Estimate impulse responses via heteroskedasticity-based IV local projections

Estimates impulse response functions (IRFs) using recursive heteroskedasticity-IV identification (Rigobon, 2003; Rigobon and Sack, 2004; Lewis, 2022; Burri and Kaufmann, 2026a, 2026b) combined with local projections (Jorda, 2005). Identification exploits the difference in variance between policy event days and control days to construct instruments for the endogenous variables.

Usage

hetiv(
  y,
  O,
  X = NULL,
  Ind,
  P,
  H,
  E = 1,
  norm = 1,
  interact = FALSE,
  cum = FALSE,
  Hstep = 1,
  cov_type = "HC0",
  details = FALSE
)

Arguments

y

Numeric matrix of stationary outcome variables (T x N). The effect on the first variable in each dimension is normalized to unity at horizon 0. These variables are also used to construct heteroskedasticity-based instruments and for recursive ordering to identify multiple dimensions.

O

Numeric matrix of information set variables (T x M). May be identical to y. Included as lags 1 through P.

X

Numeric matrix of deterministic variables (T x K). For example, time trend, seasonal dummies or other deterministic controls. Included as is (no lags). A constant is included by default.

Ind

Integer vector of length T, event indicator:

• 0 Control day (no event)

• 1 Policy day (event)

• 2 Contaminated control day (excluded from estimation)

P

Integer. Maximum lag order for the information set. Set to 0 for no lags (regression on deterministic terms only).

H

Integer. Maximum horizon (in periods) up to which IRFs are estimated.

E

Integer. Number of shock dimensions to identify via recursive ordering.

norm

Numeric scalar. Normalize the impact response of the first variable to a specific value. Set to 1 for standard unit-effect normalization.

interact

Logical. If TRUE, lagged information set variables are interacted with event/non-event dummies.

cum

Logical vector of length N. For each variable in y, whether to report the cumulative impulse response instead of the level response. If only one provided, applied to all impulse responses.

Hstep

Integer. Step size between horizons. The default 1 estimates all horizons 0 through H - 1. Values greater than 1 estimate only the selected horizons.

cov_type

Covariance estimator for local-projection standard errors: "HC0" (default) for heteroskedasticity-robust standard errors or "NW" for Newey-West HAC standard errors. "HC0" is the default because Montiel Olea et al. (2025) show that heteroskedasticity-robust standard errors suffice for local-projection impulse responses under weak conditions, even though multi-step forecast errors are typically serially correlated. "NW" remains available as an optional HAC robustness check.

details

Logical. If TRUE, code saves detailed IV results, which is slightly slower. if set to FALSE, returns only impulse response and standard error (e.g. for bootstrap)

Value

A named list with the following elements:

irf

Array (H x N x E) of estimated impulse responses.

se

Array (H x N x E) of local-projection standard errors.

IVRes

List of ivreg model objects, one per horizon, variable, and shock dimension.

Obs

Data frame with observation counts: Tp (policy days), Tc (control days), To (contaminated days), Tt (total used).

Method

Character string "Heteroscedasticity-IV".

et

Data frame of OLS residuals on event days (used for covariance estimation and shock extraction).

Sig

Covariance matrix of residuals on event days (used for shock extraction).

SigR

Covariance matrix of residuals on control days, or NA if unavailable (used for shock extraction).

Psi

Impact matrix (N x E), equal to irf[1, , ]. By the package's indexing convention HSeries starts at 1, so the first LP uses lead(y, 0) (the contemporaneous value) and is labelled horizon 0; irf[1, , ] is therefore always the impact response.

WeakData

Data frame of endogenous variables and instruments for the Lewis-Mertens (2025) weak instrument test.

Details

For E > 1, identification is recursive and order-dependent: the column order of y defines both the shock ordering and the normalization variable for each shock dimension.

References

Burri, M. and D. Kaufmann (2026a). Measuring monetary policy shocks. IRENE Working Papers 24-03, IRENE Institute of Economic Research, University of Neuchatel.

Burri, M. and D. Kaufmann (2026b). Multiple monetary policy shocks from daily data: A heteroskedasticity IV approach. Economics Letters, 268, 113091. doi:10.1016/j.econlet.2026.113091

Jorda, O. (2005). Estimation and inference of impulse responses by local projections. American Economic Review, 95(1), 161-182.

Lewis, D. J. (2022). Robust inference in models identified via heteroskedasticity. Review of Economics and Statistics, 104(3), 510-524.

Lewis, D. J. and Mertens, K. (2025). A robust test for weak instruments for 2SLS with multiple endogenous regressors. Review of Economic Studies, DOI: 10.1093/restud/rdaf103

Montiel Olea, J. L., M. Plagborg-Moller, E. Qian, and C. K. Wolf (2025). Local projections or VARs? A primer for macroeconomists. NBER Working Paper No. 33871.

Rigobon, R. (2003). Identification through heteroskedasticity. Review of Economics and Statistics, 85(4), 777-792.

Rigobon, R. and Sack, B. (2004). The impact of monetary policy on asset prices. Journal of Monetary Economics, 51(8), 1553-1575.

Examples

set.seed(1)
y <- matrix(rnorm(80), ncol = 2)
Ind <- rep(0L, nrow(y))
Ind[seq(5, nrow(y), by = 5)] <- 1L
res <- hetiv(y = y, O = y, Ind = Ind, P = 1, H = 3, details = TRUE)
dim(res$irf)
#> [1] 3 2 1