Systems of simultaneous equations in LES
Posted: Sun Feb 08, 2015 12:06 pm
hi
I have price and quantity demanded data on 16 commodities for more than 150 households. I want to estimated parameters of Linear Expenditure System to get demand elasticities, but I am facing problem of having negative value of R-Square for some commodities. can someone please help me
Thank you
the equation system i am using is: (pls check is it very right?)
x1=c(1)+c(101)*m/p1+c(101)*c(1)*p1/p1+c(101)*c(2)*p2/p1+c(101)*c(3)*p3/p1+c(101)*c(4)*p4/p1+c(101)*c(5)*p5/p1+c(101)*c(6)*p6/p1+c(101)*c(7)*p7/p1+c(101)*c(8)*p8/p1+c(101)*c(9)*p9/p1+c(101)*c(10)*p10/p1+c(101)*c(11)*p11/p1+c(101)*c(12)*p12/p1+c(101)*c(13)*p13/p1+c(101)*c(14)*p14/p1+c(101)*c(15)*p15/p1+c(101)*c(16)*p16/p1
x2=c(2)+c(102)*m/p2+c(102)*c(1)*p1/p2+c(102)*c(2)*p2/p2+c(102)*c(3)*p3/p2+c(102)*c(4)*p4/p2+c(102)*c(5)*p5/p2+c(102)*c(6)*p6/p2+c(102)*c(7)*p7/p2+c(102)*c(8)*p8/p2+c(102)*c(9)*p9/p2+c(102)*c(10)*p10/p2+c(102)*c(11)*p11/p2+c(102)*c(12)*p12/p2+c(102)*c(13)*p13/p2+c(102)*c(14)*p14/p2+c(102)*c(15)*p15/p2+c(102)*c(16)*p16/p2
x3=c(3)+c(103)*m/p3+c(103)*c(1)*p1/p3+c(103)*c(2)*p2/p3+c(103)*c(3)*p3/p3+c(103)*c(4)*p4/p3+c(103)*c(5)*p5/p3+c(103)*c(6)*p6/p3+c(103)*c(7)*p7/p3+c(103)*c(8)*p8/p3+c(103)*c(9)*p9/p3+c(103)*c(10)*p10/p3+c(103)*c(11)*p11/p3+c(103)*c(12)*p12/p3+c(103)*c(13)*p13/p3+c(103)*c(14)*p14/p3+c(103)*c(15)*p15/p3+c(103)*c(16)*p16/p3
x4=c(4)+c(104)*m/p4+c(104)*c(1)*p1/p4+c(104)*c(2)*p2/p4+c(104)*c(3)*p3/p4+c(104)*c(4)*p4/p4+c(104)*c(5)*p5/p4+c(104)*c(6)*p6/p4+c(104)*c(7)*p7/p4+c(104)*c(8)*p8/p4+c(104)*c(9)*p9/p4+c(104)*c(10)*p10/p4+c(104)*c(11)*p11/p4+c(104)*c(12)*p12/p4+c(104)*c(13)*p13/p4+c(104)*c(14)*p14/p4+c(104)*c(15)*p15/p4+c(104)*c(16)*p16/p4
x5=c(5)+c(105)*m/p5+c(105)*c(1)*p1/p5+c(105)*c(2)*p2/p5+c(105)*c(3)*p3/p5+c(105)*c(4)*p4/p5+c(105)*c(5)*p5/p5+c(105)*c(6)*p6/p5+c(105)*c(7)*p7/p5+c(105)*c(8)*p8/p5+c(105)*c(9)*p9/p5+c(105)*c(10)*p10/p5+c(105)*c(11)*p11/p5+c(105)*c(12)*p12/p5+c(105)*c(13)*p13/p5+c(105)*c(14)*p14/p5+c(105)*c(15)*p15/p5+c(105)*c(16)*p16/p5
x6=c(6)+c(106)*m/p6+c(106)*c(1)*p1/p6+c(106)*c(2)*p2/p6+c(106)*c(3)*p3/p6+c(106)*c(4)*p4/p6+c(106)*c(5)*p5/p6+c(106)*c(6)*p6/p6+c(106)*c(7)*p7/p6+c(106)*c(8)*p8/p6+c(106)*c(9)*p9/p6+c(106)*c(10)*p10/p6+c(106)*c(11)*p11/p6+c(106)*c(12)*p12/p6+c(106)*c(13)*p13/p6+c(106)*c(14)*p14/p6+c(106)*c(15)*p15/p6+c(106)*c(16)*p16/p6
x7=c(7)+c(107)*m/p7+c(107)*c(1)*p1/p7+c(107)*c(2)*p2/p7+c(107)*c(3)*p3/p7+c(107)*c(4)*p4/p7+c(107)*c(5)*p5/p7+c(107)*c(6)*p6/p7+c(107)*c(7)*p7/p7+c(107)*c(8)*p8/p7+c(107)*c(9)*p9/p7+c(107)*c(10)*p10/p7+c(107)*c(11)*p11/p7+c(107)*c(12)*p12/p7+c(107)*c(13)*p13/p7+c(107)*c(14)*p14/p7+c(107)*c(15)*p15/p7+c(107)*c(16)*p16/p7
x8=c(8)+c(108)*m/p8+c(108)*c(1)*p1/p8+c(108)*c(2)*p2/p8+c(108)*c(3)*p3/p8+c(108)*c(4)*p4/p8+c(108)*c(5)*p5/p8+c(108)*c(6)*p6/p8+c(108)*c(7)*p7/p8+c(108)*c(8)*p8/p8+c(108)*c(9)*p9/p8+c(108)*c(10)*p10/p8+c(108)*c(11)*p11/p8+c(108)*c(12)*p12/p8+c(108)*c(13)*p13/p8+c(108)*c(14)*p14/p8+c(108)*c(15)*p15/p8+c(108)*c(16)*p16/p8
x9=c(9)+c(109)*m/p9+c(109)*c(1)*p1/p9+c(109)*c(2)*p2/p9+c(109)*c(3)*p3/p9+c(109)*c(4)*p4/p9+c(109)*c(5)*p5/p9+c(109)*c(6)*p6/p9+c(109)*c(7)*p7/p9+c(109)*c(8)*p8/p9+c(109)*c(9)*p9/p9+c(109)*c(10)*p10/p9+c(109)*c(11)*p11/p9+c(109)*c(12)*p12/p9+c(109)*c(13)*p13/p9+c(109)*c(14)*p14/p9+c(109)*c(15)*p15/p9+c(109)*c(16)*p16/p9
x10=c(10)+c(100)*m/p10+c(100)*c(1)*p1/p10+c(100)*c(2)*p2/p10+c(100)*c(3)*p3/p10+c(100)*c(4)*p4/p10+c(100)*c(5)*p5/p10+c(100)*c(6)*p6/p10+c(100)*c(7)*p7/p10+c(100)*c(8)*p8/p10+c(100)*c(9)*p9/p10+c(100)*c(10)*p10/p10+c(100)*c(11)*p11/p10+c(100)*c(12)*p12/p10+c(100)*c(13)*p13/p10+c(100)*c(14)*p14/p10+c(100)*c(15)*p15/p10+c(100)*c(16)*p16/p10
x11=c(11)+c(111)*m/p11+c(111)*c(1)*p1/p11+c(111)*c(2)*p2/p11+c(111)*c(3)*p3/p11+c(111)*c(4)*p4/p11+c(111)*c(5)*p5/p11+c(111)*c(6)*p6/p11+c(111)*c(7)*p7/p11+c(111)*c(8)*p8/p11+c(111)*c(9)*p9/p11+c(111)*c(10)*p10/p11+c(111)*c(11)*p11/p11+c(111)*c(12)*p12/p11+c(111)*c(13)*p13/p11+c(111)*c(14)*p14/p11+c(111)*c(15)*p15/p11+c(111)*c(16)*p16/p11
x12=c(12)+c(121)*m/p12+c(121)*c(1)*p1/p12+c(121)*c(2)*p2/p12+c(121)*c(3)*p3/p12+c(121)*c(4)*p4/p12+c(121)*c(5)*p5/p12+c(121)*c(6)*p6/p12+c(121)*c(7)*p7/p12+c(121)*c(8)*p8/p12+c(121)*c(9)*p9/p12+c(121)*c(10)*p10/p12+c(121)*c(11)*p11/p12+c(121)*c(12)*p12/p12+c(121)*c(13)*p13/p12+c(121)*c(14)*p14/p12+c(121)*c(15)*p15/p12+c(121)*c(16)*p16/p12
x13=c(13)+c(131)*m/p13+c(131)*c(1)*p1/p13+c(131)*c(2)*p2/p13+c(131)*c(3)*p3/p13+c(131)*c(4)*p4/p13+c(131)*c(5)*p5/p13+c(131)*c(6)*p6/p13+c(131)*c(7)*p7/p13+c(131)*c(8)*p8/p13+c(131)*c(9)*p9/p13+c(131)*c(10)*p10/p13+c(131)*c(11)*p11/p13+c(131)*c(12)*p12/p13+c(131)*c(13)*p13/p13+c(131)*c(14)*p14/p13+c(131)*c(15)*p15/p13+c(131)*c(16)*p16/p13
x14=c(14)+c(141)*m/p14+c(141)*c(1)*p1/p14+c(141)*c(2)*p2/p14+c(141)*c(3)*p3/p14+c(141)*c(4)*p4/p14+c(141)*c(5)*p5/p14+c(141)*c(6)*p6/p14+c(141)*c(7)*p7/p14+c(141)*c(8)*p8/p14+c(141)*c(9)*p9/p14+c(141)*c(10)*p10/p14+c(141)*c(11)*p11/p14+c(141)*c(12)*p12/p14+c(141)*c(13)*p13/p14+c(141)*c(14)*p14/p14+c(141)*c(15)*p15/p14+c(141)*c(16)*p16/p14
x15=c(15)+c(151)*m/p15+c(151)*c(1)*p1/p15+c(151)*c(2)*p2/p15+c(151)*c(3)*p3/p15+c(151)*c(4)*p4/p15+c(151)*c(5)*p5/p15+c(151)*c(6)*p6/p15+c(151)*c(7)*p7/p15+c(151)*c(8)*p8/p15+c(151)*c(9)*p9/p15+c(151)*c(10)*p10/p15+c(151)*c(11)*p11/p15+c(151)*c(12)*p12/p15+c(151)*c(13)*p13/p15+c(151)*c(14)*p14/p15+c(151)*c(15)*p15/p15+c(151)*c(16)*p16/p15
x16=c(16)+c(161)*m/p16+c(161)*c(1)*p1/p16+c(161)*c(2)*p2/p16+c(161)*c(3)*p3/p16+c(161)*c(4)*p4/p16+c(161)*c(5)*p5/p16+c(161)*c(6)*p6/p16+c(161)*c(7)*p7/p16+c(161)*c(8)*p8/p16+c(161)*c(9)*p9/p16+c(161)*c(10)*p10/p16+c(161)*c(11)*p11/p16+c(161)*c(12)*p12/p16+c(161)*c(13)*p13/p16+c(161)*c(14)*p14/p16+c(161)*c(15)*p15/p16+c(161)*c(16)*p16/p16
I have price and quantity demanded data on 16 commodities for more than 150 households. I want to estimated parameters of Linear Expenditure System to get demand elasticities, but I am facing problem of having negative value of R-Square for some commodities. can someone please help me
Thank you
the equation system i am using is: (pls check is it very right?)
x1=c(1)+c(101)*m/p1+c(101)*c(1)*p1/p1+c(101)*c(2)*p2/p1+c(101)*c(3)*p3/p1+c(101)*c(4)*p4/p1+c(101)*c(5)*p5/p1+c(101)*c(6)*p6/p1+c(101)*c(7)*p7/p1+c(101)*c(8)*p8/p1+c(101)*c(9)*p9/p1+c(101)*c(10)*p10/p1+c(101)*c(11)*p11/p1+c(101)*c(12)*p12/p1+c(101)*c(13)*p13/p1+c(101)*c(14)*p14/p1+c(101)*c(15)*p15/p1+c(101)*c(16)*p16/p1
x2=c(2)+c(102)*m/p2+c(102)*c(1)*p1/p2+c(102)*c(2)*p2/p2+c(102)*c(3)*p3/p2+c(102)*c(4)*p4/p2+c(102)*c(5)*p5/p2+c(102)*c(6)*p6/p2+c(102)*c(7)*p7/p2+c(102)*c(8)*p8/p2+c(102)*c(9)*p9/p2+c(102)*c(10)*p10/p2+c(102)*c(11)*p11/p2+c(102)*c(12)*p12/p2+c(102)*c(13)*p13/p2+c(102)*c(14)*p14/p2+c(102)*c(15)*p15/p2+c(102)*c(16)*p16/p2
x3=c(3)+c(103)*m/p3+c(103)*c(1)*p1/p3+c(103)*c(2)*p2/p3+c(103)*c(3)*p3/p3+c(103)*c(4)*p4/p3+c(103)*c(5)*p5/p3+c(103)*c(6)*p6/p3+c(103)*c(7)*p7/p3+c(103)*c(8)*p8/p3+c(103)*c(9)*p9/p3+c(103)*c(10)*p10/p3+c(103)*c(11)*p11/p3+c(103)*c(12)*p12/p3+c(103)*c(13)*p13/p3+c(103)*c(14)*p14/p3+c(103)*c(15)*p15/p3+c(103)*c(16)*p16/p3
x4=c(4)+c(104)*m/p4+c(104)*c(1)*p1/p4+c(104)*c(2)*p2/p4+c(104)*c(3)*p3/p4+c(104)*c(4)*p4/p4+c(104)*c(5)*p5/p4+c(104)*c(6)*p6/p4+c(104)*c(7)*p7/p4+c(104)*c(8)*p8/p4+c(104)*c(9)*p9/p4+c(104)*c(10)*p10/p4+c(104)*c(11)*p11/p4+c(104)*c(12)*p12/p4+c(104)*c(13)*p13/p4+c(104)*c(14)*p14/p4+c(104)*c(15)*p15/p4+c(104)*c(16)*p16/p4
x5=c(5)+c(105)*m/p5+c(105)*c(1)*p1/p5+c(105)*c(2)*p2/p5+c(105)*c(3)*p3/p5+c(105)*c(4)*p4/p5+c(105)*c(5)*p5/p5+c(105)*c(6)*p6/p5+c(105)*c(7)*p7/p5+c(105)*c(8)*p8/p5+c(105)*c(9)*p9/p5+c(105)*c(10)*p10/p5+c(105)*c(11)*p11/p5+c(105)*c(12)*p12/p5+c(105)*c(13)*p13/p5+c(105)*c(14)*p14/p5+c(105)*c(15)*p15/p5+c(105)*c(16)*p16/p5
x6=c(6)+c(106)*m/p6+c(106)*c(1)*p1/p6+c(106)*c(2)*p2/p6+c(106)*c(3)*p3/p6+c(106)*c(4)*p4/p6+c(106)*c(5)*p5/p6+c(106)*c(6)*p6/p6+c(106)*c(7)*p7/p6+c(106)*c(8)*p8/p6+c(106)*c(9)*p9/p6+c(106)*c(10)*p10/p6+c(106)*c(11)*p11/p6+c(106)*c(12)*p12/p6+c(106)*c(13)*p13/p6+c(106)*c(14)*p14/p6+c(106)*c(15)*p15/p6+c(106)*c(16)*p16/p6
x7=c(7)+c(107)*m/p7+c(107)*c(1)*p1/p7+c(107)*c(2)*p2/p7+c(107)*c(3)*p3/p7+c(107)*c(4)*p4/p7+c(107)*c(5)*p5/p7+c(107)*c(6)*p6/p7+c(107)*c(7)*p7/p7+c(107)*c(8)*p8/p7+c(107)*c(9)*p9/p7+c(107)*c(10)*p10/p7+c(107)*c(11)*p11/p7+c(107)*c(12)*p12/p7+c(107)*c(13)*p13/p7+c(107)*c(14)*p14/p7+c(107)*c(15)*p15/p7+c(107)*c(16)*p16/p7
x8=c(8)+c(108)*m/p8+c(108)*c(1)*p1/p8+c(108)*c(2)*p2/p8+c(108)*c(3)*p3/p8+c(108)*c(4)*p4/p8+c(108)*c(5)*p5/p8+c(108)*c(6)*p6/p8+c(108)*c(7)*p7/p8+c(108)*c(8)*p8/p8+c(108)*c(9)*p9/p8+c(108)*c(10)*p10/p8+c(108)*c(11)*p11/p8+c(108)*c(12)*p12/p8+c(108)*c(13)*p13/p8+c(108)*c(14)*p14/p8+c(108)*c(15)*p15/p8+c(108)*c(16)*p16/p8
x9=c(9)+c(109)*m/p9+c(109)*c(1)*p1/p9+c(109)*c(2)*p2/p9+c(109)*c(3)*p3/p9+c(109)*c(4)*p4/p9+c(109)*c(5)*p5/p9+c(109)*c(6)*p6/p9+c(109)*c(7)*p7/p9+c(109)*c(8)*p8/p9+c(109)*c(9)*p9/p9+c(109)*c(10)*p10/p9+c(109)*c(11)*p11/p9+c(109)*c(12)*p12/p9+c(109)*c(13)*p13/p9+c(109)*c(14)*p14/p9+c(109)*c(15)*p15/p9+c(109)*c(16)*p16/p9
x10=c(10)+c(100)*m/p10+c(100)*c(1)*p1/p10+c(100)*c(2)*p2/p10+c(100)*c(3)*p3/p10+c(100)*c(4)*p4/p10+c(100)*c(5)*p5/p10+c(100)*c(6)*p6/p10+c(100)*c(7)*p7/p10+c(100)*c(8)*p8/p10+c(100)*c(9)*p9/p10+c(100)*c(10)*p10/p10+c(100)*c(11)*p11/p10+c(100)*c(12)*p12/p10+c(100)*c(13)*p13/p10+c(100)*c(14)*p14/p10+c(100)*c(15)*p15/p10+c(100)*c(16)*p16/p10
x11=c(11)+c(111)*m/p11+c(111)*c(1)*p1/p11+c(111)*c(2)*p2/p11+c(111)*c(3)*p3/p11+c(111)*c(4)*p4/p11+c(111)*c(5)*p5/p11+c(111)*c(6)*p6/p11+c(111)*c(7)*p7/p11+c(111)*c(8)*p8/p11+c(111)*c(9)*p9/p11+c(111)*c(10)*p10/p11+c(111)*c(11)*p11/p11+c(111)*c(12)*p12/p11+c(111)*c(13)*p13/p11+c(111)*c(14)*p14/p11+c(111)*c(15)*p15/p11+c(111)*c(16)*p16/p11
x12=c(12)+c(121)*m/p12+c(121)*c(1)*p1/p12+c(121)*c(2)*p2/p12+c(121)*c(3)*p3/p12+c(121)*c(4)*p4/p12+c(121)*c(5)*p5/p12+c(121)*c(6)*p6/p12+c(121)*c(7)*p7/p12+c(121)*c(8)*p8/p12+c(121)*c(9)*p9/p12+c(121)*c(10)*p10/p12+c(121)*c(11)*p11/p12+c(121)*c(12)*p12/p12+c(121)*c(13)*p13/p12+c(121)*c(14)*p14/p12+c(121)*c(15)*p15/p12+c(121)*c(16)*p16/p12
x13=c(13)+c(131)*m/p13+c(131)*c(1)*p1/p13+c(131)*c(2)*p2/p13+c(131)*c(3)*p3/p13+c(131)*c(4)*p4/p13+c(131)*c(5)*p5/p13+c(131)*c(6)*p6/p13+c(131)*c(7)*p7/p13+c(131)*c(8)*p8/p13+c(131)*c(9)*p9/p13+c(131)*c(10)*p10/p13+c(131)*c(11)*p11/p13+c(131)*c(12)*p12/p13+c(131)*c(13)*p13/p13+c(131)*c(14)*p14/p13+c(131)*c(15)*p15/p13+c(131)*c(16)*p16/p13
x14=c(14)+c(141)*m/p14+c(141)*c(1)*p1/p14+c(141)*c(2)*p2/p14+c(141)*c(3)*p3/p14+c(141)*c(4)*p4/p14+c(141)*c(5)*p5/p14+c(141)*c(6)*p6/p14+c(141)*c(7)*p7/p14+c(141)*c(8)*p8/p14+c(141)*c(9)*p9/p14+c(141)*c(10)*p10/p14+c(141)*c(11)*p11/p14+c(141)*c(12)*p12/p14+c(141)*c(13)*p13/p14+c(141)*c(14)*p14/p14+c(141)*c(15)*p15/p14+c(141)*c(16)*p16/p14
x15=c(15)+c(151)*m/p15+c(151)*c(1)*p1/p15+c(151)*c(2)*p2/p15+c(151)*c(3)*p3/p15+c(151)*c(4)*p4/p15+c(151)*c(5)*p5/p15+c(151)*c(6)*p6/p15+c(151)*c(7)*p7/p15+c(151)*c(8)*p8/p15+c(151)*c(9)*p9/p15+c(151)*c(10)*p10/p15+c(151)*c(11)*p11/p15+c(151)*c(12)*p12/p15+c(151)*c(13)*p13/p15+c(151)*c(14)*p14/p15+c(151)*c(15)*p15/p15+c(151)*c(16)*p16/p15
x16=c(16)+c(161)*m/p16+c(161)*c(1)*p1/p16+c(161)*c(2)*p2/p16+c(161)*c(3)*p3/p16+c(161)*c(4)*p4/p16+c(161)*c(5)*p5/p16+c(161)*c(6)*p6/p16+c(161)*c(7)*p7/p16+c(161)*c(8)*p8/p16+c(161)*c(9)*p9/p16+c(161)*c(10)*p10/p16+c(161)*c(11)*p11/p16+c(161)*c(12)*p12/p16+c(161)*c(13)*p13/p16+c(161)*c(14)*p14/p16+c(161)*c(15)*p15/p16+c(161)*c(16)*p16/p16