# Econ2206 Notes

Topics: Normal distribution, Estimator, Scientific method Pages: 292 (9594 words) Published: August 21, 2013
ECON2206
Revision
Notes
W2
–
SIMPLE
REGRESSION
MODEL

MOTIVATION
Much
of
applied
econometric
analysis
are
interested
in
“explaining
y
in
terms
of
x”
and
confront
three
issues:
1) Since
there
is
never
an
exact
relationship
between
y
and
x,
how
do
we
account
for
the
“other
unobserved”
variables?
2) What
is
the
function
relationship
between
y
and
x?
3) How
do
we
invoke
a
ceteris
paribus
relationship
or
a
causal
effect
between
y
an
x?

The
simple
linear
regression
model
is:
y
=
β0
+
β1x
+
u

-­‐ “u”
is
the
stochastic
error
or
disturbance
term
and
represents
all
those
unobserved
factors
or
other
factors
other
than
x.

-­‐ If
all
other
factors
(u)
is
held
fixed,
so
that
change
in
u
is
zero,
we
can
observe
the
function
relationship
between
y
and
x.
-­‐ If
we
take
the
expected
value
of
the
model,
(Δu
=
0
and
Δβ0),
then
we
can
see
that
x
has
a
linear
effect
on
y.

We
will
only
get
reliable
estimates
of
β0
and
β1
if
we
make
restricting
assumptions
on
u.
As
long
as
β0
is
included
in
the
model,
nothing
is
lost
by
making
the
assumption
that
the
expected
value
of
u
in
the
population
is
zero;
E(u)
=
0.

ZCM
Our
crucial
assumption
is
by
defining
the
conditional
distribution
of
u
given
any
value
of
x.
This
crucial
assumption
is,
the
average
value
of
u
does
not
depend
on
the
value
of
x.

E(u|x)
=
E(u)
=
0

This
is
the
zero-­conditional
mean
assumption
(ZCM)
-­‐ The
average
value
of
the
unobserved
factors
is
the
same
across
the
population.

-­‐ An
important
implication
of
ZCM
is
that
u
and
x
are
uncorrelated.

OLS
Ordinary
Least
Squares
(OLS)
is
a
method
for
estimating
the
unknown
parameters
in
a
linear
regression
model.
The
estimates
for
β0
and
β1
are
found
by
minimizing
the
sum
of
squared
residuals.
That
is,
the
distance
between
the
observations
in
the
sample
and
the
responses
predicted.

-­‐ Fitted
values
and
estimates
are
denoted
by
a
HAT
-­‐ The
values
predicted
for