St-Amant (1996) Decomposing U.S. Nominal Interest Rates into Expected Inflation and Ex Ante Real Interest Rates Using Structural VAR Methodology

Summary

St-Amant (1996) applies Blanchard-Quah long-run restriction structural VAR (SVAR) to decompose U.S. 1-year and 10-year government bond rates into an expected inflation component and an ex ante real interest rate component. The single identifying restriction — ex ante real rate shocks have no permanent effect on nominal rates — follows from the long-run Fisher effect: nominal rates and inflation expectations are cointegrated (1,1), and the real rate is stationary. Both shocks matter at medium horizons; at short horizons, real rate shocks dominate the 10-year rate (75%). The 1970s–early 1980s rate rise reflected inflation expectations; the 1994–95 fluctuations reflected real rates.

Key Claims

• Identification: The long-run impact matrix $A(1) = C(1)A_0$ is restricted so that $A(1)_{i,\text{real}} = 0$: ex ante real rate shocks have zero long-run effect on the nominal interest rate level. Combined with $A_0 A_0' = \Sigma$, this recovers the two-shock SVAR.
• System: $x_t = (\Delta i_t,\ r_t)'$ where $r_t = i_{t,k} - \pi_t$ (nominal rate minus contemporaneous inflation). The two variables are I(1) and I(0) respectively; $i_t$ and $\pi_t$ are cointegrated (1,1) — the long-term Fisher effect (Mishkin 1992).
• Lag length: DeSerres-Guay (1995) finding that the Akaike/Schwarz information criteria (AIC/SIC) under-select motivates likelihood-ratio (LR) general-to-specific selection: 17 lags (10-year VAR) and 19 lags (1-year VAR). Too-short lag structures significantly bias structural component estimates.
• Advantage over Beveridge-Nelson: The BN approach forces the transitory component of permanent shocks to zero; the SVAR approach does not — it is less restrictive.
• Variance decomposition (1-year rate): roughly 50/50 between inflation expectations and real rate at all short/medium horizons, converging to 100/0 long run.
• Variance decomposition (10-year rate): real rate shocks dominate at short horizons (75% at 1 month), converging to 80/20 by 4 years.
• Impulse responses: real rate shocks die out within ~2 years; inflation expectation shocks build gradually, consistent with slow monetary regime adjustment.
• Historical episodes: 1970s–early 1980s rate rise = inflation expectations; 1994–95 = ex ante real rate (inflation expectations stable, confirmed by Michigan survey comparison).
• Mean real rates: 2.65% (10-year) and 1.9% (1-year) over the sample.

Concepts Introduced or Extended

• Fisher Hypothesis
• Structural Identification
• Vector Autoregression

Entities Mentioned

• Christopher Sims
• Mark W. Watson

Quotes

"An increase in long-term interest rates reflecting an increase in inflation expectations might be a signal for the monetary authority to tighten its policy. An increase in long-term interest rates reflecting higher ex ante real interest rates may have different implications."

My Take

A clean, policy-relevant application of Blanchard-Quah identification to the Fisher decomposition problem. The main innovation is using the long-run Fisher cointegration as an identifying restriction rather than as an ex-post hypothesis to be tested — turning the established empirical regularity into a structural tool. The 1994–95 finding (rate movement = real rates, not inflation expectations) is well-supported by the Michigan survey comparison. Wide confidence intervals are the main limitation; with 17–19 lags and only 450 monthly observations, the impulse responses carry substantial uncertainty, as the 90% bands in Charts 2–5 make clear. The paper is candid about this.