although the relevant coefficients lack significance for some of the output measures, the
signs of the relevant coefficients in all the regressions are in line with these two theories.
For minutes played, negative binomial regression results are reported in column 2 of
Table 5.36 The coefficient of qualified * natteam(1 — natteam) is positive and significant
at the 5% level. The coefficient of qualified * natteam is negative and significant at the
1% level. Interestingly, the interactions of natteam and natteam(1 — natteam) with the
variable af ter that indicates the treatment period are significant as well, but have the
opposite signs of the interactions with qualif ied. We interpret this as a consequence
of the substitution effect between different player groups described above: for the total
number of minutes to remain constant, some players in the treatment group must be
affected. Our results suggest that the impact on players in the control group depends on
their ability which in turn is correlated with natteam; teams seem to substitute minutes
between players in treatment and the control group of roughly similar abilities.
Given the non-linear nature of the estimator, marginal effects depend on the values of
all variables, and interpreting interaction terms is more difficult than before. The ratio of
the marginal effects of any two regressors are constant, however, and equal to the ratio of
the estimated coefficients. This property permits us to evaluate the sign of the impact of
the Euro Cup treatment on a player, given his value of natteam. The relative sizes of the
estimated coefficients of qualif ied * natteam and qualif ied * natteam(1 — natteam) imply
that if 0 < natteam < 0.59 then the effect of the Euro Cup treatment is positive, but it
is negative for higher values of natteam. Hence, the results again confirm the nomination
contest theory as well as the injury theory.
Table 8 reports results of regressions on output per minute played that test for dif-
ferential treatment effects depending on age. For several output measures, we find that
ceteris paribus the treatment effect is stronger the younger a player, and that the av-
erage effect is positive for players of below-average age but negative for older players.
For minutes played, reported in the third column of Table 5, the estimated coefficient is
again negative but insignificant. Results of regressions using age dummies for different
percentiles of the age distribution instead of the (demeaned) age variable exhibit similar
patterns: the effect is weaker and often even negative for older players than for younger
players. We found no consistent evidence of a stronger effect for players of median age as
compared to the youngest players, as the theoretical results illustrated in Figure 2 would
36 OLS estimates of the same regression equations with ln (minutes played + 1) as the dependent vari-
able are qualitatively similar.
34