The
Development Dataset is from:
http://www.ssc.upenn.edu/~cheibub/data/Default.htm
We use the following
variables:
LEVEL – Real GDP per capita,
1985 international price.
EDT – Cummulative years of
education of average member of the labor force
OPENC – Exports and imports
as a share of the GDP
FEMSEC – Gross enrollment
ratio, secondary, female
Our model will have LEVEL as
the dependent variable, and EDT, OPENC as the independent variables.
LEVEL = a + b1 *
EDT + b2 * OPENC + e
Assume we want to use FEMSEC
as the instrumental variable for EDT.
(1) First Approach
Step
1, Regress EDT on FEMSEC and OPENC, and save the predicted values.
[in
SPSS, click on Analyze – Regression – Linear…, a Linear Regression box will
open. Move EDT to the Dependent Box, move FEMSEC and OPENC to the Independent
box. Click on Save and check the Predicted Values Unstandardized. Click on
Continue and back to the Linear Regression box. Click on OK to get the results.
Your saved predicted values will be the last column of your data and be names
as pres_1 variable.]
(take a look at the regression results to ensure that FEMSEC has significant impact on EDT that we do have a strong IV)
Step
2, Regress LEVEL on OPENC and the new variable – save predicted values.
[in
SPSS, click on Analyze – Regression – Linear …, a Linear Regression box will
open. Move LEVEL to the dependent box, move OPENC and Pre_1 to the independent
box.]
Coefficients(a)
|
Model |
|
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|
|
B |
Std. Error |
Beta
|
||||
|
|
|
|
|
|
|
|
|
(Constant) |
2783.008 |
82.888 |
|
33.576 |
.000 |
|
|
OPENC |
.560 |
1.221 |
.007 |
.458 |
.647 |
|
|
|
Unstandardized Predicted Value |
1032.314 |
30.305 |
.484 |
34.065 |
.000 |
a Dependent Variable: LEVEL
(here
the “unstandardized predicted value” is to replace EDT)
(2) Approach 2
In
SPSS, click on Analyze – Regression – 2 Stage Least Squares …. A 2-stage Least Squares box will open.
Please move LEVEL to the Dependent box, move EDT and OPENC to the Explanatory
box, move FEMSEC and OPENC to the Instrumental box.
------------------
Variables in the Equation ------------------
Variable B SE B Beta T
Sig T
EDT 1032.314354 68.748638 1.996364 15.016
.0000
OPENC .559922
2.770729 .006514 .202
.8399
(Constant) 2783.008163
188.038477
14.800 .0000
As
we can see, the results are very close to each other. The coefficients
estimated (the Bs) are almost identical.
But, the estimated std errors are different.
NOTE: we just use
this example to demonstrate the computational procedures.