AT: Average treatment effect of a binary endogenous variable

Description

AT can be used to calculate the unconditional average treatment effect (ATE) and average treatment effect on the treated (ATT) of a binary endogenous predictor/treatment, with corresponding confidence intervals calculated either using the delta method or via posterior simulation.

Usage

AT(x, eq, nm.bin="", E=TRUE, treat=TRUE, delta=TRUE, sig.lev=0.05, 
   s.meth="svd", n.sim=1000)

Arguments

A fitted SemiParBIVProbit object as produced by SemiParBIVProbit().

Equation containing the binary endogenous predictor of interest.

nm.bin

Name of the binary endogenous variable.

If TRUE, then AT calculates the ATE. If FALSE, then it calculates the ATT.

treat

If TRUE, then AT calculates the ATT. If FALSE, then it calculates the average treatment effect on the control group. This only makes sense if used jointly with E=FALSE.

delta

If TRUE then the delta method is used for confidence interval calculation, otherwise Bayesian posterior simulation is employed.

sig.lev

Significance level.

n.sim

Number of simulated coefficient vectors from the posterior distribution of the estimated model parameters. This is used when delta=FALSE.

s.meth

Matrix decomposition used to determine the matrix root of the covariance matrix. This is used when delta=FALSE.See the documentation of the mvtnorm package for further details.

Value

resIt returns three values: lower confidence interval limit, estimated AT and upper confidence interval limit.
sig.levSignificance level used.

Details

AT measures the average causal difference in outcomes under the treatment (the binary predictor/treatment assumes value 1) and under the control (the binary treatment assumes value 0). The corresponding confidence intervals are calculated either using the delta method or via posterior simulation from the posterior distribution of the estimated model parameters. See the references below for details.

References

Marra G. and Radice R. (2011), Estimation of a Semiparametric Recursive Bivariate Probit in the Presence of Endogeneity. Canadian Journal of Statistics, 39(2), 259-279. Marra G., Papageorgiou G. and Radice R. (in press), Estimation of a Semiparametric Recursive Bivariate Probit Model with Nonparametric Mixing. Australian & New Zealand Journal of Statistics.

Examples

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## see examples for SemiParBIVProbit

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