## Supply chain inflation and firms’ expectations and price-setting (wpiea2022161-print-pdf)

## Source details

**Canonical URL:** [Supply chain inflation and firms’ expectations and price-setting (wpiea2022161-print-pdf)](https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022161-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2022/english/wpiea2022161-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2022/english/wpiea2022161-print-pdf.pdf.json)

---

### Cross-firm heterogeneity in input vs sales price inflation
- Firms buy and sell different—and possibly unrelated—products and services, leading to markedly different conditions along the supply chain.
- Measured dispersion (interdecile range) over the sample period:
  - Input price inflation: minimum -17 percent, maximum 62 percent.
  - Sales price inflation: minimum -10 percent, maximum 50 percent.
- Excluding the post-COVID-19 period:
  - Interdecile range of input price inflation before 2020 is as large as 75 percentage points.
  - Interdecile range of sales price inflation before 2020 is 46 percentage points.

### Distributional shape and skewness
- At any given point in time the distributions of input and sales price inflation are right skewed.
- For input price inflation:
  - About 3/4 of the data points are within the 0–20 percent range.
  - Risks of large deviations from the median are more on the upside than on the downside.
- For sales price inflation:
  - Dispersion is much smaller than for input prices, but larger upside deviations remain visible.

### Temporal volatility relative to CPI inflation
- Both input and sales price inflation display significant volatility over time compared to CPI inflation.
- Input price inflation for the median firm hovered between 3.7 and 22.6 percent during 2015–2021 with a standard deviation of 23.8 percent.
- Sales price inflation moved between 1.4 and 9.5 percent with a standard deviation of 17.5 percent.
- CPI inflation benchmark moved between 1.4 and 5.2 percent with a standard deviation of 0.9 percent.
- Correlation with CPI inflation:
  - Input price inflation correlation coefficient is 35 percent (significant at 5 percent significance level).
  - Sales price inflation correlation coefficient is 69 percent (significant at 5 percent significance level).
- Distributional note: a 10 percent increase in input (sales) price inflation is about four (three) times more likely than a 10 percent decline.

### Measurement and construction of firm-level trade-adjusted inflation indicators
- Firm-product unit price: p*_{i,j,t} = (p*_{i,j,t} q*_{i,j,t})/q*_{i,j,t}; compute log difference of the median price at firm-product-month level, π* ,50_{i,j,t}.
- Firm-level import/export price inflation: π*_{it} = Σ_j (p*_{ijt} q*_{ijt} / p*_{it} q*_{it}) π_{50,*ijt}.
- Observations outside the [−30,100] percent change band are dropped.
- Domestic and imported input price inflation: weighted average of input price inflation and import price inflation, weights = share of domestic purchases and imports.
- Domestic and export sales price inflation: weighted average of sales price inflation and export price inflation, weights = share of domestic sales and exports.
- Sample facts: 45 percent of firms do not import inputs; another large fraction imports only a small share.

### Evidence on correlation and pass-through (visual and binned scatter evidence)
- Domestic input price inflation and sales price inflation: positively albeit weakly correlated; pass-through visually higher for small increases in input costs; input price declines tend to translate into (small) sales price increases.
- Including international trade: domestic+imported input price inflation positively correlated with domestic+export sales price inflation.

### Disagreement and inattention among firms
- Cross-sectional dispersion in firms’ 1-year CPI inflation expectations is generally wide; interdecile range exceeds 2 percentage points at times and collapses to about 0.5 percentage points when actual inflation approaches the central bank target.
- Correlation between firms’ predictions and inflation outcome: 11 percent (significant at 5 percent significance level).
- Inattention measure: in more than 40 percent of firm-month observations, firms did not change inflation predictions after a change in previous period CPI inflation (changes smaller than half of CPI standard deviation are classified as unchanged).
- Directional surprises: more than one-fifth of firms predict a change in inflation opposite to the direction of the previous-month actual CPI change.
- Responses to real GDP growth changes: firms often attribute changes in real GDP growth to supply shocks (e.g., after a decline in real GDP growth, more firms forecast an increase in CPI inflation than a decline).

### Empirical strategy to test whether supply chain inflation affects firm inflation expectations
- Local projections specification (horizon h = [0,...,24]):

  E_{i,t+h} π_{t+h+12} − E_{i,t−1} π_{t−1+12}
  = α^h_i + Σ_{p=1}^P γ^h_p π_{i,t−p} + Σ_{p=1}^P β^h_p π_{t−p} + Σ_{p=1}^P θ^h_p X_{i,t−p} + ε_{i,t+h}

  - Dependent variable: cumulative change in firm i beliefs about next year’s CPI inflation.
  - Key coefficients: γ^h_p (supply chain inflation effects orthogonal to CPI), β^h_p (CPI inflation effects).
  - Controls X_{i,t−p}: two lags of dependent variable, one lag of quarterly real GDP growth (repeated for three months), two lags of firms’ real sales.
  - Firm fixed effects included; time fixed effects excluded to avoid collinearity with CPI inflation and aggregate activity.
  - Standard errors clustered at firm and time level.

### Main causal findings: supply chain shocks affect expectations
- Response to input price inflation (conditional on CPI inflation):
  - A 10 percentage point increase in input price inflation leads to a 0.02 percentage point increase in firms’ inflation expectations five months after the shock.
  - In terms of a 1 standard deviation shock, effect ≈ 0.1 percentage point increase in expectations.
  - Effect persists up to about 14 months and then dies out.
- Response to CPI inflation (controlling for input price inflation):
  - A one percentage point increase in CPI inflation leads firms to increase their next-year inflation expectations by almost 0.5 percentage point one month after the shock.
  - In terms of a 1 standard deviation CPI shock, the peak increase in expectations reaches 0.4 percentage points.
  - CPI-driven response dies out within 6 months.
- Results robust when replacing domestic input price inflation with domestic+imported input price inflation.

### Industry-level inflation and comparison
- Augmented specification adds industry inflation π_{s,t−p}:
  - Industry inflation innovations lead firms to forecast higher CPI inflation (significant at some horizons).
  - Controlling for industry inflation, input price inflation effect remains generally significant and becomes somewhat larger (e.g., a 10 percentage point increase in input price inflation → 0.04 percentage point higher expectations 10 months after the shock, about one third larger than without industry control).
- Interpretation: firms observe supplier-level prices more directly than aggregate industry indices; industry inflation can be an imprecise proxy for firm-level observed prices.

### Test of full-information rational-expectations (FIRE) hypothesis
- Firm-by-firm predictive regressions: π_{t+h} = ι_i + Σ_{p=1}^P γ_{i,h,p} π_{i,t−p} + Σ_{p=1}^P β_{i,h,p} π_{t−p} + ν_{i,t+h}.
- Finding: at any horizon, only a small share of firms has a statistically significant γ_{i,h} (95 percent level). At least 80 percent of firms’ supply chain inflation does not predict future CPI inflation once current CPI inflation is controlled for.
- Re-estimating baseline excluding firms where supply chain inflation predicts future CPI inflation yields similar responses as baseline.
- Conclusion: evidence indicates a violation of the full-information rational-expectations benchmark—firms assign weight to supply chain shocks that are orthogonal to future CPI inflation.

### Heterogeneity: frequency, sign, and size of input price changes
- Frequency-weighted input price inflation (weights by number of transactions n_{ijt}) vs value-weighted:
  - Regressions for horizons h = 4, 5, 6 months show: frequency-based measure has no significant effect; value-weighted input price inflation remains significant and similar in magnitude to baseline.
  - Evidence does not support perceptual-learning-style frequency effects for firms.
- Sign asymmetry:
  - Firms respond to positive input price changes by forecasting higher CPI inflation; they do not significantly adjust expectations when input prices decline (downward rigidity in expectations).
- Size (nonlinearity) test:
  - Adding squared term of input price inflation: squared term not statistically significant for h = 4 and h = 6; for h = 5 it is significant at 10 percent and negative, providing some support for rational inattention predictions over salience.

### Robustness checks
- Placebo test: construct placebo supply chain inflation series (least predictive other firms’ series) and include it in regressions; placebo coefficients are indistinguishable from zero at all horizons.
- Excluding firms potentially exerting monopsony power: drop firm-months where median number of suppliers’ buyers < 25th percentile (230 buyers); results similar to baseline.
- Lag structure variations:
  - Including up to four lags of all variables: results unchanged.
  - Removing the second lag of independent and dependent variables: results unchanged.
- Controlling for import price inflation: input price inflation remains significant.
- Alternative standard errors:
  - Driscoll-Kraay correction (accounts for cross-sectional dependence): results align with baseline.
  - Clustering only at firm level: results robust.

### Firm-level Phillips curve and price-setting behavior
- Micro-founded New Keynesian Phillips relation under Rotemberg price adjustment and constant returns:

  π_{i,t} = β E_{i,t} π_{i,t+1} + (θ ψ / γ) ẑψ_{i,t}

  with assumption E_{i,t} π_{i,t+1} = E_{i,t} π_{t+1} + ω_{i,t}.
- Estimation specification:

  π_{i,t} = α_i + β E_{i,t} π_{t+1} + δ ̃ψ_{i,t} + u_{i,t}

- Main NKPC estimation results (firm fixed effects; standard errors clustered at firm and time):
  - Using sales price inflation (full sample): lag of inflation expectations coefficient = 1.353*** (standard error 0.386).
  - Using sales price inflation (sample with input price inflation available): coefficient = 0.992* (standard error 0.528).
  - Using weighted average of domestic sales and export sales (full sample): coefficient = 1.371*** (standard error 0.365).
  - Using weighted average of domestic sales and export sales (restricted sample): coefficient = 1.204** (standard error 0.480).
  - Wald tests: cannot reject coefficient = 1 in these specifications (e.g., Wald F-test values reported such as 0.830, 0.000, 1.030, 0.180).
  - Real marginal costs coefficient borderline insignificant across specifications.
  - R-squared values range from 0.196 to 0.243 depending on specification.
- Hybrid Phillips curve (adding lagged dependent variable):
  - Lagged sales price inflation coefficient positive and significant (~0.039 to 0.046).
  - Coefficient on inflation expectations remains positive and significant (0.935 to 1.293), again not statistically different from one.

### Policy-relevant conclusions and implications
- Firms extract aggregate inflation signals from local supply chain price changes even when those changes are contemporaneously unrelated to CPI inflation.
- Firms act on such expectations: estimated pass-through of a 1 percentage point increase in expected inflation to sales prices is between about 1 and 1.4 percentage points (full pass-through not rejected).
- Information frictions consistent with an “island” view (Lucas, 1972), heterogeneity in observed supply chain conditions, forecast disagreement, and inattention:
  - Using input price inflation to forecast CPI inflation can increase dispersion in inflation expectations across firms.
  - Dispersion in expectations can translate into welfare-costly price dispersion.
  - Information frictions weaken the effectiveness of the expectation channel of monetary policy.
- Policy implication emphasized: improvements in central bank communication aimed at reducing firms’ inattention are key to dampen undesirable effects of information frictions and preserve transmission via the expectation channel.

### Appendix A — Key descriptive statistics (selected)
- Firm‑level variables (Obs, Mean, St. dev., Min, Max)
  - Inflation expectations: 19,163; 3.4; 0.9; -5.8; 15.0
  - Input price inflation: 48,349; 14.1; 23.8; -30.0; 100.0
  - Sales price inflation: 37,540; 7.8; 17.5; -30.0; 100.0
  - Import price inflation: 25,187; 6.8; 20.1; -30.0; 100.0
  - Export price inflation: 10,638; 6.5; 19.7; -30.0; 100.0
  - Weighted avg. input‑import price inflation: 50,244; 10.7; 20.9; -30.0; 100.0
  - Weighted avg. sales‑export price inflation: 37,780; 7.5; 17.3; -30.0; 100.0
  - Real marginal cost: 41,335; 0.2; 2.3; -18.8; 23.3
  - Real marginal cost including trade: 43,274; 0.4; 2.1; -16.8; 20.0
  - Sales growth: 44,825; 5.6; 26.5; -50.0; 100.0
- Country‑level variables
  - CPI inflation: 813; 3.1; 0.9; 1.4; 5.2
  - GDP growth: 811; 1.8; 5.8; -15.4; 16.6

*Source: wpiea2022161-print-pdf (IMF working paper content unit).*

### 23.6 percent for the former and 16.7 percent for the latter, suggesting that firms observe

### wpiea2022161-print-pdf - 23.6 percent for the former and 16.7 percent for the latter, suggesting that firms observe

### Cross-firm heterogeneity in input vs sales price inflation
- Firms buy and sell different—and possibly unrelated—products and services, leading to markedly different conditions along the supply chain.
- Measured dispersion (interdecile range) over the sample period:
  - Input price inflation: minimum -17 percent, maximum 62 percent.
  - Sales price inflation: minimum -10 percent, maximum 50 percent.
- Excluding the post-COVID-19 period:
  - Interdecile range of input price inflation before 2020 is as large as 75 percentage points.
  - Interdecile range of sales price inflation before 2020 is 46 percentage points.

### Distributional shape and skewness
- At any given point in time the distributions of input and sales price inflation are right skewed.
- For input price inflation:
  - About 3/4 of the data points are within the 0–20 percent range.
  - Risks of large deviations from the median are more on the upside than on the downside.
- For sales price inflation:
  - Dispersion is much smaller than for input prices, but larger upside deviations remain visible.

### Temporal volatility relative to CPI inflation
- Both input and sales price inflation display significant volatility over time compared to CPI inflation.
- Input price inflation for the median firm hovered between 3.7 and

*Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022161-print-pdf.pdf*

### 22.6 percent during 2015–2021 with a standard deviation of 23.8 percent.  Sales price

### Supply chain inflation and firms’ expectations and price-setting (wpiea2022161-print-pdf)

### Key descriptive facts on supply chain and CPI inflation
- Input price inflation: moved between 0.0 and 22.6 percent during 2015–2021 with a standard deviation of 23.8 percent.
- Sales price inflation: fluctuated between 1.4 and 9.5 percent with a standard deviation of 17.5 percent.
- CPI inflation benchmark: moved between 1.4 and 5.2 percent with a standard deviation of 0.9 percent.
- Correlation with CPI inflation: input price inflation correlation coefficient is 35 percent; sales price inflation correlation coefficient is 69 percent (both significant at 5 percent significance level).
- Distributional note: a 10 percent increase in input (sales) price inflation is about four (three) times more likely than a 10 percent decline.

### Measurement and construction of firm-level trade-adjusted inflation indicators
- Firm-product unit price: p*_{i,j,t} = (p*_{i,j,t} q*_{i,j,t})/q*_{i,j,t}; then compute log difference of the median price at firm-product-month level, π* ,50_{i,j,t}.
- Firm-level import/export price inflation: π*_{it} = Σ_j (p*_{ijt} q*_{ijt} / p*_{it} q*_{it}) π_{50,*ijt}.
- Observations outside the [−30,100] percent change band are dropped.
- Domestic and imported input price inflation: weighted average of input price inflation and import price inflation, weights = share of domestic purchases and imports.
- Domestic and export sales price inflation: weighted average of sales price inflation and export price inflation, weights = share of domestic sales and exports.
- Sample facts: 45 percent of firms do not import inputs; another large fraction imports only a small share.

### Evidence on correlation and pass-through (visual and binned scatter evidence)
- Domestic input price inflation and sales price inflation: positively albeit weakly correlated; pass-through visually higher for small increases in input costs; input price declines tend to translate into (small) sales price increases.
- Including international trade: domestic+imported input price inflation positively correlated with domestic+export sales price inflation.

### Disagreement and inattention among firms
- Cross-sectional dispersion in firms’ 1-year CPI inflation expectations is generally wide; interdecile range exceeds 2 percentage points at times and collapses to about 0.5 percentage points when actual inflation approaches the central bank target.
- Correlation between firms’ predictions and inflation outcome: 11 percent (significant at 5 percent significance level).
- Inattention measure: in more than 40 percent of firm-month observations, firms did not change inflation predictions after a change in previous period CPI inflation (changes smaller than half of CPI standard deviation are classified as unchanged).
- Directional surprises: more than one-fifth of firms predict a change in inflation opposite to the direction of the previous-month actual CPI change.
- Responses to real GDP growth changes: firms often attribute changes in real GDP growth to supply shocks (e.g., after a decline in real GDP growth, more firms forecast an increase in CPI inflation than a decline).

### Empirical strategy to test whether supply chain inflation affects firm inflation expectations
- Local projections specification (horizon h = [0,...,24]):

  E_{i,t+h} π_{t+h+12} − E_{i,t−1} π_{t−1+12}
  = α^h_i + Σ_{p=1}^P γ^h_p π_{i,t−p} + Σ_{p=1}^P β^h_p π_{t−p} + Σ_{p=1}^P θ^h_p X_{i,t−p} + ε_{i,t+h}

  - Dependent variable: cumulative change in firm i beliefs about next year’s CPI inflation.
  - Key coefficients: γ^h_p (supply chain inflation effects orthogonal to CPI), β^h_p (CPI inflation effects).
  - Controls X_{i,t−p}: two lags of dependent variable, one lag of quarterly real GDP growth (repeated for three months), two lags of firms’ real sales.
  - Firm fixed effects included; time fixed effects excluded to avoid collinearity with CPI inflation and aggregate activity.
  - Standard errors clustered at firm and time level.

### Main causal findings: supply chain shocks affect expectations
- Response to a 1 percentage point increase in input price inflation (conditional on CPI inflation):
  - A 10 percentage point increase in input price inflation leads to a 0.02 percentage point increase in firms’ inflation expectations five months after the shock.
  - In terms of a 1 standard deviation shock, effect ≈ 0.1 percentage point increase in expectations.
  - Effect persists up to about 14 months and then dies out.
- Response to a 1 percentage point increase in CPI inflation (controlling for input price inflation):
  - A one percentage point increase in CPI inflation leads firms to increase their next-year inflation expectations by almost 0.5 percentage point one month after the shock.
  - In terms of a 1 standard deviation CPI shock, the peak increase in expectations reaches 0.4 percentage points.
  - CPI-driven response dies out within 6 months.
- Results robust when replacing domestic input price inflation with domestic+imported input price inflation.

### Industry-level inflation and comparison
- Augmented specification adds industry inflation π_{s,t−p}:
  - Industry inflation innovations lead firms to forecast higher CPI inflation (significant at some horizons).
  - Controlling for industry inflation, input price inflation effect remains generally significant and becomes somewhat larger (e.g., a 10 percentage point increase in input price inflation → 0.04 percentage point higher expectations 10 months after the shock, about one third larger than without industry control).
- Interpretation: firms observe supplier-level prices more directly than aggregate industry indices; industry inflation can be an imprecise proxy for firm-level observed prices.

### Test of full-information rational-expectations (FIRE) hypothesis
- Concern: supply chain inflation may predict future CPI inflation (violating orthogonality).
- Firm-by-firm predictive regressions: π_{t+h} = ι_i + Σ_{p=1}^P γ_{i,h,p} π_{i,t−p} + Σ_{p=1}^P β_{i,h,p} π_{t−p} + ν_{i,t+h}.
- Finding: at any horizon, only a small share of firms has a statistically significant γ_{i,h} (95 percent level). At least 80 percent of firms’ supply chain inflation does not predict future CPI inflation once current CPI inflation is controlled for.
- Re-estimating baseline excluding firms where supply chain inflation predicts future CPI inflation yields similar responses as baseline.
- Conclusion: evidence indicates a violation of the full-information rational-expectations benchmark—firms assign weight to supply chain shocks that are orthogonal to future CPI inflation.

### Heterogeneity: frequency, sign, and size of input price changes
- Frequency-weighted input price inflation (weights by number of transactions n_{ijt}) vs value-weighted:
  - Regressions for horizons h = 4, 5, 6 months show: frequency-based measure has no significant effect; value-weighted input price inflation remains significant and similar in magnitude to baseline.
  - Evidence does not support perceptual-learning-style frequency effects for firms.
- Sign asymmetry:
  - Firms respond to positive input price changes by forecasting higher CPI inflation; they do not significantly adjust expectations when input prices decline (downward rigidity in expectations).
- Size (nonlinearity) test:
  - Adding squared term of input price inflation: squared term not statistically significant for h = 4 and h = 6; for h = 5 it is significant at 10 percent and negative, providing some support for rational inattention predictions over salience.

### Robustness checks
- Placebo test: construct placebo supply chain inflation series (least predictive other firms’ series) and include it in regressions; placebo coefficients are indistinguishable from zero at all horizons.
- Excluding firms potentially exerting monopsony power: drop firm-months where median number of suppliers’ buyers < 25th percentile (230 buyers); results similar to baseline.
- Lag structure variations:
  - Including up to four lags of all variables: results unchanged.
  - Removing the second lag of independent and dependent variables: results unchanged.
- Controlling for import price inflation: input price inflation remains significant.
- Alternative standard errors:
  - Driscoll-Kraay correction (accounts for cross-sectional dependence): results align with baseline.
  - Clustering only at firm level: results robust.

### Firm-level Phillips curve and price-setting behavior
- Micro-founded New Keynesian Phillips relation under Rotemberg price adjustment and constant returns:

  π_{i,t} = β E_{i,t} π_{i,t+1} + (θ ψ / γ) ẑψ_{i,t}

  with assumption E_{i,t} π_{i,t+1} = E_{i,t} π_{t+1} + ω_{i,t}.

- Estimation specification:

  π_{i,t} = α_i + β E_{i,t} π_{t+1} + δ ̃ψ_{i,t} + u_{i,t}

- Main NKPC estimation results (firm fixed effects; standard errors clustered at firm and time):
  - Using sales price inflation (full sample): lag of inflation expectations coefficient = 1.353*** (standard error 0.386).
  - Using sales price inflation (sample with input price inflation available): coefficient = 0.992* (standard error 0.528).
  - Using weighted average of domestic sales and export sales (full sample): coefficient = 1.371*** (standard error 0.365).
  - Using weighted average of domestic sales and export sales (restricted sample): coefficient = 1.204** (standard error 0.480).
  - Wald tests: cannot reject coefficient = 1 in these specifications (e.g., Wald F-test values reported such as 0.830, 0.000, 1.030, 0.180).
  - Real marginal costs coefficient borderline insignificant across specifications.
  - R-squared values range from 0.196 to 0.243 depending on specification.
- Hybrid Phillips curve (adding lagged dependent variable):
  - Lagged sales price inflation coefficient positive and significant (~0.039 to 0.046).
  - Coefficient on inflation expectations remains positive and significant (0.935 to 1.293), again not statistically different from one.

### Policy-relevant conclusions and implications
- Firms extract aggregate inflation signals from local supply chain price changes even when those changes are contemporaneously unrelated to CPI inflation.
- Firms act on such expectations: estimated pass-through of a 1 percentage point increase in expected inflation to sales prices is between about 1 and 1.4 percentage points (full pass-through not rejected).
- Information frictions consistent with an “island” view (Lucas, 1972), heterogeneity in observed supply chain conditions, forecast disagreement, and inattention:
  - Using input price inflation to forecast CPI inflation can increase dispersion in inflation expectations across firms.
  - Dispersion in expectations can translate into welfare-costly price dispersion.
  - Information frictions weaken the effectiveness of the expectation channel of monetary policy.
- Policy implication emphasized: improvements in central bank communication aimed at reducing firms’ inattention are key to dampen undesirable effects of information frictions and preserve transmission via the expectation channel.

*Source: wpiea2022161-print-pdf (IMF working paper content unit).*

### References

### References and Appendix (wpiea2022161-print-pdf)

### References (selected)
- Albagli, Elías; Mauricio Calani; Metodij Hadzi‑Vaskov; Mario Marcel; Mr Luca A Ricci.2020. “Comfort in floating: Taking stock of twenty years of freely‑floating exchange rate in chile.” IMF Working Papers 100.
- Alfaro‑Urena, Alonso; Mariany Fuentes Fuentes; Isabela Manelici; José P Vásquez.2018. “Costa Rican production network: stylized facts.” Documento de Investigación N. 002.
- Andrade, Philippe; Olivier Coibion; Erwan Gautier; Yuriy Gorodnichenko.2022. “No firm is an island? How industry conditions shape firms’ expectations.” Journal of Monetary Economics, 125: 40–56.
- Bems, Rudolfs; Francesca Caselli; Francesco Grigoli; Bertrand Gruss.2021. “Expectations’ anchoring and inflation persistence.” Journal of International Economics, 132: 103516.
- Bernanke, Ben.2007. “Inflation expectations and inflation forecasting.” Speech delivered at the Monetary Economics Workshop of the NBER Summer Institute, Cambridge, MA.
- Bordalo, Pedro; Nicola Gennaioli; Yueran Ma; Andrei Shleifer.2020. “Overreaction in macroeconomic expectations.” American Economic Review, 110(9): 2748–82.
- Born, Benjamin; Zeno Enders; Manuel Menkhoff; Gernot J Müller; Knut Niemann.2021. “How economic expectations react to news: Evidence from German firms.” Mimeo. University of Tuebingen.
- Candia, Bernardo; Olivier Coibion; Yuriy Gorodnichenko.2020. “Communication and the beliefs of economic agents.” NBER Working Paper No. 27800.
- Candia, Bernardo; Olivier Coibion; Yuriy Gorodnichenko.2021. “The inflation expectations of US firms: Evidence from a new survey.” NBER No. 28836.
- Candia, Bernardo; Olivier Coibion; Yuriy Gorodnichenko.2022. “The macroeconomic expectations of firms.” NBER Working Paper No. 30042.
- Capistrán, Carlos; Manuel Ramos‑Francia.2010. “Does inflation targeting affect the dispersion of inflation expectations?” Journal of Money, Credit and Banking, 42(1): 113–134.
- Cardoza, Marvin; Francesco Grigoli; Nicola Pierri; Cian Ruane.2020. “Worker mobility and domestic production networks.” IMF Working Papers 205.
- Cavallo, Alberto; Guillermo Cruces; Ricardo Perez‑Truglia.2017. “Inflation expectations, learning, and supermarket prices: Evidence from survey experiments.” American Economic Journal: Macroeconomics, 9(3): 1–35.
- Cloyne, James; Lena Boneva; Martin Weale; Tomasz Wieladek.2016. “Firms’ expectations and price setting: Evidence from micro data.” Bank of England, External MPC Unit Discussion Paper 48.
- Coibion, Olivier; Yuriy Gorodnichenko.2012. “What can survey forecasts tell us about information rigidities?” Journal of Political Economy, 120(1): 116–159.
- Coibion, Olivier; Yuriy Gorodnichenko.2015a. “Information rigidity and the expectations formation process: A simple framework and new facts.” American Economic Review, 105(8): 2644–78.
- Coibion, Olivier; Yuriy Gorodnichenko.2015b. “Is the Phillips curve alive and well after all? Inflation expectations and the missing disinflation.” American Economic Journal: Macroeconomics, 7(1): 197–232.
- Coibion, Olivier; Yuriy Gorodnichenko; Mauricio Ulate.2019. “Is inflation just around the corner? The Phillips curve and global inflationary pressures.” Vol. 109, 465–69.
- Coibion, Olivier; Yuriy Gorodnichenko; Michael Weber.2022. “Monetary policy communications and their effects on household inflation expectations.” Journal of Political Economy, 130(6): 000–000.
- Coibion, Olivier; Yuriy Gorodnichenko; Saten Kumar.2018. “How do firms form their expectations? New survey evidence.” American Economic Review, 108(9): 2671–2713.
- Demertzis, Maria; Massimiliano Marcellino; Nicola Viegi.2012. “A credibility proxy: Tracking US monetary developments.” The BE Journal of Macroeconomics, 12(1).
- Dovern, Jonas; Ulrich Fritsche; Jiri Slacalek.2012. “Disagreement among forecasters in G7 countries.” Review of Economics and Statistics, 94(4): 1081–1096.
- Driscoll, John C; Aart C Kraay.1998. “Consistent covariance matrix estimation with spatially dependent panel data.” Review of Economics and Statistics, 80(4): 549–560.
- D’Acunto, Francesco; Ulrike Malmendier; Juan Ospina; Michael Weber.2021. “Exposure to grocery prices and inflation expectations.” Journal of Political Economy, 129(5): 1615–1639.
- Fuster, Andreas; Basit Zafar.2022. “Survey experiments on economic expectations.” NBER Working Paper No. 29750.
- Galí, Jordi; Mark Gertler.1999. “Inflation dynamics: A structural econometric analysis.” Journal of Monetary Economics, 44(2): 195–222.
- Georganas, Sotiris; Paul J Healy; Nan Li.2014. “Frequency bias in consumers’ perceptions of inflation: An experimental study.” European Economic Review, 67: 144–158.
- Grigoli, Francesco; Emiliano Luttini; Damiano Sandri.2021. “Idiosyncratic shocks and aggregate fluctuations in an emerging market.” IMF Working Papers, 2021(289).
- Jordà, Òscar.2005. “Estimation and inference of impulse responses by local projections.” American Economic Review, 95(1): 161–182.
- Kuchler, Theresa; Basit Zafar.2019. “Personal experiences and expectations about aggregate outcomes.” The Journal of Finance, 74(5): 2491–2542.
- Kumar, Saten; Hassan Afrouzi; Olivier Coibion; Yuriy Gorodnichenko.2015. “Inflation targeting does not anchor inflation expectations: Evidence from firms in New Zealand.” NBER Working Paper No. 21814.
- Lucas, Jr Robert.1972. “Expectations and the Neutrality of Money.” Journal of Economic Theory, 4(2): 103–124.
- Mackowiak, Bartosz; Mirko Wiederholt.2009. “Optimal sticky prices under ratio‑nal inattention.” American Economic Review, 99(3): 769–803.
- Mankiw, N Gregory; Ricardo Reis.2002. “Sticky information versus sticky prices: A proposal to replace the New Keynesian Phillips Curve.” Quarterly Journal of Economics, 117(4): 1295–1328.
- Pasten, Ernesto; Raphael Schoenle.2016. “Rational inattention, multi‑product firms and the neutrality of money.” Journal of Monetary Economics, 80: 1–16.
- Rotemberg, Julio J.1982. “Sticky prices in the United States.” Journal of Political Economy, 90(6): 1187–1211.
- Salle, Isabelle.2022. “Comment on ‘No firm is an island? How industry conditions shape firms’ expectation’ by Philippe Andrade, Olivier Coibion, Erwan Gautier and Yuriy Gorodnichenko.” Journal of Monetary Economics, 125: 57–61.
- Sims, Christopher A.2003. “Implications of rational inattention.” Journal of Monetary Economics, 50(3): 665–690.
- Watanabe, Takeo; Jose E Nanez; Yuka Sasaki.2001. “Perceptual learning without perception.” Nature, 413(6858): 844–848.

### Appendix A — Descriptive statistics (Table A.1 key figures)
- Firm‑level variables (Obs, Mean, St. dev., Min, Max)
  - Inflation expectations: 19,163; 3.4; 0.9; -5.8; 15.0
  - Input price inflation: 48,349; 14.1; 23.8; -30.0; 100.0
  - Sales price inflation: 37,540; 7.8; 17.5; -30.0; 100.0
  - Import price inflation: 25,187; 6.8; 20.1; -30.0; 100.0
  - Export price inflation: 10,638; 6.5; 19.7; -30.0; 100.0
  - Weighted avg. input‑import price inflation: 50,244; 10.7; 20.9; -30.0; 100.0
  - Weighted avg. sales‑export price inflation: 37,780; 7.5; 17.3; -30.0; 100.0
  - Real marginal cost: 41,335; 0.2; 2.3; -18.8; 23.3
  - Real marginal cost including trade: 43,274; 0.4; 2.1; -16.8; 20.0
  - Sales growth: 44,825; 5.6; 26.5; -50.0; 100.0
- Country‑level variables
  - CPI inflation: 813; 3.1; 0.9; 1.4; 5.2
  - GDP growth: 811; 1.8; 5.8; -15.4; 16.6

### Appendix B — Signal extraction problem (model summary)
- Setup
  - N islands, firm i charges p_i so aggregate price p_t = 1/N ∑_N p_{i,t}.
  - Firm production response: y_{i,t} = γ(p_{i,t} − p_t).
  - Under imperfect information firms observe p_{i,t} but not p_t; they form E(p_t | I_{i,t−1}).
- Noisy decomposition under rational expectations
  - p_t = E(p_t | I_{i,t−1}) + ε_t with ε_t ∼ N(0, σ).
  - Island price deviation: p_{i,t} = p_t + z_t with z ∼ (0, τ).
  - Proportion of composite shock due to z: θ = τ^2/(σ^2 + τ^2).
- Firm inference and expectation expression
  - E(p_t | I_{i,t−1}, p_{i,t}) = (1−θ)p_{i,t} + θ E(p_t | I_{i,t−1})
  - In first differences:
    - E(π_t | I_{i,t−1}, p_{i,t−1}) = (1−θ)π_{i,t} + θ E(π_t | I_{i,t−1})
- Implication: firms use observed trade prices (local prices) to form beliefs about future aggregate inflation.

### Appendix C — Regression results (highlights from Tables C.1 and C.2)
- Estimation details (notes)
  - Results reported for contemporaneous effect and at the end of each quarter.
  - All regressions include firm fixed effects.
  - Clustered standard errors at the firm and time level in parentheses.
  - Significance: ***p <0.01, **p <0.05, *p <0.1.
- Baseline results for input price inflation (Table C.1) — coefficients for Lag of change in inflation expectations (horizons h = 0, 4, 8, 12, 16, 20, 24)
  - h= 0: -0.468*** (0.038)
  - h= 4: -0.524*** (0.036)
  - h= 8: -0.512*** (0.057)
  - h= 12: -0.479*** (0.082)
  - h= 16: -0.571*** (0.063)
  - h= 20: -0.520*** (0.052)
  - h= 24: -0.303*** (0.068)
- Selected additional coefficients from Table C.1
  - Lag 2 of change in inflation expectations:
    - h=0: -0.202*** (0.030)
    - h=24: -0.034 (0.081)
  - Lag of input price inflation:
    - h=0: 0.000 (0.000)
    - h=4: 0.002*** (0.000)
    - h=8: 0.002*** (0.001)
  - Lag 2 of input price inflation:
    - h=4: 0.002*** (0.000)
    - h=8: 0.001* (0.001)
  - Lag of CPI inflation:
    - h=0: 0.147*** (0.050)
    - h=4: 0.415*** (0.146)
  - Lag 2 of CPI inflation:
    - h=0: -0.099** (0.047)
    - h=24: -0.954*** (0.279)
  - Firms and observations:
    - Firms: from 340 to 229 across specifications
    - Observations: 7,812; 7,383; 6,775; 6,163; 5,666; 5,163; 4,688
  - R‑squared: 0.262; 0.354; 0.272; 0.303; 0.515; 0.440; 0.439
- Baseline results for weighted average of input and import price inflation (Table C.2) — Lag of change in inflation expectations (horizons)
  - h= 0: -0.469*** (0.038)
  - h= 4: -0.525*** (0.036)
  - h= 8: -0.513*** (0.057)
  - h= 12: -0.481*** (0.082)
  - h= 16: -0.571*** (0.063)
  - h= 20: -0.520*** (0.052)
  - h= 24: -0.303*** (0.068)
- Selected additional coefficients from Table C.2
  - Lag 2 of change in inflation expectations:
    - h=0: -0.202*** (0.030)
    - h=24: -0.033 (0.081)
  - Lag of input and import price inflation:
    - h=4: 0.002*** (0.000)
    - h=8: 0.001** (0.000)
    - h=12: 0.002*** (0.001)
  - Lag 2 of input and import price inflation:
    - h=0: 0.001** (0.000)
    - h=4: 0.001** (0.000)
    - h=8: 0.001** (0.000)
  - Lag of CPI inflation:
    - h=0: 0.146*** (0.050)
    - h=4: 0.413*** (0.146)
  - Lag 2 of CPI inflation:
    - h=0: -0.098** (0.047)
    - h=24: -0.952*** (0.279)
  - Firms and observations:
    - Firms: from 340 to 229 across specifications
    - Observations: 7,812; 7,383; 6,775; 6,163; 5,666; 5,163; 4,688
  - R‑squared: 0.263; 0.353; 0.271; 0.303; 0.515; 0.441; 0.439
- Notes on Table C.2 computation
  - Input and import price inflation is computed as the weighted average where the weights are the respective shares in total purchases.

*Inflation Expectations and the Supply Chain — Working Paper No. WP/2022/161*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022161-print-pdf.pdf_