ivreg: Instrumental-Variable Regression

In AER: Applied Econometrics with R

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 of the formula.
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.

Regressors and instruments for ivreg are most easily specified in a formula with two parts on the right-hand side, e.g., y ~ x1 + x2 | z1 + z2 + z3, where x1 and x2 are the regressors and z1, z2, and z3 are the instruments. Note that exogenous regressors have to be included as instruments for themselves. For example, if there is one exogenous regressor ex and one endogenous regressor en with instrument in, the appropriate formula would be y ~ ex + en | ex + in. Equivalently, this can be specified as y ~ ex + en | . - en + in, i.e., by providing an update formula with a . in the second part of the formula. The latter is typically more convenient, if there is a large number of exogenous regressors.

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.
nobs	number of observations with non-zero weights.
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.
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", package = "AER")
CigarettesSW <- transform(CigarettesSW,
  rprice  = price/cpi,
  rincome = income/population/cpi,
  tdiff   = (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)
summary(fm, vcov = sandwich, df = Inf, diagnostics = TRUE)

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

AER documentation built on Sept. 28, 2024, 9:07 a.m.