In light – and darkness – of recent international developments, it seems inevitable that inflation will claw its way back into front-page headlines, just as it dominated coverage in the aftermath of the Covid-19 pandemic. A key lesson from that episode is that large cost shocks do more than simply nudge prices upward – they drive inflation into a distinctly nonlinear regime once they breach a critical threshold. Figure 1 brings this to life. Using firm-level data on prices and production costs, we construct a cost index aggregating year-over-year changes in nominal variable costs (labour and intermediate inputs costs) across Belgian manufacturers between 1999 and 2023. Plotting this index (x-axis) against year-over-year domestic PPI inflation in the Belgian manufacturing sector (y-axis) reveals a roughly proportional pass-through for small shocks, and a marked steepening once shocks become large. Based on our analysis (discussed below), these nonlinearities seem to kick in for annual cost shocks of about 20% or higher (equivalently, a persistent 5% quarterly shock).
Figure 1 Nonlinear passthrough of costs into inflation
Notes: Each dot in the graph represents the joint realisation of year-over-year change in a production-cost index (x-axis) against year-over-year PPI inflation (y-axis) for Belgian manufacturing in the same quarter, covering 2000:q1–2023:q4.
This nonlinearity raises a central question: Which firm-level mechanisms cause the switch from proportional to amplified pass-through once shocks become large? And do these mechanisms operate differently when shocks are small?
We address these questions in a recent paper (Gagliardone et al. 2025c). Using firm-level data on prices and production costs, we examine cost–price dynamics in both normal periods and inflation surges. A central finding is the state-dependent nature of pricing: when shocks push firms away from their optimal markups, they adjust more frequently (extensive margin) and by larger magnitudes (intensive margin). Although both margins operate simultaneously, the extensive margin only becomes quantitatively significant under large aggregate cost shocks, generating nonlinear cost–price dynamics. By contrast, in normal times – when shocks are small – adjustment probabilities remain roughly constant, and the data conform to time-dependent models (e.g. Calvo 1983), as discussed in Gagliardone et al. (2025a, 2025b). Feeding an empirically derived path of aggregate cost shocks into a generalised state-dependent pricing model reproduces both the low, stable pre-pandemic inflation and the nonlinear surge during the pandemic.
The recent surge in inflation well illustrates these points. Figure 2 plots year-over-year producer price inflation in Belgian manufacturing alongside the average frequency of price adjustments. Before the pandemic, both series were low and stable, consistent with a linear mapping between expected price changes and price gaps in time-dependent models. Beginning in early 2021, however, adjustment frequency rose sharply in tandem with inflation – a hallmark of state-dependent pricing and nonlinear cost–price dynamics (Cavallo et al. 2023).
Figure 2 Aggregate inflation and frequency of price adjustment
Notes: Year-over-year PPI inflation (left axis, black solid line) and the rolling four-quarter average of firms’ price-adjustment frequency (right axis, red dashed line) for Belgian manufacturing, 2000q1–2023q4.
Three facts on the nature of cost-price dynamics in the microdata
We begin by analysing the relationship between price gaps and the frequency of price adjustment – the defining distinction between state- and time-dependent pricing models. To do so, it is useful to introduce the notion of the price gap, which measures the percentage difference between the price that a firm would set in a frictionless given today’s economic conditions (e.g. the cost of production and competitors’ prices) and the price set by the firm in the previous period.
In all models featuring nominal rigidities, the price gap determines firms’ pricing behaviour as it reflects accumulated cost and demand shocks since the last adjustment. What distinguishes different theoretical frameworks is how changes in the price gap map into price changes, with important implications for aggregate inflation.
Time-dependent models (e.g. Taylor 1980, Calvo 1983) – the simplest and most widely adopted model of nominal rigidities – assume prices have a fixed (i.e. exogenous) adjustment probability or duration. Upon adjustment, firms reset to the optimal price, yielding a linear relationship between expected price changes and price gaps. In contrast, state-dependent pricing models (e.g. Golosov and Lucas 2007, Le Bihan et al. 2014) make both the adjustment probability and the conditional size of price changes endogenous in the gap. The combination of intensive and extensive marginal adjustment results in a nonlinear cost-price pass-through.
To test these competing predictions, we construct a firm-level empirical measure of the price gap using rich microdata on Belgian manufacturing firms. Remarkably, this dataset provides firm-level prices, output, and production-cost data on a quarterly basis.
Fact #1: We bin firms by price-gap quantile and plot each bin’s average gap (x-axis) against its average frequency of price adjustment (y-axis) for firms in the bin. The solid black line shows the density of price gaps in the data. Firms in the tails of the distribution have listed prices that deviate most from their optimal price – either too high or too low. The red curve shows the empirical fraction adjusting; the black dotted line is a quadratic fit from regressing bin-level adjustment frequency on a constant and the square of the average gap.
The data reveal a pronounced U-shaped relationship: firms with larger absolute gaps adjust more frequently. A simple quadratic in the gap captures over 90% of the variation in adjustment probabilities, confirming the state-dependent prediction that the extensive margin intensifies as gaps widen.
Figure 3 Probability of price adjustment and price gaps
Notes: The figure plots the probability density function of the distribution of price gaps in the data. After grouping firms into bins based on the quantile of the distribution to which they belong, we plot the average price gap for bin against the empirical probability of price adjustment for firms in the quantile. The black dotted line is the fitted value obtained from a cross-sectional regression of the frequency of price adjustment of a given bin on a constant and the square of the average price gap of the same bin.
Fact #2: Next, we turn to average price changes (accounting for both intensive and extensive margin effects) and how they vary in the cross-section of price gaps. We again sort observations into quantiles (bins) spanning the price gap distribution and plot the average price change (i.e., inflation) within the same bin (y-axis) as a function of the average price gap in the bin (x-axis) in Figure 4. The mapping between expected price changes and price gaps is ‘S-shaped’: approximately linear at small gaps with a slope that matches the average frequency of price adjustment, and highly nonlinear at large gaps with a steeper slope.
Consider first the central bins (25th–75th percentiles). Observations in this range are characterised by relatively small price gaps, meaning moderate deviations of their prices from the target prices. We can think of this set as representing the mapping between gaps and price changes in ‘normal times’ with low inflation and small aggregate shocks. As we can see, over this range of the price gap distribution, the mapping between inflation and price gaps is essentially linear, as in the Calvo model. Interestingly, the gradient between price changes and price gaps (0.27) is nearly identical to the average quarterly adjustment probability before the pandemic (Gagliardone et al. 2025a).
Figure 4 Nonlinear price dynamics
Notes: This figure presents a scatterplot of the average price gap for each bin of the price gap distribution (x-axis) against the corresponding average inflation (the logarithmic price change) with the bin (y-axis). The black dashed line represents a linear fit of price changes on price gaps, estimated on the subsample of bins covering firms between the 25th and 75th percentiles of the price gap distribution, with the estimated slope reported in black. The red dashed line represents the fit of a third-order polynomial in price gaps, estimated using bins across the entire price gap distribution. The average slope of the third-order polynomial fit in the tails of the distribution (below the 25th and above the 75th percentiles) is reported in red.
Extending to the full distribution reveals pronounced nonlinearity driven by state-dependent pricing. In the tails – when gaps widen after large shocks – the slope rises to 0.43, a 60% increase over the central-range gradient. This amplification stems from the higher frequency of price adjustment in large-gap regimes, underscoring firms’ state-dependent pricing behaviour.
Fact #3: The final interesting fact emerging from the micro data relates to the effect that aggregate shocks have on the distribution of price gaps (and consequently on the frequency of price changes). Figure 5 compares the price-gap distribution before the pandemic (solid black) with that in 2022 Q2 (red dashed). In 2022 Q2, firms’ marginal costs jumped by an average of 6.2% quarter-on-quarter, shifting the entire gap distribution rightward. As theory predicts, larger gaps raise the cost of inaction; as a result, consistent with Fact #1, the average adjustment probability nearly doubles in 2022:q2 relative to normal periods.
Figure 5 Impact of aggregate cost shocks on the price gap distribution and average frequency of price adjustment
Notes: The solid black curve is the pre-pandemic (1999–2019) density of price gaps; the red dashed curve is the 2022:q2 density. Vertical lines mark the average gaps in the pre-pandemic period and in 2022:q2. Horizontal lines show average adjustment probabilities in each period.
Aggregate cost-price dynamics
We have shown in Figures 1 and 2 that, consistent with firms’ state-dependent pricing documented in the microdata, cost-price dynamics are highly nonlinear when shocks are large, driven by the acceleration in price adjustments when gaps widen. This mechanism is not at work in ‘normal times’. For example, in the pre-pandemic period – characterised by low, stable inflation – the price-gap distribution was steady, adjustment frequencies were roughly constant, and the gap–price change relationship remained linear.
We can assess how well time- and state-dependent pricing models replicate the actual path of inflation. Using an empirically recovered sequence of aggregate cost shocks, we simulate both a Calvo (time-dependent) model and a menu-cost (state-dependent) model to generate model-implied series of aggregate inflation. Figure 6 compares year-over-year PPI inflation in Belgian manufacturing (data) with the two model simulations.
Figure 6 Inflation and frequency of price adjustment: Model versus data
Notes: This figure contrasts the dynamics of PPI manufacturing inflation in the data to the inflation dynamics generated by the Calvo and menu-cost models, after feeding the model a sequence of aggregate nominal marginal cost shocks that matched the one observed in the data.
Three key observations emerge. First, the menu-cost model (black line) closely tracks inflation – in moderate ‘normal times’, throughout the post-pandemic surge, and during the ensuing rapid decline. Second, in normal times, the menu-cost and Calvo models are nearly indistinguishable, reflecting stable adjustment frequencies and linear dynamics. Third, when large cost shocks hit, accounting for nonlinearities becomes critical. The menu-cost model captures the full magnitude of the surge, while the Calvo model not only underestimates the peak by about one-third but also predicts a more sluggish disinflation than observed in the data
Authors’ note: The views expressed in this contribution are those of the authors and do not necessarily reflect the views of the National Bank of Belgium, the Eurosystem, or any other institution with which the authors are affiliated.
References
Calvo, A G (1983), “Staggered prices in a utility-maximizing framework”, Journal of Monetary Economics 12(3): 383–398.
Cavallo, A, F Lippi, and K Miyahara (2023), “Large shocks travel fast”, CEPR Discussion Paper 18413.
Gagliardone, L, M Gertler, S Lenzu, and J Tielens (2025a),“Anatomy of the Phillips curve: Micro evidence and macro implications”, American Economic Review, forthcoming.
Gagliardone, L, M Gertler, S Lenzu, and J Tielens (2025b), “Anatomy of the Phillips curve”, VoxEU.org, 5 June.
Gagliardone, L, M Gertler, S Lenzu, and J Tielens (2025c),“Micro and macro cost-price dynamics in normal times and during inflation surges”, NBER Working Paper 33478.
Golosov, M and R E Lucas (2007), “Menu costs and Phillips curves”, Journal of Political Economy 115(2): 171–199.
Le Bihan, H, F Lippi, and F Alvarez (2014), “Modelling sticky prices and the effect of monetary shocks”, VoxEU.org, 30 September.
Taylor, B J (1980), “Aggregate dynamics and staggered contracts”, Journal of Political Economy 88(1): 1–23.
