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Systems of Regression Equations

This study by Boot and deWitt (1960) examines investment demand using Grunfeld's data on 10 firms over 20 years, focusing on gross investment as the dependent variable and firm value and plant/equipment stock as independent variables. It explores various regression model special cases, cross-sectional correlation over time, autocorrelated errors, and random regression coefficients.

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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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