| Library: | metrics |
| See also: | gls |
| Quantlet: | seq | |
| Description: | Estimates a simultaneous equations model by 3-stage least squares |
| Usage: | {d3sls,cov3,d2sls} = seq(seqlist1,seqlist2) | |
| Input: | ||
| seqlist1 | list of matrices. If there are M equations then seqlist1 will be a list of M+2 matrices. The first matrix is comprised of the vectors of observations of the left-hand side variables. The next M matrices consist of the observations of the right-hand-side variables of the M equations. The last matrix contains the observations of the exogenous variables of the system. | |
| seqlist2 | list of string vectors. If there are M equations then seqlist2 will be a list of M+2 string (column) vectors. Each vector contains the names of the variables of the corresponding matrix from seqlist1. | |
| Output: | ||
| d3sls | 3-stage lest squares coefficient estimates | |
| cov3 | vector | |
| d2sls | estimated covariance matrix of the 3sls-estimator | |
| n/a | matrix | |
| n/a | 2-stage lest squares coefficient estimates | |
| n/a | vector | |
; simulated data for a supply-and-demand model
n=50
randomize(101)
sp = #(1,-0.7)~#(-0.7,1) ; covariance matrix
mp = #(4,4) ; mean vector
pcompete = qfc(2*matrix(n,1),uniform(n)) ; price of competitor
income = qfc(3*matrix(n,1),uniform(n))
praw = qfc(matrix(n,1),uniform(n)) ; price of inputs
one = matrix(n,1)
randomize(102)
u2=uniform(n) ; uniform random numbers used for error term
n2=1.2*qfn(u2)
randomize(103)
u3=uniform(n)
n3=1.2*qfn(u3)
; price and quantity computed as solutions of 2-equation system
price=1/1.5*(34+.25*pcompete+0.5*income+0.75*praw+-0.8*qfn(u3))
q=40-price+.25*pcompete[,2]+0.5*income+n2
/* structural equations */
;qd=40-price+.25*pcompete+0.5*income+n2
;qs=6+0.5*price-.75*praw+n3
; setting up the matrices for seqlist1
lhs=q~q
z1=one~price~pcompete~income
z2=one~price~praw
x=one~pcompete~income~praw
seqlist1=list(lhs,z1,z2,x)
; setting up the string vectors for seqlist2
yl="quantity demanded"|"quantity supplied"
zl1="one"|"price"|"pcompete"|"income"
zl2="one"|"price"|"praw"
xl="one"|"pcompete"|"income"|"praw"
seqlist2=list(yl,zl1,zl2,xl)
{d3,s,d2}=seq(seqlist1,seqlist2)
d3~d2
You will find the following output in the output window Contents of output2sls [ 1,] "=====================================================" [ 2,] "2stage Least-squares estimates" [ 3,] "=====================================================" [ 4,] " EQ dep. var. R2 " [ 5,] "=====================================================" [ 6,] " 1 quantity 0.244 " [ 7,] " 2 quantity -0.068 " [ 8,] "=====================================================" [ 9,] "VARIABLE Coef.Est. Std.Err. t" [10,] "--------------------------------------------------" [11,] "one 28.296 6.727 28.296" [12,] "price -0.495 0.291 -0.495" [13,] "pcomp 0.113 0.112 0.113" [14,] "incom 0.345 0.139 0.345" [15,] "-------------------------------------------------------- [16,] "one 7.513 6.412 7.513" [17,] "price 0.421 0.267 0.421" [18,] "praw -0.364 0.172 -0.364" [19,] "=====================================================" Contents of output3sls [ 1,] "=====================================================" [ 2,] " 3stage Least-squares estimates" [ 3,] "=====================================================" [ 4,] " EQ dep. var. R2 " [ 5,] "=====================================================" [ 6,] " 1 quantity 0.244 " [ 7,] " 2 quantity -0.068 " [ 8,] "=====================================================" [ 9,] "VARIABLE Coef.Est. Std.Err. t" [10,] "--------------------------------------------------" [11,] "one 28.365 6.439 4.405" [12,] "price -0.498 0.278 -1.791" [13,] "pcomp 0.128 0.059 2.175" [14,] "incom 0.341 0.132 2.589" [15,] "------------------------------------------------------- [16,] "one 7.513 6.217 1.209" [17,] "price 0.421 0.258 1.630" [18,] "praw -0.364 0.167 -2.176" [19,] "=====================================================" Contents of _tmp [1,] 28.365 28.296 [2,] -0.49837 -0.49493 [3,] 0.12777 0.11271 [4,] 0.34135 0.3446 [5,] 7.5132 7.5132 [6,] 0.42127 0.42127 [7,] -0.36355 -0.36355