Economics 310

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Economics 310

• Lecture 19
• Identification

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General Notation
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Identification Problem

• By the identification problem we mean whether
  numerical estimates of the parameters of a
  structural equation can be obtained from the
  estimated reduced-form coefficients.
• If this can be done, we say the equation is
  identified.
• If this cannot be done, we say the equation is
  unidentified or underidentified.

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Identification Problem

• An identified equation may be either exactly (or
  fully or just) identified or overidentified.
• It is said to be exactly identified if unique
  numerical values of the structural parameters can
  be obtained.
• It is said to be overidentified if more than one
  numberical value can be obatained for some of the
  parameters of the structural equations.

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Identification Problem

• The identification problem arises because
  different sets of structural coefficients may be
  compatible with the same set of data.
• A given reduced-form equation may be compatible
  with different structural equations or different
  hypotheses (models).

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Underidentification
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Underidentification
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Another way to view identification
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What is happening
P
S
S
a
b
D
D
Q
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Just Identification
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Just identified
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What is happening
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What is happening
P
S
b
a
D
D
Q
Demand identifies supply
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Just Identified
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Just Identified
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What is happening
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Over-identified
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Over-identified
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What is happening
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Understanding identificationInstrumental
Variable estimation
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Supply in matrix form
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Instrumental Variable Estimation
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Instrumental Variable Estimation
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Instrumental Variable Estimation
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Counting Rule for identification

• Let g be number of endogenous variables in
  equation
• Let k be number exogenous variables in equation
• Let K be number of exogenous or predetermined
  variables in system

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Counting Rule for identification

• gk-1ltK or g-1ltK-k then the equation is
  overidentified.
• gk-1K or g-1K-k then the equation is just
  identified.
• gk-1gtK or g-1gtK-k then the equation is
  underidentified.

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Variance-covariance matrix for IV estimator