econ-130 lecture 01 - kids in prison programecon 130 •content of the class –lectures •provide...
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ECON 130
Welcome to Econometrics
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What is Econometrics?
• Econometrics is about how we use theory and
data from economics, business and the social
sciences, along with tools from statistics, to
answer “how much” type questions.
• Econometrics is about estimating economic
relationships and predicting economic
outcomes using data.
• Econometrics is the application of statistical
methods to economics.
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ECON 130
• Content of the class– Lectures
• Provide overall structure, direction & content
• Derive and develop statistical and econometric theories and techniques
• Work on projects
– Sections/Labs • Stat Problems
• Econometrics Problems
• Gretl practice and problems
• Work on projects
– Reading• Principles of Econometrics, Hill, Griffiths and Lim, 4th edition.
(can buy used online)
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ECON 130
Grading System
• A 92 – 100
• A- 89 - 91
• B+ 86 – 88
• B 82 – 85
• B- 79 - 81
• C+ 76 – 78
• C 72 – 75
• C- 69 – 71
Grading Rules:• Grades are final; no changes
• No curves
• Test problems can be tossed
• Missed tests can be made up but with a loss of 2 points per midterm &1 point/quiz
• How to get a good grade:
– Attend all classes and labs
– Keep up with the work
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Econometrics• Requirements for the class:
Requirement % of Grade Critical Dates
STAT Quiz 10% 9/10
Problems/Exercises 10% Most Labs
GRETL Practice
First Midterm 30% 10/15
Second Midterm 25% 11/12
Project 25% 12/16
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ECON 130• The PROJECT
–Most challenging part of the class.
–We want 15 teams, with 3 – 5 members.
–We will spend considerable time in both the
class and labs working on it.
–Please start early (forming groups, picking
topics).
–Everyone must participate including final
presentation (or – 5 points!)
No FREERIDING!!!
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ECON 130• The project schedule
End SEP Create your 3-5 person Group
MID OCT Define your topic (economic problem)
~NOV 5 Identify data sources
~NOV 19 Present data, summary statistics
DEC 1 - 9 Literature review, meet with SS
12/16 Final presentations, projects due
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ECON 130
• Basic Class Structure:
–50 minute – 1 hour (1st lecture)
• Short break
–40 minute – 50 minute (2nd lecture)
• Questions, comments.
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What is Econometrics?
• Here is a basic microeconomics problem:
• The law of demand states that when “the price
of a good rises, the quantity demanded of the
good falls . . . .”
• Assume the following demand curve:
• Pd = 10 – ½ Qd. How many units are
demanded at P = 2, 6 and 10?
• Answers: Q(P = 2) = 16, Q(P = 6) = 8 and
Q(P = 10) = 0.
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What is Econometrics?
Price Quantity
2 2 = 10 – ½ Q-8 = - ½ Q Q = 16
6 6 = 10 – ½ Q-4 = - ½ Q Q = 8
10 10 = 10 – ½ Q0 = - ½ Q Q = 0
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What is Econometrics?
• Here is a basic microeconomics
problem:
• The law of demand states that
when “the price of good rises
the quantity demanded of the
good falls.”
• Assume the following demand
curve:
• Pd = 10 – ½ Qd. How many units
are demanded at P = 2, 6 and 10?
• Answers: Q(P = 2) = 16, Q(P = 6)
= 8 and Q(P = 10) = 0.
• NOTICE: All these are
given to you.
– Law of Demand
– Marginal Relationship
(the demand function)
– Prices
• What if there were no
one to provide this
information?
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What is Econometrics?
This is what Econometrics and ECON 130
is all about.
–Where do we get data to do this analysis?
–How do we create the model relating the
data?
–How do we relate data to one another?
–How do we evaluate these relationships?
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What is Econometrics?
• How do economists talk about economic
behavior?
• How do they argue something is “true”?
–Theory
–Anecdote
–Statistical (Econometrics)
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What is Econometrics?
• Theoretical – Law of Demand
–Explains behavior: with all else being
equal, when price of a good rises, the
quantity demanded of the good falls,
and when price falls, the quantity
demanded rises.
–How do we know this is true?
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What is Econometrics?
• A SPECIFIC EXAMPLE of a certain
type of economic behavior is a second
way economists talk about the economy.
This is “anecdotal” evidence.
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What is Econometrics?
• Econometrics offers a third way to talk
about the economy, one which is tied to
actual measurable data derived from
economic and social activities.
• This is important, because it adds a
precision to economic analysis that
approaches the scientific.
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What is Econometrics?
• Basic Linear Economic model
Y = 1 2X + e (e.g., P = A - BQ)
• Y is endogenous or dependent variable
• X is exogenous or independent variable
• A 1 the intercept; 2 is slope (marginal
affects) and e is error term (uncertainty)
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What is Econometrics?
Y = 12X + e
Endogenous Intercept Slope Exogenous Error (uncertainty)
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What is Econometrics?
• 1 and2 are parameters. We can’t know
them
• We ESTIMATE these values.
• Y = b1 + b2
• Our primary method of estimation is called
ordinary least squares (OLS).
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What is Econometrics
• Consider this model of housing prices. It
relates the size of a house to its price.
• Model:
–PRICE = 1 + 2SQUAREFOOTAGE + e
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What is Econometrics?SQUARE FOOTAGE SALE PRICE (000)
1065 199.9
1254 228
1300 235
1577 285
1600 239
1750 293
1800 285
1870 365
1935 295
1948 290
2254 385
2600 505
2800 425
3600 415
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What is Econometrics?
0
100
200
300
400
500
600
0 500 1000 1500 2000 2500 3000 3500
Square Footage
Pric
e (
00
0)
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What is Econometrics?
0
100
200
300
400
500
600
0 500 1000 1500 2000 2500 3000 3500
Square Footage
Pri
ce (
00
0)
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What is Econometrics?
Using OLS, the parameters 1 and 2 are
estimated:
PRICE = 52.351 + .13875X(1.404) (7.41)
R2 = .821
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What is Econometrics?
Issues:
–Where do we get data to do this analysis?
–How do we create the model relating the
data?
–How do we relate data to one another?
–How do we evaluate these relationships?
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What is Econometrics?
Issues:
–Where do we get data to do this analysis?
–How do we create the model relating the
data?
–How do we relate data to one another?
–How do we evaluate these relationships?
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Statistics Review
• We now begin our Statistics Review.
–Where do we get data to do this analysis?
–How do we create the model relating the
data?
–How do we relate data to one another?
–How do we evaluate these relationships?
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Statistics Review
• Random Variables (RV)
• Mean, variance and
covariance
• Normal Distributions
• Empirical Rule
• Standardized Normal
(Z) Distribution
– How it’s derived
– Applications
• Samples
• Chi-Square
• t distribution
• F distribution
• p-Value
• Hypothesis Testing
• Confidence Intervals
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Statistics Review
• Random Variables (RV)
• Mean, variance and covariance
• Normal Distributions
• Empirical Rule
• Standard Normal (Z) Distribution
– How it’s derived
– Applications
• Samples
• Chi Square
• t distribution
• F distribution
• p-Value
• Hypothesis Testing
• Confidence Intervals
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Statistics ReviewWe begin with random variables (RV). Begin with X, a
random variable; x are individual members.
• A random variable is a variable whose value is
unknown until it is observed. I.e., the value that this
variable takes (when realized) is one of many possible
values and which value it takes is uncertain (random).
• A discrete random variable can take only a limited, or
countable, number of values.
• A continuous random variable can take any value on an
interval such as [0,1] (the unit interval) or (-∞,∞) (the
real line).
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Statistics Review
• A random variable, X, is associated with a
probability distribution (f(x)) that determines
the likelihood that it will take a particular
value in specified intervals.
• f(x) = probability density = P(X=x)
• We summarize the probabilities of possible
outcomes using a probability density function
(pdf).
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Statistics Review
• Descriptions of probability distributions:
–Mean μ
–Variance σ2
–Covariance sxy
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Statistics Review• Equation for mean
The mean, or expected value, is the most-used
measure of the “center” of a probability
distribution.
• For a discrete random variable the expected
value is:
1 1 2 2
1
[ ] ( ) ( ) ( )
( ) ( )
n n
n
i ii x
E X x f x x f x x f x
x f x xf x
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Statistics Review
• Other Equations
– If c is a constant, E(c ) = c
– If c is a constant, E[cg(X)] = c E[g(X)]
–E [u(X) + v(X)] = E[u(X)] + E[v(X)]
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Statistics Review
• The variance of a random variable is important
in characterizing the spread of the probability
distribution.
• Algebraically, letting E(X) = μ,
= S(x – )2 f(x)
22 2 2var( ) [ ]X E X E X s
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Statistics Review
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Statistics Review
• Definition: Standard deviation is the square
root of the variance
• Standard deviation = σ = (σ2) 1/2 = (Var(X))1/2
• Note: Variance is always non-negative, so it
can take the square root and obtain a non-
negative standard deviation.
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Statistics Review
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Statistics Review
• The Mean
• The Variance
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Statistics Review
• Mean and variance for linear equations:
• E (a + bX) = a + b E(X)
• Var (a + bX) = b2Var(X)
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Statistics Review
• When we are dealing with two random
variables (X,Y) it is often important to
determine how closely they are related.
• Covariance measures the joint association
between two variables.
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Statistics Review
Covariance measures how variables move
together.
– If they move together (one goes up, other tends to
go up), then Cov>0
– If move in opposite directions, then Cov<0
= S(x – x) fx (y - y) fy
cov( , ) XY X Y X YX Y E X Y E XY s
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Statistics Review
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Statistics Review
• A related concept is correlation:
cov ,
var( ) var( )
XY
X Y
X Y
X Y
s
s s
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Statistics Review
• Normal Distribution N~(μ, σ2)
• Equation
• Properties:
– Symmetric around mean
– Bell shaped
2
22
1 ( )( ) exp ,
22
xf x x
ss
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Statistics Review
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Statistics Review
• Empirical Rule: Area under normal
curve:
– +/- s = 68.26% of area
– +/- 2 s = 95.44% of area
– +/- 3 s = 99.74% of area
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ECON 130
• Next Week we will review various
statistical methods that will be ultimately
be used to evaluate those last questions.
• Please read Chapters 1 and 3 of the text.
• Week 3 we will have a short Statistics
Quiz and then we will begin developing
the techniques to estimate parameters .