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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


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