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 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 ( ) Dependent Variable:  Gross Investment (Y, in millions of 1947 $) Independent Variables:  Value of Firm (X 1, in millions of 1947 $)  Stock of Plant/Equipment (X 2, in millions of 1947 $)

Regression Model

Special Cases - I

Special Cases - II

Equal , Equal  , Independent  ijt

Equal , Unequal  , Independent  ijt

Equal , Unequal  , Independent  ijt - Iterated (ML)

Cross-Sectional Correlation Over Time - I

Cross-Sectional Correlation Over Time - II

Cross-Sectional Correlation- Iterated EGLS – (ML)

Autocorrelated Errors - I

Autocorrelated Errors - II

Autocorrelated Errors - III

Autocorrelated Errors - IV

Cross-Sectional and Autocorrelation - I

Cross-Sectional and Autocorrelation - II

Random Regression Coefficients - I

Random Regression Coefficients - II

Random Regression Coefficients - III

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

Firm Results - II

RCR – Best Linear Unbiased Predictors

Firm Results – BLUP’s

Test for Equal  s ( 

Seemingly Unrelated Regressions (SUR)

Firm Example - I

Firm Example - II Estimated GLS ML (Iterated GLS)