José Luis Montiel Olea | Macro Paper Warehouse

Decision Theory for Treatment Choice Problems with Partial Identification

This paper applies classical statistical decision theory (Wald 1950) to treatment choice problems where the data only partially identify payoff-relevant parameters. The policy maker chooses an action a in [0,1] — interpreted as the share of the population assigned to a new policy — to maximize welfare that is linear in the action. The data are Gaussian, and the key departure from prior literature is that the mean function mapping parameters to data need not be injective, so even infinite data may not reveal the optimal action.

Double Robustness of Local Projections and Some Unpleasant VARithmetic

This paper provides formal theoretical results on the relative robustness of local projection (LP) and vector autoregression (VAR) confidence intervals for impulse response inference when the data generating process (DGP) is locally misspecified. The research question is whether the widely held belief that LP estimators are more robust to misspecification than VARs is theoretically justified, and if so, precisely under what conditions and with what consequences for VAR inference.

The analytical framework models the DGP as a stationary structural VARMA(1, ∞) that is local to an SVAR(1), of the form y_t = Ay_{t-1} + H[I + T^{-ζ}α(L)]ε_t, where the MA component T^{-ζ}α(L)ε_t represents misspecification that vanishes at rate T^{-ζ} as sample size T grows. The key rate parameter is ζ ∈ (1/4, 1/2), which corresponds to misspecification large enough to be detected with probability approaching 1 by conventional Hausman-type specification tests, yet small enough that the bias-variance trade-off between LP and VAR remains non-trivial asymptotically. The framework encompasses under-specification of lag length, omitted variables, temporal aggregation, measurement error, and failure of shock invertibility — essentially all sources of dynamic misspecification relevant to linearized DSGE models.

Local Projection Inference Is Simpler and More Robust Than You Think

This 2021 Econometrica paper by José Luis Montiel Olea and Mikkel Plagborg-Møller studies what inference procedure applied researchers should use for local-projection (LP) estimates of impulse response functions, and argues that a specific variant, lag-augmented LP (LA-LP) paired with ordinary Eicker-Huber-White (EHW) heteroskedasticity-robust standard errors, is both simpler to implement than commonly assumed and uniformly valid across a much wider range of data persistence than previously understood. The key theoretical mechanism, worked out first in an AR(1) setting, is that adding a single extra lag as a control (regressing y_{t+h} on both y_t and y_{t-1} rather than on y_t alone) makes the resulting regression scores serially uncorrelated even though the LP residual itself follows an MA(h-1) process, so heteroskedasticity-robust standard errors alone suffice for correct coverage: no HAC long-run-variance estimator or bandwidth choice is needed. Extending this to a general VAR(p) system, Proposition 1 shows the LA-LP estimator’s studentized statistic converges uniformly to a standard normal distribution across the entire parameter space of stationary, near-unit-root, and unit-root processes (each variable’s persistence parameter ρ_i ranging over [-1,1]) and across every horizon h that grows no faster than the sample size (h̄_T/T → 0), so the resulting confidence intervals have correct asymptotic coverage without the researcher pretesting for unit roots or tailoring the procedure to the persistence regime. Monte Carlo evidence (T = 240, 5,000 replications, nominal 90% coverage) shows LA-LP combined with a wild recursive-VAR bootstrap achieves approximately nominal coverage across all persistence/horizon combinations examined, including the unit-root case and long horizons, whereas a delta-method confidence interval built from an estimated AR(1) badly under-covers at longer horizons when the process is persistent, and a bootstrap confidence interval built from an augmented AR model achieves coverage only by becoming extremely wide near the unit root (e.g., a reported median CI length of 23.050 for the augmented-AR bootstrap versus 0.942 for LA-LP at ρ = 0.95, h = 60 under homoscedastic innovations, with the gap growing far more extreme under ARCH innovations). The efficiency ranking between LA-LP and its competitors is not uniform, however: LA-LP is more efficient than the augmented-AR estimator for persistent processes at long horizons, and more efficient than non-augmented LP (which is biased near unit roots) for large |ρ|, but for stationary processes at short horizons the ranking is ambiguous and AR-based estimators can be tighter. On this basis the authors recommend LA-LP with EHW standard errors, or the wild bootstrap, as a default inference procedure for LP-based impulse responses, recommend choosing the lag length conservatively (more lags rather than fewer, with the theory accommodating lag order growing at rate T^{1/3} or slower), and note that the results concern pointwise, single-horizon confidence intervals rather than confidence bands that are simultaneously valid across a whole range of horizons.

Simultaneous Confidence Bands: Theory, Implementation, and an Application to SVARs

This 2019 Journal of Applied Econometrics paper by José Luis Montiel Olea and Mikkel Plagborg-Møller addresses a practical problem in applied time-series econometrics: which “simultaneous” (joint, across-parameter) confidence band should researchers use by default when reporting an entire vector of estimated quantities – such as impulse responses across horizons from a structural VAR – rather than one interval per parameter reported separately. The authors set up a general framework in which a possibly nonlinear transformation theta = h(mu) of an asymptotically normal estimator mu-hat is to be covered jointly, and show that a wide class of popular bands (pointwise, Bonferroni, Sidak, projection, and the “sup-t” band) can all be written as members of a single “one-parameter class” that scales every pointwise standard error by one common critical value c. Within this class, the sup-t band – whose critical value is the quantile of the maximum absolute studentized draw from the estimator’s joint asymptotic distribution – is the narrowest band that still achieves exact asymptotic simultaneous coverage, and the paper adds a decision-theoretic result (Proposition 1) showing it uniquely minimizes worst-case regret across all degree-one-homogeneous loss functions, which makes it a defensible default when the researcher does not know which feature of the band matters most to different readers. The paper gives three computationally convenient ways to construct it – a plug-in (delta-method) simulation algorithm, a bootstrap algorithm, and a Bayesian algorithm delivering exact finite-sample simultaneous credibility – and notes all three are first-order asymptotically equivalent. In an empirical application to a monthly U.S. SVAR (July 1979-June 2012, 12 lags; identified two ways, via a recursive/Cholesky scheme and via a Gertler-Karadi (2015)-style external instrument using federal-funds-futures surprises from January 1990) with industrial production, CPI, a one-year bond yield, and the excess bond premium, the sup-t band is substantially narrower than the Bonferroni or Sidak bands – around 35% narrower in the external-instrument specification at 68% confidence – and the narrowing is not merely cosmetic: at the 68% simultaneous level the plug-in sup-t band excludes zero for the industrial-production response at horizons of roughly 13-36 months, letting the authors reject the no-effect null at some horizon in that range, whereas the Bonferroni band does not permit that rejection; conversely, an output response that looks pointwise significant at the 2-month horizon is no longer simultaneously significant once the sup-t multiple-comparison adjustment is applied. A companion Monte Carlo study of bivariate VARs finds the sup-t band 20-25% narrower than Bonferroni/Sidak at 68% confidence and 10-20% narrower at 90% confidence, though for highly persistent data only the Bayesian sup-t implementation is reported to achieve satisfactory finite-sample coverage. The theory is developed for point-identified models with a continuously differentiable transformation h(.); partially identified (e.g., sign-restricted) SVARs require additional considerations, though the authors suggest the Bayesian sup-t band may still be usable there for subjective Bayesian analysis.