Systems of Regression Equations

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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

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Grunfelds Investment Data

• Cross-Section n10 Firms (GM, US Steel, GE,
  Chrysler, Atlantic Refining, IBM, Union Oil,
  Westinghouse, Goodyear, Diamond Match)
• Time Series T20 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
  )

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Regression Model
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Special Cases - I
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Special Cases - II
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Equal b, Equal s2, Independent eijt
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Equal b, Unequal s2, Independent eijt
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Equal b, Unequal s2, Independent eijt - Iterated
(ML)
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Cross-Sectional Correlation Over Time - I
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Cross-Sectional Correlation Over Time - II
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Cross-Sectional Correlation- Iterated EGLS (ML)
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Autocorrelated Errors - I
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Autocorrelated Errors - II
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Autocorrelated Errors - III
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Autocorrelated Errors - IV
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Cross-Sectional and Autocorrelation - I
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Cross-Sectional and Autocorrelation - II
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Random Regression Coefficients - I
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Random Regression Coefficients - II
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Random Regression Coefficients - III
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Firm Results - I
Note Gamma estimate does not Subtract off the
average of the V matrices (not positive definite)

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Firm Results - II
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RCR Best Linear Unbiased Predictors
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Firm Results BLUPs
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Test for Equal bs (G0)
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Seemingly Unrelated Regressions (SUR)
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Firm Example - I
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Firm Example - II
Estimated GLS
ML (Iterated GLS)