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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

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Cross equation constraints l.jpg

Cross Equation Constraints


Stone geary utility function linear expenditure system l.jpg

Stone-Geary Utility FunctionLinear expenditure system

  • U= (q1 - 1) (q2 - 2)

    •  + =1

    •  and  are expenditure shares (above subsistence)

    • i subsistence quantity of good I


Stone geary utility function l.jpg

Stone-Geary Utility Function

  • 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)


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Stone-Geary Utility Function

  • 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


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    Stone-Geary Utility Function

    • 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


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    Constraints in Stata

    • 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


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    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


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    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)


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