Long-term inflation expectations and the transmission of monetary policy shocks: Evidence from a SVAR analysis

The paper asks whether U.S. long-term inflation expectations actually respond to monetary policy shocks the way a “re-anchoring channel” would predict, and if so, how much of monetary policy’s effect on inflation and unemployment runs through that channel. This matters because well-anchored long-term expectations are widely viewed as central to how monetary policy transmits to the real economy, but earlier structural VAR work (e.g., Gertler and Karadi 2015, using a proxy SVAR) found essentially no response of long-term expectations to policy shocks – often because those studies imposed a zero contemporaneous response of expectations as part of their identification (a Cholesky ordering), which mechanically rules out the channel rather than testing for it. Diegel and Nautz instead identify a monetary policy shock without restricting how expectations respond on impact, leaving open whether re-anchoring occurs.

The system includes quarterly U.S. inflation (annual CPI growth), the unemployment rate, a policy-rate variable, and the Survey of Professional Forecasters’ median 10-year-ahead CPI inflation expectation, estimated over 1991Q4-2019Q4 with four lags (a lag length supported by an LM test for residual autocorrelation). The policy-rate variable splices the federal funds rate with the Krippner (2013) shadow rate from 2008M8-2015M11 to handle the zero lower bound. The structural model is estimated using the Bayesian algorithm of Arias, Caldara, and Rubio-Ramírez (2018) – a uniform prior over rotation matrices, an uninformative normal prior on the reduced-form coefficients, and an inverse-Wishart prior on the residual covariance matrix – with 5,000 accepted posterior draws underlying all reported results.

The monetary policy shock is identified by standard sign restrictions (inflation falls, unemployment rises, the policy rate rises, on impact) plus, distinctively, a restriction on the systematic component of the policy rule itself: the contemporaneous reaction coefficient on long-term inflation expectations, ψ_π^e, must be non-negative, meaning the central bank raises rates when long-term expectations rise. Unlike the other three variables, the response of inflation expectations to the monetary policy shock is left completely unrestricted in sign – so any expectations response the model finds is a result, not an assumption. The authors motivate the systematic-component restriction by appeal to Arias, Caldara, and Rubio-Ramírez (2019) and Wolf (2020), who argue restrictions on the policy rule’s systematic component sharpen identification when one variable’s impulse response is deliberately left free. They show the restriction is far from innocuous: without it, only about 50% of posterior draws would satisfy ψ_π^e > 0, so imposing it “significantly shrinks the identified set.”

A second, expectations-specific shock is identified by zero restrictions: long-term inflation expectations are assumed not to respond contemporaneously to current-quarter inflation or unemployment (a_{0,21} = a_{0,22} = 0), while their response to the policy rate and to the expectations shock itself is left free. The justification is timing: Survey of Professional Forecasters respondents submit their forecasts before the second-month release of current-quarter CPI and unemployment data, so their information set typically excludes those current-quarter realizations. The authors acknowledge this timing assumption “cannot be perfectly verified.”

The posterior median reaction coefficients are ψ_π = 0.5 (68% credible interval [0.13, 1.2]) on inflation, ψ_u = -2.18 ([-4.11, -1.08]) on unemployment, and ψ_π^e = 3.77 ([1.07, 9.74]) on long-term inflation expectations – so the policy rate reacts roughly seven times as strongly, in absolute terms, to a one-unit move in long-term expectations as to a one-unit move in current inflation. The paper reports that this reaction coefficient implies “a median long-run response coefficient of monetary policy to the rate of inflation of 1.14,” reflecting the indirect channel through which current inflation affects future expectations and hence future policy.

A one-standard-deviation contractionary monetary policy shock causes long-term inflation expectations to fall significantly and immediately, with an effect the authors describe as persistent but ultimately transitory – “in contrast to earlier studies” that found no such response. Inflation itself falls in a negative, hump-shaped pattern that troughs around three quarters out and returns near zero by year three; unemployment rises by roughly 0.2 percentage points in a hump shape. Variance decompositions show monetary policy shocks account for a non-trivial share of long-term expectations’ forecast-error variance at every horizon examined: about 16% on impact, rising to around 26-28% at one- to two-year horizons, and settling around 26% at the ten-year horizon – credible intervals are wide, but the authors read this as showing monetary policy “has a sizable impact on the dynamics of long-term inflation expectations,” contrary to assumptions in earlier literature.

No – a counterfactual that shuts down the re-anchoring channel (holding expectations fixed via a sequence of offsetting expectations shocks) shows the channel is economically important for inflation but has “virtually no effect” on the unemployment or policy-rate paths. With the channel active, monetary policy shocks account for about 15% of inflation’s forecast-error variance on impact and roughly 28-34% at one-year-plus horizons; with the channel shut off, those contributions collapse to under 1% on impact and only about 4-13% at longer horizons. The authors conclude the re-anchoring channel is “economically relevant at all forecasting horizons” for inflation transmission specifically, while unemployment’s response to monetary policy runs through the conventional interest-rate channel instead.

Using a structural scenario analysis (following the Antolín-Díaz et al. 2021 methodology) over the period since the Federal Reserve’s January 2012 inflation-target announcement, the authors find that had the Fed not systematically responded to expectations shocks, median counterfactual inflation would have been about 57 basis points lower and median counterfactual unemployment about 99 basis points higher on average. They interpret this as evidence that the Fed’s actual, estimated reaction to below-target long-term inflation expectations has itself helped stabilize both inflation and unemployment over this period.

The authors report the results are broadly stable across several checks, though with some nuance. Replacing the Krippner shadow rate with the Lombardi-Zhu (2019) or Wu-Xia (2016) alternatives leaves the expectations response “nearly unaffected.” Restricting the sample to the pre-ZLB period (1992Q4-2008Q2) yields expectations-shock results “very similar to full sample results.” Using the University of Michigan Survey of Consumers’ 5-year-5-year household expectations measure instead of the SPF preserves the main qualitative conclusions, though the household-based response may be stronger on impact and less persistent. Replacing the sign restrictions on inflation and unemployment with alternative systematic-component restrictions (ψ_π ≥ 0, ψ_u ≤ 0), in the spirit of Uhlig (2005), leaves the inflation and expectations results unaffected but makes the unemployment impulse response insignificant. The output gap can also replace unemployment without changing the main conclusions.