ch07nonlinearrelationships

ch07nonlinearrelationships - ECON 6002 Econometrics...

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ECON 6002 Econometrics Memorial University of Newfoundland Adapted from Vera Tabakova’s
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7.1 Polynomials 7.2 Dummy Variables 7.3 Applying Dummy Variables 7.4 Interactions Between Continuous Variables 7.5 Log-Linear Models
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7.1.1 Cost and Product Curves Figure 7.1 (a) Total cost curve and (b) total product curve
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Figure 7.2 Average and marginal (a) cost curves and (b) product curves
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2 1 2 3 AC Q Q e = β +β + 2 3 1 2 3 4 TC Q Q Q e = α + α + α + α + 2 3 ( ) 2 dE AC Q dQ = β + β 2 2 3 4 ( ) 2 3 dE TC Q Q dQ = α + α + α
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1 2 3 WAGE EDUC EXPER+ EXPER e = β +β β + 2 4 3 4 ( ) 2 E WAGE EXPER EXPER = β + β
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· 18 ( ) .3409 2( .0051)18 .1576 EXPER E WAGE EXPER = = + - = 3 4 2 .3409 / 2( .0051) 33.47 EXPER = -β β = - - = The turning point of the relationship is given by At the sample median of age (18 years old) the estimated marginal effect is:
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1 2 PRICE SQFT e = β +β + 1 if characteristic is present 0 if characteristic is not present D = 1 if property is in the desirable neighborhood 0 if property is not in the desirable neighborhood D =
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1 2 PRICE D SQFT e = β + δ + 1 2 1 2 ( ) when 1 ( ) when 0 SQFT D E PRICE SQFT D β + δ +β = = β +β =
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Figure 7.3 An intercept dummy variable
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1 if property is not in the desirable neighborhood 0 if property is in the desirable neighborhood LD = 1 2 PRICE LD SQFT e = β + λ + 1 2 PRICE D LD SQFT e = β + δ + λ + But would this Second version Work?
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1 2 ( ) PRICE SQFT SQFT D e = β +β + γ × + ( 29 1 2 1 2 1 2 ( ) when 1 ( ) when 0 SQFT D E PRICE SQFT SQFT D SQFT D β + β + γ = = β +β + γ × = β +β = 2 2 when 1 ( ) when 0 D E PRICE D SQFT β + γ = = β =
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Figure 7.4 (a) A slope dummy variable. (b) A slope and intercept dummy variable
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