econ-130 lecture 01 - kids in prison programecon 130 •content of the class –lectures •provide...

ECON 130

Welcome to Econometrics

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.

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)

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

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

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!!!

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

ECON 130

• Basic Class Structure:

–50 minute – 1 hour (1st lecture)

• Short break

–40 minute – 50 minute (2nd lecture)

• Questions, comments.


• 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.


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


• 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?


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?


• How do economists talk about economic

behavior?

• How do they argue something is “true”?

–Theory

–Anecdote

–Statistical (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?


• A SPECIFIC EXAMPLE of a certain

type of economic behavior is a second

way economists talk about the economy.

This is “anecdotal” evidence.


• 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.


• 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)


Y = 12X + e

Endogenous Intercept Slope Exogenous Error (uncertainty)


• 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).

What is Econometrics

• Consider this model of housing prices. It

relates the size of a house to its price.

• Model:

–PRICE = 1 + 2SQUAREFOOTAGE + e

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


0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000 3500

Square Footage

Pric

e (

00

0)


0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000 3500

Square Footage

Pri

ce (

00

0)


Using OLS, the parameters 1 and 2 are

estimated:

PRICE = 52.351 + .13875X(1.404) (7.41)

R2 = .821


Issues:



data?



Statistics Review

• We now begin our Statistics Review.



data?



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

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

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).

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).

Statistics Review

• Descriptions of probability distributions:

–Mean μ

–Variance σ2

–Covariance sxy

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

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)]

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

Statistics Review

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.

Statistics Review

Statistics Review

• The Mean

• The Variance

Statistics Review

• Mean and variance for linear equations:

• E (a + bX) = a + b E(X)

• Var (a + bX) = b2Var(X)

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.

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

Statistics Review

Statistics Review

• A related concept is correlation:

cov ,

var( ) var( )

XY

X Y

X Y

X Y

s

s s

Statistics Review

• Normal Distribution N~(μ, σ2)

• Equation

• Properties:

– Symmetric around mean

– Bell shaped

2

22

1 ( )( ) exp ,

22

xf x x

ss

Statistics Review

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

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 .

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