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.