1. Economics 310 Lecture 7 Testing Linear Restrictions

2. Single Linear Restriction

3. Cigarette Demand Example VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 24 DF P-VALUE CORR. COEFFICIENT AT MEANS LNY 0.25768 0.1303 1.977 0.060 0.374 0.5930 2.7090 LNP -0.21669 0.1070 -2.024 0.054-0.382 -0.4693 -0.1927 LNQLAG 0.62464 0.1541 4.053 0.000 0.637 0.6500 0.6215 CONSTANT -1.6892 0.9206 -1.835 0.079-0.351 0.0000 -2.1377 VARIANCE-COVARIANCE MATRIX OF COEFFICIENTS LNY 0.16986E-01 LNP -0.12665E-01 0.11459E-01 LNQLAG -0.15970E-01 0.10230E-01 0.23747E-01 CONSTANT -0.11965 0.89111E-01 0.10681 0.84744 LNY LNP LNQLAG CONSTANT

4. Test Homogeneity

5. Testing Multiple Linear Restrictions

6. Selecting Models Economic Theory and logic Use of t- and F-tests Coefficient of Determination Models with different dependent variables Models with different number regressors Models without constant term Adjusted Coefficient of Determination Akaike Information Criterion J-test for non-nest hypothesis Ramsey Reset for non-linearity

7. Selecting Models

8. Ramsey Reset Test Test functional form of model Regress Y on independent variables and square and cubic of predictions of Y from linear model. TV Ad yield example

9. J-Test Test for best model between 2 non- nested models. J-Test Example

10. Testing linear versus log-linear