Vector autoregressions transformed empirical macroeconomics by letting data speak with minimal theoretical impositions. Yet the transition from reduced-form VARs to structural interpretations requires identifying assumptions that fundamentally shape conclusions. These assumptions often remain implicit, obscured by technical sophistication that masks substantive economic restrictions.

The identification problem is not merely technical—it reflects deep epistemological challenges in recovering causal relationships from observational data. When central banks assess whether their policy actions affect output and inflation, they rely on structural VAR evidence. When fiscal policy effectiveness is debated, competing structural VAR studies reach opposing conclusions. The divergence typically traces not to data disagreements but to different identifying restrictions, each embedding distinct views about how the economy operates.

Understanding these identification strategies—their foundations, limitations, and implicit commitments—is essential for interpreting empirical macroeconomic evidence. Recursive orderings impose timing restrictions. Sign restrictions constrain impulse responses. Narrative approaches leverage historical information. Each strategy purchases identification at a price, trading assumptions for conclusions. The sophistication lies not in eliminating assumptions but in understanding which assumptions drive which results. This analysis examines the major identification strategies, evaluates their theoretical foundations, and demonstrates how identification choices shape substantive conclusions about monetary policy effectiveness.

A reduced-form VAR estimates the joint dynamics of macroeconomic variables—output, inflation, interest rates—capturing their statistical relationships without structural interpretation. The innovation covariance matrix reveals contemporaneous correlations among forecast errors, but these correlations reflect the combined effect of all structural disturbances, not individual shocks. The fundamental problem: infinitely many structural representations are observationally equivalent to any reduced-form VAR.

Formally, if the reduced-form innovations have covariance matrix Σ, any structural shock matrix B satisfying BB' = Σ generates identical likelihood values. The Cholesky decomposition provides one such B, but it represents merely one point in a continuous space of observationally equivalent decompositions. Each decomposition implies different structural shocks, different impulse responses, and different policy conclusions. The data alone cannot discriminate among them.

This identification failure is not a statistical nuisance awaiting better estimation methods—it reflects a fundamental logical impossibility. Correlation cannot establish causation without additional structure. Observing that interest rates and output move together reveals nothing about whether monetary policy affects output, output movements prompt policy responses, or both respond to common shocks. The correlational evidence is consistent with all three interpretations simultaneously.

The reduced-form VAR honestly summarizes what the data contain: conditional forecasts and residual correlations. Structural conclusions require going beyond the data, imposing restrictions that identify particular shocks. These restrictions constitute maintained hypotheses, not testable implications. Their validity cannot be assessed by statistical criteria but depends on theoretical reasoning and institutional knowledge about economic mechanisms.

Recognizing this limitation clarifies what structural VAR exercises actually accomplish. They answer conditional questions: if the identifying assumptions hold, then the structural impulse responses follow. The empirical content lies in the reduced-form estimates; the structural interpretation derives entirely from the identifying restrictions. Conflating these distinct components—confusing statistical precision about correlations with certainty about causal effects—represents a fundamental category error in applied macroeconomics.

Takeaway

Reduced-form VARs capture correlations with statistical precision, but structural interpretations depend entirely on identifying assumptions that data cannot verify—making assumption transparency essential for credible inference.

Recursive identification, popularized by Sims's seminal work, achieves exact identification through Cholesky decomposition of the innovation covariance matrix. This imposes a triangular structure: variables ordered earlier respond contemporaneously to their own shocks and those of predecessors, but not to innovations in variables ordered later. For monetary policy analysis, placing the policy rate last implies that monetary authorities observe and respond to current output and inflation, while the real economy responds to policy only with a lag.

The timing assumptions underlying recursive identification carry substantive economic content. Placing output before the policy rate assumes central bankers observe current GDP—questionable given publication lags and real-time data uncertainty. Different orderings generate different identified shocks and impulse responses. The Cholesky decomposition's apparent objectivity masks an ordering choice that substantially affects conclusions. When researchers report results for a single ordering without sensitivity analysis, they suppress evidence about how conclusions depend on maintained assumptions.

Sign restrictions, developed by Uhlig and extended by subsequent researchers, achieve set identification by constraining impulse response signs rather than imposing exact contemporaneous restrictions. A contractionary monetary shock might be defined as one that raises interest rates and does not increase inflation or output on impact. This approach avoids specific timing assumptions but introduces different commitments: it rules out the identification of shocks that might violate conventional theoretical predictions, potentially excluding empirically relevant scenarios.

The set-identified nature of sign restrictions means they deliver bounds on structural objects rather than point estimates. Multiple structural decompositions satisfy the sign constraints, each generating different impulse responses. Reporting a single impulse response from this identified set—typically a posterior median—obscures the actual uncertainty about structural effects. The identified set's size measures identification strength: narrow sets indicate identifying assumptions do substantial work; wide sets reveal the data's limited capacity to discriminate among structural interpretations.

Narrative identification leverages historical information to tag specific observations as particular shock realizations. Romer and Romer's monetary policy shock series uses Federal Reserve records to identify exogenous policy actions. This approach achieves identification through information auxiliary to the VAR, avoiding purely statistical restrictions. However, narrative approaches require that historical interpretations correctly classify shock types and that identified episodes represent the same structural phenomenon—assumptions that themselves resist formal testing.

Takeaway

Each identification strategy—recursive orderings, sign restrictions, narrative approaches—purchases structural interpretation through different assumptions; understanding which assumptions drive which conclusions is more valuable than any single point estimate.

The extensive literature on monetary policy effects illustrates how identification choices generate substantive disagreements. Studies using recursive identification with interest rates ordered last typically find significant output effects from monetary shocks, supporting policy effectiveness. However, reordering variables or modifying the information set substantially alters these conclusions. The policy effectiveness evidence is identification-dependent, not identification-robust.

Sign restriction approaches to monetary policy identification often yield wide identified sets for output responses, indicating substantial uncertainty about policy effects even conditional on the maintained restrictions. Studies reporting tight confidence intervals around a median response understate true structural uncertainty. The identified set itself constitutes the honest answer to what sign restrictions reveal about monetary policy effects. When this set spans both positive and negative output responses, the identification strategy cannot determine the sign of monetary policy's real effects.

The Romer and Romer narrative approach produces different monetary shock series than recursive or sign-restricted alternatives. These different series correlate imperfectly, implying they identify different structural objects. The divergence is not statistical—it reflects fundamentally different maintained hypotheses about what constitutes an exogenous monetary shock. If policy responds systematically to information not captured in standard VAR specifications, recursive and sign-restricted shocks confound endogenous and exogenous policy variation. The narrative approach potentially avoids this contamination but introduces different concerns about shock classification.

Recent high-frequency identification uses asset price movements in narrow windows around policy announcements to isolate monetary surprises. This strategy assumes financial markets respond immediately to policy news and that announcement windows contain no other significant information. These assumptions enable identification without VAR estimation, but the identified shocks may capture only the surprise component of policy, missing predictable monetary policy effects operating through systematic response functions.

The monetary policy effectiveness debate cannot be resolved by accumulating more VAR evidence. Different identification strategies yield different conclusions, and no purely empirical criterion adjudicates among them. Progress requires either theoretical restrictions that narrow the class of admissible structural models or explicit recognition that current evidence cannot resolve substantive policy questions. Claiming robust evidence for policy effectiveness when results depend critically on identification choices misrepresents the state of knowledge.

Takeaway

Monetary policy effectiveness conclusions vary substantially across identification strategies—the honest assessment acknowledges this dependence rather than reporting preferred results as if they were identification-robust.

Structural VAR analysis represents a sophisticated approach to empirical macroeconomics, but its sophistication lies in making identification assumptions explicit rather than eliminating them. Every structural impulse response embeds maintained hypotheses about shock transmission, contemporaneous relationships, or historical classification. These assumptions do not contaminate otherwise pure empirical evidence—they constitute the bridge from correlation to causation.

For researchers and policymakers evaluating structural VAR evidence, the essential question is not which identification strategy is correct but which assumptions are defensible for which purposes. Recursive orderings suit contexts where timing restrictions have theoretical support. Sign restrictions accommodate theoretical uncertainty but deliver set identification requiring honest communication of bounds. Narrative approaches leverage institutional knowledge but depend on correct historical interpretation.

The discipline structural VAR methods impose—requiring explicit identification assumptions—represents methodological progress. The remaining challenge is interpretive: recognizing that empirical precision about reduced-form objects does not transfer to structural conclusions, and that substantive debates often concern maintained assumptions rather than statistical evidence.