bayesm (version 1.1-2)

rivGibbs: Gibbs Sampler for Linear "IV" Model

Description

rivGibbs is a Gibbs Sampler for a linear structural equation with an arbitrary number of instruments.

Usage

rivGibbs(Data, Prior, Mcmc)

Arguments

Data

list(z,w,x,y)

Prior

list(md,Ad,mbg,Abg,nu,V) (optional)

Mcmc

list(R,keep) (R required)

Value

• a list containing:
• deltadraw
  R/keep x dim(delta) array of delta draws
• betadraw
  R/keep x 1 vector of beta draws
• gammadraw
  R/keep x dim(gamma) array of gamma draws
• Sigmadraw
  R/keep x 4 array of Sigma draws

concept

• Instrumental Variables
• Gibbs Sampler
• bayes
• endogeneity
• simultaneity
• MCMC

Details

Model: $x=z'delta + e1$. $y=beta*x + w'gamma + e2$. $e1,e2$ $\sim$ $N(0,Sigma)$. Priors: $delta$ $\sim$ $N(md,Ad^{-1})$. $vec(beta,gamma)$ $\sim$ $N(mbg,Abg^{-1})$ $Sigma$ $\sim$ IW(nu,V) List arguments contain:

• z

{ matrix of obs on instruments} y{ vector of obs on lhs var in structural equation} x{ "endogenous" var in structural eqn} w{ matrix of obs on "exogenous" vars in the structural eqn} md{ prior mean of delta (def: 0)} Ad{ pds prior prec for prior on delta (def: .01I)} mbg{ prior mean vector for prior on beta,gamma (def: 0)} Abg{ pds prior prec for prior on beta,gamma (def: .01I)} nu{ d.f. parm for IW prior on Sigma (def: 5)} V{ pds location matrix for IW prior on Sigma (def: nuI)} R{ number of MCMC draws} keep{ MCMC thinning parm: keep every keepth draw (def: 1)}

Examples

##
if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10}

set.seed(66)
simIV = function(delta,beta,Sigma,n,z,w,gamma) {
eps = matrix(rnorm(2*n),ncol=2) %*% chol(Sigma)
x = z %*% delta + eps[,1]; y = beta*x +  eps[,2] + w%*%gamma
list(x=as.vector(x),y=as.vector(y)) }
n = 200 ; p=1 # number of instruments
z = cbind(rep(1,n),matrix(runif(n*p),ncol=p))
w = matrix(1,n,1)
rho=.8
Sigma = matrix(c(1,rho,rho,1),ncol=2)
delta = c(1,4); beta = .5; gamma = c(1)
simiv = simIV(delta,beta,Sigma,n,z,w,gamma)

Mcmc=list(); Prior=list(); Data = list()
Data$z = z; Data$w=w; Data$x=simiv$x; Data$y=simiv$y
Mcmc$R = R
Mcmc$keep=1
out=rivGibbs(Data=Data,Prior=Prior,Mcmc=Mcmc)

cat("deltadraws ",fill=TRUE)
mat=apply(out$deltadraw,2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(delta,mat); rownames(mat)[1]="delta"; print(mat)
cat("betadraws ",fill=TRUE)
qout=quantile(out$betadraw,probs=c(.01,.05,.5,.95,.99))
mat=matrix(qout,ncol=1)
mat=rbind(beta,mat); rownames(mat)=c("beta",names(qout)); print(mat)
cat("Sigma draws",fill=TRUE)
mat=apply(out$Sigmadraw,2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(as.vector(Sigma),mat); rownames(mat)[1]="Sigma"; print(mat)