ivreg.fit: Fitting Instrumental-Variable Regressions by 2SLS, 2SM, or...

In ivreg: Instrumental-Variables Regression by '2SLS', '2SM', or '2SMM', with Diagnostics

Fitting Instrumental-Variable Regressions by 2SLS, 2SM, or 2SMM Estimation

Description

Fit instrumental-variable regression by two-stage least squares (2SLS). This is equivalent to direct instrumental-variables estimation when the number of instruments is equal to the number of predictors. Alternative robust-regression estimation is also supported, based on M-estimation (22M) or MM-estimation (2SMM).

Usage

ivreg.fit(
  x,
  y,
  z,
  weights,
  offset,
  method = c("OLS", "M", "MM"),
  rlm.args = list(),
  ...
)

Arguments

x	regressor matrix.
y	vector for the response 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.
method	the method used to fit the stage 1 and 2 regression: "OLS" for traditional 2SLS regression (the default), "M" for M-estimation, or "MM" for MM-estimation, with the latter two robust-regression methods implemented via the rlm function in the MASS package.
rlm.args	a list of optional arguments to be passed to the rlm function in the MASS package if robust regression is used for the stage 1 and 2 regressions.
...	further arguments passed to lm.fit or lm.wfit, respectively.

Details

ivreg is the high-level interface to the work-horse function ivreg.fit. ivreg.fit is essentially a convenience interface to lm.fit (or lm.wfit) for first projecting x onto the image of z, then running a regression of y on the projected x, and computing the residual standard deviation.

Value

ivreg.fit returns an unclassed list with the following components:

coefficients	parameter estimates, from the stage-2 regression.
residuals	vector of model residuals.
residuals1	matrix of residuals from the stage-1 regression.
residuals2	vector of residuals from the stage-2 regression.
fitted.values	vector of predicted means for the response.
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.
p	number of columns in the model matrix x of regressors.
q	number of columns in the instrumental variables model matrix z
rank	numeric rank of the model matrix for the stage-2 regression.
df.residual	residual degrees of freedom for fitted model.
cov.unscaled	unscaled covariance matrix for the coefficients.
sigma	residual standard error; when method is "M" or "MM", this is based on the MAD of the residuals (around 0) — see mad.
x	projection of x matrix onto span of z.
qr	QR decomposition for the stage-2 regression.
qr1	QR decomposition for the stage-1 regression.
rank1	numeric rank of the model matrix for the stage-1 regression.
coefficients1	matrix of coefficients from the stage-1 regression.
df.residual1	residual degrees of freedom for the stage-1 regression.
exogenous	columns of the "regressors" matrix that are exogenous.
endogenous	columns of the "regressors" matrix that are endogenous.
instruments	columns of the "instruments" matrix that are instruments for the endogenous variables.
method	the method used for the stage 1 and 2 regressions, one of "OLS", "M", or "MM".
rweights	a matrix of robustness weights with columns for each of the stage-1 regressions and for the stage-2 regression (in the last column) if the fitting method is "M" or "MM", NULL if the fitting method is "OLS".
hatvalues	a matrix of hatvalues. For method = "OLS", the matrix consists of two columns, for each of the stage-1 and stage-2 regression; for method = "M" or "MM", there is one column for each stage-1 regression and for the stage-2 regression.

See Also

ivreg, lm.fit, lm.wfit, rlm, mad

Examples

## data
data("CigaretteDemand", package = "ivreg")

## high-level interface
m <- ivreg(log(packs) ~ log(rprice) + log(rincome) | salestax + log(rincome),
  data = CigaretteDemand)

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

ivreg documentation built on April 3, 2025, 9:34 p.m.