What is Econometrics

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What is Econometrics?

• A set of techniques for measuring economic
  relationships.
• What is an economic relationship? It is a
  relationship among economic variables, where an
  economic variable is one that measures some
  aspect of the economy.
• Examples
• The relationship between economic activity and
  interest rates
• The relationship between savings and tax refunds
• The relationship between education and earnings
• The relationship between crime and wages
• The relationship between advertising expenditures
  and market share
• The relationship between teacher salaries and
  test scores (student learning)

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What is Econometrics ? (cont)

• 2. How do we measure these relationships?
• We use
• economic theory about how economic agents make
  decisions
• data on the economic variables to model and
  estimate the economic relationship

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Understanding Economic Relationships
money supply
Dow-Jones Stock Index
federal budget
short term treasury bills
inflation
trade deficit
Federal Reserve Discount Rate
unemployment
power of labor unions
capital gains tax
rent control laws
crime rate
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The Consumption Function

• From economic theory we know that consumption, c,
  is some function of income, i
• c f(i)
• For applied econometric analysis this consumption
  function must be specified more precisely, such
  as
• c ?1 ?2i
• What is ?2?
• Use econometric techniques to estimate ?1 and ?2
  

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Demand Model
Demand, qd, for an individual commodity
qd f( p, pc, ps, i )
p own price pc price of complements ps
price of substitutes i income
If quantity demanded is a linear function
qd ?1 ?2 p ?3 ps ?4 pc ?5 i
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How Much?

• If we understand the nature of a relationship
  between economic variables then we can answer the
  how much question
• Bernanke asks by how much will economic activity
  fall if we raise interest rates by a quarter
  point?
• CEO of Pepsi asks by how much (if any) will
  market share increase if Pepsi increases
  advertising expenditures by 100 million?
• The Mayor asks by how much will crime fall if
  local wages increase by 20?

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To Answer How Much

• The model is unknown, so
• We theorize about it and
• We use data to test our theories and to make
  predictions about how much

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Constructing an econometric model

• Start with c f(i) but it is too general
• Use theory to argue for c ?1 ?2 i (linear
  relshp)
• But ?1 and ?2 are unknown
• And there may be other variables that influence
  c. (The relationship isnt exact)
• Econometric Model
• c ?1 ?2 i e
• (?1 ?2 i) is the average, systematic,
  deterministic part.
• e is the random error term that measures all
  other factors.

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Econometric Model of Consumption
Actual systematic part random error
c f(i) e
c ?1 ?2 i e
Consumption, c, is a function of income, i, with
error, e
Systematic part provides prediction, f(i), but
the prediction will miss the actual value by a
random error, e.
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A General Econometric Model
y ?1 ?2 X2 ?3 X3 e

• Dependent variable, y, is focus of study
• (predict or explain changes in dependent
  variable).

• Explanatory variables, X2 and X3, help us
  explain
• observed changes in the dependent variable.

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Econometric model

• Systematic or Deterministic Portion
• (non-random) economic variables
• and parameters.
• Error Term
• Random variable with a probability
• distribution.
• Data
• observed values of the variables.

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Research Format

• 1. It all starts with a problem or question
• 2. Economic theory gives us a way of thinking
  about the problem What economic variables are
  involved and what is the possible direction of
  the relationship(s)?
• 3. The working economic model leads to an
  econometric model. We must choose a functional
  form and make some assumptions about the nature
  of the error term.
• 4. Sample data are obtained, and a desirable
  method of statistical analysis chosen, based on
  our initial assumptions, and our understanding of
  how the data were collected.

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• 5. Estimates of the unknown parameters are
  obtained with the help of a statistical software
  package, predictions are made and hypothesis
  tests are performed.
• 6. Model diagnostics are performed to check the
  validity of assumptions weve made. For example,
  were all of the right-hand-side explanatory
  variables relevant? Was the correct functional
  form used?
• 7. The economic consequences and the implications
  of the empirical results are analyzed and
  evaluated. What economic resource allocation and
  distribution results are implied, and what are
  their policy-choice implications? What remaining
  questions might be answered with further study ?

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