Estimate impulse responses via proxy-IV local projections

Estimates impulse response functions (IRFs) using user-provided external instruments (proxies) combined with local projections (Jordà, 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(). d only).

Usage

proxyiv(
  y,
  O,
  Z,
  X = NULL,
  Ind,
  P,
  H,
  E = 1,
  norm = 1,
  cum = FALSE,
  Hstep = 1,
  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) are retained so that those observations remain available for shock prediction even when the instrument is unobserved.

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 are intended only for fast testing; they are only safe when Hstep >= H (a single horizon is stored). For complete IRF estimation always use Hstep = 1. Default 1.

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 HC0 heteroscedasticity-robust 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 (total used).
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.

References

Jordà, Ò. (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. The 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.

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.