## Friday, May 11, 2018

### 2-Stage Least Squares Regression (SPSS)

Often used in Econometrics, The 2-Stage Least Squares Regression method is a technique which is utilized to create a predictive model which is influenced by, but does not contain, outside variables. These “outside variables” are better known by their proper term, “instrumental variables”.

The definition of an “instrumental variable” is as follows:

“A variable used to estimate casual relationships when controlled experiments are not feasible, or when a treatment is not successfully delivered to every unit in a randomized experiment.” *

In simplified terms, what this essentially means, is that a variable is factored into the regression model which impacts the dependent variables, and as a consequence of such, also impacts the independent variable. Within the model, there can be more instrumental variables than independent variables. However, there cannot be more independent variables than instrumental variables.

Assembling this model manually is rather difficult when synthesizing it by hand. Thankfully, modern technology has granted us the ability to easily create the model within SPSS.

Example (SPSS):

Below is our sample data set:

To begin our analysis, we must select, from the topmost menu, “Analyze”, then “Regression”, followed by “2-Stage Least Squares”.

This sequence of actions should cause the following menu to appear:

Using the topmost arrow button, assign “Z” as a ”Dependent” variable. Once this has been completed, utilize the center arrow button to assign the variables (“Y”, “X”) as “Factor(s)”. Finally, utilize the bottom center arrow button to designate the variables (“Y”, “X”) as “Instrumental” variables.

Next, click on the button labeled “Options”, this should populate the following menu:

From this interface, beneath the header labeled, “Save New Variables”, select the following option: “Predicted”.

Once this has been completed, click the box labeled “Continued”, then select the box labeled “OK”.

This should produce the following output:

The output indicates that the model generated through the utilization of the 2-Stage Least Squares Regression is of extremely poor quality. This is illustrated in the R-Square value (.001), the significance values of the predictor variables (.923, .952, .953), and extremely high correlation value (-.996).

Assuming that the model did serve as a decent predictor, and therefore as such, you desired to use it as a predictive tool, the equation to generate dependent variable values would be as follows:

Dependent Variable Value = (X * 8.369) + (Y * -4.555) + 507.242

SPSS computes the predicted values of the dependent variables from the application of the model as it pertains to the original data set. This is a result of the “Save” option being selected earlier. These predicted values are output into a column within the original data set.

*- https://en.wikipedia.org/wiki/Instrumental_variables_estimation