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Last data update: 2014.03.03

R: Instrumental-Variable Regression

ivreg

R Documentation

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 `NA`s. 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.

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)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(AER)
Loading required package: car
Loading required package: lmtest
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

Loading required package: sandwich
Loading required package: survival
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/AER/ivreg.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ivreg
> ### Title: Instrumental-Variable Regression
> ### Aliases: ivreg print.ivreg
> ### Keywords: regression
> 
> ### ** 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)

Call:
ivreg(formula = log(packs) ~ log(rprice) + log(rincome) | log(rincome) + 
    tdiff + I(tax/cpi), data = CigarettesSW, subset = year == 
    "1995")

Residuals:
       Min         1Q     Median         3Q        Max 
-0.6006931 -0.0862222 -0.0009999  0.1164699  0.3734227 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)    9.8950     1.0586   9.348 4.12e-12 ***
log(rprice)   -1.2774     0.2632  -4.853 1.50e-05 ***
log(rincome)   0.2804     0.2386   1.175    0.246    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1879 on 45 degrees of freedom
Multiple R-Squared: 0.4294,	Adjusted R-squared: 0.4041 
Wald test: 13.28 on 2 and 45 DF,  p-value: 2.931e-05 

> summary(fm, vcov = sandwich, df = Inf, diagnostics = TRUE)

Call:
ivreg(formula = log(packs) ~ log(rprice) + log(rincome) | log(rincome) + 
    tdiff + I(tax/cpi), data = CigarettesSW, subset = year == 
    "1995")

Residuals:
       Min         1Q     Median         3Q        Max 
-0.6006931 -0.0862222 -0.0009999  0.1164699  0.3734227 

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)    9.8950     0.9288  10.654  < 2e-16 ***
log(rprice)   -1.2774     0.2417  -5.286 1.25e-07 ***
log(rincome)   0.2804     0.2458   1.141    0.254    

Diagnostic tests:
                 df1 df2 statistic p-value    
Weak instruments   2  44   228.738  <2e-16 ***
Wu-Hausman         1  44     3.823  0.0569 .  
Sargan             1  NA     0.333  0.5641    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1879 on Inf degrees of freedom
Multiple R-Squared: 0.4294,	Adjusted R-squared: 0.4041 
Wald test: 34.51 on 2 DF,  p-value: 3.214e-08 

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

Model 1: log(packs) ~ log(rprice) + log(rincome) | log(rincome) + tdiff + 
    I(tax/cpi)
Model 2: log(packs) ~ log(rprice) | tdiff
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     45 1.5880                           
2     46 1.6668 -1 -0.078748 1.3815  0.246
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>