measure weighted to reflect the largest 300 publicly-traded firms using the probability weights discussed in Appendix Section 3.1. By using both the probability weights and the alternate stock option assumption, this series reflects our best estimate of the long-run trend in compensation in large publicly-traded firms. Although the combination of reweighting and adjusted stock option grants reduces our estimates of compensation by about ten percent in the years prior to 1990, this decrease does not alter the long-run trend in executive pay in any meaningful way. Therefore, we conclude that the unweighted statistics we present in the main body of the paper accurately reflect the trends in compensation in the 300 largest publicly-traded firms in the economy.

Because our data present a reasonably accurate picture of compensation in large firms, we can approximate alternate sampling schemes by assigning different weights to the firms in our sample. In Appendix Table A5, we report sampling schemes that are inversely proportional to either the firm’s market share or the firm’s share of aggregate sales. These weights would be appropriate if a firm’s probability of selection was proportional to its market value or to its value of sales, respectively. The table reports median total pay separately for firms ranked in the top 100 and for firms ranked between 100 and 300. For comparison, we also report medians for each of these groups using weights based on the probability of selection into our sample, as described in Section 3.1. All columns in the table use the alternate estimate of option grants based on the Hall-Liebman data. The trends in pay are similar for all weighting schemes.

Appendix Table A5 reveals some interesting differences between the largest publiclytraded firms and the somewhat smaller firms. The differential in pay between these two groups was roughly stable from 1950 to 1979, but has widened noticeably during the past 25 years. This gap was also larger prior to World War II. In fact, median compensation in the smaller group increased from the 1930s to the 1940s while the level of pay in the largest firms fell. Therefore, the decline in the real value of compensation that we document for this period in the main body of this paper was concentrated in the very largest firms in the economy. More generally, differentials in pay by firm size have followed the well-documented U-shaped pattern in income inequality over the course of the century, contracting during World War II and widening in recent decades.

4. Correcting pay-to-performance estimates for growth in firm size The two main statistics used to measure pay-to-performance—the Jensen-Murphy statistic and the value of equity at stake—are both correlated with firm size. Because the scale of firms has increased substantially over the course of the century, it is important to account for changes in firm size when analyzing the long-run trends in pay-to-performance. We use a regression-based method to correct our pay-to-performance estimates for changes in the size of firms. The basic idea of this strategy is to estimate pay-to-performance correlations for firms in specific size categories in each decade, and then to compare estimates for a given firm size from one decade to the next.

** To adjust the Jensen-Murphy statistic we interact the change in market value in equation [2] with a spline function based on quintiles of the firm-size distribution, as follows:**

Δ( Exec. Wealth) ijt = α tJM + β tJM Δ( Shareholder Value) jt + + ∑ β tJM, s Δ( Shareholder Value) jt I s + ∑ θ ts I st + ε ijt s s where Is are dummy variables for quintiles of the distribution of firm size in each decade. We measure firm size as the average market value of the firm during the previous three years. For each firm in our sample, we predict a Jensen-Murphy statistic as the fitted value from this regression. We also predict an alternative Jensen-Murphy statistic for each firm using the coefficient estimates and the distribution of firm size from the previous decade. The difference between these two estimates reflects the change in the Jensen-Murphy statistic for each firm of a given size.

For example, a firm with a market value of $3.1 billion in the 1960s falls in the 24th percentile for that decade, and so it would have a predicted Jensen-Murphy statistic of β 60 + β 60,21− 40. The same firm would have fallen in the 57th percentile of the 1950 distribution JM JM of firm size, and so its predicted Jensen-Murphy statistic for prior decade would be β 50 + β 50,41−60. The difference between these two statistics reflects the change in pay-forJM JM performance from the 1950s to the 1960s for this firm.

This method generates a range of estimates of changes in pay-to-performance based on the distribution of firm sizes in our data. Appendix Table A6 reports the mean and median change in pay-to-performance across all of the firms in our sample, along with the predicted change in pay-to-performance at the median firm size in each decade. All three statistics provide a similar picture of the evolution of pay-to-performance over time.74 The index shown in Figure 8 of the paper is based on the average across firms, because we believe the average provides the The only exception is that the median percent change in the Jensen-Murphy statistic appears to be lower in the 2000s than in the 1990s, while it is higher for all the other statistics of pay-to-performance.

best estimate of the typical change in pay-to-performance in our sample.75 We follow a similar technique to adjust the value of equity at stake for changes in firm size.76 The median change in pay-to-performance may not be representative of a typical firm since it may occur in a firm that is unusually large or unusually small for that decade. We prefer the average change over the change at the median firm size because the former uses information across the entire distribution of firm sizes, rather than information only at a single point.

An alternative methodology would be to compare the pay-for-performance estimates in two successive decades using a subsample of firms of similar size. One problem with this method is that the type of firms that appear in the upper part of the distribution in one decade may be systematically different from small firms in the subsequent decade. Nevertheless, results are similar when we follow this strategy.

Note. The change in the pay-to-performance correlation for each firm is the percent change in simulated pay-to-performance correlations from the previous decade to the current decade. Simulated correlations for each firm are the fitted values from a regression including interactions of firm performance with a spline function of firm size (using five size categories). Simulated values for the previous decade are the coefficient estimates from the previous decade multiplied by an indicator variable for the firm’s position in the previous decade’s distribution of firm size. Estimates are based on median regressions estimated separately for each decade. Firm size is defined as average market value in the prior three years. The change in executive wealth is defined as the sum of total compensation and the revaluation of stock and stock option holdings. The year 1946 is excluded from all calculations; see footnote 42 for details.

Note: Based on the three highest-paid executives in the largest 50 firms in 1940, 1960, and 1990.