An alternative explanation of the price puzzle

This 2004 Journal of Monetary Economics paper by Paolo Giordani offers an analytical and empirical alternative to the Sims (1992) forward-looking-information explanation of the “price puzzle” — the finding that prices rise, rather than fall, after a contractionary monetary policy shock in standard VARs — by showing that the puzzle can be generated purely by omitting the output gap from the VAR, even when the resulting misspecified system still produces optimal forecasts of inflation at every horizon. Using a backward-looking Svensson (1997) IS/Phillips-curve/Taylor-rule model as the data-generating process, Giordani shows analytically that a VAR excluding the output gap (retaining only output, inflation, and the policy rate) does not admit a finite-order VAR representation — it is instead a VARMA(2,1) — that the variance attributed to the recovered “monetary policy shock” is strictly positive even when the true policy rule is deterministic, and that the interest rate loads with a positive coefficient in the misspecified inflation equation because movements in the policy rate help retrieve the omitted output gap on which the Taylor rule responds, generating a spurious positive inflation response to what is identified as a contractionary shock. Empirically, using quarterly U.S. data from 1966Q1 to 2001Q3 with a recursively (Cholesky) identified three-variable VAR(3), funds rate ordered last, a system using Federal Reserve capacity utilization as the output-gap proxy (“VARgap”: capacity utilization, CPI inflation, federal funds rate) produces an inflation response to a contractionary shock that is never significantly positive and is significantly negative for several quarters, whereas the otherwise identical system using log real GDP in place of the gap reproduces “a huge price puzzle.” Variance decompositions show monetary policy shocks account for only 2.1% of the 8-quarter-ahead inflation forecast-error variance in VARgap, versus 3.5% at the 2-quarter horizon in the misspecified VAR (where cost-push/supply shocks dominate at 92.1%), and the estimated standard deviation of the monetary policy shock is about 12% lower in VARgap, consistent with the theoretical prediction that omitting the gap inflates the estimated policy-shock variance. The paper further argues that the standard Sims (1992) fix — adding a commodity price index — reduces the puzzle not because it improves inflation forecasts (an F-test shows the commodity index PcomCEE is redundant once capacity utilization is included, p = 0.41, while capacity utilization is not redundant given the commodity index, p ≈ 0.0000) but because commodity prices are themselves correlated with the output gap (r = 0.58 with capacity utilization, 1970Q1–1998Q4) and so act as a cyclical proxy for it. The results are reported as robust to lag lengths 1–8, using CPI in log levels or the GDP deflator, reordering capacity utilization and inflation, adding M2, and using several alternative output-gap measures (linear/quadratic detrending, the CBO gap, unemployment, HP-filtered output), though the fix is less clean in a pre-1979 subsample and in monthly data, and the paper flags remaining measurement-error and gap-construction caveats, including a check that adding leads of GDP to the misspecified VAR does not eliminate the puzzle, addressing the concern that capacity utilization’s construction embeds future information.

Paolo Giordani | Macro Paper Warehouse

An alternative explanation of the price puzzle