# ivreg

0th

Percentile

##### Instrumental-Variable Regression by 2SLS

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 regressors.

Keywords
regression
##### 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. These components are necessary for computing regression diagnostics.

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, predict, residuals, terms, model.matrix, bread, estfun) is available and described in ivregMethods. For methods related to regression diagnotics, see ivregDiagnostics.

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 explanatory variables and z1, z2, and z3 are the instrumental variables. 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" that inherits from class "lm", 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 deviation.

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.residual

residual degrees of freedom for fitted model.

call

the original function call.

formula

the model formula.

na.action

function applied to missing values in the model fit.

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.

ivreg.fit, ivregDiagnostics, ivregMethods, lm, lm.fit

• ivreg
##### Examples
# NOT RUN {
## data
data("CigaretteDemand", package = "ivreg")

## model
m <- ivreg(log(packs) ~ log(rprice) + log(rincome) | salestax + log(rincome),
data = CigaretteDemand)
summary(m)
summary(m, vcov = sandwich::sandwich, df = Inf)

## ANOVA
m2 <- update(m, . ~ . - log(rincome) | . - log(rincome))
anova(m, m2)
car::Anova(m)

# }

Documentation reproduced from package ivreg, version 0.5-0, License: GPL (>= 2)

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