Studenmund(2006) Chapter 7

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Lecture 7
Studenmund(2006) Chapter 7
Objective
Applications of Dummy Independent Variables
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Qualitative information
Gender male and female Regional HK Island,
Kowloon NT Zone East, South, West, North,
Center Time/period peace
and war, before after crisis Age young,
middle, elder Education Post-graduate, College,
High, Element Others
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Example Gender issue of whether discrimination
is existing for salary
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Separate sample of male
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Separate sample of female
Female sample (Gujarati-1995, Table 15.1 15.5)
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D1 D2 1 D1 1 - D2
Each dummy identify two different categories,
but when sum up two dummies it
cannot identify which is male or female
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(Dummy variable trap)
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Use two dummy variables to identify two different
qualitative categories in one model will be fall
into the trap of perfect multicollinearity.
General rule To avoid the perfect
multicollinearity
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Separate Examples for female and male
The two regression results performed differently
in slope and intercept. But are they really
statistically different? We cannot answer from
these two separate regression results unless you
test with the F.
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Set two different dummies for the Example
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One qualitative variable with more than two
categories
D2 1 if high school education 0
otherwise D3 1 if college education
0 otherwise
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One Qualitative variable with many categories
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Qualitative variable with many categories (Cont.)
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One Qualitative variable with many categories
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Qualitative variable with many categories
(Cont.)
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Two qualitative variables
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(3) Mean salary for white female teacher



Y (?0 ?0 D2) ?1 X ?1D2X that
are D1 0, D2 1

(4) Mean salary for white male teacher
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Different types of dummy regression
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Reconstruction (46-54) Yt A0 A1 Xt
?1t Pastreconstruction (55-63) Yt B0 B1 Xt
?2t
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Interactive effects between the two qualitative
variables
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Concurrent model (or Covariance, or Slope shift
model)
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Shifts in both intercept and slope
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Quarterly effect is same as seasonal effect
Control quarter is the 4th quarter
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(2) Structural Test based on Dummy variables
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The Chow test on the Unemployment rate-capacity
utilization rate
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Restriction F-test procedures
H0 No structural change H1 Yes
F gt Fc gt reject H0
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Using the dummy variable to identify the
structural change
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(2) Structural stability test based on dummy
variables
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Whether intercept and slope change?
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1946 - 1954 -0.2662 0.047 Income
D1 1
1955 - 1963 -1.750 0.150 Income
D1 0
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The use of Dummy variables in the Pooled data
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(ii) Y ?0 ?1 X1 ?2 X2 ?3 D ?4 D X2 ?5
D X3 ?
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Chow Test - structural stability Test Using
dummy variables approach
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GENR dummy 0 for 1946-1954 dummy 1 for
1955-1963
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Using the dummy variable to identify the
structural instability
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Read the estimated results from the dummy
regressions
For the period of 1946-1954 Savings
-0.2662 0.0470 Income
For the period of 1955-1963 savings (-0.2662
- 1.4839) (0.0470 0.1034)
-1.7501 0.1504 Income