<s>
In	O
statistics	O
,	O
a	O
fixed	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
is	O
a	O
statistical	O
model	O
in	O
which	O
the	O
model	O
parameters	O
are	O
fixed	O
or	O
non-random	O
quantities	O
.	O
</s>
<s>
This	O
is	O
in	O
contrast	O
to	O
random	B-General_Concept
effects	I-General_Concept
models	I-General_Concept
and	O
mixed	B-General_Concept
models	I-General_Concept
in	O
which	O
all	O
or	O
some	O
of	O
the	O
model	O
parameters	O
are	O
random	O
variables	O
.	O
</s>
<s>
In	O
many	O
applications	O
including	O
econometrics	O
and	O
biostatistics	O
a	O
fixed	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
refers	O
to	O
a	O
regression	O
model	O
in	O
which	O
the	O
group	O
means	O
are	O
fixed	O
(	O
non-random	O
)	O
as	O
opposed	O
to	O
a	O
random	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
in	O
which	O
the	O
group	O
means	O
are	O
a	O
random	O
sample	O
from	O
a	O
population	O
.	O
</s>
<s>
The	O
group	O
means	O
could	O
be	O
modeled	O
as	O
fixed	O
or	O
random	B-General_Concept
effects	I-General_Concept
for	O
each	O
grouping	O
.	O
</s>
<s>
In	O
a	O
fixed	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
each	O
group	O
mean	O
is	O
a	O
group-specific	O
fixed	O
quantity	O
.	O
</s>
<s>
In	O
panel	O
data	O
where	O
longitudinal	O
observations	O
exist	O
for	O
the	O
same	O
subject	O
,	O
fixed	B-General_Concept
effects	I-General_Concept
represent	O
the	O
subject-specific	O
means	O
.	O
</s>
<s>
In	O
panel	O
data	O
analysis	O
the	O
term	O
fixed	B-General_Concept
effects	I-General_Concept
estimator	I-General_Concept
(	O
also	O
known	O
as	O
the	O
within	B-General_Concept
estimator	I-General_Concept
)	O
is	O
used	O
to	O
refer	O
to	O
an	O
estimator	O
for	O
the	O
coefficients	O
in	O
the	O
regression	O
model	O
including	O
those	O
fixed	B-General_Concept
effects	I-General_Concept
(	O
one	O
time-invariant	O
intercept	O
for	O
each	O
subject	O
)	O
.	O
</s>
<s>
There	O
are	O
two	O
common	O
assumptions	O
made	O
about	O
the	O
individual	O
specific	O
effect	O
:	O
the	O
random	B-General_Concept
effects	I-General_Concept
assumption	O
and	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
assumption	O
.	O
</s>
<s>
The	O
random	B-General_Concept
effects	I-General_Concept
assumption	O
is	O
that	O
the	O
individual-specific	O
effects	O
are	O
uncorrelated	O
with	O
the	O
independent	O
variables	O
.	O
</s>
<s>
The	O
fixed	B-General_Concept
effect	I-General_Concept
assumption	O
is	O
that	O
the	O
individual-specific	O
effects	O
are	O
correlated	O
with	O
the	O
independent	O
variables	O
.	O
</s>
<s>
If	O
the	O
random	B-General_Concept
effects	I-General_Concept
assumption	O
holds	O
,	O
the	O
random	B-General_Concept
effects	I-General_Concept
estimator	I-General_Concept
is	O
more	O
efficient	O
than	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
estimator	I-General_Concept
.	O
</s>
<s>
However	O
,	O
if	O
this	O
assumption	O
does	O
not	O
hold	O
,	O
the	O
random	B-General_Concept
effects	I-General_Concept
estimator	I-General_Concept
is	O
not	O
consistent	O
.	O
</s>
<s>
The	O
Durbin	B-General_Concept
–	I-General_Concept
Wu	I-General_Concept
–	I-General_Concept
Hausman	I-General_Concept
test	I-General_Concept
is	O
often	O
used	O
to	O
discriminate	O
between	O
the	O
fixed	O
and	O
the	O
random	B-General_Concept
effects	I-General_Concept
models	I-General_Concept
.	O
</s>
<s>
Unlike	O
the	O
random	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
where	O
the	O
unobserved	O
is	O
independent	O
of	O
for	O
all	O
,	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
(	O
FE	O
)	O
model	O
allows	O
to	O
be	O
correlated	O
with	O
the	O
regressor	O
matrix	O
.	O
</s>
<s>
The	O
FE	O
estimator	O
is	O
then	O
obtained	O
by	O
an	O
OLS	B-General_Concept
regression	I-General_Concept
of	O
on	O
.	O
</s>
<s>
This	O
is	O
numerically	O
,	O
but	O
not	O
computationally	O
,	O
equivalent	O
to	O
the	O
fixed	B-General_Concept
effect	I-General_Concept
model	I-General_Concept
and	O
only	O
works	O
if	O
the	O
sum	O
of	O
the	O
number	O
of	O
series	O
and	O
the	O
number	O
of	O
global	O
parameters	O
is	O
smaller	O
than	O
the	O
number	O
of	O
observations	O
.	O
</s>
<s>
The	O
FD	O
estimator	O
is	O
then	O
obtained	O
by	O
an	O
OLS	B-General_Concept
regression	I-General_Concept
of	O
on	O
.	O
</s>
<s>
When	O
,	O
the	O
first	O
difference	O
and	O
fixed	B-General_Concept
effects	I-General_Concept
estimators	I-General_Concept
are	O
numerically	O
equivalent	O
.	O
</s>
<s>
If	O
the	O
error	O
terms	O
are	O
homoskedastic	B-General_Concept
with	O
no	O
serial	O
correlation	O
,	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
estimator	I-General_Concept
is	O
more	O
efficient	O
than	O
the	O
first	O
difference	O
estimator	O
.	O
</s>
<s>
For	O
the	O
special	O
two	O
period	O
case	O
(	O
)	O
,	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
(	O
FE	O
)	O
estimator	O
and	O
the	O
first	O
difference	O
(	O
FD	O
)	O
estimator	O
are	O
numerically	O
equivalent	O
.	O
</s>
<s>
To	O
see	O
this	O
,	O
establish	O
that	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
estimator	I-General_Concept
is	O
:	O
</s>
<s>
Gary	O
Chamberlain	O
's	O
method	O
,	O
a	O
generalization	O
of	O
the	O
within	B-General_Concept
estimator	I-General_Concept
,	O
replaces	O
with	O
its	O
linear	B-Algorithm
projection	I-Algorithm
onto	O
the	O
explanatory	O
variables	O
.	O
</s>
<s>
Writing	O
the	O
linear	B-Algorithm
projection	I-Algorithm
as	O
:	O
</s>
<s>
then	O
the	O
values	O
and	O
standard	O
deviations	O
for	O
and	O
can	O
be	O
determined	O
via	O
classical	O
ordinary	B-General_Concept
least	I-General_Concept
squares	I-General_Concept
analysis	O
and	O
variance-covariance	O
matrix	O
.	O
</s>
<s>
Random	B-General_Concept
effects	I-General_Concept
estimators	I-General_Concept
may	O
be	O
inconsistent	O
sometimes	O
in	O
the	O
long	O
time	O
series	O
limit	O
,	O
if	O
the	O
random	B-General_Concept
effects	I-General_Concept
are	O
misspecified	O
(	O
i.e.	O
</s>
<s>
the	O
model	O
chosen	O
for	O
the	O
random	B-General_Concept
effects	I-General_Concept
is	O
incorrect	O
)	O
.	O
</s>
<s>
However	O
,	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
may	O
still	O
be	O
consistent	O
in	O
some	O
situations	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
the	O
time	O
series	O
being	O
modeled	O
is	O
not	O
stationary	O
,	O
random	B-General_Concept
effects	I-General_Concept
models	I-General_Concept
assuming	O
stationarity	O
may	O
not	O
be	O
consistent	O
in	O
the	O
long-series	O
limit	O
.	O
</s>
<s>
In	O
situations	O
like	O
these	O
where	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
is	O
known	O
to	O
be	O
consistent	O
,	O
the	O
Durbin-Wu-Hausman	B-General_Concept
test	I-General_Concept
can	O
be	O
used	O
to	O
test	O
whether	O
the	O
random	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
chosen	O
is	O
consistent	O
.	O
</s>
