Leontief’s Input-Output Representation of Regression Coefficients
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This paper formally establishes tighter-than-known connectivity between Least Squares (LS) estimators and Leontief’s input-output (I/O) model. First, this study shows that the nexus between partial and total derivatives of the general function of a given number of independent variables is identical to the one between LS estimators of regression coefficients. Second, this study presents that the nexus between the coefficients is exactly represented by Leontief’s I/O model. Third, this study shows that the Leontief matrix therefrom is positive-definite as long as regressor collinearity is less than perfect, satisfying the Hawkins-Simon condition. Finally, this study derives Cramer/Leontief alternative to Frisch/Waugh/Lovell theorem.
Abstract
This paper formally establishes tighter-than-known connectivity between Least Squares (LS) estimators and Leontief’s input-output (I/O) model. First, this study shows that the nexus between partial and total derivatives of the general function of a given number of independent variables is identical to the one between LS estimators of regression coefficients. Second, this study presents that the nexus between the coefficients is exactly represented by Leontief’s I/O model. Third, this study shows that the Leontief matrix therefrom is positive-definite as long as regressor collinearity is less than perfect, satisfying the Hawkins-Simon condition. Finally, this study derives Cramer/Leontief alternative to Frisch/Waugh/Lovell theorem.
참고문헌 (9)
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