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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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stone geary utility function linear expenditure system
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
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)
stone geary utility function4
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
stone geary utility function5
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
constraints in stata
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
seemingly unrelated regressions in stata
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 regressions in stata8
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)