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The Cost of Inflation

Vipin P Veetil

TL;DR

This paper develops a production-network model to study how inflation propagates through an economy where firms are linked by input-output relationships. Using a state-dependent price hazard that combines duration and network exposure, it derives closed-form, analytic characterizations of transient and steady-state inflation dynamics, highlighting the roles of the spectral gap $1-\lambda_2$, degree-tail exponent $\alpha$, and assortativity $\nu^2$. The key findings show that inflation can generate large relative-price distortions even when the average size of price changes tracks inflation, with distortions rising with network heterogeneity and propagation persistence; under fully flexible prices these distortions scale as $\omega\sim\pi$ and $\psi\sim\pi^2$ with topology-dependent constants. The results extend beyond equilibrium analysis by detailing the entire adjustment path and by demonstrating Gaussian concentration for distortion measures, making the predictions robust to randomness in the production network. Overall, the paper provides a Cantillonian mechanism for monetary transmission through networks and clarifies why price-change frequencies can rise with inflation even as cross-sectional mispricing worsens due to network structure.

Abstract

Empirical evidence suggests that there is little to no correlation between the rate of inflation and the size of price change. Economists have hitherto taken this to mean that monetary shocks do not generate much deviation in relative prices and therefore inflation does not hurt the economy by impeding the workings of the price system. This paper presents a production network model of inflationary dynamics in which it is well possible for inflation to have near-zero correlation with the size of price change yet cause significant distortion of relative prices. The relative price distortion caused by inflation critically depends on the spectral gap, degree distribution, and assortativity of the production network.

The Cost of Inflation

TL;DR

This paper develops a production-network model to study how inflation propagates through an economy where firms are linked by input-output relationships. Using a state-dependent price hazard that combines duration and network exposure, it derives closed-form, analytic characterizations of transient and steady-state inflation dynamics, highlighting the roles of the spectral gap , degree-tail exponent , and assortativity . The key findings show that inflation can generate large relative-price distortions even when the average size of price changes tracks inflation, with distortions rising with network heterogeneity and propagation persistence; under fully flexible prices these distortions scale as and with topology-dependent constants. The results extend beyond equilibrium analysis by detailing the entire adjustment path and by demonstrating Gaussian concentration for distortion measures, making the predictions robust to randomness in the production network. Overall, the paper provides a Cantillonian mechanism for monetary transmission through networks and clarifies why price-change frequencies can rise with inflation even as cross-sectional mispricing worsens due to network structure.

Abstract

Empirical evidence suggests that there is little to no correlation between the rate of inflation and the size of price change. Economists have hitherto taken this to mean that monetary shocks do not generate much deviation in relative prices and therefore inflation does not hurt the economy by impeding the workings of the price system. This paper presents a production network model of inflationary dynamics in which it is well possible for inflation to have near-zero correlation with the size of price change yet cause significant distortion of relative prices. The relative price distortion caused by inflation critically depends on the spectral gap, degree distribution, and assortativity of the production network.
Paper Structure (30 sections, 7 theorems, 73 equations)

This paper contains 30 sections, 7 theorems, 73 equations.

Table of Contents

  1. Introduction
  2. Related Literature
  3. State-dependent pricing within a production network
  4. Cross-price variation and price stickiness.
  5. Monetary dynamics on networks
  6. Organization of the Paper
  7. Model
  8. The general equilibrium framework
  9. Transient dynamics
  10. Price hazard function
  11. Price gap and nominal dominance.
  12. Reset probability and reduced-form separability.
  13. Network exposure index.
  14. Finite-horizon saturation of duration dependence.
  15. Large-economy asynchrony.
  16. ...and 15 more sections

Key Result

Theorem 1

Assume fully flexible prices and a constant-rate monetary injection of size $\pi$. Let $\phi_T$ denote the degree-weighted average size of price change at time $T$ (using the weighting exponent $\zeta$; see Def. def:size_price_change). Under the standing assumptions stated earlier, there exists a th Moreover, the threshold $\zeta^{*}$ is characterized in closed form by where $\alpha$ is the tail

Theorems & Definitions (12)

  • Remark 1
  • Remark 2
  • Definition 1: Average Size of Price Change
  • Theorem 1: Bounded price-index growth in the transient under flexible prices
  • Definition 2: Relative price gap
  • Definition 3: Relative price entropy
  • Theorem 2: Relative price distortion in a network economy
  • Lemma 1: Transitory component of monetary shocks
  • Proposition 1: Injection tilt implies $C_t\ge 0$
  • Lemma 2: Gaussian concentration of $\phi_T$ in steady state
  • ...and 2 more