CHAPTER 7 FUNCTIONAL FORM AND STRUCTURAL CHANGE Chapter 7 Functional Form and Structural Change 7.1 Using binary variable Example 1 Earnings equation for married women In earnings=B,+ B2age+ B3age+ Education Skids +a =0. no kids =1. kids Variable Coefficient se Age0.200600.08862.39 -0.00231470.00098688-2.345 Education0.0674720.0252482.672 Kid 351190.14753-2380 The earnings of women with children are 35% less than those without Model with one dummy variable Here di takes value either l or 0 depending on the category. We may use several dummy variables Example 2(Seasonal effects) quarterly de yt=B,+BXL+5,DIt+&2D2t +53 D3t+Et Here x does not contain 1 spreng 0. othe if if fa 0, di denote seasonal effects Alternatively, we may use BXt+61D1t+62D2+63D3x+64DCHAPTER 7 FUNCTIONAL FORM AND STRUCTURAL CHANGE 1 Chapter 7 Functional Form and Structural Change 7.1 Using binary variables Example 1 Earnings equation for married women ln earnings = β1 + β2age + β3age2 + β4 education + β5kids + ε kids =
= 0, no kids = 1, kids Variable Coefficient s.e. t Age 0.20056 0.08386 2.392 Age2 —0.0023147 0.00098688 —2.345 Education 0.067472 0.025248 2.672 Kids —0.35119 0.14753 —2.380 The earnings of women with children are 35% less than those without. Model with one dummy variable yi = X ′ iβ + δdi + εi Here di takes value either 1 or 0 depending on the category. We may use several dummy variables. Example 2 (Seasonal effects) Suppose yt is a quarterly data yt = β1 + β ′Xt + δ1D1t + δ2D2t + δ3D3t + εt . Here Xt does not contain 1. D1t
= 1, if spring = 0, otherwise D2t
= 1, if summer = 0, otherwise D3t
= 1, if fall = 0, otherwise δi denote seasonal effects. Alternatively, we may use yt = β ′Xt + δ1D1t + δ2D2t + δ3D3t + δ4D4t + εt