Economics 310

Lecture 7Testing Linear Restrictions

Single Linear Restriction

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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

Test Homogeneity

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Testing Multiple Linear Restrictions

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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

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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

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