Estimate impulse responses via proxy-IV local projections

Estimates impulse response functions (IRFs) using user-provided external instruments (proxies) combined with local projections (Jorda, 2005). The proxy variables serve directly as instruments for the endogenous shock variables. Optionally imposes recursive zero restrictions across shock dimensions and supports deterministic controls following the same conventions as hetiv().

Usage

proxyiv(
  y,
  O,
  Z,
  X = NULL,
  Ind,
  P,
  H,
  E = 1,
  norm = 1,
  cum = FALSE,
  Hstep = 1,
  cov_type = "HC0",
  recursive = FALSE,
  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 norm at horizon 0. These variables are also used as the endogenous regressors instrumented by the columns of Z.

O

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

Z

Numeric matrix of external instruments (T x E). Column e is used as the proxy for shock dimension e. Missing values on control days (Ind == 0) are treated as contaminated and excluded from estimation. Missing values on policy days (Ind == 1) remain labelled as events for residual-based shock prediction, but are necessarily dropped from IV regressions that use the missing proxy.

X

Numeric matrix of deterministic variables (T x K), or NULL (default). May include a constant, time trend, or seasonal dummies. Included as-is (no lags).

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 constant only).

H

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

E

Integer. Number of shock dimensions to identify. Default 1.

norm

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

cum

Logical scalar or vector of length N. If TRUE for variable i, the cumulative IRF is reported. A single value is recycled to all variables. Default FALSE.

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. Default 1.

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.

recursive

Logical. If TRUE, imposes recursive zero restrictions across shock dimensions: for shock e > 1, the variables and instruments from dimensions 1, ..., e-1 are added as controls. Default FALSE.

details

Logical. If TRUE, returns detailed results including IV model objects, OLS residuals, and covariance matrices. If FALSE (default), returns only impulse responses and standard errors (faster; use for bootstrap).

Value

A named list. Always contains:

irf

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

se

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

Method

Character string "Proxy-IV".

With details = TRUE, additionally contains:

IVRes

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

OLSRes

List of OLS model objects used for residual-based covariance estimation, one per outcome variable.

Obs

Data frame with observation counts: Tp (policy days), Tc (control days), To (contaminated days), Tt (labelled event or control days), and Tiv (complete observations available to the IV regression at the impact horizon).

et

Data frame of OLS residuals on event days.

Sig

Covariance matrix of residuals on event days.

SigR

Covariance matrix of residuals on control days, or NA if unavailable.

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 can be order-dependent: the column order of y defines the endogenous shock variables and normalizations, the column order of Z assigns proxies to shock dimensions, and recursive = TRUE imposes restrictions in that order.

References

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

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

Mertens, K. and Ravn, M. O. (2013). The dynamic effects of personal and corporate income tax changes in the United States. American Economic Review, 103(4), 1212-1247.

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.

Stock, J. H. and Watson, M. W. (2018). Identification and estimation of dynamic causal effects in macroeconomics using external instruments. Economic Journal, 128(610), 917-948.

Examples

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