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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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Φ ( Z ) = cumulative probability function for the normal distribution Except for the dividend rate, the interest rate, and the standard deviation of stock returns, the proxy statements generally contain all of the information necessary to implement the BlackScholes formula. However, we impute the values of an option’s duration or exercise price in some cases where this information is missing. Before 1964, the typical stock option plan granted options that expired after ten years and had an exercise price ranging from 95 to 100 percent of the market price of the stock on the day it was granted. These characteristics were fairly standard because an option with these characteristics was subject to capital gains tax rates instead of income tax rates under the 1950 Revenue Act. When the 1964 Revenue Act replaced “restricted” with “qualified” stock options, these requirements were changed to an exercise price of 100% and duration of five years. The majority of the firms in our sample revised their stock option plans to conform to these new rules. As the tax incentive to grant stock options diminished during the 1970s, firms began granting a larger number of non-qualified options with a 10-year duration. Therefore, when information on the duration of an option is missing, we assume that it was ten years if the option was granted prior to 1964 or between 1974 and 1992, and five years if it was granted between 1964 and 1973. This imputation is made for 16 percent of the sample prior to 1992, with most missing information occurring during the 1970s and 1980s. Compustat does not report the duration of option grants, so we assume a horizon of seven years for all options granted after 1992.61 Because the vast majority of the options granted after 1950 had an exercise price equal to the stock price on the day of the grant, we assume that the stock price on the day of the award is equal to the exercise price for all options grants after this year.62 For years prior to 1950, a much larger number of options were granted in-the-money.

However, we frequently do not know the exact grant date of these options so we are unable to calculate their value on the day they were granted. Instead, we value these options using the end-of-fiscal year market price.

We also impute the number of options granted in cases where the firm reported only the total number of options awarded to each executive during the previous three or five years, a reporting practice what was common from the late 1960s to the late 1980s. Wherever possible, we combine these cumulative option awards with information on annual grants and exercises from previous proxy statements to estimate the amounts granted for each executive in an individual year. However, this imputation cannot be made for executives who do not appear in all of the previous three or five proxy statements, or if the proxy statement for an intervening year is missing.63 Because roughly 27 percent of the firms in the 1970s and 20 percent of the firms in the 1980s reported options in this manner, excluding this information would severely bias downward our estimates of option grants. Instead, when we can not impute the grants and exercises for a given year, we assume that one-fifth of the 5-year totals were granted in each of We assume 7 years instead of 10 to be consistent with prior work (for example, Hall and Liebman 1998).

See Smith and Zimmerman (1976) and Murphy (1985) for further evidence that firms fix the exercise price equal to the current stock price.

We are able to back out annual data for 11 percent of the cases where only multi-year totals are reported.

the past five years, or one-third of the 3-year totals in each of the past three years. We assume that the exercise price of these options was equal to the end–of-fiscal-year stock price.

Appendix Figure A1 shows the frequency of stock option grants both including and excluding these imputed values. Our procedure raises the probability of receiving an option by 20 to 30 percentage points during the 1970s and 1980s. Including the imputations also alters the trend in the use of options, making the rise in stock option grants steeper in the 1960s and flatter in the 1980s. During periods when a large fraction of option grants are imputed, our assessment of the correlation between annual option grants (and therefore total compensation) and firm performance will be less accurate.64 Despite the substantial impact on our estimates of the frequency of option grants, this imputation strategy has only a minor effect on the value of total compensation (see Appendix Figure A2). These imputations raise the median real value of total compensation by less than \$0.1 million for most of our sample, and do not appreciably alter the long-run trend.

Options exercised: Proxy statements issued from the 1950s to the 1970s generally report the number of options exercised, the exercise price (adjusted for stock splits) and the market value of the stock on the date of purchase. Using this information, we value gains from exercising options as the difference between the exercise price and the average stock price on the day the option was exercised. The exercise price is only missing for less than two percent of the observations on stock option exercises, so we do not impute values for these cases. Proxy statements issued during the 1980s and 1990s generally report the total gains from exercising options, but not the number. In these cases, we assume the executive exercised his oldest options first in order to back out the number exercised (which is needed to estimate each executive’s stock option holdings).

Analogous to the reporting of option grants, the number of options exercised were also reported in 3- and 5-year totals during the 1970s and 1980s. We impute the number exercised from these totals using a procedure similar to the one used for option grants. Appendix Figure A3 shows the frequency of option exercises including and excluding these imputations. In this case, the biggest effect of our imputations is from the late 1960s to the late 1970s, when it raises our estimates of the frequency of options exercised by about ten percentage points.

Stock option holdings: We calculate the number of options held by an executive as the number he held the previous year plus the number granted, less the number exercised and the number that expired during the year. To value these holdings using the Black-Scholes formula, we need the exercise price and remaining duration of each option included in these holdings. These statistics are not generally reported in proxy statements, so we gather this information by following the exercise price and duration of the options each executive receives and exercises in each year. In cases for which information on the exercise price or remaining duration of an option grant is missing, we assume that the exercise price is the closing price at the end of the fiscal year of the grant year and that options granted before 1964 or after 1974 have a duration of ten years, while options granted between 1964 and 1974 have a duration of five years. This method may underestimate an executive’s total stock option holdings because many executives are likely to have been granted stock options before we observe them in our data. However, during the 1970s most firms also began to report the total number of options held by each For example, it is possible that many of the grants we attribute to the mid-1970s were actually granted in the late 1960s or early 1970s, which were times when firms were earning higher rates of return.

executive. About one third of our estimates match the reported totals exactly, and we adjust our calculated holdings to match the reported totals for the other two thirds (following Hall and Liebman 1998). Our estimates do not appear to be significantly biased, as the average difference between our estimates and the reported totals is 586 options (0.2 percent of the average number of options held for executives with positive holdings) and the median difference is zero. In cases where our estimates are greater than the reported totals, we assume that the oldest options in the portfolio were exercised first. In cases where we calculate fewer option holdings than reported, we assume that the missing options were granted in the year prior to the first year that we observe the executive.

2.4 Equity holdings Equity holdings are valued with the stock price at the end of the fiscal year. We include shares that are held by family members and associates. Equity holdings were only reported in proxy statements for officers who were also directors, and occasionally only for directors who were also up for re-election. Nonetheless, we observe stock holdings for 88 percent of our sample from 1942-2005. Because 10-K reports did not list the equity held by officers and directors, stock holdings for the 1935-41 period are based on the bi-monthly reports of the SEC, Official Summary of Security Transactions and Holdings. These reports record the equity purchases and sales of every officer and director in publicly-traded corporations and public utilities. At the time of a transaction, an officer’s total holdings of company stock are also reported. Using these reports, we collected information on the holdings of company stock of any officer who made a transaction during a year. If an officer did not appear in any reports for a given year, we assume he owned the same amount of stock as in the previous year. We obtain an initial estimate of stock holdings in 1935 from the Official Summary of Holdings of Officers, Directors and Principal Stockholders, which reports the holdings of all officers in each firm for that year. If an individual was not an officer or director in 1935, we will not observe his equity holdings until the first year in which he makes a transaction. Thus, our estimates during the 1936-41 period may be biased upward if officers with less tenure in the company held smaller shares of stock. We are able to assess the magnitude of this bias by comparing our estimated stock holding to the proxy statements issued in the 1936-41 period that did report officers’ equity holdings. Our estimated stock holdings match the proxy statements’ data about 50 percent of the time, and they do not appear to be significantly biased. The average difference between our estimates and the reported totals is 2000 shares (20 percent of the average number of shares held) and the median difference is 50 shares (three percent of the median number of shares held).

3. Evaluating the Representativeness of our Sample

3.1 Salary and Bonus Appendix Table A3 shows the distribution of the firms in our sample ranked by their market value.65 To calculate these rankings, we define the universe of firms as those in Compustat listed as being traded on the S&P, NYSE, ASE or NASDAQ. For the years prior to 1951, the universe is all firms listed in CRSP. Most firms are ranked among the 100 largest, but the sample also includes smaller firms that will either become large in future years or that were large in the past.

Despite a decline in our firms’ rankings over time, nearly half of them still ranked among the top 100 by the end of our sample period.

Results are similar when we rank firms according to their sales.

Because our sample is heavily weighted towards large firms, a natural concern is that the trends we document are not representative of the typical publicly-traded firm.66 Therefore, we evaluate the representativeness of our sample by comparing it to three other datasets that reflect compensation in the S&P 500. The first sample is the Forbes survey, which has reported the pay levels for CEOs in the 800 largest publicly-traded corporations since 1970. The second sample is from Hall & Liebman (1998), who collected data on CEO compensation from 1980 to 1994 using a random sample of 478 firms from the Forbes 500 rankings.67 Finally, we use ExecuComp, which provides data on the compensation of the highest-paid officers in the S&P 500 for the 1992-1993 period, and in the S&P 1500 since 1994. As far as we are aware, no comprehensive dataset would provide us with a useful comparison group prior to the 1970s.

Appendix Figure A4 compares the median real value of salaries and bonuses of CEOs in our sample to these three other samples for firms in three different size categories according to their market value: firms among the largest 100, firms ranked 100 to 300, and firms ranked 300 to 500. Although the level of pay in the two smaller size categories is somewhat higher in our data than in the broader samples, the trends are similar.68 From 1970 to 2005, median salary and bonus in the largest firm-size category in our sample increased at an annual rate of 4.8 percent, compared with 4.0 percent in the more representative samples. The corresponding growth rates for the mid-sized category are 2.4 percent and 2.3 percent, respectively, while they are 2.6 percent and 2.1 percent respectively for the smallest category.69 If we assume that the differential between our data and the broader samples was similar in earlier time periods, we can estimate nationally-representative trends in cash compensation for our entire sample period by reweighting firms according to the national distribution of firm size.

Appendix Figure A5 shows the trends in median compensation —again defined only as current salary and bonus payments—where each firm is assigned a weight inversely proportional to its probability of being in our sample.70 These probabilities are calculated as the fraction of firms of a given size category in our sample relative to the total number of firms in that group. We define five size categories: the largest 50, firms ranked 50-100, firms ranked 100-200, firms ranked 200-300 and firms ranked 300-500.71 Because the smallest firms in our sample are the least likely to be representative of other firms of similar size, we also consider weights scaled to reflect only the largest 300 publicly-traded firms. For most of our sample period, the median of our unweighted sample is similar to the median of the top 300 firms in the economy, while it is somewhat higher than the median of the top 500 firms. Therefore, we conclude that our data on salaries and bonuses are broadly representative of the largest 300 publicly-traded firms in the economy.

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