Instrumental variables and GMM estimation for R with built-in
diagnostics, designed to reproduce Stata’s ivreg2
output (Baum, Schaffer & Stillman, 2003, 2007).
# install.packages("devtools")
devtools::install_github("restatr/ivreg2r")library(ivreg2r)
data(card)
fit <- ivreg2(lwage ~ exper + expersq + black + smsa + south + smsa66 +
reg662 + reg663 + reg664 + reg665 + reg666 + reg667 +
reg668 + reg669 | educ | nearc2 + nearc4,
data = card, vcov = "robust", small = TRUE)
tidy(fit)
#> # A tibble: 16 × 7
#> term estimate std.error statistic p.value conf.low conf.high
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 3.24 0.884 3.66 2.56e- 4 1.50 4.97
#> 2 educ 0.157 0.0526 2.99 2.83e- 3 0.0540 0.260
#> 3 exper 0.119 0.0230 5.18 2.41e- 7 0.0738 0.164
#> 4 expersq -0.00236 0.000368 -6.40 1.83e-10 -0.00308 -0.00163
#> 5 black -0.123 0.0516 -2.39 1.70e- 2 -0.225 -0.0220
#> 6 smsa 0.101 0.0314 3.20 1.37e- 3 0.0391 0.162
#> 7 south -0.143 0.0303 -4.73 2.34e- 6 -0.203 -0.0838
#> 8 smsa66 0.0151 0.0212 0.712 4.77e- 1 -0.0264 0.0566
#> 9 reg662 0.103 0.0379 2.71 6.79e- 3 0.0284 0.177
#> 10 reg663 0.150 0.0371 4.04 5.51e- 5 0.0771 0.223
#> 11 reg664 0.0476 0.0457 1.04 2.98e- 1 -0.0420 0.137
#> 12 reg665 0.154 0.0509 3.03 2.44e- 3 0.0546 0.254
#> 13 reg666 0.173 0.0535 3.23 1.25e- 3 0.0680 0.278
#> 14 reg667 0.142 0.0524 2.71 6.75e- 3 0.0393 0.245
#> 15 reg668 -0.0951 0.0588 -1.62 1.06e- 1 -0.210 0.0201
#> 16 reg669 0.103 0.0427 2.41 1.59e- 2 0.0193 0.187Three-part formula:
y ~ exogenous | endogenous | excluded_instruments. Each
variable appears once; exogenous regressors are automatically included
as instruments.
| Part | Contents | Example |
|---|---|---|
| LHS | Dependent variable | lwage |
| 1st RHS | Exogenous regressors | exper + expersq + black + smsa + ... |
| 2nd RHS | Endogenous regressors | educ |
| 3rd RHS | Excluded instruments | nearc2 + nearc4 |
A one-part formula (y ~ x1 + x2) estimates OLS.
Estimators: OLS, 2SLS, LIML, Fuller, k-class, two-step efficient GMM, CUE
Standard errors: classical, robust, one- and two-way clustering, HAC/AC (8 kernels), Kiefer, Driscoll-Kraay, cluster+kernel
Diagnostics: weak identification (Kleibergen-Paap rk, Cragg-Donald, Stock-Yogo critical values), underidentification, overidentification (Sargan, Hansen J), endogeneity, first-stage F/partial R-squared, Anderson-Rubin, Stock-Wright S, orthogonality, redundancy
Integration: tidy(),
glance(), augment() via broom
summary() prints the complete ivreg2
output, including the automatic diagnostics described above, for the
model fit in the example:
summary(fit)
#>
#> 2SLS Estimation
#>
#> Call:
#> ivreg2(formula = lwage ~ exper + expersq + black + smsa + south +
#> smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 + reg667 +
#> reg668 + reg669 | educ | nearc2 + nearc4, data = card, vcov = "robust",
#> small = TRUE)
#>
#> Observations: 3,010
#> VCV type: Robust, small-sample corrected
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 3.2367114 0.8842788 3.660 0.000256 ***
#> educ 0.1570593 0.0525525 2.989 0.002825 **
#> exper 0.1188149 0.0229516 5.177 2.41e-07 ***
#> expersq -0.0023565 0.0003684 -6.397 1.83e-10 ***
#> black -0.1232778 0.0516278 -2.388 0.017010 *
#> smsa 0.1007530 0.0314458 3.204 0.001369 **
#> south -0.1431945 0.0302678 -4.731 2.34e-06 ***
#> smsa66 0.0150626 0.0211683 0.712 0.476792
#> reg662 0.1027473 0.0379324 2.709 0.006793 **
#> reg663 0.1499316 0.0371230 4.039 5.51e-05 ***
#> reg664 0.0475676 0.0456953 1.041 0.297972
#> reg665 0.1544801 0.0509365 3.033 0.002444 **
#> reg666 0.1729728 0.0535430 3.231 0.001249 **
#> reg667 0.1420355 0.0523988 2.711 0.006753 **
#> reg668 -0.0950611 0.0587578 -1.618 0.105801
#> reg669 0.1029760 0.0426891 2.412 0.015915 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> ---
#> R-squared: 0.1702
#> Adj. R-squared: 0.1660
#> F(15, 2994): 51.4 (p < 2.2e-16)
#> Root MSE: 0.4053
#>
#> Underidentification test (Kleibergen-Paap rk LM statistic):
#> Chi-sq(2) = 16.37 (p = 0.0003)
#>
#> Weak identification test:
#> Cragg-Donald Wald F: 7.89
#> Kleibergen-Paap rk Wald F: 8.32
#> (Stock-Yogo critical values are for iid errors)
#> Stock-Yogo critical values (IV size):
#> 10% maximal IV size 19.93
#> 15% maximal IV size 11.59
#> 20% maximal IV size 8.75
#> 25% maximal IV size 7.25
#>
#> Overidentification test (Hansen J):
#> Chi-sq(1) = 1.27 (p = 0.2600)
#>
#> Weak-instrument-robust inference:
#> H0: B1=0 and orthogonality conditions are valid
#> Anderson-Rubin Wald F(2,2993) = 5.28 (p = 0.0051)
#> Anderson-Rubin Wald Chi-sq(2) = 10.63 (p = 0.0049)
#> Stock-Wright LM S Chi-sq(2) = 10.61 (p = 0.0050)
#>
#> Endogeneity test:
#> Chi-sq(1) = 2.83 (p = 0.0925)
#> Tested: educ
#>
#> First-stage diagnostics:
#> Endogenous F-stat p-value Partial R2 Shea PR2 SW F AP F
#> educ 8.32 0.0002 0.0052 0.0052 8.32 8.32
#>
#> Instrumented: educ
#> Included instruments: exper, expersq, black, smsa, south, smsa66, reg662, reg663, reg664, reg665, reg666, reg667, reg668, reg669
#> Excluded instruments: nearc2, nearc4Every estimator, variance estimator, and diagnostic is tested against
output generated by Stata’s ivreg2 itself. Checked-in Stata
scripts run each specification and write the results to machine-readable
fixture files; the R test suite then reproduces them at tight, centrally
documented tolerances. See How ivreg2r
is validated against Stata for more details.
Common translations (see vignette("introduction") for
the full
table and intentional
differences):
| Stata | R (ivreg2r) |
|---|---|
ivreg2 y x (endo = z1 z2) |
ivreg2(y ~ x \| endo \| z1 + z2, data = d) |
ivreg2 ..., robust |
ivreg2(..., vcov = "robust") |
ivreg2 ..., robust small |
ivreg2(..., vcov = "robust", small = TRUE) |
ivreg2 ..., cluster(g) |
ivreg2(..., clusters = ~ g) |
ivreg2 ..., cluster(g) small |
ivreg2(..., clusters = ~ g, small = TRUE) |
ivreg2 ..., liml |
ivreg2(..., method = "liml") |
ivreg2 ..., gmm2s |
ivreg2(..., method = "gmm2s") |
vignette("introduction") — OLS, 2SLS, diagnostics,
robust/cluster SEs, weights, broom integration, Stata migration
referencevignette("advanced-iv") — LIML, Fuller, k-class, COVIV,
two-way clustering, reduced-form, model comparisonvignette("time-series-gmm") — HAC/AC, Kiefer,
Driscoll-Kraay, GMM, CUE, partialling, user matricescitation("ivreg2r")
DiTraglia F (2026). _ivreg2r: Extended Instrumental Variables
Estimation with Diagnostics_. R package,
<https://github.com/restatr/ivreg2r>.
The Stata ivreg2 command that inspired this package is described in:
Baum C, Schaffer M, Stillman S (2003). "Instrumental Variables and
GMM: Estimation and Testing." _The Stata Journal_, *3*(1), 1-31.
doi:10.1177/1536867X0300300101
<https://doi.org/10.1177/1536867X0300300101>.
Baum C, Schaffer M, Stillman S (2007). "Enhanced Routines for
Instrumental Variables/Generalized Method of Moments Estimation and
Testing." _The Stata Journal_, *7*(4), 465-506.
doi:10.1177/1536867X0800700402
<https://doi.org/10.1177/1536867X0800700402>.
To see these entries in BibTeX format, use 'print(<citation>,
bibtex=TRUE)', 'toBibtex(.)', or set
'options(citation.bibtex.max=999)'.ivreg2r is part of restatr, a project that uses LLM
assistance to port user-contributed Stata modules from the SSC Archive to R
and Python. The package was developed with Claude Code, working from the
original GPL-3-licensed ivreg2
Stata source code, created by Baum, Schaffer, and Stillman. Every
package feature has been numerically validated against the Stata
original. For more details see How ivreg2r
is validated against Stata.
GPL-3. Adapted from the Stata package ivreg2 by
Christopher F Baum, Mark E Schaffer, and Steven Stillman, also
distributed under GPL-3.