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Dummy Regression Modeling - Econometric Modeling - Lecture Notes, Study notes of Econometrics and Mathematical Economics

Dr. Bhim Rao Ambedkar University Econometrics and Mathematical Economics

Econometric models are statistical models used in econometric. This modelling tool help economist develop future economy plan for the company. This lecture note discuss important points for understanding Econometric modelling, it includes Dummy, Variables, Modeling, Analysis, Seasonal, Sectional, Use

Typology: Study notes

2011/2012

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MODULE OBJECTIVE

This module attempts to emphasize on qualitative response regression modelling.

The earlier discussion, related to econometric modelling, is based on the assumption that

variables are quantitative in nature. But in reality, some the variables are qualitative in nature. In

this case, the principles of econometric modelling are little bit different. The qualitative variable

is otherwise called dummy or categorical variable. It may be under dependent group or

independent groups. If the independent variable is qualitative, it is called as dummy independent

technique. On the contrary, if the dependent variable is qualitative, it is called as dummy

dependent technique.

In this section, we highlight the followings:

1. WHAT IS A DUMMY VARIABLE?

2. MODELING ON DUMMY INDEPENDENT VARIABLES

3. MODELLING ON DUMMY DEPENDENT VARIABLE

4. USE OF DUMMY VARIABLES IN CROSS SECTIONAL ANALYSIS

5. USE OF DUMMY VARIABLES IN SEASONAL ANALYSIS

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MODULE OBJECTIVE

This module attempts to emphasize on qualitative response regression modelling.

The earlier discussion, related to econometric modelling, is based on the assumption that

variables are quantitative in nature. But in reality, some the variables are qualitative in nature. In

this case, the principles of econometric modelling are little bit different. The qualitative variable

is otherwise called dummy or categorical variable. It may be under dependent group or

independent groups. If the independent variable is qualitative, it is called as dummy independent

technique. On the contrary, if the dependent variable is qualitative, it is called as dummy

dependent technique.

In this section, we highlight the followings:

1. WHAT IS A DUMMY VARIABLE?

2. MODELING ON DUMMY INDEPENDENT VARIABLES

3. MODELLING ON DUMMY DEPENDENT VARIABLE

4. USE OF DUMMY VARIABLES IN CROSS SECTIONAL ANALYSIS

5. USE OF DUMMY VARIABLES IN SEASONAL ANALYSIS

WHAT IS A DUMMY VARIABLE?

Dummy variable is a variable, which can classifying the structure into various subgroups based

on qualities or attributes and implicitly allows one to run individual regressions for each group.

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. In some cases, it can be presented with the code 1, 2, 3, 4

and alike. For instance, if we like to study the impact of religion on income, the religion will be

categorical (qualitative) and in this context, we take the value like 1, 2, 3, etc.

MODELING ON DUMMY INDEPENDENT VARIABLES

The model starts with the assumption that at least one of the independent variable is categorical

or binary. For example, suppose we like to investigate the relationship between income (Y) and

years of experience (X) of workers in a particular industry. In this case, the simple econometric

model will be

Y = α + β X + u

Where, Y is income and X is years of experience in the industry.

However, if we add one more objective/ constraints into this system, which is categorical, then

the problem becomes dummy independent technique. For instance, let us assume that female

earnings are much higher than male earnings. To test it, we can introduce a dummy variable to

distinguish between the observations for male and female workers in the regression. That means

we can introduce gender is a third variable into the system and by default, gender is binary

variable with 0 for male and female for 1 indication. In such a case, the above model can de

modified and it is presented as follows:

The topics above have been briefly discussed below:

There are various statistical techniques to compare two or more mean values which generally go

by the name analysis of variance or ANOVA .Regression models containing a admixture of

quantitative and qualitative variables are called analysis of covariance or ANCOVA models

which are nothing but an extension of ANOVA models providing a statistical method of

controlling the effects of quantitative regressors called control variables. The process of

removing seasonal component from the time series is called the deseasonalisation and we further

try to know about the method of dummy variables for deseasonalisation .With time series data

we can have impulse dummies- just affecting a particular period and step dummies- affect

remains on for a number of periods. We might also have seasonal dummies. For instance,

lnQt = β 0 + β 1 lnYt + β 2 lnPt + δ 1 D1t + δ 2 D2t + δ 3 D3t + ut

Where, D1 = 1 for quarter 1 observations, 0 otherwise; D2 = 1 for quarter 2 observations, 0

otherwise; D3 = 1 for quarter 3 observations, 0 otherwise.

There may be interaction between two qualitative variables. Their effects on the mean Y may not

be simply additive but multiplicative as well. These are called interaction dummy. In general, we

can extend this model to multivariate model. This can be represented as follows.

Dummy modelling, in practice, has lots of applications. In finance/ economics, we can use this

technique for studying the structural break. We use the Chow test measure the structural stability

of the regression model. In case of Chow test the pooling technique assumes homoscedasticity.

Here we find out the differential intercept and the differential slope coefficient to find out the

Y   1 D 1 ... kDk  e

Dummy Regression Modeling - Econometric Modeling - Lecture Notes, Study notes of Econometrics and Mathematical Economics

Related documents

Partial preview of the text

Download Dummy Regression Modeling - Econometric Modeling - Lecture Notes and more Study notes Econometrics and Mathematical Economics in PDF only on Docsity!

MODULE OBJECTIVE

This module attempts to emphasize on qualitative response regression modelling.

The earlier discussion, related to econometric modelling, is based on the assumption that

variables are quantitative in nature. But in reality, some the variables are qualitative in nature. In

this case, the principles of econometric modelling are little bit different. The qualitative variable

is otherwise called dummy or categorical variable. It may be under dependent group or

independent groups. If the independent variable is qualitative, it is called as dummy independent

technique. On the contrary, if the dependent variable is qualitative, it is called as dummy

dependent technique.

In this section, we highlight the followings:

1. WHAT IS A DUMMY VARIABLE?

2. MODELING ON DUMMY INDEPENDENT VARIABLES

3. MODELLING ON DUMMY DEPENDENT VARIABLE

4. USE OF DUMMY VARIABLES IN CROSS SECTIONAL ANALYSIS

5. USE OF DUMMY VARIABLES IN SEASONAL ANALYSIS

WHAT IS A DUMMY VARIABLE?

Dummy variable is a variable, which can classifying the structure into various subgroups based

on qualities or attributes and implicitly allows one to run individual regressions for each group.

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. In some cases, it can be presented with the code 1, 2, 3, 4

and alike. For instance, if we like to study the impact of religion on income, the religion will be

categorical (qualitative) and in this context, we take the value like 1, 2, 3, etc.

MODELING ON DUMMY INDEPENDENT VARIABLES

The model starts with the assumption that at least one of the independent variable is categorical

or binary. For example, suppose we like to investigate the relationship between income (Y) and

years of experience (X) of workers in a particular industry. In this case, the simple econometric

model will be

Y = α + β X + u

Where, Y is income and X is years of experience in the industry.

However, if we add one more objective/ constraints into this system, which is categorical, then

the problem becomes dummy independent technique. For instance, let us assume that female

earnings are much higher than male earnings. To test it, we can introduce a dummy variable to

distinguish between the observations for male and female workers in the regression. That means

we can introduce gender is a third variable into the system and by default, gender is binary

variable with 0 for male and female for 1 indication. In such a case, the above model can de

modified and it is presented as follows:

The topics above have been briefly discussed below:

There are various statistical techniques to compare two or more mean values which generally go

by the name analysis of variance or ANOVA .Regression models containing a admixture of

quantitative and qualitative variables are called analysis of covariance or ANCOVA models

which are nothing but an extension of ANOVA models providing a statistical method of

controlling the effects of quantitative regressors called control variables. The process of

removing seasonal component from the time series is called the deseasonalisation and we further

try to know about the method of dummy variables for deseasonalisation .With time series data

we can have impulse dummies- just affecting a particular period and step dummies- affect

remains on for a number of periods. We might also have seasonal dummies. For instance,

lnQt = β 0 + β 1 lnYt + β 2 lnPt + δ 1 D1t + δ 2 D2t + δ 3 D3t + ut

Where, D1 = 1 for quarter 1 observations, 0 otherwise; D2 = 1 for quarter 2 observations, 0

otherwise; D3 = 1 for quarter 3 observations, 0 otherwise.

There may be interaction between two qualitative variables. Their effects on the mean Y may not

be simply additive but multiplicative as well. These are called interaction dummy. In general, we

can extend this model to multivariate model. This can be represented as follows.

Dummy modelling, in practice, has lots of applications. In finance/ economics, we can use this

technique for studying the structural break. We use the Chow test measure the structural stability

of the regression model. In case of Chow test the pooling technique assumes homoscedasticity.

Here we find out the differential intercept and the differential slope coefficient to find out the

difference in diagrammatic representations between the two time periods. The introduction of

dummy variables brings about the change in the intercept and the slope.