Economics 310 Lecture 7 Testing Linear Restrictions

Single Linear Restriction

Cigarette Demand Example VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 24 DF P-VALUE CORR. COEFFICIENT AT MEANS LNY LNP LNQLAG CONSTANT VARIANCE-COVARIANCE MATRIX OF COEFFICIENTS LNY E-01 LNP E E-01 LNQLAG E E E-01 CONSTANT E LNY LNP LNQLAG CONSTANT

Test Homogeneity

Testing Multiple Linear Restrictions

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

Selecting Models

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

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

Testing linear versus log-linear