Package 'clusterIV'

Cluster-jackknife instrumental variables estimation (CJIVE)

Description

Computes the cluster-jackknife IV estimator of Frandsen, Leslie and McIntyre (2025) for a single endogenous regressor in a just-identified design, with cluster-robust inference. The first-stage value for each observation is fitted from a regression that leaves out the observation's entire cluster, which removes the many-instrument bias that survives clustering.

Usage

cjive(y, ...)

## Default S3 method:
cjive(
  y,
  x,
  z,
  cluster,
  controls = NULL,
  weights = NULL,
  level = 0.95,
  intercept = TRUE,
  method = c("auto", "dense", "leaveout_mean"),
  ...
)

## S3 method for class 'formula'
cjive(
  formula,
  data,
  cluster,
  controls = NULL,
  weights = NULL,
  level = 0.95,
  intercept = TRUE,
  method = c("auto", "dense", "leaveout_mean"),
  ...
)

## S3 method for class 'cjive'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'cjive'
summary(object, ...)

## S3 method for class 'summary.cjive'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'cjive'
coef(object, ...)

## S3 method for class 'cjive'
vcov(object, ...)

## S3 method for class 'cjive'
confint(object, parm, level = 0.95, ...)

Arguments

y	Outcome (numeric vector), or a two-sided formula y ~ x | z for the formula method (the bar separates the endogenous regressor from the instruments).
...	Unused.
x	Single endogenous regressor (numeric vector); or, for the print methods, a fitted "cjive" object.
z	Instruments: a numeric vector/matrix, or a factor/character grouping vector for a judge design (expanded internally to a dummy design with one reference level dropped, the intercept supplying the rest).
cluster	Cluster identifiers (length n). For the formula method a one-sided formula (~ g) or a column name is also accepted.
controls	Optional covariates (FLM's $X$): a matrix or data frame, or a one-sided formula in the formula method. May be rank deficient (fixed effects are allowed). An intercept is added unless intercept = FALSE.
weights	Optional strictly positive precision weights.
level	Confidence level for the reported interval.
intercept	Logical; partial out an intercept (default TRUE).
method	One of "auto", "dense", "leaveout_mean". "auto" and "dense" both use the dense Frisch-Waugh-Lovell block-jackknife and are the default. "leaveout_mean" evaluates FLM's printed leave-cluster-out group-mean form and is available only for a grouping-factor z with intercept-only controls; it differs from the default by an O(1/n_g) intercept term and is never selected automatically.
formula	A formula y ~ x | z1 + z2.
data	A data frame in which to evaluate the formula.
object	A fitted "cjive" object.
digits	Number of significant digits to print.
parm	Ignored (a single coefficient is estimated).

Details

The estimator is the covariance ratio $\hat\delta = \widehat{Cov}(Y,\hat p)/\widehat{Cov}(D,\hat p)$ with the cluster-jackknife constructed instrument $\hat p$. Covariates are handled by Frisch-Waugh-Lovell: $Y$, $D$ and each instrument are residualised on the covariates (with an intercept) once, up front, then the estimator runs on the residuals. This dense route is the single convention everywhere, so cjive() and iv_compare return the identical CJIVE for any design. The leave-cluster-out fits are computed by a Woodbury block update (one Cholesky of $Z'Z$ plus a small solve per cluster), exact against the brute-force definition, and collapsing to observation-level JIVE when every cluster is a singleton.

Value

An object of class "cjive": a list with coefficient, se, statistic, p.value, conf.low, conf.high, level, the diagnostics n, G, p, path ("dense" or "leaveout_mean") and maxlev (the maximum within-cluster leverage $\max_g \lambda_{\max}(H_g)$, a conditioning diagnostic; NA on the mean path), and the call.

Methods (by class)

• cjive(default): matrix/vector interface.

• cjive(formula): formula interface y ~ x | z.

• print(cjive): Print a concise summary of the fit.

• summary(cjive): Build a summary object.

• print(summary.cjive): Print method for the summary object.

• coef(cjive): Extract the point estimate.

• vcov(cjive): Extract the cluster-robust (co)variance.

• confint(cjive): Confidence interval for the coefficient.

References

Frandsen, B., Leslie, E. and McIntyre, S. (2025). Cluster Jackknife Instrumental Variables Estimation. Review of Economics and Statistics.

Examples

set.seed(1)
G  <- 40; ng <- 6; n <- G * ng
cl <- rep(seq_len(G), each = ng)
j  <- factor(rep(rep(1:4, length.out = ng), G))   # judge identity
u  <- rnorm(G)[cl]
x  <- as.numeric(j) + u + rnorm(n)
y  <- 1.5 * x + u + rnorm(n)
fit <- cjive(y, x, j, cluster = cl)
print(fit)

## formula interface
dat <- data.frame(y = y, x = x, j = j, cl = cl)
cjive(y ~ x | j, data = dat, cluster = ~cl)

---

Compare IV estimators on a common cluster-robust SE (FLM Table 1)

Description

Returns OLS, 2SLS, JIVE and CJIVE for the same design, each reported with the identical just-identified cluster-robust IV sandwich standard error; only the constructed instrument differs between rows. This reproduces the shape of Table 1 in Frandsen, Leslie and McIntyre (2025).

Usage

iv_compare(
  y,
  x,
  z,
  cluster,
  controls = NULL,
  weights = NULL,
  level = 0.95,
  intercept = TRUE
)

Arguments

y	Outcome (numeric vector).
x	Single endogenous regressor (numeric vector).
z	Instruments (numeric matrix/vector or a grouping factor).
cluster	Cluster identifiers (length n). For the formula method a one-sided formula (~ g) or a column name is also accepted.
controls	Optional covariates (FLM's $X$): a matrix or data frame, or a one-sided formula in the formula method. May be rank deficient (fixed effects are allowed). An intercept is added unless intercept = FALSE.
weights	Optional strictly positive precision weights.
level	Confidence level for the reported interval.
intercept	Logical; partial out an intercept (default TRUE).

Details

The constructed instruments are: OLS, the residualised $x$ itself; 2SLS, the full-sample fit $Z\hat\pi$; JIVE, the leave-one-out fit $(\hat x - h x)/(1 - h)$; CJIVE, the leave-cluster-out block fit. The CJIVE row equals cjive(..., method = "dense") on the same design.

Value

A data frame with one row per estimator (in the order OLS, 2SLS, JIVE, CJIVE) and columns estimator, coefficient, se, statistic, p.value, conf.low, conf.high.

References

Frandsen, B., Leslie, E. and McIntyre, S. (2025). Cluster Jackknife Instrumental Variables Estimation. Review of Economics and Statistics.

Examples

set.seed(2)
G <- 50; ng <- 5; n <- G * ng
cl <- rep(seq_len(G), each = ng)
z  <- matrix(rnorm(n * 3), n, 3)
u  <- rnorm(G)[cl]
x  <- z %*% c(1, -1, 0.5) + u + rnorm(n)
y  <- 2 * x + u + rnorm(n)
iv_compare(y, x, z, cluster = cl)

---