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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.

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Presentation on theme: "Cross Equation Constraints. Stone-Geary Utility Function Linear expenditure system U= (q 1 -  1 )  (q 2 -  2 )  –  +  =1 –  and  are expenditure."— Presentation transcript:

1 Cross Equation Constraints

2 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

3 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 )

4 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

5 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

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 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

8 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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