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Systems of Regression Equations

Systems of Regression Equations. Cross-Sectional Time Series of Investment Data Boot, J. and G. deWitt (1960). “Investment Demand: An Empirical Contribution to the Aggregation Problem,” International Economic Review , Vol. 1, pp. 3-30. Grunfeld’s Investment Data.

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Systems of Regression Equations

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  1. Systems of Regression Equations Cross-Sectional Time Series of Investment Data Boot, J. and G. deWitt (1960). “Investment Demand: An Empirical Contribution to the Aggregation Problem,” International Economic Review, Vol. 1, pp. 3-30

  2. Grunfeld’s Investment Data • Cross-Section: n=10 Firms (GM, US Steel, GE, Chrysler, Atlantic Refining, IBM, Union Oil, Westinghouse, Goodyear, Diamond Match) • Time Series: T=20 years per firm (1935-1954) • Dependent Variable: • Gross Investment (Y, in millions of 1947 $) • Independent Variables: • Value of Firm (X1, in millions of 1947 $) • Stock of Plant/Equipment (X2, in millions of 1947 $)

  3. Regression Model

  4. Special Cases - I

  5. Special Cases - II

  6. Equal b, Equal s2, Independent eijt

  7. Equal b, Unequal s2, Independent eijt

  8. Equal b, Unequal s2, Independent eijt - Iterated (ML)

  9. Cross-Sectional Correlation Over Time - I

  10. Cross-Sectional Correlation Over Time - II

  11. Cross-Sectional Correlation- Iterated EGLS – (ML)

  12. Autocorrelated Errors - I

  13. Autocorrelated Errors - II

  14. Autocorrelated Errors - III

  15. Autocorrelated Errors - IV

  16. Cross-Sectional and Autocorrelation - I

  17. Cross-Sectional and Autocorrelation - II

  18. Random Regression Coefficients - I

  19. Random Regression Coefficients - II

  20. Random Regression Coefficients - III

  21. Firm Results - I Note: Gamma estimate does not Subtract off the average of the V matrices (not positive definite)

  22. Firm Results - II

  23. RCR – Best Linear Unbiased Predictors

  24. Firm Results – BLUP’s

  25. Test for Equal bs (G=0)

  26. Seemingly Unrelated Regressions (SUR)

  27. Firm Example - I

  28. Firm Example - II Estimated GLS ML (Iterated GLS)

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