WLS Regressions with Constraints
Posted: Mon May 24, 2010 5:04 am
Hi
My name is Rafael Alencar and I am decomposing the industry and country effects of index returns from countries and industry sectors of countries (using Eviews) in WLS Regression with dummy variables that is necessary the use of constraints. The follow equation model is used:
Ric = α + β1Iic1+ β2Iic2 +… β36Iic36 + γ1Cic1+ γ2Cic2 +… γ48Cic48+ ei
Where Ric n is the return on the industry value-weighted index “i“ in country “c”. The coefficients Betas (β) which could be interpreted as the “pure industry effects” of 36 industry sectors, and the coefficient Gamma (γ) that can be interpreted as the “pure country effect” of the 48 countries. And where “ic” denotes the index ic, and "I" equals 1 if index “ic” is in the first of “n” industry, and "C" equals to 1 if index “ic” is in the first of the “m” countries.
To avoid interpretation problems of an arbitrary benchmark with unrealistic values, I have to insert constrains that the value weighted sum of the industry coefficients equal zero and that the value weighted sum of the country coefficients equal zero.
∑wi βi = 0
The sum of all Betas (β) value weighted in the industry must be = 0, where "wi" is the value weights of industry i in the world market portfolio.
∑vc γc = 0
The sum of all Gammas (γ) value weighted in the industry must be = 0, where "vc" is the value weights of country c in the world market portfolio.
How can I insert those constraints, even in a manual way that I can perform this calculus on Eviews?
Thank you very much for your attention.
Rafael Alencar
My name is Rafael Alencar and I am decomposing the industry and country effects of index returns from countries and industry sectors of countries (using Eviews) in WLS Regression with dummy variables that is necessary the use of constraints. The follow equation model is used:
Ric = α + β1Iic1+ β2Iic2 +… β36Iic36 + γ1Cic1+ γ2Cic2 +… γ48Cic48+ ei
Where Ric n is the return on the industry value-weighted index “i“ in country “c”. The coefficients Betas (β) which could be interpreted as the “pure industry effects” of 36 industry sectors, and the coefficient Gamma (γ) that can be interpreted as the “pure country effect” of the 48 countries. And where “ic” denotes the index ic, and "I" equals 1 if index “ic” is in the first of “n” industry, and "C" equals to 1 if index “ic” is in the first of the “m” countries.
To avoid interpretation problems of an arbitrary benchmark with unrealistic values, I have to insert constrains that the value weighted sum of the industry coefficients equal zero and that the value weighted sum of the country coefficients equal zero.
∑wi βi = 0
The sum of all Betas (β) value weighted in the industry must be = 0, where "wi" is the value weights of industry i in the world market portfolio.
∑vc γc = 0
The sum of all Gammas (γ) value weighted in the industry must be = 0, where "vc" is the value weights of country c in the world market portfolio.
How can I insert those constraints, even in a manual way that I can perform this calculus on Eviews?
Thank you very much for your attention.
Rafael Alencar