ivpml function

Estimate Instrumental Variable Probit model by Maximum Likelihood.

Estimation of Probit model with one endogenous and continuous variable by Maximum Likelihood.

ivpml(formula, data, messages = TRUE, ...)

## S3 method for class 'ivpml'
terms(x, ...)

## S3 method for class 'ivpml'
model.matrix(object, ...)

## S3 method for class 'ivpml'
estfun(x, ...)

## S3 method for class 'ivpml'
bread(x, ...)

## S3 method for class 'ivpml'
vcov(object, ...)

## S3 method for class 'ivpml'
df.residual(object, ...)

## S3 method for class 'ivpml'
coef(object, ...)

## S3 method for class 'ivpml'
logLik(object, ...)

## S3 method for class 'ivpml'
print(x, ...)

## S3 method for class 'ivpml'
summary(object, eigentol = 1e-12, ...)

## S3 method for class 'summary.ivpml'
print(x, digits = max(3, getOption("digits") - 2), ...)

## S3 method for class 'ivpml'
predict(object, newdata = NULL, type = c("xb", "pr", "stdp"), asf = TRUE, ...)

Arguments

• formula: a symbolic description of the model of the form y ~ x | z where y is the binary dependent variable, x includes the exogenous and the endogenous continuous variable, and z is the complete set of instruments.
• data: the data of class data.frame.
• messages: if TRUE, then additional messages for the estimation procedure are displayed.
• ...: arguments passed to maxLik.
• x, object: an object of class ivpml.
• eigentol: the standard errors are only calculated if the ratio of the smallest and largest eigenvalue of the Hessian matrix is less than eigentol. Otherwise the Hessian is treated as singular.
• digits: the number of digits.
• newdata: optionally, a data frame in which to look for variables with which to predict.
• type: the type of prediction required. The default, type = xb, is on the linear prediction. If type = pr, the predicted probabilities of a positive outcome is returned. Finally, if type = stdp the standard errors of the linear predictions for each individual is returned.
• asf: if TRUE, the average structural function is used. This option is not allowed with xb or stdp.

Details

The IV probit for cross-sectional data has the following structure:

with

where $y_{1i}^*$ is the latent (unobserved) dependent variable for individual $i = 1,...,N$; $y_{2i}$ is the endogenous continuous variable; $z_i$ is the vector of exogenous variables which also includes the instruments for $y_{2i}$; and $(\epsilon, \upsilon)$ are normal jointly distributed.

The model is estimated using the maxLik function from maxLik package using analytic gradient.

Examples

# Data
library("AER")
data("PSID1976")
PSID1976$lfp  <- as.numeric(PSID1976$participation == "yes")
PSID1976$kids <- with(PSID1976, factor((youngkids + oldkids) > 0,
                                      levels = c(FALSE, TRUE), 
                                      labels = c("no", "yes")))
                                      
# IV probit model by MLE
# (nwincome is endogenous and heducation is the additional instrument)
PSID1976$nwincome <- with(PSID1976, (fincome - hours * wage)/1000)
fiml.probit <- ivpml(lfp ~  education + experience + I(experience^2) + age + 
                            youngkids + oldkids + nwincome |
                            education + experience + I(experience^2) + age + 
                            youngkids + oldkids + heducation, 
                     data = PSID1976)
summary(fiml.probit)

References

Greene, W. H. (2012). Econometric Analysis. 7 edition. Prentice Hall.

Author(s)

Mauricio Sarrias.