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.