CHAPTER 7 FUNCTIONAL FORM AND STRUCTURAL CHANGE 2. Semilog model Iny=61+B2t+E If =t, B, is the average growth rate of y. If r is a dummy variable, y is 100 x B2% higher(lower if B2<0) when 3=1 3. Polynomial equation y=B1+A2x+B3x2+…+B2x2-1+e 4. Interaction model Example 5 D=B1+B2S+B3W+BSW+E D: breaking distance road wetness ee OE DIS, WI aS B2+Baw If B4>0, the marginal effect of higher speed on breaking distance is increased when the road is wetter Example 6 Y=1+B2D2+3D3+4D2D3+BX+e Y: log annual salary of a bank clerk in HK D23= if Huent in English 1 if fluent in Putonghua 0 otherwise X: work experience B4: effect of fluency in both English and Putonghua on salaryCHAPTER 7 FUNCTIONAL FORM AND STRUCTURAL CHANGE 4 2. Semilog model ln y = β1 + β2x + ε If x = t, β2 is the average growth rate of y. If x is a dummy variable, y is 100×β2% higher (lower if β2 < 0) when x = 1. 3. Polynomial equation y = β1 + β2x + β3x 2 + · · · + βpx p−1 + ε. 4. Interaction model Example 5 D = β1 + β2S + β3W + β4SW + ε D : breaking distance W : road wetness S : speed ∂E [D|S, W] ∂S = β2 + β4W If β4 > 0, the marginal effect of higher speed on breaking distance is increased when the road is wetter. Example 6 Y = β1 + β2D2 + β3D3 + β4D2D3 + β5X + ε Y : log annual salary of a bank clerk in HK D2
= 1 if fluent in English = 0 otherwise D3
= 1 if fluent in Putonghua = 0 otherwise X : work experience β4 : effect of fluency in both English and Putonghua on salary