Faust-Swanson-Wright (2004) Identifying VARs Based on High Frequency Futures Data

Summary

Faust, Swanson, and Wright (2004) use daily changes in federal funds futures on Federal Open Market Committee (FOMC) meeting days to estimate the term structure of the funds rate impulse response to a monetary policy shock, then impose this as identifying restrictions on the Christiano-Eichenbaum-Evans (CEE) six-variable vector autoregression (VAR). Because the rank of the resulting restriction matrix is approximately three — not six — the approach only partially identifies the impulse vector; inference uses Stock-Wright (2000) S-sets combined with Bonferroni bounds for ≥90% asymptotic coverage. The main findings are that the CEE recursive identification is rejected by the futures data, the price puzzle disappears under the weaker identification, and monetary policy shocks explain at most 0–29% of output forecast-error variance at 60 months — confirming the small-variance-share conclusion under far weaker structural assumptions than CEE.

Key Claims

Two-step identification: On FOMC days, futures rate changes at horizon $h$ must be proportional to the policy shock's effect on the funds rate path: $\Delta f_d^h = (r_h/r_0)\Delta f_d^0$ . Regressing $\Delta f_d^h$ on the FOMC surprise $\Delta f_d^0$ estimates $r_h$ , the funds rate impulse response at month $h$ . Imposing $B_{h,ff}\alpha = r_h$ for $h = 0,\ldots,5$ gives $R\alpha = r$ .
Gradual funds rate persistence (Table 2, FOMC days only): $r_{t+1}=0.80$ , $r_{t+2}=0.66$ , $r_{t+3}=0.60$ , $r_{t+4}=0.61$ , $r_{t+5}=0.55$ — the funds rate effect decays slowly over five months; fast-reverting identifications (which imply large output variance shares) are inconsistent with these estimates.
Partial identification: Tests reject rank $L\leq 2$ of $R$ but not $L=3$ ( $p=0.89$ ), meaning $R\alpha=r$ does not point-identify $\alpha$ . The allowable set $A^+$ combines the rank-3 restriction with sign bounds on industrial production (IP), consumer price index (CPI), commodity prices (PCOM), non-borrowed reserves (NBR), total reserves (TR), and the federal funds rate (FF): $IP, CPI\in[-0.1,0]$ ; $PCOM, NBR, TR\in[-0.25,0]$ ; $FF=+0.25$ .
S-set confidence intervals: $A = \{\alpha\in A^+: S(\alpha)\leq F_{\chi^2}\}$ where the continuous-updating generalized method of moments (GMM) objective is $S(\alpha) = T(\hat{R}\alpha-\hat{r})'[(\alpha\otimes I_K)\hat{V}_R(\alpha'\otimes I_K)+\hat{V}_r]^{-1}(\hat{R}\alpha-\hat{r})$ ; 10 million uniform draws from $A^+$ used to trace the boundary of $A$ ; Bonferroni bounds across the two uncertainty sources give ≥90% coverage for scalar functions.
CEE recursive identification rejected: The Cholesky impulse vector lies outside the Faust-Swanson-Wright (FSW) confidence set $A$ .
Zero contemporaneous price effect rejected: Imposing $CPI$ contemporaneous response = 0 makes $A$ empty — the standard zero restriction is inconsistent with the futures evidence.
Small variance shares confirmed: 90% confidence interval (CI) for output forecast-error-variance (FEV) share is $[0, 0.15]$ at 12 months and $[0, 0.29]$ at 60 months — monetary policy explains little output variance under these weaker assumptions.
Price puzzle eliminated: Confidence intervals for the price response lie strictly below zero at all horizons; the anomalous price increase in recursive VARs is an artifact of the zero contemporaneous price restriction.
Futures efficiency validated: Regressions of $h$ -month-ahead funds rate on futures-implied prediction give intercept ≈ 0, slope ≈ 1 for $h=1,\ldots,5$ (Table 5); target surprises are uncorrelated with subsequent macro data releases (Table 6), supporting the clean-shock interpretation.

Concepts Introduced or Extended

Entities Mentioned

Quotes

"We find that many commonly used identifying assumptions are inconsistent with the futures data. In particular, the Cholesky factorization used by CEE is rejected."

"When the price restriction is imposed, the confidence set is empty, indicating that this restriction is also inconsistent with the futures data."

My Take

The paper's central contribution is methodological: external instrument restrictions can be imposed on a VAR without requiring point identification, using confidence sets throughout. The rejection of the zero contemporaneous price restriction is particularly striking — the price puzzle in recursive VARs is not merely a data problem but a failure of a specific structural zero restriction. The gradual funds rate persistence (55–80% of impact effect remaining at months 1–5) is the key empirical input: it rules out the fast-reversing identifications that Faust (1998) showed imply large output variance shares. The overall result — small variance shares under weak restrictions — strengthens the credibility of the CEE quantitative conclusion even as it rejects the CEE identification mechanism. The futures-based clean-shock strategy, and the use of confidence sets under partial identification, anticipate the Nakamura-Steinsson (2018) tradition of high-frequency monetary identification.