Dummy Variables in Financial Econometrics: Applications and Interpretation, Summaries of Introduction to Econometrics

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Dummy Variables

Introduction

Discuss the use of dummy variables in

Financial Econometrics.

Examine the issue of normality and the

use of dummy variables to correct any

problem

Show how dummy variables affect the

regression

Assess the use of intercept and slope

dummy variables

Bera-Jarque Test

• This test for normality in effect tests for the

coefficients of skewness and excess kurtosis

being jointly equal to 0

numberof observatio ns

coefficient of excess kurtosis

coefficient of skewness

]

24

( 3 )

6

[

2

1

2

2

2

1









 

T

b

b

b b

W T

Bera-Jarque Test

• The statistic follows the chi-squared distribution

with 2 degrees of freedom.

• The null hypothesis is that the distribution is

normal.

• i.e. if we get a Bera-Jarque statistic of 4.78, the

critical value is 5.99 (5%), then as 4.78<5.99 we

would accept the null hypothesis that the error

term is normally distributed.

• Most computer programmes report this statistic.

Non-normality

The use of this type of dummy variable is

controversial, as some argue it is an

artificial method of improving the

regression, by in effect removing the

influence of this particular observation.

However an outlier can have an

excessively strong effect on a model,

giving an unrealistic result, so needs to be

taken into account.

Dummy Variable for Single Outlier

• In a regression of stock prices against income for

the UK, an outlier was noticed for 1992 month 9,

when the UK left the ERM. A dummy variable was

added to account for this. This produced the

following result:

1 var 1992 9.

R 0. 78 , 1. 87.

2

D dummy iable for m

DW

s y D

t t t

Dummy Variables

• Dummy variables are discrete variables taking a

value of ‘0’ or ‘1’. They are often called ‘on’ ‘off’

variables, being ‘on’ when they are 1.

• Dummy variables can be used either as

explanatory variables or as the dependent

variable.

• When they act as the dependent variable there

are specific problems with how the regression is

interpreted, however when they act as

explanatory variables they can be interpreted in

the same way as other variables.

Types of Explanatory Dummy

Variable

• Qualitative dummy variables: i.e. age, sex, race,

health.

• Seasonal dummy variables: depends on the

nature of the data, so quarterly data requires

three dummy variables etc.

• Dummy variables that represent a change in

policy:

• Intercept dummy variables, that pick up a change in

the intercept of the regression

• Slope dummy variables, that pick up a change in the

slope of the regression

Dummy Variables

This produces an average salary for a

smoker of E( y/Di =0) = .

The average salary of a non-smoker will

be E( y/Di = 1) =  + .

This suggests that non-smokers receive a

higher salary than smokers.

Dummy Variables

• Equally we could have used the dummy

variable in a model with other explanatory

variables. In addition to the dummy variable

we could also add years of experience ( x) ,

to give:

i i i t

y     D   x  u

Seasonal Dummy Variables

• The use of seasonal dummy variables is widespread in

finance due to the ‘day of the week’ effect on asset

prices.

• They take the same format as other dummy variables,

i.e. a January dummy variable would consist of 0, except

every observation in January which has the value of 1.

• For monthly data, we include 11 dummy variables,

quarterly data 3 etc. i.e. we have as many dummies as

months, quarters etc minus 1.

• The excluded month acts as the reference category, i.e.

all the other dummies refer to differences between

themselves and this reference month.

Seasonal Dummy variables

• If we have the following model of share prices for a

gas and electricity firm, where the share price is

regressed against 3 dummy variables. (Using

quarterly data)

t t

t t

t t

t

t t

Q s y y

Q s y y

Q s y y

Q s y

s D D D y

2 3 4

Slope Dummy Variables

• The type of dummy variable considered so far is

the intercept dummy variable, we could also use

dummy variables to model changes in the slope

of the regression line, these are known as slope

or interaction dummy variables.

• We can include either types of dummy variable

or more commonly both types in a regression, to

account for changes in the intercept and slope of

the regression line.

Slope Dummy Variables

• The slope dummy variable consists of a term

which is the product of an explanatory variable

and dummy variable ( Dx ):

t t t

t

t t t

t

t t t t t t

y x u

When D

y x u

When D

y D x D x u

    



  



    

( ) ( )

1

0

0 1 1 2

0 1

0 1 1 2

   

 

   