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

Studies that focus solely on compensation and ignore revaluations of equity and option holdings often report a third measure of incentives: the percentage change in compensation for a 1 percent change in firm value (the elasticity of compensation). An analogous measure that includes revaluations of wealth would be the elasticity of wealth to firm performance (i.e. the percentage change in wealth for a percentage change in firm value). A log-log functional form for incentives can be obtained theoretically as the optimal contract if utility is CRRA (Himmelberg and Hubbard 2000) or from a model that embeds incentive pay in a competitive labor market (Edmans, Gabaix, and Landier 2007).39 However, calculating this measure is problematic because we do not observe the level of an executive’s total wealth but only firmrelated wealth. If non-firm-related assets trended upward or downward over the century, ignoring these forms of wealth would lead to a systematic bias in our estimates of the level of total wealth, and consequently a bias in estimates of the percent change in wealth. Therefore, we focus on the Jensen-Murphy statistic and the value of equity at stake, but we return to this issue in Section 5.5 by calculating the elasticity of changes in wealth to firm performance.40

5.3 Estimating pay-to-performance correlations An additional benefit to calculating the elasticity is that it is not sensitive to changes in firm size, as are the other two measures we consider.

This concern is less important for the other two measures of pay-to-performance because the correlation between changes in non-firm related wealth and firm performance is less likely to have changed over time.

The value of equity at stake is the dollar value of wealth that an executive has at risk for a one

**percent change in firm value. We estimate this statistic as β tES from the following regression:**

where the firm’s j (real) rate of return during fiscal year t, r jt, measures the percentage change in firm market value.41 To assess how βtES has changed over time, we estimate the regression separately for the periods 1937-40, 1941-1949 (excluding 1946), 1950-59, 1960-69, 1970-1979, 1980-1989 and 1990-1999, and 2000-2005.42 The dependent variable is the change in the real value of all types of an executive’s firm-related wealth, calculated as the sum of total compensation (salaries, bonuses, long-term incentive pay and stock option grants), changes in the value of stock option holdings, and changes in the value of firm stock holdings.

We use a similar regression to estimate the Jensen-Murphy statistic, where the firm’s rate

**of return is replaced by the dollar change in the market value of the firm:**

where we measure the dollar change in shareholder value as r jtV j,t −1, firm’s j rate of return during fiscal year t multiplied by firm’s j market value in the previous year.

Because the distributions of compensation and wealth are highly skewed, OLS regressions will not provide an accurate picture of the pay-to-performance sensitivity facing the We ignore issues of repurchases of shares during the fiscal year, and use the rate of return to approximate the percentage change in firm value.

The distribution of rates of return in our sample of firms is unusually low and highly skewed in 1946, possibly due to the end of war contracts. Therefore, we exclude this year from all regressions. When this year is included, the Jensen-Murphy statistic estimated over the 1944-1948 period falls from $0.44 to $0.24, and the value of equity at stake goes from $8,664 to $7,822. Therefore, our finding of an unusually low pay-to-performance correlation in the 1940s would only be strengthened by including 1946.

typical executive in our sample.43 Therefore, we estimate equations [2] and [3] using a quantile regression to fit the conditional medians of the data.44 Table 7 reports coefficient estimates and standard errors for the Jensen-Murphy statistic and the value of equity at stake.45 With the exception of the first and last decades of the sample, the magnitude of the standard errors suggests that the coefficients are significantly different from one another.46 In accordance with prior research, both measures show a large increase in pay-to-performance during the 1980s and 1990s (Hall and Liebman 1998, Murphy 1999).47 However, a historical perspective reveals a more nuanced picture. The value of equity at stake trended upward over time, while the JensenMurphy statistic followed a U-shaped pattern over the century.48 The correlation between pay and performance has been mainly driven by stock and stock option revaluations (see Table 8). Prior to the 1970s, equity holdings were the primary factor linking executive wealth to firm performance. Pay-to-performance has strengthened over time with the increase in the number of options held by executives, and options have become the most important type of wealth tying pay to performance in recent decades. However, the role of equity holdings is still significant, and their correlation with firm performance has also increased in recent decades.

For example, Aggarwall and Samwick (1999) find that OLS estimates of pay-performance sensitivities are between 2 to 7 times larger than those obtained from median regression.

Alternatively, we computed a robust regression that uses Huber and biweight iterations to down-weight large outliers (the rreg command in Stata), and estimated an OLS regression after trimming the highest and lowest percentiles from the distribution of changes in wealth. These methods yielded similar results.

Standard errors are bootstrapped, and account for correlation of observations within the firm.

The estimates for the 1930s do not appear to be significantly different from the 1940s, and the 2000s may not be different from the 1990s. The larger standard errors in these decades may be due to smaller sample sizes in these periods. Extreme heteroskedasticity prevents estimation of the entire sample in one regression to directly test the significance of the changes in the coefficients over time.

Our estimates of the value of equity at stake are consistent with those reported by Hall and Liebman (1998), but the Jensen-Murphy statistic is smaller. This discrepancy is partly due to larger firm size in our sample. Limiting our data to CEOs between 1993 and 1995, we obtain an estimate of $1.11 for a $1000 increase in firm value in firms among the top 100 of the S&P 500, $2.62 in firms ranked from 100 to 200, and $3.37 for the smallest firms in our sample. Hall and Liebman report a sensitivity of $5.29 for 1994, which is based on a random sample of about 500 of the largest firms between 1980 and 1994.

The trends in pay-to-performance are similar for both CEOs and other top executives.

5.4 Accounting for changes in the size of firms over time The divergence between these two measures of pay-to-performance prior to the 1970s is partly due to growth in the size of firms. While the Jensen-Murphy statistic tends to be negatively correlated with firm size, the value of equity at stake is higher for larger firms.49 Because the average market value of the firms in our sample increased by a factor of 3.5 from 1936 to 1970, it is not surprising that the value of equity at stake increased while the Jensen-Murphy statistic declined over this period. On the other hand, both measures rose from the 1970s to the 2000s despite another 3.5-fold increase in firm size. Thus, the growth in pay-to-performance during the past 30 years was strong enough to offset the natural downward trajectory of the Jensen-Murphy statistic as firms became larger.

To correct the long-run trends in pay-to-performance for the secular increase in firm size, we develop a regression-based method that relies on estimating pay-to-performance correlations for firms in specific size categories in each decade, and then comparing estimates for a given firm size from one decade to the next (see Appendix Section 4 for details). Since our firm-size adjustments are formed by comparing pay-to-performance correlations in subsequent decades, they do not provide size-adjusted estimates of the level of these correlations but only estimates of how these correlations would have changed over time if firm size had remained the same.

Therefore, we index both the Jensen-Murphy statistic and the value of equity at stake to equal one in the 1930s and use average size-adjusted growth rates in pay-to-performance to obtain a new index value in each successive decade (see Figure 6). For comparison, the dashed lines in Figure 6 show indexes based on growth in the unadjusted statistics.

Executives’ wealth constraints and risk aversion are plausible explanations for the well-known negative correlation between the Jensen-Murphy statistic and firm size (Demsetz and Lehn 1985, Schaefer 1998). See Baker and Hall (1998) for further discussion of the value of equity at stake.

Adjusted for firm size, pay-to-performance followed a W-shaped pattern from the 1930s to the 1980s: its magnitude was about the same in the 1930s, the 1950s, the 1960s and the 1980s, and was somewhat lower in the 1940s and the 1970s. This pattern is largely driven by

strengthened considerably in the 1990s and 2000s, mostly due to a rising contribution from stock option wealth. Thus, even after accounting for changes in firm size, the pay-to-performance correlation was higher in the last 15 years of our sample than in any previous period.50 The unusually low correlations in the 1940s and 1970s are not easy to explain. Although the correlation in the 1940 to 1945 period may have been held down by war-related compensation practices, we find low pay-to-performance for the 1946 to 1949 period as well.

Thus, the war could only explain this lower correlation if its effects persisted for the entire decade. Alternatively, the decline in incentives in the 1940s and 1970s might be driven by a prevalence of negative economic shocks if executives’ wealth responds more strongly to improvements than to deterioration in firm performance. However, this explanation is also unlikely because we obtain the same W-shaped pattern when estimating pay-to-performance with only positive changes in firm outcomes.51

5.5 Quantifying the size of the pay-to-performance correlation In the standard principal-agent model, the optimal degree of managerial incentives is based on a number of unobservable factors such as the agents’ risk aversion and the cost of managerial effort. Therefore, there is no theoretical benchmark of the “optimal” degree of pay-toThe small sample size for the 2000-2005 period makes it difficult to tell whether this increase reflects a transitory spike in pay-to-performance or whether it will be long lasting.

Jensen and Murphy (1990) interpret the low degree of pay-to-performance in the 1970s relative to the late 1930s as the result of political constraints following the increase in pay disclosure in 1942. The significantly higher correlations that we find in the 1950s and 1960s suggest that this was not the case.

performance against which to contrast our results (Haubrich 1994). Nevertheless, we gauge the strength of incentives by calculating an executive’s monetary return for a meaningful improvement in firm performance. Following Hall and Liebman (1998), we define a meaningful (but modest) improvement in firm performance as a movement from the median rate of return to the 70th percentile rate of return.

To estimate the wealth at stake from this improvement, we calculate the dollar change in each executive’s stock and option holdings if the price of the firm increased from the median rate of return in our sample (8.4 percent) to the 70th percentile rate of return (22.7 percent).52 The median change in wealth across executives was over $2 million in the 1990s and 2000s, but considerably smaller in earlier decades (col. 1 of Table 9). Even though the dollar value of these changes in wealth rose significantly over time, the upward trend is not as steep when comparing these dollar values to a broad measure of compensation that includes salaries, bonuses, stock option grants, and revaluations of stock and options holdings at the median rate of return (col. 2).

With the exception of the 1940s, an improvement in firm performance from the 50th to the 70th percentile has typically led to at least a 30 percent increase in this broad measure of compensation.53 Moreover, the executive’s return to this improvement in firm outcomes was about 50 percent of broad compensation in the 1960s, about as high as it was in the 1990s. Thus, the incentive for an executive to undertake actions leading to an improvement in firm performance of this magnitude has been substantial for most of our sample period. In other words, it appears that managerial incentives have not been “wildly inefficient” for most of the 20th century, to paraphrase Hall and Liebman.

Table 8 shows that revaluations of stock and stock options account for virtually all of the relationship between wealth and performance. Therefore, we ignore changes in compensation for this exercise.

Although the median percent increases in the 1970s and in the 1980s are about the same, the pattern is U-shaped from the early 1970s to the late 1980s. Thus, we find a steady increase in managerial incentives from the mid-1970s to the late 1990s, a result consistent with Hall and Liebman’s 1980-1994 estimates.

Finally, we divide the percent increase in compensation broadly defined (col. 2 of Table

9) by the improvement in the rate of return from the median to the 70th percentile of performance. Because the numerator is calculated from changes in wealth as opposed the level of wealth, this measure reflects the elasticity of changes in wealth, a concept related to the elasticity of wealth discussed above. This elasticity was greater than 1.9 for every decade in our sample except the 1940s, and almost as large in the 1960s as it was in the 1990s and 2000s.

Thus, this measure of pay-to-performance also suggests that managerial incentives were not small for most of the 20th century.