CHAPTER6ECONOMETRICSx

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Dummy Variable Regression Models

Dummy, or indicator, variables take on values of 0 or 1to indicate the presence or absence of a quality.

Yi = B1 + B2 Di + B3Xi + ui

Di = 1 for female0 for male

They can be included in regressionsjust like quantitative variables.

Di = 1 for prior to 20010 for 2001 and later

OR

A Dummy Variable Indicates Change in Intercept

Yi = 60 + 30 Di - 0.4 Xi + ui

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Y If D = 0

Y = 60 + 30 D - 0.4 X

Y = 60 – 0.4 X

D = 0

D = 1

If D = 1

Y = 60 + 30 D - 0.4 X

Y = 90 - 0.4 X

B2=30 is the differential intercept coefficient.

A Dummy Variable Can Allow for Change in Slope, Too

Yi = 60 + 30 Di – 0.4 Xi + 0.3(DiXi) + ui

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Y If D = 0

Y = 60 + 30 D – 0.4 X + 0.3 DX

Y = 60 – 0.4 X

D = 0

D = 1

B4=0.3 is the differential slope coefficient.

If D = 1

Y = 60 + 30 D – 0.4 X + 0.3 DX

Y = 60 – 0.1 X

Yi = B1 + B2 Di + B3Xi + ui

Di = 0 for first quarter 2 for third quarter1 for second quarter 3 for fourth quarter

Variables with More than Two Classes

Don’t allow the dummy variable to take on multiple values:

This assumes a pattern in the effect that might not exist.

Instead, use several indicator variables.

D2i = 1 if 2nd qrt0 otherwise

Yi = B1 + B2 D2i + B3D3i + B4D4i + B5Xi + ui

D3i = 1 if 3rd qrt0 otherwise

D4i = 1 for 4th qrt0 otherwise