SemiParBIVProbit (version 3.7-1)

AT: Average treatment effect of a binary or continuous endogenous variable

Description

AT can be used to calculate the treatment effect of a binary or continuous endogenous predictor/treatment, with corresponding interval obtained using posterior simulation.

Usage

AT(x, nm.end, E = TRUE, treat = TRUE, type = "bivariate", ind = NULL,  n.sim = 100, prob.lev = 0.05, length.out = NULL, hd.plot = FALSE, te.plot = FALSE,  main = "Histogram and Kernel Density of Simulated Average Effects",  xlab = "Simulated Average Effects", ...)

Arguments

x

A fitted SemiParBIVProbit object as produced by SemiParBIVProbit().

nm.end

Name of the endogenous variable.

E

If TRUE then AT calculates the sample ATE. If FALSE then it calculates the sample AT for the treated individuals only.

treat

If TRUE then AT calculates the AT using the treated only. If FALSE then it calculates the effect on the control group. This only makes sense if E = FALSE.

type

This argument can take three values: "naive" (the effect is calculated ignoring the presence of observed and unobserved confounders), "univariate" (the effect is obtained from the univariate model which neglects the presence of unobserved confounders) and "bivariate" (the effect is obtained from the bivariate model which accounts for observed and unobserved confounders).

ind

Binary logical variable. It can be used to calculate the AT for a subset of the data. Note that it does not make sense to use ind when some observations are excluded from the AT calculation (e.g., when using E = FALSE).

n.sim

Number of simulated coefficient vectors from the posterior distribution of the estimated model parameters. This is used when delta = FALSE. It may be increased if more precision is required.

prob.lev

Overall probability of the left and right tails of the AT distribution used for interval calculations.

length.out

Ddesired length of the sequence to be used when calculating the effect that a continuous treatment has on a binary outcome.

hd.plot

If TRUE then a plot of the histogram and kernel density estimate of the simulated average effects is produced. This can only be produced when when binary responses are used.

te.plot

For the case of continuous endogenous variable and binary outcome, if TRUE then a plot showing the treatment effects that the binary outcome is equal to 1 for each incremental value of the endogenous variable and respective intervals is produced.

main

Title for the plot.

xlab

Title for the x axis.

...

Other graphics parameters to pass on to plotting commands. These are used only when hd.plot = TRUE.

Value

res

It returns three values: lower confidence interval limit, estimated AT and upper interval limit.

prob.lev

Probability level used.

sim.AT

It returns a vector containing simulated values of the average treatment effect. This is used to calculate intervals.

Effects

For the case of continuous endogenous variable and binary outcome, it returns a matrix made up of three columns containing the effects for each incremental value in the endogenous variable and respective intervals.

Details

AT measures the average difference in outcomes under treatment (the binary predictor or treatment assumes value 1) and under control (the binary treatment assumes value 0). Posterior simulation is used to obtain a confidence/credible interval. See the references below for details.

AT can also calculate the effect that a continuous endogenous variable has on a binary outcome. In this case the effect will depend on the unit increment chosen (as shown by the plot produced).

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.

See Also

SemiParBIVProbit-package, SemiParBIVProbit, summary.SemiParBIVProbit

Examples

## see examples for SemiParBIVProbit