Definition
The price puzzle is the empirical anomaly in which a structural vector autoregression (SVAR) identifies a contractionary monetary policy shock that is followed by a rise in the price level — the opposite of what monetary theory predicts. A tightening that raises interest rates should reduce aggregate demand and lower inflation; prices rising in response indicates misspecification or misidentification.
Key Ideas
- Symptom of omitted forward-looking information: Sims (1992) showed the puzzle arises when the model's information set Ωt omits the Fed's forward-looking indicators. The Fed raises rates partly in anticipation of commodity-price-driven inflation; without a commodity price index (PCOMt) in the VAR, the policy shock absorbs the anticipated inflation signal and appears expansionary.
- Resolution via commodity prices: Adding PCOMt as a leading indicator of inflation to the slow block controls for the Fed's forward-looking behavior, and prices fall after a contractionary shock as expected. This fix became standard in the Christiano-Eichenbaum-Evans (1999) six-variable benchmark.
- Sign restriction approach: Sign Restriction Identification (Uhlig 2004) rules out the price puzzle by construction — the identifying restriction requires prices to not rise after a contractionary shock. This avoids the puzzle but does so by assumption rather than by explanation.
- High-frequency identification: Faust-Swanson-Wright (2004) use Federal Open Market Committee (FOMC)-day changes in fed funds futures to identify the policy shock without imposing any zero restriction on prices. The resulting confidence intervals for the price response lie strictly below zero at all horizons — the price puzzle vanishes entirely. The key mechanism: recursive identification's implicit zero contemporaneous price restriction is rejected outright by the futures-based evidence (the confidence set is empty when this restriction is imposed).
- Diagnostic of model quality: The presence of a price puzzle is now a standard check: its appearance signals an incomplete information set, a mis-ordered Cholesky decomposition, or an incorrect sample period.
Why It Matters
The price puzzle exposed a fundamental weakness of Cholesky-recursive identification: ordering restrictions can cause structural shocks to embed systematic forecast errors belonging to other shocks. Its resolution via commodity prices revealed that the Fed's information set matters as much as its actions, and led to the inclusion of leading indicators as standard practice in monetary policy VARs.
Open Questions
- Alternative resolutions: Information-robust identification (external instruments, heteroskedasticity-based methods) also typically resolve the price puzzle without requiring commodity prices, suggesting multiple valid approaches.
- Post-2000 reappearance: Some studies find the price puzzle reemerges in post-2000 samples even with commodity prices included, potentially reflecting structural changes in monetary transmission near the zero lower bound.
- Global commodity price channels: In open-economy VARs, international commodity price dynamics may require additional treatment beyond a single domestic commodity price index.
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