# Cross Equation Constraints

## Presentation on theme: "Cross Equation Constraints"— Presentation transcript:

Cross Equation Constraints

Stone-Geary Utility Function Linear 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 - p11 - p22) M is money income pi is price of good i q2 = 2 + (/p2)(M - p11 - p22)

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 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/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)