SASHA-LEE NELSON ECOH 617 0737692353
ECON 617
CHAPTER 9
DUMMY VARIABLES
INTRODUCTION: THE NATURE OF QUALITATIVE INFORMATION
An assumption made implicitly up to this point has been that we can always obtain a set of
numerical values for all the variables we want to use in our models.
However, there are variables that can play a very important role in the explanation of an
econometric model but are not numerical or easy to quantify.
Some variables are not numerical, e.g.:
Gender may be important in determining salary levels.
Different ethnic groups may fallow diverse patterns regarding consumption and
savings.
The level of education can affect earnings from employment.
Being a member of a labour union may imply different treatment/attitudes than not
belonging to the union.
= All these typical cases in cross-section data.
Not easily quantifiable (or in general qualitative) information could arise within a time series
econometric framework.
Time-series examples:
Change in political dispensation/regime may affect production processes or
employment conditions.
A War can have an impact on all aspects of economic activity.
Certain Day-of-the-week or month in a year can have different effects on stock
prices and.
Seasonal patterns/effects frequently observed in the demand for particular
products; for example, ice cream in the summer, furs during the winter.
= All these typical cases in Time-series data.
To account for this (qualitative variables), we use dummy variables = dichotomous variables.
The next session present the possible effects of qualitative variables in regression equation
and how to use them.
We then present special cases of dummy variables and the chow test for structural stability.
, SASHA-LEE NELSON ECOH 617 0737692353
THE USE OF DUMMY VARIABLES
(A) INTERCEPT DUMMY VARIABLES
Consider cross-sectional regression:
Yi 1 2 X 2i u i
What does 1 tell us? Is it realistic?
It is the constant term and measures the mean value of Y i when X2i is equal to 0.
The important thing here is that this regression equation assumes that the value of
1 will be same for all observations in the data set.
The coefficient may be different, depending on different aspects of the data set.
For example, regional differences might exist in the values of Y i; or Yi might
represent the growth of GDP for EU countries.
Differences in growth rates are quite possible between core and peripheral countries.
The question is, how can we quantify this information in order to enter it in the
regression equation and check for viability of this differences?
The answers: with the use of a special type of variable – dummy (or fake) that
captures qualitative effects by coding the different possible outcomes with numerical
values.
= Capture qualitative differences with dummy (or fake) variable!
This can be done by coding the variable with numerical values of 1 and 0, e.g.
1 for male
D or D = 1 for core country/0 peripheral country
0 for female
Note that the choice of which of the alternatives outcomes is to assign the value of 1 does
not alter the results in an important way, as we shall show later.
Our estimating equation becomes by entering this dummy in our regression:
Yi 1 2 X 2i 3 Di u i
In order to obtain the interpretation of Di consider the two possible values of D and how
these will affect the specification of the above equation.
If D=0, then
Yi 1 2 X 2i u i or
E Yi X 2 i , Di 0 1 2 X 2 i
If D=1, then
Yi 1 2 X 2i 3 (1) u i or
E Yi X 2 i , Di 1 1 2 X 2 i 3 (1)
E Yi X 2i , Di 1 ( 1 3 ) 2 X 2i
The constant is I now different 1 and equal to (β1 + β3).
We can see that by including the dummy variable the value of the intercept changed,
shifting the function (and therefore the regression line) up or down, depending on whether
the observation in question correspond to male or female.
, SASHA-LEE NELSON ECOH 617 0737692353
= Dummy variable change the intercept! See graphs p. 204
β
The figures show two possibilities for 3:
o The first being positive and shifting the regression line up, suggesting that (X2i is
investment rates) the mean GDP growth for core countries is greater than peripheral
countries for any given level of investment
o A second being negative, suggesting the opposite conclusion.
β
Only if 3 is significant different from 0 can we conclude that we have relationship such
depicted above.
(B) SLOPE DUMMY VARIABLES
The implicit assumption here underlining this is that the relationship between Y and X’s is
not effected by the inclusion of the qualitative dummy.
The relationship tween Y and X’s is represented by the derivatives 9slope) of the function in
the simple linear regression model, and by the partial derivatives in the multiple regression
model.
Sometimes, however the slope coefficient might be affected by differences in dummy
variables.
= Intercept dummies assume relationship between X and Y not affected by qualitative
differences.
= Is it always the case?
= Think of example when not?
Consider, for example, Consumption function model, relating consumer expenditure (Y t) to
disposable income (X2t).
Consider time series regression:
Yt 1 2 X 2t ut
ECON 617
CHAPTER 9
DUMMY VARIABLES
INTRODUCTION: THE NATURE OF QUALITATIVE INFORMATION
An assumption made implicitly up to this point has been that we can always obtain a set of
numerical values for all the variables we want to use in our models.
However, there are variables that can play a very important role in the explanation of an
econometric model but are not numerical or easy to quantify.
Some variables are not numerical, e.g.:
Gender may be important in determining salary levels.
Different ethnic groups may fallow diverse patterns regarding consumption and
savings.
The level of education can affect earnings from employment.
Being a member of a labour union may imply different treatment/attitudes than not
belonging to the union.
= All these typical cases in cross-section data.
Not easily quantifiable (or in general qualitative) information could arise within a time series
econometric framework.
Time-series examples:
Change in political dispensation/regime may affect production processes or
employment conditions.
A War can have an impact on all aspects of economic activity.
Certain Day-of-the-week or month in a year can have different effects on stock
prices and.
Seasonal patterns/effects frequently observed in the demand for particular
products; for example, ice cream in the summer, furs during the winter.
= All these typical cases in Time-series data.
To account for this (qualitative variables), we use dummy variables = dichotomous variables.
The next session present the possible effects of qualitative variables in regression equation
and how to use them.
We then present special cases of dummy variables and the chow test for structural stability.
, SASHA-LEE NELSON ECOH 617 0737692353
THE USE OF DUMMY VARIABLES
(A) INTERCEPT DUMMY VARIABLES
Consider cross-sectional regression:
Yi 1 2 X 2i u i
What does 1 tell us? Is it realistic?
It is the constant term and measures the mean value of Y i when X2i is equal to 0.
The important thing here is that this regression equation assumes that the value of
1 will be same for all observations in the data set.
The coefficient may be different, depending on different aspects of the data set.
For example, regional differences might exist in the values of Y i; or Yi might
represent the growth of GDP for EU countries.
Differences in growth rates are quite possible between core and peripheral countries.
The question is, how can we quantify this information in order to enter it in the
regression equation and check for viability of this differences?
The answers: with the use of a special type of variable – dummy (or fake) that
captures qualitative effects by coding the different possible outcomes with numerical
values.
= Capture qualitative differences with dummy (or fake) variable!
This can be done by coding the variable with numerical values of 1 and 0, e.g.
1 for male
D or D = 1 for core country/0 peripheral country
0 for female
Note that the choice of which of the alternatives outcomes is to assign the value of 1 does
not alter the results in an important way, as we shall show later.
Our estimating equation becomes by entering this dummy in our regression:
Yi 1 2 X 2i 3 Di u i
In order to obtain the interpretation of Di consider the two possible values of D and how
these will affect the specification of the above equation.
If D=0, then
Yi 1 2 X 2i u i or
E Yi X 2 i , Di 0 1 2 X 2 i
If D=1, then
Yi 1 2 X 2i 3 (1) u i or
E Yi X 2 i , Di 1 1 2 X 2 i 3 (1)
E Yi X 2i , Di 1 ( 1 3 ) 2 X 2i
The constant is I now different 1 and equal to (β1 + β3).
We can see that by including the dummy variable the value of the intercept changed,
shifting the function (and therefore the regression line) up or down, depending on whether
the observation in question correspond to male or female.
, SASHA-LEE NELSON ECOH 617 0737692353
= Dummy variable change the intercept! See graphs p. 204
β
The figures show two possibilities for 3:
o The first being positive and shifting the regression line up, suggesting that (X2i is
investment rates) the mean GDP growth for core countries is greater than peripheral
countries for any given level of investment
o A second being negative, suggesting the opposite conclusion.
β
Only if 3 is significant different from 0 can we conclude that we have relationship such
depicted above.
(B) SLOPE DUMMY VARIABLES
The implicit assumption here underlining this is that the relationship between Y and X’s is
not effected by the inclusion of the qualitative dummy.
The relationship tween Y and X’s is represented by the derivatives 9slope) of the function in
the simple linear regression model, and by the partial derivatives in the multiple regression
model.
Sometimes, however the slope coefficient might be affected by differences in dummy
variables.
= Intercept dummies assume relationship between X and Y not affected by qualitative
differences.
= Is it always the case?
= Think of example when not?
Consider, for example, Consumption function model, relating consumer expenditure (Y t) to
disposable income (X2t).
Consider time series regression:
Yt 1 2 X 2t ut
