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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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**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**• q1 = 1 + (/p1)(M - p11 - p22) • M is money income • pi is price of good i • q2 = 2 + (/p2)(M - p11 - p22)**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 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**• 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)

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