5/26/2010
1
Interpreting Results  I
•
How do we interpret results in Probit and Logit models?
The
estimated Probit regression line is:
•
Since the Bought
i
is binary, the predicted/expected value of
Bought
i
is equal to the
probability
that Bought
i
= 1 (given any
value of Price
i
).
•
So if Price
i
=0.70, the results say that the probability of purchase
is
Φ
(1.371.26*0.7) =
Φ
(2.25) = 0.012, or 1.2%
•
If Price
i
=0.60, the probability of purchase is
Φ
(1.371.26*0.6)
=
Φ
(2.13) = 0.017, or 1.7%
•
If Price
i
=1.00, the probability of purchase is
Φ
(1.371.26*1) =
Φ
(2.63) = 0.004, or 0.4% (Note: this is not less than zero like in
the LPM!)
circumflexnosp4char
(
29
Bought =
1.37
1.26Price
i
i
Φ 

Interpreting Results  II
•
The estimated Logit regression line is:
•
So if Price
i
=0.70, this says that the probability of purchase is
1/(1+exp((1.913.44*0.7))) = 1/(1+exp(4.32)) = 0.013, or 1.3%
•
If Price
i
=0.60, the probability of purchase is 1/(1+exp((1.91
3.44*0.6))) = 1/(1+exp(3.97)) = 0.019, or 1.9%
•
If Price
i
=1.00, the probability of purchase is 1/(1+exp((1.91
3.44*1))) = 1/(1+exp(5.35)) = 0.005, or 0.5%
circumflexnosp4char
(
29
(
29
1
Bought
=
1
exp
1.91
3.44Price
i
i
+
 

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5/26/2010
2
Interpreting Results  III
•
Note that since both the Probit and Logit models are
nonlinear (in contrast to the linear probability model,
which is linear):
•
1) The estimated “slope” coefficient
β
1
does not
directly measure the effect of changing
X
i
on
Pr(
Y
i
=1
X
i
) (recall that
Z
i
= Pr(
Y
i
=1
X
i
))
•
2) The effect of changing
X
i
on Pr(
Y
i
=1
X
i
) varies
depending on what
X
i
is.
For example, in the above
Probit model:
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 Spring '07
 SandraBlack
 Econometrics, Regression Analysis, Logit, Probit, Logit Models

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