Instrumental-Variable Regression

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.

Arguments

formula

specification(s) of the regression relationship
instruments

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. Using instruments is not recommended with zelig.
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 methods. See also zelig.

Source

ivreg is from Christian Kleiber and Achim Zeileis (2008). Applied Econometrics with R. New York: Springer-Verlag. ISBN 978-0-387-77316-2. URL https://CRAN.R-project.org/package=AER

Details

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.

Methods

zelig(formula, data, model = NULL, ..., weights = NULL, by, bootstrap = FALSE)

The zelig function estimates a variety of statistical models

See also

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

Examples

library(AER) # for sandwich vcov
library(dplyr) # for the pipe operator %>%

# load and transform data
data("CigarettesSW")
CigarettesSW$rprice <- with(CigarettesSW, price/cpi)
CigarettesSW$rincome <- with(CigarettesSW, income/population/cpi)
CigarettesSW$tdiff <- with(CigarettesSW, (taxs - tax)/cpi)

# log second stage independent variables, as logging internally for ivreg is
# not currently supported
CigarettesSW$log_rprice <- log(CigarettesSW$rprice)
CigarettesSW$log_rincome <- log(CigarettesSW$rincome)

# estimate model
z.out1 <- zelig(log(packs) ~ log_rprice + log_rincome |
                    log_rincome + tdiff + I(tax/cpi),
                    data = CigarettesSW, subset = year == "1995",
                    model = "ivreg")
#> Error in eval(substitute(subset), data, env): object 'year' not found
summary(z.out1)
#> Model: 
#> 
#> Call:
#> z5$zelig(formula = log(packs) ~ log_rprice + log_rincome | log_rincome + 
#>     tdiff + I(tax/cpi), data = CigarettesSW, subset = year == 
#>     "1995")
#> 
#> Residuals:
#>        Min         1Q     Median         3Q        Max 
#> -0.6006931 -0.0862222 -0.0009999  0.1164699  0.3734227 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   9.8950     1.0586   9.348 4.12e-12
#> log_rprice   -1.2774     0.2632  -4.853 1.50e-05
#> log_rincome   0.2804     0.2386   1.175    0.246
#> 
#> Residual standard error: 0.1879 on 45 degrees of freedom
#> Multiple R-Squared: 0.4294,	Adjusted R-squared: 0.4041 
#> Wald test: 13.28 on 2 and 45 DF,  p-value: 2.931e-05 
#> 
#> Next step: Use 'setx' method
from_zelig_model(z.out1) %>% summary(vcov = sandwich, df = Inf,
                                     diagnostics = TRUE)
#> 
#> Call:
#> `z5$zelig`(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 
#> 
# simulate and plot quantities of interest
z.out1 %>% setx() %>% sim() %>% plot()

# ANOVA
z.out2 <- zelig(log(packs) ~ log_rprice |
                tdiff, data = CigarettesSW, subset = year == "1995",
                model = "ivreg")
#> Error in eval(substitute(subset), data, env): object 'year' not found
anova(from_zelig_model(z.out1), from_zelig_model(z.out2))
#> 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