ivbma (version 1.05)

ivbma: Instrumental Variable Bayesian Model Averaging via Conditional Bayes Factors

Description

This function estimates an Instrumental Variable (IV) system while incorporating model uncertainty and performing model averaging using an MC3-within-Gibbs Sampler.

Usage

ivbma(Y, X, Z, W, s = 1000, b = round(s/10), full = FALSE, 
    odens = min(c(5000, s - b)), print.every = round(s/10), run.diagnostics = FALSE)

Arguments

Y

n x 1 matrix. Response variable

X

n x r matrix. Endogenous variables

W

n x p matrix. Further explanatory variables. You are responsible for including an intercept.

Z

n x q matrix. Instrumental variables

s

integer. Number of iterations

b

integer. Number of iterations to discard as burn-in.

full

If full is TRUE then model selection is not performed

odens

Output density. How many samples from the posterior should be returned? Note that posterior expectations are taken over every sample after burn-in

print.every

After how many iterations should the progress be printed?

run.diagnostics

If TRUE, this will compute experimental diagnostics to assess the validity of the instruments in use. Note that this adds a non-negligible amount of computing time.

Value

• rho
  An odens x (r + p) matrix with sampled values for the outcome stage. Endogenous variables come first.
• rho.bar
  Posterior expectation of the outcome stage taken over all iterations
• lambda
  A (p + q) x r x odens array with sampled values for the parameters of the first stage regressions. Instruments come first.
• lambda.bar
  Posterior expectation of each first stage taken over all iterations
• Sigma
  odens sampled realizations of Sigma
• Sigma.bar
  Posterior expectation of Sigma taken over all iterations
• M
  Sampled first stage models
• M.bar
  Posterior first stage inclusion probabilities
• L
  Sampled second stage models
• L.bar
  Posterior second stage inclusion probabilities
• If run.diagnostics was set to TRUE then you also receive
• Sargan
  Model averaged Sargan p-values. Lower values indicate lack of instrument validity
• Bayesian.Sargan
  An _Experimental_ Bayesian Sargan diagnostic based on Conditional Bayes Factors. Same direction as above

Details

The function estimates the parameters based on the model $$Y = [X W] * \rho + \epsilon$$ $$X = [Z W] * \lambda + \eta$$ with $$(\epsilon_i, \eta_i)^T \sim N_2 ( 0,\Sigma)$$ and its extension to multiple endogenous variables. If full is set to FALSE model uncertainty is included using conditional Bayes factors.

References

Anna Karl and Alex Lenkoski (2012). "Instrumental Variable Bayesian Model Averaging via Conditional Bayes Factors" http://arxiv.org/abs/1202.5846

See Also

summary.ivbma ivbma.cv.study

Examples

set.seed(1)
data(growth)
attach(growth)
## To replicate KL, set s to 1e5
a <- ivbma(Y, X, Z, W, s = 1e2)
summary(a, nms.U = c(names(Z), names(W)),nms.V = c(names(X), names(W)))
detach(growth)

set.seed(1)
data(margarine)
attach(margarine)
## To replicate KL, set s to 2.5e5
a <- ivbma(Y, X, Z, W, s=1e2)
summary(a, nms.U = c(names(Z), names(W)),nms.V = c(names(X), names(W)))
detach(margarine)