AER (version 0.2-2)

ivreg: 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

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.

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.

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.

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)