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# Cross Equation Constraints - PowerPoint PPT Presentation

Cross Equation Constraints. Stone-Geary Utility Function Linear expenditure system. U= (q 1 -  1 )  (q 2 -  2 )   + =1  and  are expenditure shares (above subsistence)  i subsistence quantity of good I. Stone-Geary Utility Function.

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### Cross Equation Constraints

Stone-Geary Utility FunctionLinear expenditure system

• U= (q1 - 1) (q2 - 2)

•  + =1

•  and  are expenditure shares (above subsistence)

• i subsistence quantity of good I

• q1 = 1 + (/p1)(M - p11 - p22)

• M is money income

• pi is price of good i

• q2 = 2 + (/p2)(M - p11 - p22)

• q1 = 1 (1- )+ (M/p1)- (p2 /p1)  2

• q1 = a0 + a1 (M/p1) + a2 (p2 /p1) + 1

• q2 = 2  + (M/p2)- (p1 /p2)  1

• q2 = b0 + b1 (M/p2) + b2 (p1 /p2) + 2

• Constraints

• a1 + b1 = 1

• a2 = b0

• a0 = b2

• q1 = a0 + a1 (M/p1) + a2 (p2 /p1) + 1

• q2 = b0 + b1 (M/p2) + b2 (p1 /p2) + 2

• Constraint define # “condition”

• example 1:

• constraint define 1 var1=var2

• coefficient on var1 equals coefficient on var2

• example 2:

• constraint define 2 [q1]constant = [q2]var3

• constant in q1 equation equals coefficient on var3 in q2 equation

Seemingly Unrelated Regressionsin Stata

• SUREG ([eqname1]: depvar1 indvar11 indvar12…, noconstant) ([eqname2]: depvar2 indvar21 indvar22…, noconstant), constraint(constraint numbers)

• eqname is optional

• noconstant is optional

• constraint(.) is optional

Seemingly Unrelated Regressionsin Stata

• SUREG ([q1]: q1 M/p1 p2/1) ([q2]: q2 M/p2 p1/2)

• test [q1]constant = [q2] p1/2

• constraint define 2 [q1]constant=[q2] p1/2

• SUREG ([q1]: q1 M/p1 p2/1) ([q2]: q2 M/p2 p1/2), constraint(2)