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Cross Equation Constraints

Cross Equation Constraints

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Cross Equation Constraints

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  1. 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

  3. 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)

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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)