56 K. Li and N.R. Prabhala
- Panel data with fixed effects
In self-selection models, the central issue is that unobserved attributes that lead firms to
self-select could explain variation in outcomes. In panel data settings, we have multiple
observations on the same firm over different periods. If the unobservable attributes are
fixed over time, we can control for them by including firm fixed effects. Applications
of fixed effect models in corporate finance includeHimmelberg, Hubbard and Palia
(1999), Palia (2001), Schoar (2002), Bertrand and Mullainathan (2003), andÇolak and
Whited (2005). There are undoubtedly many more. One question is whether the use of
such fixed effect models alleviates self-selection issues. Not necessarily, as we discuss
next.
There are two main issues with using firm fixed effects to rule out unobservables. One
is that the unobservables should be time invariant. When time invariant effects exist and
ought to be controlled for, fixed effect models are effective. However, time invariance is
unlikely to be an appropriate modeling choice for corporate events where unobservables
are not only time varying but also related to the event under consideration. Furthermore,
unobservables often have a causal role in precipitating the corporate finance event being
studied. For instance, in the framework ofMaksimovic and Phillips (2002),firmsdiver-
sify or focus because they receive an unobserved shock that alters the optimal scope
of the firm. Thus, in studying conglomerate diversification or spinoffs, the central un-
observable of importance is the scope-altering shock. It is time varying and it leads to
the event of interest—diversification. Including time-invariant firm fixed effects does
nothing to address such event-related unobservable shocks. This point also applies to
the difference-in-difference methods related to fixed effects. They do not account for
event-related self-selection. Such methods are just not designed to capture time-varying
and event-related unobservables, which are, in contrast, the central focus of selection
models.^18
A second issue with fixed effect models is statistical power. Models with fixed effects
rely on time variation in RHS variables and LHS outcomes for a given firm. Thus,
fixed effect models often have limited power when the underlying variables vary slowly
over time. In this scenario, causal effects, if any, are primarily manifested in the cross-
section rather than time series.Zhou (2001)presents an argument on these lines with an
empirical application. Thus, it appears especially important to take a more careful look
at the lack of power as an explanation for insignificant results when using fixed effects.
It should also be pointed out that the regressionR^2 in fixed effects regressions could
easily lead to misleading impressions of the strength of an economic relation.^19
(^18) A related issue is the use of period-by-period estimates of Heckman-style selection models in panel data.
Imposing such a structure imposes the assumption that the period-by-period disturbances are pairwise uncor-
related with next-period disturbances, which may not necessarily be realistic.
(^19) Most cross-sectional studies in corporate finance with reasonable sample sizes report a modestR (^2) when
there are no fixed effects. However when one adds fixed effects, there is often an impressive improvement in