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The full model of Example 2.3 may be written in logarithmic terms as lnG/pop = α + βp ln Pg + βy lnY + γnc ln Pnc + γuc ln Puc + γpt ln Ppt + β year + δd ln Pd + δn ln Pn + δs ln Ps + ε. Consider the hypothesis that the microelasticities are a constant proportion of the elasticity with respect to their corresponding aggregate. Thus, for some positive θ (presumably between 0 and 1), γnc = θδd, γuc = θδd, γpt = θδs. The first two imply the simple linear restriction γnc = γuc. By taking ratios, the first (or second) and third imply the nonlinear restriction
a. Describe in detail how you would test the validity of the restriction.
b. Using the gasoline market data in Table F2.2 , test the restrictions separately and jointly. |
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