ivreg {AER}R Documentation

Instrumental-Variable Regression

Description

Fit instrumental-variable regression by two-stage least squares. This is equivalent to direct instrumental-variables estimation when the number of instruments is equal to the number of predictors.

Usage

ivreg(formula, instruments, data, subset, na.action, weights, offset,
  contrasts = NULL, model = TRUE, y = TRUE, x = FALSE, ...)

Arguments

formula, instruments formula specification(s) of the regression relationship and the instruments. Either instruments is missing and formula has three parts as in y ~ x1 + x2 | z1 + z2 + z3 (recommended) or formula is y ~ x1 + x2 and instruments is a one-sided formula ~ z1 + z2 + z3 (only for backward compatibility).
data an optional data frame containing the variables in the model. By default the variables are taken from the environment from which ivreg is called.
subset an optional vector specifying a subset of observations to be used in fitting the model.
na.action a function that indicates what should happen when the data contain NAs. The default is set by the na.action option.
weights an optional vector of weights to be used in the fitting process.
offset an optional offset that can be used to specify an a priori known component to be included during fitting.
contrasts an optional list. See the contrasts.arg of model.matrix.default.
model, x, y logicals. If TRUE the corresponding components of the fit (the model frame, the model matrices , the response) are returned.
... further arguments passed to ivreg.fit.

Details

ivreg is the high-level interface to the work-horse function ivreg.fit, a set of standard methods (including print, summary, vcov, anova, hatvalues, predict, terms, model.matrix, bread, estfun) is available and described on summary.ivreg.

Value

ivreg returns an object of class "ivreg", with the following components:

coefficients parameter estimates.
residuals a vector of residuals.
fitted.values a vector of predicted means.
weights either the vector of weights used (if any) or NULL (if none).
offset either the offset used (if any) or NULL (if none).
n number of observations.
rank the numeric rank of the fitted linear model.
df.residual residual degrees of freedom for fitted model.
cov.unscaled unscaled covariance matrix for the coefficients.
sigma residual standard error.
hatvalues regression hat values.
call the original function call.
formula the model formula.
terms a list with elements "regressors" and "instruments" containing the terms objects for the respective components.
levels levels of the categorical regressors.
contrasts the contrasts used for categorical regressors.
model the full model frame (if model = TRUE).
y the response vector (if y = TRUE).
x a list with elements "regressors", "instruments", "projected", containing the model matrices from the respective components (if x = TRUE). "projected" is the matrix of regressors projected on the image of the instruments.

References

Greene, W. H. (1993) Econometric Analysis, 2nd ed., Macmillan.

See Also

ivreg.fit, lm, lm.fit

Examples

## data
data("CigarettesSW")
CigarettesSW$rprice <- with(CigarettesSW, price/cpi)
CigarettesSW$rincome <- with(CigarettesSW, income/population/cpi)
CigarettesSW$tdiff <- with(CigarettesSW, (taxs - tax)/cpi)

## model 
fm <- ivreg(log(packs) ~ log(rprice) + log(rincome) | log(rincome) + tdiff + I(tax/cpi),
  data = CigarettesSW, subset = year == "1995")
summary(fm)

## ANOVA
fm2 <- ivreg(log(packs) ~ log(rprice) | tdiff, data = CigarettesSW, subset = year == "1995")
anova(fm, fm2)

[Package AER version 1.1-2 Index]