Statistical conventions in ivreg2r

ivreg2r is a translation of Stata's ivreg2, and it follows Stata's statistical conventions rather than those of R's lm()/vcov() ecosystem. This topic collects those conventions in one place. The API itself is idiomatic R (formula interface, tidyverse-friendly output); only the statistical choices below lean on Stata. See ivreg2() for the estimation function and ivreg2r-glossary for the diagnostic acronyms printed by summary().

Default VCE and small-sample corrections

vcov defaults to "iid" (classical) and small defaults to FALSE, matching Stata's ivreg2 defaults. With small = FALSE, inference uses z and chi-squared statistics and the large-sample variance normalization. Set small = TRUE for t and F statistics and the finite-sample N - K correction, matching Stata's small option. small is the single, uniform control for finite-sample corrections across every VCE type ("iid", "robust", "HAC", "AC"); it is not a VCE selector. There are no "HC0"/"HC1" values — use vcov = "robust" and toggle small.

Three statistics sit outside that uniform control, all matching Stata: the first-stage F statistics (first_stage()) always use small-sample degrees of freedom regardless of small; the overidentification (Sargan/Hansen J) and endogeneity (C-statistic) tests are never small-sample corrected, even when small = TRUE; and the stored reduced-form variance-covariance matrix (reduced_form) always applies OLS-style small-sample scaling regardless of the main model's small.

Sigma (RMSE) normalization

Under small = FALSE, \(\sigma^2 = RSS / (N - dofminus)\). Under small = TRUE, \(\sigma^2 = RSS / (N - K - dofminus - sdofminus)\). This differs from lm(), which always divides the residual sum of squares by its residual degrees of freedom. Because ivreg2r reports the large-sample sigma by default, its RMSE and any quantity built from sigma differ from lm() unless small = TRUE.

Standard errors relative to lm()

Coefficients match lm() for OLS. Standard errors and the full variance-covariance matrix match lm() only when small = TRUE; the default small = FALSE reports Stata-convention standard errors without the N - K finite-sample correction. Under analytic ("aweight") or probability ("pweight") weights, sigma additionally differs from lm(..., weights = w) by a factor of sqrt(N / sum(w)), because lm() uses raw (unnormalized) weights while ivreg2r normalizes them (see below).

Weight normalization

Analytic and probability weights are normalized internally to sum to N, following Stata. This makes sigma scale-invariant for those types: multiplying every weight by a constant leaves all coefficients, standard errors, and test statistics unchanged. Frequency ("fweight") and importance ("iweight") weights are not normalized; they redefine N as sum(weights), so their scale is meaningful by construction. Probability weights force a robust VCE. See the weight_type argument of ivreg2().

Degrees-of-freedom adjustments

dofminus is a large-sample adjustment subtracted from N in large-sample variance formulas (for example when fixed effects have been partialled out upstream). sdofminus is a small-sample adjustment subtracted from the residual degrees of freedom alongside K (for example the count of regressors removed by partial). Both mirror Stata's dofminus() and sdofminus() options. Stata's own source labels dofminus a large-sample adjustment (e.g. number of fixed effects) and sdofminus a small-sample one (e.g. number of partialled-out regressors).

Confidence intervals and test statistics

confint() and the model Wald test use the standard normal and chi-squared distributions when small = FALSE, and the t and F distributions when small = TRUE. The reported model test is therefore a chi-squared Wald statistic by default and an F statistic under small = TRUE.