文档介绍：CHAPTER 7 FUNCTIONAL FORM AND STRUCTURAL CHANGE 1
Chapter 7 Functional Form and Structural Change
Using binary variables
Example 1 Earnings equation for married women
2
ln earnings = β1 + β2age + β3age + β4education + β5kids + ε
= 0, no kids
kids =
= 1, kids
Variable Coefficient . t
Age
Age2 — —
Education
Kids — —
The earnings of women with children are 35% less than those without.
Model with one dummy variable
′
yi = Xiβ+ 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.
= 1, if spring
D1
t = 0, otherwise
= 1, if summer
D2
t = 0, otherwise
= 1, if fall
D3
t = 0, otherwise
δi denote seasonal effects.
Alternatively, we may use
′
yt = β Xt + δ1D1t + δ2D2t + δ3D3t + δ4D4t + εt.
CHAPTER 7 FUNCTIONAL FORM AND STRUCTURAL CHANGE 2
But we should NOT use
′
yt = β1 + β Xt + δ1D1t + δ2D2t + δ3D3t + δ4D4t + εt
since
D1t + D2t + D3t + D4t = 1,
we run into a multicollinearity problem.
Example 3 (Threshold effects and categorical variables)
e = β1 + β2age + δBB + δM M + δP P + ε
= 1, Bachelor’s degree only
B
= 0,