ECF 322/422: ECONOMETRICS II AND TIME SERIES ECONOMETRICS
TOPIC ONE:DUMMY INDEPENDENT VARIABLE MODELS
1.1 Introduction to dummy independent variables
1.2 Incorporating dummy variables in a regression model
1.3 Interaction effects of dummy variables (intercept and slope effects)
1.4 ANOVA and ANCOVA models
1.5 The dummy variable approach to the chow test
TOPIC TWO: DUMMY DEPENDENT VARIABLE MODELS
1.1 introduction to dummy dependent variables
1.2 the Linear Probability Model
1.3 the logit and probit model (Binary cases)
1.4 Marginal effects for Dummy dependent Variable models
1.5 Goodness of fit for dummy dependent variable models
TOPIC THREE: SIMULTANEOUS EQUATION MODELS
3.1 Introduction to simultaneous equations
3.2 Endogenous versus Exogenous variables
3.3 Structural equations and reduced form equations
3.4 The Simultaneity bias in OLS estimation
3.5 Identification of Simultaneous equations – Order and Rank conditions
3.6 Methods of estimating simultaneous equations
TOPIC FOUR: TIME SERIES ECONOMETRICS
4.1 Introduction to Time series Econometrics
4.2 Characteristics of time series
4.3 Data generating processes
4.4 Stationary and non stationary series: Unit roots
4.5 Testing for stationarity of time series and remedial measures for non-stationary series
4.6 Integrated time series
4.7 Cointergration and Error-correction Model
TOPIC FIVE: PANEL DATA ANALYSIS
Page 1 of 82
, 5.1 Introduction to Panel Data
5.2 Merits and demerits of Panel Data
5.3 Types of panel data
5.4 Models for estimation of Panel Data
5.5 Fixed Effects and Random effects: The Hausman Test
2. ASSESSMENT
The course will be assessed as follows: Class Assignments (15%), Sit-in CAT (15%) and Final
semester Examination (70%).
3. RECOMMENDED TEXT BOOK
Students are encouraged to read widely on the subject, and any textbook on Econometrics will be
useful. However, text books by Gujarati Damodar, Maddala G and Stock and Watson will form
the main reference material for the course.
SUCCESS IN YOUR STUDIES
EES 401: FUNDAMENTALS OF ECONOMETRICS II
TOPIC ONE: DUMMY INDEPENDENT VARIABLE MODELS
1. INTRODUCTION TO DUMMY VARIABLES
A dummy variable is one that takes on discrete values only, that is 0, 1, 2,
3… rather than continuous numbers. Thus, a binary dummy will have only
two possible values: 0 and 1 to indicate the absence and presence of a
particular characteristic respectively.
Dummy variables are also known as categorical variables, discrete variables
or binary variables.
In regression analysis, dummy variables are mainly used to capture
qualitative attributes or characteristics, such as gender, religion,
employment status, marital status, political party membership, and so on.
Page 2 of 82
,Since these variables cannot be measured but they do influence the
dependent variable in a regression model, then we need to find a way of
capturing them in the model, and this is done usually through the process of
CODING. In coding, we assign specific numerical values to each particular
attribute. For example:
- Gender: male (0), female (1)
- Employment status: unemployed (0), employed (1)
- Voting in elections: no (0), yes (1), undecided (2)
- Political party membership: republican (0), democrat (1), others (2)
- Marital status: single (0), married (1), divorced (2), separated (3),
widowed (4), etc.
Dummy variables thus sort the data into mutually exclusive categories. They
are thus useful in helping us to incorporate into a model:
(i) Qualitative characteristics,
(ii) Seasonal and regional analysis,
(iii) Occurrence of major events,
(iv) Changes in regimes, and so on.
The main concepts in the topic are: how to incorporate dummy variables in a
regression model, the interaction effects of dummy variables – i.e., intercept,
slope and both intercept and slope, the dummy variable trap, and the
dummy regression concepts of ANOVA and ANCOVA.
2. INCORPORATING DUMMY VARIABLES IN A REGRESSION MODEL
Dummy variables are incorporated in regression models, in the same way as
other quantitative explanatory variables are included.
For example, consider the following model for salary of employees as a
function of gender and level of education:
Salary = 0 + 1 Gender + 2 Education +ut
Where: Salary is measured in thousands of Kenya shillings;
Gender = 1 if female, and 0 otherwise.
Education is measured by the number of years spent in school.
Page 3 of 82
, From the above regression model, we note that salary and education are
quantitative variables, whereas gender is a qualitative or dummy variable.
A binary dummy explanatory variable such as gender, can take only two
values, 0 and 1 as shown. The category assigned value 0 (i.e., male in this
case) is assumed to have no role in influencing the dependent variable. Such
a category given a value of zero is thus omitted from the regression model,
and is thus called the REFERENCE CATEGORY or BASE CATEGORY or
BENCHMARK CATEGORY. The omitted category is the category to which no
dummy is assigned, and thus, it is the category against which comparisons
are made. This is why it is referred to as the reference or base or benchmark
category.
On the other hand, the category given a value of 1 (i.e., female in this case)
will affect the regression model and it acts by CHANGING THE INTERCEPT OF
THE REGRESSION MODEL. This is demonstrated as shown below:
MALE REGRESSION: Salary = 0 + 1 (0) + 2 Education +ut
Salary = 0 + 2 Education +ut
FEMALE REGRESSION: Salary = 0 + 1 (1) + 2 Education +ut
Salary = (0 + 1) + 2 Education +ut
The intercept for male regression model is 0 while that for female is 0 + 1.
However, the slopes for the two regression models are constant (2), and
thus the regression lines for MALE and FEMALE will be parallel to each other.
The diagram below illustrates the dummy variable effect for change in
intercept:
Figure 1: dummy variable effect for change in intercept
Page 4 of 82
TOPIC ONE:DUMMY INDEPENDENT VARIABLE MODELS
1.1 Introduction to dummy independent variables
1.2 Incorporating dummy variables in a regression model
1.3 Interaction effects of dummy variables (intercept and slope effects)
1.4 ANOVA and ANCOVA models
1.5 The dummy variable approach to the chow test
TOPIC TWO: DUMMY DEPENDENT VARIABLE MODELS
1.1 introduction to dummy dependent variables
1.2 the Linear Probability Model
1.3 the logit and probit model (Binary cases)
1.4 Marginal effects for Dummy dependent Variable models
1.5 Goodness of fit for dummy dependent variable models
TOPIC THREE: SIMULTANEOUS EQUATION MODELS
3.1 Introduction to simultaneous equations
3.2 Endogenous versus Exogenous variables
3.3 Structural equations and reduced form equations
3.4 The Simultaneity bias in OLS estimation
3.5 Identification of Simultaneous equations – Order and Rank conditions
3.6 Methods of estimating simultaneous equations
TOPIC FOUR: TIME SERIES ECONOMETRICS
4.1 Introduction to Time series Econometrics
4.2 Characteristics of time series
4.3 Data generating processes
4.4 Stationary and non stationary series: Unit roots
4.5 Testing for stationarity of time series and remedial measures for non-stationary series
4.6 Integrated time series
4.7 Cointergration and Error-correction Model
TOPIC FIVE: PANEL DATA ANALYSIS
Page 1 of 82
, 5.1 Introduction to Panel Data
5.2 Merits and demerits of Panel Data
5.3 Types of panel data
5.4 Models for estimation of Panel Data
5.5 Fixed Effects and Random effects: The Hausman Test
2. ASSESSMENT
The course will be assessed as follows: Class Assignments (15%), Sit-in CAT (15%) and Final
semester Examination (70%).
3. RECOMMENDED TEXT BOOK
Students are encouraged to read widely on the subject, and any textbook on Econometrics will be
useful. However, text books by Gujarati Damodar, Maddala G and Stock and Watson will form
the main reference material for the course.
SUCCESS IN YOUR STUDIES
EES 401: FUNDAMENTALS OF ECONOMETRICS II
TOPIC ONE: DUMMY INDEPENDENT VARIABLE MODELS
1. INTRODUCTION TO DUMMY VARIABLES
A dummy variable is one that takes on discrete values only, that is 0, 1, 2,
3… rather than continuous numbers. Thus, a binary dummy will have only
two possible values: 0 and 1 to indicate the absence and presence of a
particular characteristic respectively.
Dummy variables are also known as categorical variables, discrete variables
or binary variables.
In regression analysis, dummy variables are mainly used to capture
qualitative attributes or characteristics, such as gender, religion,
employment status, marital status, political party membership, and so on.
Page 2 of 82
,Since these variables cannot be measured but they do influence the
dependent variable in a regression model, then we need to find a way of
capturing them in the model, and this is done usually through the process of
CODING. In coding, we assign specific numerical values to each particular
attribute. For example:
- Gender: male (0), female (1)
- Employment status: unemployed (0), employed (1)
- Voting in elections: no (0), yes (1), undecided (2)
- Political party membership: republican (0), democrat (1), others (2)
- Marital status: single (0), married (1), divorced (2), separated (3),
widowed (4), etc.
Dummy variables thus sort the data into mutually exclusive categories. They
are thus useful in helping us to incorporate into a model:
(i) Qualitative characteristics,
(ii) Seasonal and regional analysis,
(iii) Occurrence of major events,
(iv) Changes in regimes, and so on.
The main concepts in the topic are: how to incorporate dummy variables in a
regression model, the interaction effects of dummy variables – i.e., intercept,
slope and both intercept and slope, the dummy variable trap, and the
dummy regression concepts of ANOVA and ANCOVA.
2. INCORPORATING DUMMY VARIABLES IN A REGRESSION MODEL
Dummy variables are incorporated in regression models, in the same way as
other quantitative explanatory variables are included.
For example, consider the following model for salary of employees as a
function of gender and level of education:
Salary = 0 + 1 Gender + 2 Education +ut
Where: Salary is measured in thousands of Kenya shillings;
Gender = 1 if female, and 0 otherwise.
Education is measured by the number of years spent in school.
Page 3 of 82
, From the above regression model, we note that salary and education are
quantitative variables, whereas gender is a qualitative or dummy variable.
A binary dummy explanatory variable such as gender, can take only two
values, 0 and 1 as shown. The category assigned value 0 (i.e., male in this
case) is assumed to have no role in influencing the dependent variable. Such
a category given a value of zero is thus omitted from the regression model,
and is thus called the REFERENCE CATEGORY or BASE CATEGORY or
BENCHMARK CATEGORY. The omitted category is the category to which no
dummy is assigned, and thus, it is the category against which comparisons
are made. This is why it is referred to as the reference or base or benchmark
category.
On the other hand, the category given a value of 1 (i.e., female in this case)
will affect the regression model and it acts by CHANGING THE INTERCEPT OF
THE REGRESSION MODEL. This is demonstrated as shown below:
MALE REGRESSION: Salary = 0 + 1 (0) + 2 Education +ut
Salary = 0 + 2 Education +ut
FEMALE REGRESSION: Salary = 0 + 1 (1) + 2 Education +ut
Salary = (0 + 1) + 2 Education +ut
The intercept for male regression model is 0 while that for female is 0 + 1.
However, the slopes for the two regression models are constant (2), and
thus the regression lines for MALE and FEMALE will be parallel to each other.
The diagram below illustrates the dummy variable effect for change in
intercept:
Figure 1: dummy variable effect for change in intercept
Page 4 of 82
