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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 q 1 = 1 + ( /p 1 )(M - p 1 1 - p 2 2 ) –M is money income –p i is price of good i q 2 = 2 + ( /p 2 )(M - p 1 1 - p 2 2 )
Stone-Geary Utility Function q 1 = 1 (1- )+ (M/p 1 )- (p 2 /p 1 ) 2 q 1 = a 0 + a 1 (M/p 1 ) + a 2 (p 2 /p 1 ) + 1 q 2 = 2 + (M/p 2 )- (p 1 /p 2 ) 1 q 2 = b 0 + b 1 (M/p 2 ) + b 2 (p 1 /p 2 ) + 2
Stone-Geary Utility Function Constraints –a 1 + b 1 = 1 –a 2 = b 0 –a 0 = b 2 q 1 = a 0 + a 1 (M/p 1 ) + a 2 (p 2 /p 1 ) + 1 q 2 = b 0 + b 1 (M/p 2 ) + b 2 (p 1 /p 2 ) + 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 Regressions in 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 Stata SUREG ([q1]: q1 M/p 1 p 2/1 ) ([q2]: q2 M/p 2 p 1/2 ) test [q1]constant = [q2] p 1/2 constraint define 2 [q1]constant=[q2] p 1/2 SUREG ([q1]: q1 M/p 1 p 2/1 ) ([q2]: q2 M/p 2 p 1/2 ), constraint(2)
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