AER (version 1.2-4)

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 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.

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.

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.

References

Greene, W. H. (1993) Econometric Analysis, 2nd ed., Macmillan.

See Also

ivreg.fit, lm, lm.fit

Examples

## data
data("CigarettesSW", package = "AER")
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)
summary(fm, vcov = sandwich, df = Inf, diagnostics = TRUE)

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