Cross Equation Constraints

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Cross Equation Constraints
2
Stone-Geary Utility FunctionLinear expenditure
system

• U (q1 - ?1)? (q2 - ?2)?
• ? ?1
• ? and ? are expenditure shares (above
  subsistence)
• ?i subsistence quantity of good I

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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 var1var2
• coefficient on var1 equals coefficient on var2
• example 2
• constraint define 2 q1constant q2var3
• 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 q1constant q2 p1/2
• constraint define 2 q1constantq2 p1/2
• SUREG (q1 q1 M/p1 p2/1) (q2 q2 M/p2 p1/2),
  constraint(2)