Class Outline

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Class Outline

• What is Econometrics?
• Why to Study Econometrics?
• Methodology
• Some Examples
• Review of Statistics
• Events
• Sample Space
• Random Variables
• Probabilities
• Properties of Probabilities
• Reading Handout

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What is Econometrics?
The Social Science in which the tools of economic
theory, mathematics and statistical inference are
applied to the analysis of economic phenomena
Or, Econometrics consists of the application of
mathematical statistics to economic data to lend
empirical support to the models constructed by
mathematical economics and to obtain numerical
results.
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Why to Study Econometrics?

• Broad application beyond economics
• Instrument to test economic theories and predict
  economic issues
• Proper handling of Economic Data in work related
  applications

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Methodology
1. Creating a statement of theory or
hypothesis 2. Specifying the mathematical model
of theory 3. Specifying the statistical, or
econometric, model of theory 4. Collecting
Data 5. Estimating the parameters of the chosen
econometric model 6. Hypothesis Testing 7.
Forecasting or Prediction 8. Using the model for
control or policy purposes
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Creating a Statement of Theory or Hypothesis
We want to know the effect of economic conditions
on peoples willingness to work Hypothesis 1
when economic condition worsen people give up
looking for jobs, dropping out of the labor force
(Discouraged worker hypothesis) Hypothesis 2
When economic conditions worsen other family
members look for jobs, if the main worker in the
family loses his/her job (Added worker
hypothesis) Economic Condition
Unemployment Decision of Staying in/out Labor
Force Labor Force Participation Rate
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Collecting Data

• Time Series U.S. GDP over time
• Cross Section Form (individual or business
  series)
• Panel Data Both cross section and time series
• Levels of Aggregation
• Micro (individual economic units)
• Macro (pooling of individual data)
• Flow or Stock
• Quantitative (prices, income, quantities)
• Qualitative ( married or not, male or female)

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Specifying the Mathematical Model
InterceptB1
SlopeB2
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Statistical or Econometric Model
The relationship between Participation and
Unemployment is not perfectly linear Try drawing
a line through all of the 23 points
This is not easy to represent
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Statistical or Econometric Model
u represents all the other factors that could
help to explain the level of Participation
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Estimation of the Chosen Econometric Model
We estimate the model using Ordinary Least
Squares (OLS) According to this estimation if the
unemployment rate increases 1, the participation
rate will decrease by about 0.65 percentage
points. This suggests that the discouraged worker
effect dominates (Hypothesis 1)
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Checking for Model Adequacy
We can try other model, like the following
In this case we added the variable for the Real
Average Hourly Earnings, which could also help to
explain the Participation rate This is an example
of a Multiple Linear Regression Model The
previous one was a Simple Linear Regression Model
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Hypothesis Testing and Prediction
Testing the Hypothesis Derived from the Model
Does our model make economic sense? Are the
signs of the coefficients as expected Using the
Model for Prediction We can use this model to
predict what can happen if in the future the
unemployment rate increases or there are changes
in earnings
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Stock Market Boom Predictions
Published November 2001
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How to get There

• To get to their target of 36,000, the authors
  project dividend growth of the 30 stocks that
  make up the Dow and apply a valuation measure
  that they call PRP ("perfectly reasonable
  price").
• Many will dismiss this kind of thinking as
  wishful, but they're probably the same Chicken
  Littles who have been calling the market
  overpriced for years.
• The target of 36,000 should be reached in 5 years

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Stock Market Boom
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Experiment

• Statistical or Random Experiment any process of
  observation or measurement that has more than one
  possible outcome and for which there is
  uncertainty about the outcome.
• Example Throwing a coin or a dice

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Sample Space or Population

• Is the set of all possible outcomes of an
  experiment.
• Example Tossing two fair coins. Let H be Heads
  and T be Tail. The possible results are as follow

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Sample Space or Population
Tossing First Coin
Tossing Second Coin
Sample Space
T
T,T
T
T,H
H
T
H,T
H
H,H
H
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Sample Point and Events

• Each member, or outcome, of the sample space or
  population is a sample point
• Events
• Is a particular collection of outcomes and is
  this a subset of the sample space
• Example in our coin experiment let sample A be
  the occurrence of one head. This event has two
  outcomes HT and TH.

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Venn diagram
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Random Variables

• A variable whose (numerical) value is determined
  by the outcome of an experiment is called a
  random variable
• A discrete random variable can take only a finite
  number of values, that can be counted by using
  the positive integers.
• A continuous random variable can take any real
  value (not just whole numbers) in an interval on
  the real number line.

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Random Variables

• Example

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Probability

• Probability of an event
• If an experiment can result in n mutually
  exclusive and equally likely outcomes, and if m
  of these outcomes are favorable to event A, then
  P(A) is the ratio m/n

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Probability

• Empirical definition of Probability or relative
  frequencies
• If in n trials (or observations), m of them are
  favorable to event A, then P(A), the probability
  of event A, is simply the ratio m/n (relative
  frequency) provided n, the number of trials, is
  sufficiently large (technically infinite)

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Probability

• Example

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Properties of Probability

• The probability of an event always lies between 0
  and 1
• If A, B, C, are mutually exclusive events, the
  probability that any one of them will occur is
  equal to the sum of the probabilities of their
  individual occurrences
• P(ABC)P(A)P(B)P(C)

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Properties of Probability

• If A,B,C, are any events, they are said to be
  statistically independent if the probability of
  their occurring together is equal to the product
  of their individual probability
• If the events A, B, C, are not mutually
  exclusive, then we have that for events A and B
• P(AB)P(A)P(B)-P(AB)
• For every event A there is an event A called the
  complement of A, with these properties
• P(AA)1
• P(AA)0

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Properties of Probability

• Conditional Probability
• Assume two events A and B. We want to find out
  the probability that the event A occurs knowing
  that the event B has already occurred. This is
  the conditional probability of A P(AB)

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Properties of Probability

• Conditional and unconditional probabilities in
  general are different. If the two events are
  independent

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Properties of Probability

• Bayes Theorem The knowledge that an event B has
  occurred can be used to revise or update the
  probability that an event A has occurred