What Drives the Recent Surge in Inflation? The Historical Decomposition Roller Coaster

Layer 1: Overview

The paper addresses what drove the post-COVID inflation surge in the United States and internationally. Before answering the substantive question, the authors identify and diagnose a methodological obstacle: the standard tool used for such analysis — the historical shock decomposition in a structural VAR — can produce wildly inconsistent narratives depending on small, likelihood-inconsequential changes in the model’s parameters.

The mathematical core is the VAR decomposition of observed data into a deterministic component (DC, the model’s period-zero forecast in the absence of any realized shocks) and a stochastic component (SC, the discounted cumulative sum of shock contributions). Because DC and SC sum to data, imprecision in DC is mechanically transmitted to SC, making inferences about shock contributions unreliable. The authors establish that conditional likelihood-based estimation leaves the VAR constant C poorly identified: parameter perturbations that move the likelihood only negligibly can shift DC dramatically. This “excess volatility” in DC is distinct from the better-known overfitting problem: excess volatility is about cross-draw uncertainty in DC, not its average level, and can be severe even when overfitting is mild.

The illustrative case is a bivariate SVAR of US real GDP and the GDP deflator (log first differences, 1983:Q1–2022:Q4, four lags, sign restrictions, Jeffreys diffuse prior). The three draws closest to the point-wise median impulse response — draws whose impulse responses are virtually indistinguishable — produce entirely contradictory post-pandemic narratives: the first assigns more than two-thirds of the inflation rise to supply shocks, the second assigns more than two-thirds to demand shocks, and the third assigns roughly equal shares. The US GDP deflator peaked at 7.7 percent in 2022:Q2; euro area inflation peaked around 10 percent on an annual basis, with some European countries exceeding 15 percent in 2022.

The excess volatility problem is shown to be pervasive: it arises regardless of identification scheme (sign restrictions, Blanchard-Quah long-run restrictions, Cholesky zero-impact restrictions), persists with standard priors (Normal-Inverse Wishart and Minnesota) that shrink AR coefficients but leave the constant diffuse, worsens with longer or more heterogeneous samples (the 1949:Q1–2022:Q4 sample produces substantially larger dispersion than the baseline), and survives in larger VAR systems (the problem is if anything more severe in a 5-variable BVAR).

The preferred solution is the single-unit-root prior (Sims 1993), implemented as a dummy initial observation that constrains the VAR’s unconditional mean to the sample average. As the tightness hyperparameter δ → 0, DC converges across all posterior draws to a common value. The modal posterior value of δ, estimated data-adaptively using the approach of Giannone et al. (2015) with a Gamma prior of mode 1, is 0.0001 for US data — indicating the data strongly favor tight shrinkage. In simulations, after roughly 20 periods, all 1,000 draws of DC converge to virtually identical values regardless of data persistence or sample size.

With the single-unit-root prior, the US results are unambiguous: supply shocks were important in the initial phase of the inflation surge, but demand factors became the main driver from 2021 onward, accounting for 56 percent of inflation fluctuations in 2021 and 77 percent in 2022. Two pragmatic alternatives for frequentists — demeaning the data prior to estimation, and computing point-wise median historical decompositions — both corroborate demand dominance.

International evidence is estimated using the same bivariate SVAR and identification restrictions. For the euro area (industrial production and HICP inflation, 2001:M1–2023:M3), demand factors account for more than 50 percent of inflation fluctuations in 2022, but supply shocks remain significant through at least mid-2023, reflecting the region’s greater exposure to the Ukraine-war commodity supply shock. For four small open economies (Norway, Sweden, Canada, Australia; quarterly GDP growth and year-on-year CPI inflation, 1993:Q1–2023:Q2), the pattern closely resembles the US: supply shocks dominate in 2020, but demand forces become prevalent already in 2021 and are nearly dominant in some cases thereafter. The finding that demand factors were the primary driver of the inflation surge thus holds robustly across six economies with heterogeneous policy responses, supply-chain exposures, and Ukraine-war commodity price effects. The policy implication is that the aggressive monetary tightening implemented by central banks was appropriate given the demand-driven nature of the surge — though the paper is careful to note that its “demand shock” aggregates monetary, fiscal, and other demand-side disturbances, limiting precise policy prescriptions.

Layer 2: Deep Dive

What is the identification strategy and what are the main threats to it?

The baseline uses sign restrictions: a demand shock moves real GDP and the GDP deflator in the same direction on impact; a supply shock moves them in opposite directions. Restrictions are imposed only on impact, following Canova and De Nicolo (2002). The authors acknowledge that the demand shock bundles monetary, fiscal, and other demand-side disturbances, while the supply shock aggregates productivity, commodity, markup, and other supply-side factors. Blanchard-Quah (long-run zero restrictions) and Cholesky (impact zero restrictions) are used as alternative schemes to show the excess-volatility problem is identification-independent. The main threat to credible decompositions is not misidentification of shocks per se but rather imprecision in the VAR’s deterministic component, which contaminates all inferences about shock contributions regardless of the identification scheme.

What exactly is the excess volatility problem and why does it arise?

The VAR’s deterministic component DC_t depends on the companion matrix A and the constant vector C. Conditional likelihood-based estimation identifies A well — impulse responses are relatively precisely estimated — but leaves C poorly pinned down, because many combinations of (A, C) produce nearly identical likelihood values while implying very different unconditional means and thus very different DC paths. Even parameter perturbations negligible relative to the likelihood surface can shift DC dramatically. Because the stochastic component SC_t = Data - DC_t, imprecision in DC is mechanically transmitted to SC_t and to estimated shock contributions. The problem is a property of the reduced-form model and arises before any structural identification is imposed.

How is excess volatility distinguished from the overfitting problem?

Overfitting (Sims 1996, 2000; Giannone et al. 2019) refers to the deterministic component attributing an implausibly large share of low-frequency data variation to itself — the DC level tracks the data in-sample but implies poor out-of-sample forecasts. Excess volatility refers to the uncertainty across posterior draws in DC, not the average level of DC. A model can exhibit mild overfitting (as in the baseline bivariate model, whose DC paths stabilize after only two or three years) while having extreme excess volatility across draws. Solving the overfitting problem — for example by using the prior for the long run (Giannone et al. 2019) — does not solve the excess volatility problem. The single-unit-root prior addresses both, but for distinct reasons.

How does the single-unit-root prior solve the excess volatility problem technically?

The prior adds a dummy observation that imposes the stochastic constraint [I − A]Ȳ₀ − C = δu₀, where Ȳ₀ is set to the sample average and δ governs tightness. Substituting into the DC formula shows that, for a stationary ergodic system, A^t(Y₀ − Ȳ₀) → 0 as t grows, so DC_t converges across all posterior draws to Ȳ₀. The hyperparameter δ is estimated from the data using a Gamma prior with mode 1, following Giannone et al. (2015). The modal posterior value is 0.0001 with negligible posterior dispersion, indicating strong data support for near-exact shrinkage. The prior does not eliminate uncertainty in the stochastic component — draws of A and F still produce variation in shock contributions — but that remaining uncertainty is the same type as in impulse response estimation, making the two statistics mutually consistent.

Why do standard priors (Normal-Inverse Wishart, Minnesota) fail to solve the problem?

Standard priors shrink the AR coefficient matrices and the residual covariance matrix but leave the prior on the VAR constant C diffuse. Because the excess volatility arises specifically from poorly identified values of C, these priors leave the deterministic component as uncertain as with a diffuse prior. The paper demonstrates this directly by plotting deterministic component draws under Normal-Inverse Wishart and Minnesota priors (Figure 3, rows 2) — the dispersion remains large and whimsical historical decompositions persist.

What heterogeneity is documented across countries?

The euro area shows a more balanced demand-supply split than the US: demand and supply factors contribute roughly equally overall, with demand becoming prevalent in 2022 (exceeding 50 percent of inflation fluctuations) but supply shocks remaining significant through mid-2023. The authors attribute this persistence of supply shocks in the euro area to the region’s greater exposure to the Russia-Ukraine energy supply disruption. The four small open economies (Norway, Sweden, Canada, Australia) have outcomes surprisingly similar to the US: supply shocks drive inflation in 2020, demand becomes prevalent in 2021 and is nearly dominant in some cases in 2022. Overall, despite heterogeneity in fiscal stimulus, supply-chain exposure, and commodity price effects, demand factors are the primary driver across all six economies examined.

What robustness checks are run?

The paper runs five main robustness exercises. (1) Three identification schemes — sign restrictions, Blanchard-Quah, and Cholesky — all exhibit the same excess-volatility problem under diffuse priors and produce similar demand-dominance results with the single-unit-root prior. (2) Four prior specifications — diffuse, Normal-Inverse Wishart, Minnesota, single-unit-root — are compared using a proposed dispersion measure (max-minus-min across top 100 draws, averaged over time); the single-unit-root prior uniformly produces the smallest dispersion across all identification schemes. (3) Two sample periods for the US: the baseline 1983:Q1–2022:Q4 and an extended 1949:Q1–2022:Q4 sample; excess volatility is substantially larger with the longer, heterogeneous sample. (4) A 5-variable VAR (real GDP, GDP deflator, real private investment, federal funds rate, real wages), baseline sample and diffuse prior — the excess-volatility problem remains and is more severe for variables like inflation and the federal funds rate. (5) Two alternative approaches for frequentists (demeaning the data; computing point-wise median historical decompositions) both reproduce the demand-dominance finding.

What are the two pragmatic alternatives offered for researchers reluctant to use priors?

First, demeaning all variables before estimation and estimating the VAR without a constant. This eliminates the first term of DC (which depends on C) and forces DC to follow A^t·Y₀, which approaches zero for stationary systems. It is a partial solution — draws with different A matrices still produce different DC paths, so dispersion is reduced but not eliminated; dispersion is smaller than under a diffuse prior but larger than under the single-unit-root prior. Second, computing the point-wise median historical decomposition: across all posterior draws, take the median contribution of each shock at each date. The resulting summary is non-additive (a residual deterministic component absorbs the gap between data and the two median stochastic components) but robust to outliers and reflective of parameter uncertainty. Bergholt et al. (2023) use this approach in prior work. The paper shows that median decompositions under all four prior specifications deliver demand-dominance conclusions similar to those from the single-unit-root prior.

What dispersion measure do the authors propose, and what do the numbers show?

The authors define D_{i,j,t} as the max-minus-min spread of shock j’s contribution to variable i at time t across the 100 draws closest to the point-wise median impulse response. M_{i,j} is the time-average of D_{i,j,t}. Applied to the contribution of demand shocks to US inflation over 2020:Q2–2022:Q4, the values are: diffuse prior — 1.07 (sign), 0.88 (Blanchard-Quah), 2.33 (Cholesky); Normal-Inverse Wishart — 1.53, 1.20, 0.91; Minnesota — 0.87, 0.71, 0.61; single-unit-root — 0.68, 0.48, 0.54. The single-unit-root prior produces the smallest dispersion uniformly across all identification schemes.

How does this paper relate to and differ from closely related prior work?

Bernanke and Blanchard (2024) use a simple wage-price dynamic model and find most of the surge resulted from shocks to prices given wages. Rubbo (2023) uses disaggregated price data and finds roughly three-quarters of the CPI rise since 2021 is demand-driven. Eickmeier and Hofmann (2022) use a large factor model and find demand predominant. Ascari et al. (2023) use a Bayesian SVAR on euro area data and find demand factors crucial from fall 2020. The present paper’s demand-dominance conclusion is broadly consistent with this literature. Its distinctive contribution is not the substantive finding but the methodological diagnosis: it shows that standard VAR-based historical decompositions are whimsical under diffuse priors, explains why, and provides credible solutions. It also contributes international evidence spanning six economies with comparable methodology.

What are the policy implications and their scope conditions?

The finding that demand factors were the primary driver of the post-COVID inflation surge supports the appropriateness of the aggressive monetary tightening implemented by the Federal Reserve and other central banks. A demand-driven inflation surge calls for a different policy response than a supply-driven one; the paper’s results vindicate the central bank interpretation that monetary tightening was warranted. However, scope conditions are important: the identified ‘demand shock’ aggregates monetary, fiscal, and other demand-side disturbances; the paper cannot decompose the demand category further into, for example, fiscal stimulus versus pent-up household demand. Additionally, the bivariate model omits many potentially relevant variables. The policy implication applies to the broad nature of the shock (demand vs. supply) and does not prescribe specific instruments or magnitudes of policy response.

What future research directions are identified?

The authors note that the excess volatility problem is even more acute when separating permanent from transitory components of data, because imprecision in DC translates directly into imprecision in the level of the permanent component. In small samples, long-run shock contributions are also imprecisely estimated, compounding the problem. These issues make estimates of trend inflation poor and inflation regimes difficult to characterize. The authors flag this as a planned area of future research.

Key Concepts

Deterministic component (DC_t): The period-zero forecast of the endogenous variables in the absence of any unforecastable shock realizations — the counterfactual trajectory the VAR assigns based on its parameters and initial conditions alone. Not a statistical trend, but the baseline path the model says would have prevailed had no shocks occurred.

Stochastic component (SC_t): The discounted cumulative sum of all structural shock realizations from period 1 through period t. Together with the deterministic component, it sums to the observed data; it is the part of the observed series attributable to identified economic shocks.

Historical shock decomposition: The retrospective attribution of observed data fluctuations at each point in time to the contributions of individual identified structural shocks. Distinct from the impulse response function (which characterizes prospective shock propagation): the historical decomposition integrates shock realizations and is thus a function of the stochastic component’s draw-specific paths.

Excess volatility (of the deterministic component): The phenomenon whereby posterior draws of VAR parameters that produce nearly identical impulse response functions nevertheless imply radically different paths for the deterministic component. Caused by the likelihood surface being nearly flat with respect to the VAR constant C. Distinct from overfitting: excess volatility is cross-draw uncertainty in DC, not the average level of DC.

Single-unit-root prior (dummy initial observations prior): A prior on VAR parameters implemented by adding one artificial observation, where both current and lagged values equal (1/δ)·Ȳ₀ and the intercept equals 1/δ. As tightness parameter δ → 0, the prior constrains the VAR’s unconditional mean to equal Ȳ₀ across all posterior draws, eliminating excess volatility in DC while leaving structural shock uncertainty intact.

Dispersion measure (M_{i,j}): The authors’ proposed metric for quantifying how whimsical a historical decomposition is: the time-average of the max-minus-min spread of shock j’s contribution to variable i across the 100 draws closest to the point-wise median impulse response. Smaller values indicate more robust, less draw-dependent decompositions.

Whimsical historical decomposition: The paper’s term for a shock decomposition whose narrative about the relative importance of structural drivers changes substantially across draws that are otherwise observationally equivalent in terms of impulse responses. Caused by excess volatility in the deterministic component forcing shocks to compensate for different DC paths.