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QMT 3033
ECONOMETRICS
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Chapter 1
INTRODUCTION
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Introduction to Econometrics
 Econometrics literally means “measurement
in economics”.
 Econometrics may be defined as the social
science in which the tools of economic theory,
mathematics, and statistical inference are
applied to the analysis of economic
phenomena.
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 Econometrics is not mathematical economics.
It is about developing quantitative estimates
of economics relations or models.
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Economic Models
 A model is a simple representation of a real-
world process.
 Models have to be simple to make them
traceable.
 They also have to be general enough to be
useful.
 Models explain the relationships between
variables of interest.
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Example
 The national income identity represents a
simple economic model.
 For a closed economy, the following identity
holds,
Y=C+I+G
where all variables are flows in real terms.
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 Hypotheses about the individual parts of this
identity formed:
1) Consumption
C = f [(1-t) Y, r]
0 < f1 < 1, f2 < 0
2) Investment
I = f [(1-t) Y, r]
f1 > 0, f2 < 0
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 The model constitutes a theory about the joint
determination of C, I and Y.
 C, I and Y are endogenous.
 The explanation is conditional upon the
values of G, r and t.
 G, r and t are exogenous.
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Limits of Economic Models
 Economic models leave many questions
1)
2)
3)
4)
5)
unanswered.
Functional form.
Data definition and measurement.
Dynamic (lag) structure.
Qualitative versus quantitative implications.
Choice between competing theories.
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The Econometrics Model
 The specification of a model with a
deterministic component (the explanatory
variables) and the stochastic error component
is called the econometric model.
 It provides a link between the data and
economic theory.
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Economic vs Statistical Models
 Economic model explains the behaviour of
one variable in terms of other variables.
 Eg. Q = f(P)
 Linear: Qt = β1 + β2Pt
 Log-linear: ln Qt = β1 + β2 ln Pt
 Statistical model: Qt = β1 + β2 Pt + ut
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Writing Research Paper
 Research can be defined as an organized,
systematic, data-based, critical, objective,
specific inquiry or investigation into a
specific problem, undertaken with the purpose
of finding answers or solutions to it.
 Research provides the needed information
that guide managers to make informed
decisions to successfully deal with problems.
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Research Process
The broad
problem area
Research
design
Data
collection
Preliminary data
gathering
Hypothesis
development
Data analysis
and interpretation
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Problem
definition
Theoretical
framework
Research
report
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Review of Probability Concepts
Basic Probability Concepts
 Probability is the likelihood or chance that a
particular event will occur (always between 0
and 1).
 Event is each possible outcome of a variable.
 Simple Event is an event that can be
described by a single characteristic.
 Sample Space is the collection of all possible
events.
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Assessing Probability
1) A priori classical probability
- Probability of occurrence:
=
X
T
where
X = number of ways in which the event
occurs
T = total number of elementary outcomes
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2) Empirical Classical Probability
- Probability of occurrence.
Number of favorable outcomes observed
=
Total number of elementary observed
3) Subjective Probability
- An individual judgment or opinion about
the probability of occurrence.
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Conditional Probabilities
 A conditional probability is the probability
of one event, given that another event has
occurred:
P(A and B)
P(A | B) 
P(B)
The conditional probability of A given
that B has occurred
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P(A and B)
P(B | A) 
P(A)
The conditional probability of B given
that A has occurred
Where
P(A and B) = joint probability of A and B
P(A) = marginal probability of A
P(B) = marginal probability of B
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Bayes’ Theorem
 Conditional probability takes into account
information about the occurrence of one event
to find the probability of another event.
 This concept can be extended to revise
probabilities based on new information and to
determine the probability that a particular effect
was due to a specific cause.
 The procedure for revising these probabilities is
called Bayes’ Theorem.
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Bayes’ Theorem Formula
P(B i | A) 
P(A | B i )P(B i )
P(A | B 1 )P(B 1 )  P(A | B 2 )P(B 2 )    P(A | B k )P(B k )
Where
Bi = ith event of k mutually exclusive
and collectively exhaustive events
A = new event that might impact P(Bi)
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Discrete Probability
Binomial Distribution
 Binomial distribution is used when discrete
random variable of interest is the number of
successes obtained in a sample of n
observation.
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 Binomial distribution:
n!
n X
X
P X  
p 1  p 
X !n  X !
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Poisson Distribution
 Poisson distribution is used when you wish
to count the number of times an event
occurs in a given area of opportunity.
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Poisson Distribution Formula

e 
P( X ) 
X!
x
Where
X = number of events in an area of
opportunity
 = expected number of events
e = base of the natural logarithm system
(2.71828...)
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