ivreg.fit: Fitting Instrumental-Variable Regressions

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.fit(x, y, z, weights, offset, ...)

Value

ivreg.fit returns an unclassed list 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).
estfun: a matrix containing the empirical estimating functions.
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.

Arguments

x: regressor matrix.
y: vector with dependent variable.
z: instruments matrix.
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.
...: further arguments passed to lm.fit or lm.wfit, respectively.

Details

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

ivreg.fit is a convenience interface to lm.fit (or lm.wfit) for first projecting x onto the image of z and the running a regression of y onto the projected x.

Examples

Run this code

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

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

## low-level interface
y <- fm$y
x <- model.matrix(fm, component = "regressors")
z <- model.matrix(fm, component = "instruments")
ivreg.fit(x, y, z)$coefficients