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Economics 310

Economics 310. Lecture 19 Identification. General Notation. 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.

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Economics 310

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  1. Economics 310 Lecture 19 Identification

  2. General Notation

  3. 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.

  4. 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.

  5. 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).

  6. Underidentification

  7. Underidentification

  8. Another way to view identification

  9. What is happening P S* S’ a b D’ D* Q

  10. Just Identification

  11. Just identified

  12. What is happening

  13. What is happening P S b a D’ D* Q Demand identifies supply

  14. Just Identified

  15. Just Identified

  16. What is happening

  17. Over-identified

  18. Over-identified

  19. What is happening

  20. Understanding identificationInstrumental Variable estimation

  21. Supply in matrix form

  22. Instrumental Variable Estimation

  23. Instrumental Variable Estimation

  24. Instrumental Variable Estimation

  25. 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

  26. Counting Rule for identification • g*+k*-1<K or g*-1<K-k* then the equation is overidentified. • g*+k*-1=K or g*-1=K-k* then the equation is just identified. • g*+k*-1>K or g*-1>K-k* then the equation is underidentified.

  27. Variance-covariance matrix for IV estimator

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