Estimate impulse responses via proxy-IV local projections

Estimates impulse response functions (IRFs) using external instruments (proxies) combined with local projections (Jorda, 2005, Stock and Watson, 2018). The proxy variables serve as instruments for the endogenous variables. Optionally imposes recursive zero restrictions across shock dimensions. It also returns weak instrument tests as well as shock predictions on event days, 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,
  cov_type = "HC3",
  recursive = FALSE,
  hpredict = 0,
  pooled = FALSE,
  details = FALSE
)

Arguments

y

Numeric matrix of 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). For non-stationary variables y, it should at least include 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 for the corresponding endogenous variable. Following the proxy-SVAR literature (Mertens and Ravn, 2013), the recommended convention is to set the proxy to zero on control days (Ind == 0). These days then remain in the IV sample and sharpen the estimates of the control coefficients, while the identifying moments are unaffected. Alternatively, missing values control days are treated as contaminated and excluded from estimation, which reproduces the event-day sample of the event-study literature (Nakamura and Steinsson, 2018). With zeros, always prefer the robust first-stage statistics (F_rob, WeakTest) over the homoskedastic F, which treats the zero observations as informative. 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. Needs to be equal to the number of columns in Z

norm

Numeric scalar. Normalize the impact response of the first variable to this value. Defaults 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 applied to all variables. Default FALSE.

cov_type

Covariance estimator for local-projection standard errors: "HC3" (default) for heteroskedasticity-robust standard errors or "NW" for Newey-West HAC standard errors. "HC3" 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. This implies that the shock identified for dimension e has no impact effect on the endogenous variables from dimensions 1, ..., e-1. Default FALSE.

hpredict

Integer. Horizon of the responses and forecast errors used for shock prediction, on the same scale as the row labels of irf. Defaults to 0 (recommended; the impact response and one-step-ahead residual are used). Must lie between 0 and H - 1.

pooled

Logical. If FALSE (default), the shock prediction uses the forecast errors and responses at horizon hpredict only. If TRUE, the forecast errors of all horizons 0, ..., hpredict are stacked and used jointly (pooled prediction); see kfpredict(). With hpredict = 0 both options coincide.

details

Logical. If TRUE, saves detailed IV results, weak instrument tests, and shock prediction results, which is slightly slower. If FALSE, returns only impulse responses and standard errors.

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:

Shocks: Predicted structural shocks on event days from kfpredict(), based on the responses at horizon hpredict.
IVRes: List of ivreg model objects, one per horizon, variable, and shock dimension.
OLSRes: List of the information-set regressions whose residuals enter the shock prediction, named OLS.n<i>.h<h> by outcome variable and horizon.
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 of the first shock at the impact horizon).
FirstStage: For E = 1: data frame with one row per horizon h giving the number of observations Tobs, the homoskedastic first-stage F statistic F_hom (the squared t statistic of the proxy; Stock and Yogo, 2005) and the robust effective F statistic F_rob of Montiel Olea and Pflueger (2013), always computed with the HAC (Newey-West) covariance estimator, irrespective of cov_type. The statistics do not depend on the outcome variable. NULL for E > 1.
WeakTest: For E > 1: data frame with one row per shock dimension target (e = 1, ..., E), horizon h and outcome variable i, giving the results of gweakivtest() for the system with the first e policy variables as endogenous regressors and the first e proxies as instruments, targeting the coefficient on policy variable e: Tobs, gmin (generalized minimum eigenvalue statistic, which depends on the horizon only through the sample), cv and cv_simplified (sharp and simplified critical values, which may depend on the outcome and horizon), and the Stock-Yogo statistic sy_stat with its critical value sy_cv (NaN unless over-identified). The test always uses the HAC (Newey-West) covariance estimator, irrespective of cov_type, and the relative bias criterion (crit = "rel"), for comparability with Montiel Olea and Pflueger (2013). Rows where the outcome is a policy variable (i <= E) on impact are omitted. NULL for E = 1.
et: Data frame of forecast errors on event days used for shock prediction, one column per variable and horizon (y1.h0, ..., yN.h0, y1.h1, ...): horizon hpredict only if pooled = FALSE, horizons 0, ..., hpredict if pooled = TRUE.
Sig: Covariance matrix of et on event days.
SigR: Covariance matrix of the same residuals on control days, or NA if unavailable. A control day enters horizon h only if no event occurs in its window t + 1, ..., t + h.
Psi: Response matrix used for shock prediction, with rows matching the columns of et: irf[hpredict + 1, , ] (N x E) if pooled = FALSE, the rows 1, ..., hpredict + 1 of irf stacked if pooled = TRUE. With the default hpredict = 0 this is 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 zero restrictions in that order. If recursive = FALSE the instruments are assumed to be valid across dimensions.

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.

Nakamura, E. and Steinsson, J. (2018). High-frequency identification of monetary non-neutrality: The information effect. Quarterly Journal of Economics, 133(3), 1283-1330.

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