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DUMMY VARIABLES

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There are cases when some factors, one wouldlike to introduce, in a regression model arequalitative in nature  and are measured in

nominal scale of measurement.Examples:

1. Earning depends on schooling and one maylike to see whether gender has a role to play.

2. Relationship between ependiture and incomewith respect to ethnic differences.

!. Relationship between growth rate of "#$ percapita and foreign aid per capita in developing

countries some of which are democracies andsome are not.%ne would like to investigatewhether impact of foreign aid on growth isaffected by the type of "overnment.

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&. 'hether change in the policy at macro level has someimpact on the rate of growth of some macroeconomic(socio)economic variables while considering

a long time period.*. 'hether changes in the administrative set up in an

organisation, social upheavals, bilateral war, changesin the technology etc. over the time period have someimpact on the long term growth of some variables.

+n each of these eamples one solution is to run separateregressions for two categories or two periods and seewhether the coefficients are statistically different.

lternatively, one could run a single equation using all

the observations together and measuring the impact ofthe qualitative variables by using the qualitativevariables in a single equation.

-/0 R+3E- RE 45%'5 - #667 R+3E-.

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#667 R+3E-

#ummy +ndependent ariable

• +ntercept #ummy• -lope #ummy

+n regression analysis dependent variable is influenced

by quantitative as well as qualitative variables.

8ualitative ariables indicate presence or absence of aquality or attribute. 8uantifying such variable is by

constructing artificial variables which takes on values of

1 and 9, 9 indicating the absence of an attribute and 1

indicating presence of that.

+ndependent

#ummy#ependent

#ummy

%ne or more eplanatory

variables are qualitative#ependent variables is

qualitative

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1. +ntercept of #ummy

. 3et us consider the following data:

-tarting -alary of /ollegeTeachers ;

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+n such a case to find whether gender

plays a role in starting salary and whether

it is significant. simple intercept dummy regression

model can be used:

 7 D #i

#i  is 1 in case of 6ale and 9 in case of

@emale

The estimated equation is 7 D 1B !.29# i

;9.99=

4nown as a step function or 5% 6odel

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1.. +n the step function the assumption was

that no independent variable influenced

the starting salary.5ow consider the following model:

  7i D 1  2#1  Fi  i

'here 7i D -alary of college teachers  Fi D 7ears of teaching eperience

  #1 D 1 if male, 9 if female

The above equation uses one dummy variable

for the intercept.

/onsider -alary D f ;years of teaching

eperience=

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The epected scatter plot postulates that

the male and female college teachersG

salary functions in relation to years ofteaching eperience have same slope ;H=

but different intercepts.

⇒ -alary levels are dissimilar, but the rateof change with respect to years of

eperience is the same for both.

+f 2  is statistically significant, the nullhypothesis that Ithere is no gender

discriminationJ is reKected ;y using simple

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2. +ntercept ? -lope #ummies:

+n case we need to find whether the rate of

change differs with respect to gender we canintroduce a slope dummy which could be like

the following:

  7i

 D -alary of college teachers

  Fi D 7ears of teaching eperience

  #1 D 1 if male, 9 if female

The conclusions could be related to thestatistical difference in intercept ;level= and

;slope= rate of change.

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Intercept and Slope Dummy

• 5ow consider the following model:

•   7i D 1  2#1  Fi  #1 Fi  i

• 'here 7i D -alary of college teachers•   Fi D 7ears of teaching eperience

•   #1 D 1 if male, 9 if female

• The above equation uses one dummyvariable for the intercept and slope.

• #ata -tructure LLLLL

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Interpretation

• +f the intercept dummy is significant, there is

statistical difference in level.

• +f the slope dummy is statistically different it

may mean that the rate of change for the twogroups are different w.r.t the indep var..

• Ref. : 1. Basic Econometrics by DN

Gujarati, Ch. 9, pp 29!"2#•   2. $ntro%uction to Econometrics

by C.Dou&herty, Ch. ' pp 1" ! 19