Introduction to Econometrics

1
Introduction to Econometrics

• Lecture 6
• Testing restrictions

2
Lecture plan

• Testing restrictions about
• individual parameters
• groups of parameters

• t-tests for individual parameters
• zero value under H0
• Some other value under H0

• F-tests for groups of parameters
• the overall significance of a
• regression
• group exclusion tests
• other linear restrictions

3
t-tests of non-zero parameter values
4
F tests of zero restrictions (group exclusion
tests)
5
F tests of other linear restrictions
6
Calculating the F value

• F cal RSSR - RSSU/m
• RSSU/(n-k-1)
• where m is the number of restrictions
• RSSR is the Residual Sum of Squares in the
  restricted model
• RSSU is the Residual Sum of Squares in the
  unrestricted model
• H0 restrictions are valid
• Decision rule reject H0 if Fcal gt F(m,n-k-1)

7
Imposing restrictions by

• reparameterising the model (incorporating the
  restriction by substitution and then rearranging
  the equation)
• using Restricted Least Squares

8
Other issues concerning testing restrictions

• testing for parameter constancy - the Chow test
• testing non-linear restrictions
• tests to choose between non-nested models