Economics 241B
Endogeneity Bias  The Example of Working
The classic illustration of the biases created by endogeneity dates to Working in
1927. Consider the simple model of demand and supply (for co/ee, say)
Q
d
t
=
&
0
+
1
P
t
+
U
t
Q
s
t
=
±
0
+
±
1
P
t
+
V
t
Q
d
t
=
Q
s
t
:
The error term
U
t
demand, other than price, such as the public±s mood for co/ee. Depending on
the value of
U
t
, the demand curve in the pricequantity plane shifts up or down.
Similarly,
V
t
represents supply factors other than price. As the intercepts capture
the mean of the error terms, we assume
E
(
U
t
) = 0
and
E
(
V
t
) = 0
.
To avoid
inessential complications, we also assume
Cov
(
U
t
;V
t
) = 0
.
If we de²ne the
marketclearing quantity to be
Q
t
=
Q
d
t
=
Q
s
t
, then the system reduces to two
equations
Q
t
=
&
0
+
1
P
t
+
U
t
(demand)
Q
t
=
±
0
+
±
1
P
t
+
V
t
:
(supply)
A regressor is endogenous if it is not orthogonal to the error term, that is, if it
does not satisfy the orthogonality condition. With an intercept in the equation,
endogeneity arises if and only if the regressor is correlated with the error. In the
present example, the regressor
P
t
is necessarily endogenous in both equations. To
see why, treat the demand and supply equations as a system of two simultaneous
equations and solve for
(
P
t
;Q
t
)
as
P
t
=
±
0
&
0
1
±
1
+
V
t
U
t
1
±
1
Q
t
=
1
±
0
&
0
±
1
1
±
1
+
1
V
t
±
1
U
t
1
±
1
:
Because price is a function of the two error terms, price is clearly correlated with
each error.
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View Full DocumentWe can take the argument one step further and calculate the covariance of
price with each error. The covariance of price with the demand shifter
U
t
and
the supply shifter
V
t
is
Cov
(
P
t
;U
t
) =
V ar
(
U
t
)
1
±
1
;
Cov
(
P
t
;V
t
) =
V ar
(
V
t
)
1
±
1
:
If the demand curve is downward sloping (
1
<
0
) and the supply curve is upward
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 Fall '08
 Staff
 Economics

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