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6. x. ECONOMETRICS. x. CHAPTER. x. x. x. Dummy Variable Regression Models. Dummy, or indicator, variables take on values of 0 or 1 to indicate the presence or absence of a quality. They can be included in regressions just like quantitative variables.
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6 x ECONOMETRICS x CHAPTER x x x Dummy Variable Regression Models Dummy, or indicator, variables take on values of 0 or 1 to indicate the presence or absence of a quality. They can be included in regressions just like quantitative variables. Yi= B1 + B2 Di + B3Xi + ui Di = 1 for female 0 for male Di = 1 for prior to 2001 0 for 2001 and later OR
A Dummy Variable Indicates Change in Intercept 120 Y 100 80 60 40 20 20 40 60 80 100 120 X Yi= 60 + 30 Di - 0.4 Xi + ui If D = 0 Y = 60 + 30 D - 0.4 X Y = 60 – 0.4 X D = 1 If D = 1 Y = 60 + 30 D - 0.4 X Y = 90 - 0.4 X D = 0 B2=30 is the differential intercept coefficient.
A Dummy Variable Can Allow for Change in Slope, Too 120 Y 100 80 60 40 20 20 40 60 80 100 120 X Yi= 60 + 30 Di– 0.4 Xi + 0.3(DiXi) + ui If D = 0 Y = 60 + 30 D – 0.4 X + 0.3 DX Y = 60 – 0.4 X D = 1 If D = 1 Y = 60 + 30 D – 0.4 X + 0.3 DX Y = 60 – 0.1 X D = 0 B4=0.3 is the differential slope coefficient.
Variables with More than Two Classes Don’t allow the dummy variable to take on multiple values: Yi= B1 + B2 Di + B3Xi + ui Di = 0 for first quarter 2 for third quarter 1 for second quarter 3 for fourth quarter This assumes a pattern in the effect that might not exist. Instead, use several indicator variables. Yi= B1+ B2 D2i + B3D3i + B4D4i + B5Xi + ui D2i = 1 if 2nd qrt 0 otherwise D3i = 1 if 3rd qrt 0 otherwise D4i = 1 for 4th qrt 0 otherwise