Lecture presentation to use SAS to test for specification and determine whether a dummy variable has a significance on our outcome variable.

1. A test for structural break
Dr. Steven C. Myers
Department of Economics
College of Business Administration
The University of Akron
econdatascience.com
May 2, 2019

2. Linear models with a binary regressor
Y is the outcome variable of interest.
X in this slide is a Dummy Variable.
Expected values can be calculated and the effect of the dummy variable
on the model is beta.

3. Effect of D, a dummy variable and a continuous variable X
E[Y|D=1] - E[Y|D=0] = β2
E[Y|D=1] - E[Y|D=0] = β3X
E[Y|D=1] - E[Y|D=0] = β2 + β3X

4. Create the data set (1) read Y and (2) create variables for testing

5. Graphing the data shows that a quadratic equation seems also
reasonable.
title "PROC SGPLOT with LOESS Statement";
proc sgplot data=trData;
reg x=t y=y / CLM CLI;
loess x=t y=y / interpolation=linear /
degree=2; ;
ellipse x=t y=y;
xaxis grid; yaxis grid;
run;
Model implied by LOESS:
Y = β0 + β1T = β2T2 + u

6. Needed variables created, time, time squared, D and D*T

7. Model 1 establishes the reasonableness of the model
Model 3 shows no effect of D. Some researchers may stop here.
Model 4 shows D and DT coefficients are both significant.

8. Here we see that two competitors for best model are models 2 and 4,
the quadratic and the structural break models.
If model 2 s correct then the
intervention, D, had no effect
If module 4 is correct then the
intervention, D, Has a significant
effect where the rate of growth in Y
has doubled because of the
intervention, D.
These models are so close that a test
between may not easily reveal a
winner (closer than error)

9. Fully interactive versus quadratic model
Full sample,
linear versus
quadratic
Sub samples,
linear models

10. If the quadratic model ruled, then it would exist in the sub samples
and it does not!
Conclusion: since the quadratic model
is rejected, the fully interactive model
Rules and indeed does answer the question:
there is a structural break of some significance.
Recall that the first impulse model (model 3)
of a dummy variable suggested no such
structural break.
If the analyst hadn’t gone by the obvious the
conclusion for the business leader would
have been wrong.