on performance; third, the consistent coefficient estimate for attendance in
the fixed effect model is about half the size of the OLS estimate, indicating
that attending an extra one percent of lectures increases test score by 0.04
percentage points.
In order to provide a complete description of the relationship between at-
tendance and performance, we now turn to the analysis of class attendance.
In particular, we first examine whether class attendance has an impact on
performance comparable to that of lectures, and then whether the respec-
tive roles of lectures and classes can be identified separately. In table 5, we
report estimates obtained by replacing lecture attendance with class atten-
dance (columns 1-3) and by including classes and lectures jointly (columns
4-6), comparing in both cases the results for the OLS, RE and FE models
(all results refer to the full specification that includes the complete set of
controls).
The coefficient for class attendance is positive and statistically significant
in all models reported (table 5, columns 1 to 3). The point estimate is about
0.05 for both the OLS and RE estimators, and only slightly lower (0.037)
for the FE estimator, remarkably close to the 0.039 FE estimate for lecture
attendance reported in table 4. Interestingly, in this case the Hausman test
does not reject the random effects model against the fixed effects model. This
result indicates that, contrary to lecture attendance, class attendance is not
significantly correlated with unobservable factors. One possible explanation
for this result is that the decision to attend classes is less related to ability,
given that it is commonly believed by students that class attendance has a
higher return than lecture attendance for exam performance. Overall, the
results suggest that the effect of class attendance on performance is significant
and quantitatively similar to that of lecture attendance: an extra percentage
point of class attendance increases test score by about 0.05 percentage points.
Next, we consider the estimates obtained inserting lectures and classes
jointly in the full specification, to assess whether the respective roles of lec-
tures and classes can be identified independently. As in the previous case,
the OLS and RE estimates are quite similar (about 0.05 and 0.03 for lecture
and class attendance, respectively), and the Breusch-Pagan LM test statistic
strongly rejects OLS against RE. These results would seem to indicate that
lecture and class attendance have independent effects on performance, and
that lectures have a larger impact than classes.25 However, the Hausman
25Note, however, that the difference between the 0.051 and 0.030 estimates for lectures
15