Alternative age change groups

The definition of the three age change groups plays a key role in the present study’s examination of the occurrence and economic magnitude of the effect that CEO age has on firm risk. I base the main definition on the tercile thresholds of the distribution of the change in CEO age while sorting the threshold events into the respective lower categories. To ensure that my results are not simply driven by this particular choice, I test the following two alternative definitions.²⁹ First, I redefine the age change groups by sorting the events that lay on the tercile thresholds of -4 and -13 into the respective upper categories. The Increase/Stable group then comprises 47 events with changes in age from -4 to 20, theModerate Decrease group 43 events with changes in age from -13 to -5, and the Large Decreasegroup 41 events with changes in age from -35 to -14.

When I use these alternative tercile groups and perform the analyses from Section 2.4 again, the results remain basically unchanged.

Second, since the tercile groups to some extent still combine events that differ with respect the change in age, I define alternative groups based on quartiles. Therefore, I take the quartile thresholds of -15, -9, and -1 to define the four groupsIncrease [0;20],Decrease [-8;-1],Decrease

29Most of the results are unreported but are available upon request.

Table 2.10: Tests of the parallel trends assumption Panel A: Placebo treatments

Post, if year≥τ−2 Post, if year≥τ−1

(1) (2) (3) (4)

Volatility Volatility Volatility Volatility Treated×Postτ−3×Non-Retirement Age CEO 0.0093 -0.0152

(0.9950) (0.9923) Treated×Postτ−3×Retirement Age CEO 0.4510 1.8053

(0.8160) (0.3622)

Treated×Postτ−2×Non-Retirement Age CEO 0.3060 0.2424

(0.8621) (0.8959)

Treated×Postτ−2×Retirement Age CEO 1.1420 1.9462

(0.5404) (0.3195)

Firm Controls No Yes No Yes

Year Fixed Effects Yes Yes Yes Yes

Firm Fixed Effects Yes Yes Yes Yes

Number of Firms 166 166 166 166

Number of Observations 636 636 636 636

Adj. R-Squared 0.3175 0.3460 0.3179 0.3459

Panel B: Yearly treatment effects

Benchm. τ−3|4 Benchm. τ−2|3|4

(1) (2) (3) (4)

Volatility Volatility Volatility Volatility Treated×Yearτ−2×Non-Retirement Age CEO -1.2210 -1.3551

(0.4640) (0.4226)

Treated×Yearτ−1×Non-Retirement Age CEO -1.7627 -2.4235 -1.2883 -1.9149 (0.3317) (0.1752) (0.4296) (0.2445) Treated×Post×Non-Retirement Age CEO -2.7681 -3.4201* -2.2527 -2.8717

(0.1846) (0.0881) (0.2353) (0.1144) Treated×Yearτ−2×Retirement Age CEO -1.5430 -0.4605

(0.5143) (0.8480)

Treated×Yearτ−1×Retirement Age CEO -0.5234 0.3893 0.0875 0.6155 (0.8273) (0.8713) (0.9690) (0.7828) Treated×Post×Retirement Age CEO 5.5838* 6.2479** 6.2044** 6.4903***

(0.0736) (0.0299) (0.0209) (0.0051)

Firm Controls No Yes No Yes

Year Fixed Effects Yes Yes Yes Yes

Firm Fixed Effects Yes Yes Yes Yes

Number of Firms 166 166 166 166

Number of Observations 1,264 1,264 1,264 1,264

Adj. R-Squared 0.2818 0.3189 0.2824 0.3196

This table presents the results from tests of the parallel trends assumption. All tests in this table are performed on the subsample of long-tenured deceased CEOs and are based on the retirement age analyses. Panel A presents placebo tests on the pre-event sample with placebo treatments inτ−2 (Models (1) and (2)) andτ−1 (Models (3) and (4)). Panel B illustrates tests including yearly treatment effects for the single pre-event yearsτ−2 and τ−1 for each of the two groups. In all models, the dependent variable isVolatility. Definitions for the DID specifications can be found in the legends of Table 2.5, while Table A.2 in Appendix A.2 illustrates definitions for the (omitted) firm controls. All models include firm and year fixed effects, as well as a constant term. The p-values are based on standard errors clustered at the firm-level and are reported in parentheses, with *, **, and

*** indicating significance levels of 10%, 5%, and 1%, respectively.

[-14;-9], and Decrease [-35;-15], which comprise 30, 32, 36, and 33 events, respectively. Notably, unlike the tercile groups, this categorization explicitly differentiates between increases and decreases in CEO age. I then use these quartile groups and re-perform my analyses. Table 2.11 presents the volatility results.

Table 2.11: Effect on volatility by age change groups based on quartiles Overall Volatility Idiosyncratic Volatility

(1) (2) (3) (4)

Volatility Volatility IdioVol IdioVol Treated×Post×Increase [0;20] -5.1143** -5.0482** -4.5480** -4.5838**

(0.0197) (0.0160) (0.0251) (0.0161) Treated×Post×Decrease [-8;-1] 2.8016 2.7507 3.2088 3.1246

(0.2141) (0.2088) (0.1575) (0.1493) Treated×Post×Decrease [-14;-9] -0.5609 -1.0726 -0.9227 -1.5268

(0.7620) (0.5563) (0.5767) (0.3466) Treated×Post×Decrease [-35;-15] 4.1052* 4.8481** 3.8215 4.5271**

(0.0800) (0.0286) (0.1121) (0.0402)

Firm Controls No Yes No Yes

Year Fixed Effects Yes Yes Yes Yes

Firm Fixed Effects Yes Yes Yes Yes

Number of Firms 261 261 261 261

Number of Observations 1,929 1,929 1,929 1,929

Adj. R-Squared 0.2825 0.3040 0.2205 0.2518

This table presents DID analyses for the effect of CEO age on firm risk. In the regressions the treatment effect is split for four age change groups. In all models, the dependent variable isVolatility. Treated is a dummy variable equal to one for firms that experienced a sudden death and zero for the control firms. Postis a dummy variable equal to one for the four years after and zero for the four years prior to the event. Increase [0;20],Decrease [-8;-1], Decrease [-14;-9], andDecrease [-35;-15]are dummy variables equal to one for treated firms with a change in CEO age of 0 to 20, -8 to -1, -14 to -9, and -35 to -15, respectively, and zero otherwise. Definitions for the (omitted) firm controls can be found in Table A.2 in Appendix A.2. All models include firm and year fixed effects, as well as a constant term. Thep-values are based on standard errors clustered at the firm-level and are reported in parentheses, with *, **, and *** indicating significance levels of 10%, 5%, and 1%, respectively.

The results are in line with the findings of the main analyses. Specifically, they highlight that the effect of an increase in volatility mainly occurs when CEO age decreases to a large extent.

Moreover, they provide additional evidence for the group of firms that increased CEO age. This group experienced a decline in volatility following the CEO turnover, which further supports the notion of a negative relation between CEO age and firm risk. Besides, the (unreported) results for the tests of the two alternative explanations also generally confirm the earlier findings, albeit with slightly reduced statistical significance. Overall, the results are robust to alternative definitions of age change groups.