LECTURE 1
Introduction to Econometrics
HIEU NGUYEN
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Fall Semester, 2024
Lecturer: HIEU NGUYEN
Email: 254279@muni.cz
Lectures/Seminars: Friday 9:00 – 11:50 (VT 105)
Office hours: Fri 12:00 – 14:00
(appointment via email in advance)
INTRODUCTORY ECONOMETRICS COURSE
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Grade compositions:
• 2 home assignments (15pts * 2 = 30 pts)
• Midterm exam (30 pts, MCQs & practice exercises)
• Final exam (30 pts, MCQs & practice exercises)
• 2 in-class quizzes (5 pts * 2 = 10 points)
Materials:
• Wooldridge, J. M., Introductory Econometrics: A Modern
Approach
• Adkins, L., Using gretl for Principles of Econometrics
• Studenmund, A. H., Using Econometrics: A Practical Guide,
Chapter 16
COURSE CONTENT
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e Lectures:
 Lecture 1: Introduction, repetition of statistical
background, non-technical introduction to regression
 Lectures2 - 4: Linear regression models (OLS)
 Lectures5 - 11: Violations of standard assumptions
e In-classexercises:
 Will serve to clarify and apply concepts presented
on lectures
 Wewill use statistical software Gretl to solve the exercises
WHAT IS ECONOMETRICS?
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 Econometrics is a set of statistical tools and techniques for
quantitative measurement of actual economic and
business phenomena
 It attemptsto
1. quantify economic reality
2. bridge the gap between the abstract world of economic
theory and the real world of human activity
 It has three major uses:
1. describing economic reality
2. testing hypotheses about economic theory
3. forecasting futureeconomic activity
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EXAMPLE
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e Consumer demand for a particular commodity can be
thought of as a relationship between
 quantity demanded (Q)
 commodity’s price (P)
 price of substitute good (Ps)
 disposableincome (Y)
e Theoretical functionalrelationship:
Q = f(P, Ps, Y)
e Econometrics allows us to specify:
Q = 31.50 − 0.73P + 0.11Ps +0.23Y
LECTURE 1.
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e Introduction, repetition of statisticalbackground
 probability theory
 statistical inference
e Readings:
 Wooldridge, J. M., Introductory Econometrics: A
Modern Approach, Appendix B and C
 Studenmund, A. H., Using Econometrics: A
Practical Guide, Chapter 16
RANDOM VARIABLES
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e A random variable X is a variable whose numerical value
is determined by chance. It is a quantification of the
outcome of a random phenomenon.
e Discrete random variable: has a countable number of
possible values
Example: the number of times that a coin will be flipped
before a heads is obtained
e Continuous random variable: can take on any value in an
interval
Example: time until the first goal is scored in a football
match between Liverpool and Manchester United
DISCRETE RANDOM VARIABLES
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e Described by listing the possible values and the associated
probability that it takes on each value
e Probability distribution of a variable X that can take
values x1, x2, x3, .. . :
P(X = x1) = p1
P(X = x2) = p2
P(X = x3) = p3
..
e Cumulative mass function (CMF):
SIX-SIDED DIE: PROBABILITY MASS FUNCTION
(PMF)
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SIX-SIDED DIE: HISTOGRAM OF DATA (100 ROLLS)
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SIX-SIDED DIE: HISTOGRAM OF DATA (1000 ROLLS)
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CONTINUOUS RANDOM VARIABLES
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e Probability density function fX(x) (PDF) describes the
relative likelihood for the random variable X to take on a
particular value x
e Cumulative distribution function (CDF):
e Computationalrule:
P(X > x) = 1 − P(X ≤x)
EXPECTED VALUE AND MEDIAN
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e Expected value (mean):
Mean is the (long-run) average value of random variable
Discrete variable Continuous variable
∫
Example: calculating expectedproduction of a wind turbine
given wind speed distribution and a power curve
e Median : ”the value in themiddle”
VARIANCE AND STANDARD DEVIATION
e Variance:
Measures the extent to which the values of a random
variable are dispersed from the mean.
If values (outcomes) are far away from the mean, variance is
high. If they are close to the mean, variance is low.
e Standard deviation :
 Note: Outliers influence onvariance/sd.
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DANCING STATISTICS
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Watch the video ”Dancing statistics: Explaining the statistical
concept of variance through dance”:
https://www.youtube.com/watch?v=pGfwj4GrUlA&list=
PLEzw67WWDg82xKriFiOoixGpNLXK2GNs9&index=4
Use the ’dancing’ terminology to answer these questions:
1. How do we define variance?
2. How can we tell if variance is large or small?
3. What does it mean to evaluate variance within a set?
4. What does it mean to evaluate variance between sets?
5. What is the homogeneity of variance?
6. What is the heterogeneity of variance?
COVARIANCE, CORRELATION, INDEPENDENCE
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e Covariance:
 How, on average, two random variablesvary with
one another.
 Do the two variables move in the same or
opposite direction?
 Measures the amount of linear dependence between two
variables.
Cov(X, Y) = E[(X − E[X])(Y − E[Y])] = E[XY] − E[X]E[Y]
e Correlation:
Similar concept to covariance, but easier to interpret.
It has values between -1 and 1.
Corr(X, Y)=
Cov(X, Y)
σXσY
INDEPENDENCE OF VARIABLES
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e Independence : X and Y are independent if the conditional
probability distribution of X given the observed value of Y
is the same as if the value of Y had not been observed.
e If X and Y are independent, then Cov(X, Y) = 0 (not the
other way round in general)
e Dancing statistics: explaining the statistical concept of
correlation through dance
https://www.youtube.com/watch?v=VFjaBh12C6s&index=3&
list=PLEzw67WWDg82xKriFiOoixGpNLXK2GNs9
COMPUTATIONAL RULES
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E(aX + b) = aE(X) +b
Var(aX +b) = a2Var(X)
Var(X +Y) = Var(X) + Var(Y) + 2Cov(X, Y)
Cov(aX,bY) = Cov(bY, aX) = abCov(X, Y)
Cov(X + Z,Y) = Cov(X, Y) + Cov(Z, Y)
Cov(X,X) = Var[X]
RANDOM VECTORS
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e Example:
e Sometimes, we deal with vectors of randomvariables
e Expected value:
e Variance/covariancematrix:
STANDARDIZED RANDOM VARIABLES
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e Standardization is used for better comparison of different
variables
e Define Z to be the standardized variable ofX:
Z =
X − µX
σX
e The standardized variable Z measures how many standard
deviations X is below or above its mean
e No matter what are the expected value and variance of X,
it always holds that
E[Z] = 0 and Var[Z] = σZ
2 = 1
NORMAL (GAUSSIAN) DISTRIBUTION
e Notation : X ∼ N(µ,σ2) e E[X]= µ e Var[X] = σ2
e Dancingstatistics
https://www.youtube.com/watch?v=dr1DynUzjq0&index=2&
list=PLEzw67WWDg82xKriFiOoixGpNLXK2GNs9
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SUMMARY
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e Today, we revised some concepts from statistics that we
will use throughout our econometrics classes
e It was a very brief overview, serving only for information
what students are expected to know already
e The focus was on properties of statistical distributions and
on work with normal distribution tables
NEXT LECTURE
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e We will go through terminology of sampling and
estimation
e We will start with regression analysis and introduce the
Ordinary Least Squares estimator