Transcript DUMMY VARIABLES

DUMMY VARIABLES
BY
HARUNA ISSAHAKU
Haruna Issahaku
Definition
• Dummy variables (DV) indicate the presence
or absence of a ‘quality’ or an attribute such
as male or female, black or white, north or
south, etc.
• A dummy variable will take the value 1 or 0
according to whether or not the condition is
present or absent for a particular observation.
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1 indicates the presence of the attribute
0 indicates the absence of the attribute
Eg. 1 may represent female and 0 for male
DV are sometimes called categorical variables,
or qualitative variables or indicator variables
• ANOVA MODELS: Used to test the statistical
significance of the relationship between a
quantitative regressand and qualitative or
dummy regressors
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• ANCOVA MODELS: regression models
containing an admixture of quantitative and
dummy regressors.
– They provide a method of statistically controlling
for the effects of quantitative regressors called
covariates or control variables in a model that
includes both quantitative and qualitative
regressors
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A single dummy independent variable
• Given the wage discrimination model
W age  B o   D f  B1 edu  u
• Wage=hourly wage
• D=1 for females and 0 for males
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• is the difference in hourly wage between males and
females given the same level of education and the same
error term u.
• B o is the mean hourly wage for males (the base or
benchmark group)
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Why a single category is included in a
single DV. equation
• Using two DV would introduce perfect colinearity
because for example
• Female + male=1
• Ie. Male is a perfect colinear function of female
• Introducing DV for both male and female is the
simplest example of the so called dummy variable
trap.
• It arises when too many DV describe a given
number of groups
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Overcoming the DV trap
• One way of overcoming the DV trap is to drop
the intercept and include the two categories
• Eg.
W age  B o m ale   fem ale  B1educ .  u
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Some interpretations
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Given
Wage = 2.91 - 1.81female + 0.572educ.
Se=
(0.12) (0.26)
(0.049)
N=526
R-sqd=0.364
-males receive a mean wage of Ghc2.91 per hour
-on the average females receive Ghc1.81 less
than their male counterparts holding education
constant.
• -the average hourly wage of female is
• 2.91-1.81=Ghc1.10
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Interpreting coefficients on DV when
an explanatory v. is in log form
• Given the ff. model on the effects of training grants on
hours of training by firms
ˆ p  46.67  26.25 grant  0.98 log( sales )  6.07 log( em ploy )
hrsem
se
 (43.21) (5.59)
(3.54)
(3.54)
n  105
R  0.237
• hrsemp=hours of training per employee at the firm
level
• Grant is a DV =1 if a firm received a job training grant
and 0 otherwise
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• Sales=annual sales
• Employ=total no. of employees of the firm
• Grant coefficient of 26.25 means controlling
for sales and employment, firms that receive
grants trained each worker on the average
26.25 hours more
• The coefficient on log sales is small and
insignificant
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• The coefficient on log employ of -6.07 means
• If a firm is 1% larger it trains its workers by
0.061 (ie. 6.07/100) hours less
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Interpreting DV when dependent v. is
in log form
• 1. given the housing price equation
ˆ )  5.56  0.168( lotsize )  0.707 log( sqrft )  0.027 bdrm s  0.054 colonial
log( price
• Colonial is a DV. =1 if house is of a colonial style and 0
otherwise
• Raw interpretation: holding other factors constant the
difference in log(price) of a house of a colonial style is 0.054
• Correct interpretation: a house of the colonial style is predicted
to sell for about 5.4% more, holding other factors constant
• Ie. When the dependent v. is in log form the coefficient on the
DV multiplied by 100 is interpreted as percentage difference in
the dependent variable holding other factors constant.
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2. Given a log hourly wage equation
• Using log(wage) as the dependent v. and adding
quadratics in experience
log( w age )  0.417  0.297 fem ale  0.080 educ  0.029 exp er  0.0005 exp er
• The coefficient on female implies for the same
levels of experience and education women on the
average earn 29.7% (ie. 100*0.297) less than men
• More accurate interpretation: a more accurate
interpretation is obtained by using the formula
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• 100*[exp.(B)-1]
• Where B is the coefficient on the dummy
variable
• Thus, 100*[exp.(-0.297)-1]=25.7
• More accurately, on the average a woman’s
wage is 25.7% below a comparable man’s
wage
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• Median hourly wage for males is calculated by
taking the antilog of the intercept 0.417
• exp(0.417)=Ghc1.517
• The median hourly wage of females
• Exp[0.417+(-0.279)]=Ghc1.148
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ANOVA models with 2 DV.
• Model: hourly wage in relation to marital status and
region of residence
Yt 
8.8148 
0.997 D 2 i 
1.6729 D 3 i
se 
(0.4015)
(0.4642)
(0.4854)
t
(21.953)
(2.3688)
(0.0006)
R  0.0322
• Y=hourly wage (Ghc)
• D 2 =marital status 1=married 0=otherwise
• D 3 =region of residence 1=south 0=otherwise
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Which is the benchmark group?
Unmarried non-south residents
All comparisms are made wrt this group as ff:
-Unmarried non-south residents receive a
mean hourly wage of GhC8.81
• -Those married on average receive Ghc1.10
more than the unmarried non-south residents
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• The mean hourly wage for the married is Ghc
9.91 (ie. 8.81+1.10)
• -the hourly wage of those from the south is
lower by Ghc 1.67
• The mean hourly wage of those from the
south is Ghc7.14 (ie. -1.67+8.81)
• All are statistically significant.
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Interaction effects using DV.
• Given
log( w age )  0.321  0.110 fem ale  0.213 m ale  0.301 fem ale .m arried  u
• Female is a dummy=1 for females; 0=otherwise
• Married is a dummy 1=married 0=otherwise
• The differential effect of being a married female
is 0.301
• Married females earn 35.12% more than single
men with a mode of Ghc1.35
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• What will be the earnings for
– 1. married men?
– 2. single men?
– 3. unmarried females?
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Uses of DV in applied econometric
research
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Read Akoutsoyannis pp.281-284
1. As proxies to qualitative variables
2. As proxies for numerical factors
3. Measuring shifts of a function over time
4. Measuring the change in parameters over
time
• 5. As proxies for the dependent variable
• 6. For seasonal adjustment of time series
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Indicator vs effects coding
• Indicator coding: where the reference category is
assigned zero across the set of DV.
• Effects coding: where the reference category is
assigned a value of negative 1 across the set of DV.
• In indicator coding coefficients represent group
deviations on the dependent variable from the
reference group
• While in effect coding coefficients become group
deviations on the dependent variable from the mean
of the dependent variable across all groups
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