Berry and Fowler (2021) “Leadership or luck? Randomization inference for leader effects in politics, business, and sports” in Science Advances propose a method they call RIFLE for testing the null hypothesis that leaders have no effect on organisation performance. The method is robust to serial correlation in outcomes and leaders, but not to endogenous leader turnover, as Berry and Fowler honestly point out. The endogeneity is that the organisation’s performance influences the probability that the leader is replaced (economic growth causes voters to keep a politician in office, losing games causes a team to replace its coach).
To test whether such endogeneity is a significant problem for their results, Berry and Fowler regress the turnover probability on various measures of organisational performance. They find small effects, but this underestimates the endogeneity problem, because Berry and Fowler use linear regression, forcing the effect of performance on turnover to be monotone and linear.
If leader turnover is increased by both success (get a better job elsewhere if the organisation performs well, so quit voluntarily) and failure (fired for the organisation’s bad performance), then the relationship between turnover and performance is U-shaped. Average leaders keep their jobs, bad and good ones transition elsewhere. A linear regression finds a near-zero effect in this case even if the true effect is large. How close the regression coefficient is to zero depends on how symmetric the effects of good and bad performance on leader transition are, not how large these effects are.
The problem for the RIFLE method of Berry and Fowler is that the small apparent effect of organisation performance on leader turnover from OLS regression misses the endogeneity in leader transitions. Such endogeneity biases RIFLE, as Berry and Fowler admit in their paper.
The endogeneity may explain why Berry and Fowler find stronger leader effects in sports (coaches in various US sports) than in business (CEOs) and politics (mayors, governors, heads of government). A sports coach may experience more asymmetry in the transition probabilities for good and bad performance than a politician. For example, if the teams fire coaches after bad performance much more frequently than poach coaches from well-performing competing teams, then the effect of performance on turnover is close to monotone: bad performance causes firing. OLS discovers this monotone effect. On the other hand, if politicians move with equal likelihood after exceptionally good and bad performance of the administrative units they lead, then linear regression finds no effect of performance on turnover. This misses the bias in RIFLE, which without the bias might show a large leader effect in politics also.
The unreasonably large effect of governors on crime (the governor effect explains 18-20% of the variation in both property and violent crime) and the difference between the zero effect of mayors on crime and the large effect of governors that Berry and Fowler find makes me suspect something is wrong with that particular analysis in their paper. In a checks-and-balances system, the governor should not have that large of influence on the state’s crime. A mayor works more closely with the local police, so would be expected to have more influence on crime.