## I. THE CONQUEST OF INFLATION... AND THEN WHAT?

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---

### Background: inflation performance and policy since the mid-1990s
- The FOMC reached an internal agreement on a two percent inflation target for the personal consumption expenditure deflator at the July 1996 meeting; this corresponds to "roughly 2.3 percent in CPI terms."
- Since that decision, "core inflation has been at or above that target for only a fraction of the time."
- Post-Global Financial Crisis (GFC) features:
  - Large financial and real shocks that contributed to persistent weakness in inflation.
  - The zero lower bound (ZLB) on interest rates in many countries, constraining conventional policy.
  - Compensatory measures including forward guidance and quantitative easing designed to lower risk-free interest rates and loosen financial conditions.
  - Fiscal policy that "was, on net, only a modest support to growth" over the post-Crisis period.
- Contrary to early post-GFC concerns (inflation spike from Fed balance sheet expansion or deflation from unemployment and capacity slack), inflation "remained slightly below target for most of the period."
- After 2015 the FOMC expressed concern that "inflation expectations could become de-anchored to the downside from their long-run target" and the FOMC began to raise interest rates in December 2015; around then, many (but not all) survey measures of inflation expectations began to drift downwards.

### Methodological contributions of the paper
- Contribution 1: The model assumes "the level of long-run expected inflation has a unit root," allowing the data to more flexibly discriminate between transient and permanent movements in inflation expectations versus approaches that "impose long-run stability on the data."
- Contribution 2: The model "uses a broader selection of surveys of households and businesses than most other approaches," producing a measure indicative of cross-sector inflation expectations.

### Key findings and interpretation
- Long-run expectations of CPI inflation were "largely stable from 2000 until 2014 at levels near 2.3 percent."
- "Over the past 5 years, expectations appear to have declined to just below 2 percent," described as "well below that which would be consistent with the FOMC’s long-run target" given the Fed’s target on PCE inflation and the historical relationship with CPI inflation.
- The decline is characterized as "significant (roughly three standard deviations below the previous range)."
- Two possible interpretations:
  - Reflects "fears about large expected output gaps as a normal state of the world (driving down average inflation with constant equilibrium inflation)."
  - Agents may "now expect below target inflation and embed this into their own actions, which becomes a self-fulfilling forecast."
- Implication: Allowing a unit root for long-run expected inflation alters the econometric separation of permanent versus transitory movements, affecting inference about whether recent declines represent lasting de-anchoring.

---

### II. TERM STRUCTURE MODEL BASED ON TIPS AND SURVEYS

### Model overview and motivation
- Purpose: extract market expectations and risk premia from bond prices and surveys using a no arbitrage term structure, extended to breakeven inflation (BEI) from TIPS while allowing for differential liquidity (liq) between nominal Treasuries and TIPS.
- Key decomposition:
  - BEI_t,τ = E_t,τ[π] + irp_t,τ − liq_t,τ
- Rationale for including surveys and macro data:
  - Address short-sample, small-sample, and time-varying mean problems.
  - Surveys increase cross-sectional information and stabilize factor mean-reversion estimates.
  - Surveys can parsimoniously capture features such as the zero lower bound.
- Data used: 12-month CPI inflation, TIPS breakeven inflation rates (maturities 2, 5, 7, 10, 15, and 20 year from Gurkaynak, Sack, and Wight, 2010), surveys of economists and market participants at short and longer-term horizons, household and business surveys, de-meaned oil price changes, and the CBO’s unemployment gap.

### Model specification
- Factor structure: four factors
  - Factor 1: long-run expected level of inflation (constrained to be a unit root).
  - Factor 2: economic slack (de-meaned CBO unemployment gap).
  - Factor 3: temporary supply shocks (relative oil price inflation).
  - Factor 4: liquidity differential between TIPS and nominal Treasury securities (endogenous).
- Measurement of CPI: twelve-month inflation rate is affine in state variables with δ = [1, 1, 1, 0].
- State dynamics: X_t = μ + κ X_{t−1} + Σ e_t with μ = 0 and Σ diagonal; κ diagonal terms are estimated speeds of mean reversion. A parsimonious κ specification is used for stability.
- Observation equations: Y_{t}^i = c + β X_t + η^i. Survey βs are linked to transition dynamics; consumer/business surveys include constant terms for persistent biases.
- Market price of inflation risk: Γ_t = λ_0 + λ_1 X_t with empirical restrictions:
  - λ_0: constant prices for the first three factors; fourth (liquidity) set to zero.
  - λ_1: diagonal, each factor’s price of risk determined by its own level; liquidity factor allowed to impact pricing of the other factors.
- Bond pricing recursions under no arbitrage produce affine zero-coupon yields via A(τ), B(τ) recursions and y_{t,τ} = −(1/τ) A(τ) − (1/τ) B(τ)' X_t.
- Estimation: Kalman Filter on end-of-month data; survey results treated as missing except in survey months.

### Key empirical findings and statistics
- Factor dynamics and behavior:
  - Four factors capture long-run inflation, slack, oil-supply shocks, and TIPS liquidity.
  - Oil price shocks largely fade almost fully within a year.
  - Output gap declines relatively slowly.
- Variance decomposition (share of variance explained for BEIs; reported as covariance contribution divided by BEI variance):
  - For 5Y BEI: Expected Inflation 0.13; Inflation Risk Premium 0.01; Liquidity Premium 0.86.
  - For 10Y BEI: Expected Inflation 0.26; Inflation Risk Premium 0.23; Liquidity Premium 0.51.
  - For 20Y BEI: Expected Inflation 0.32; Inflation Risk Premium 0.52; Liquidity Premium 0.16.
- Measurement errors (standard deviations, percentage points) for TIPS BEIs:
  - 2-year: 0.498
  - 5-year: 0.080
  - 7-year: 0.000
  - 10-year: 0.059
  - 15-year: 0.071
  - 20-year: 0.133
- Survey measurement errors and related statistics:
  - 1-q: 0.319; 2-q: 0.217; 3-q: 0.175; 4-q: 0.179.
  - SPF 10-year: 0.198
  - Consensus Economics 5y5y: 0.260
  - Survey of Primary Dealers 10-year average: 0.103
  - Survey of Market Participants 10-year average: 0.045
- Table statistics (factor speeds of mean-reversion; Value and T-stat):
  - k_{2,2} Value 0.960 T-stat 180
  - k_{3,3} Value 0.760 T-stat 47.9
  - k_{4,4} Value 0.950 T-stat 45.9
- Long-run inflation expectations:
  - Declined substantially through early 1990s, stable near the FOMC’s implied target of 2.3 percent for CPI inflation from 1998-2014.
  - Began moving downwards in 2014; recent years show expectations below levels consistent with the FOMC’s target.
- Inflation risk premium:
  - Declined over time with falling realized inflation volatility; since 2016 this premium has been close to zero.
- Liquidity premium:
  - Initial TIPS illiquidity effects largely dissipated by 2005, re-emerged during the global financial crisis, and provided a modest but generally stable drag on BEIs post-GFC.
  - Liquidity effects are more impactful for short-term instruments than for longer-term bonds.
- Covid-19 episode (model results):
  - Model indicates covid shock is, on net, deflationary with 10-year inflation expectations having fallen by 20 basis points relative to pre-pandemic levels.
  - Survey responses: consumer surveys regarded the shock as inflationary; model-estimated liquidity effects during covid were roughly half as large, but much shorter-lived, than during the GFC.
- Robustness:
  - Filtered results robust to changing the cross-sectional sample (e.g., TIPS only or including different survey measures) provided macro data are included.
  - Household/business-survey–based estimates are higher and more volatile than baseline and respond more strongly to supply shocks.

### Policy-relevant implications and conclusions
- Longer-run inflation expectations have drifted down over the past six years according to model estimates integrating market pricing and surveys.
- Contributing factors: decline in neutral interest rate, persistent slack, shale oil, U.S. dollar movements, and imported disinflation.
- Monetary policy challenges:
  - Lowered inflation expectations make it more difficult for monetary policy to achieve the Fed’s 2 percent target.
  - Macroeconomic models that assume well-anchored inflation expectations may over-estimate future realized inflation.
  - With a very flat Phillips Curve, unemployment would need to be reduced to very low levels to offset the observed decline in inflation expectations.
- New strategy considerations:
  - The FOMC’s new framework (maximum employment as asymmetric and flexible average inflation targeting) may need to produce periods with medium-run expectations above 2 percent to restore anchoring.
  - Success requires running the economy “hot” enough to sustainably push inflation to, and temporarily above, 2 percent to generate a virtuous adjustment of expectations and create more monetary policy space.

---

### Appendix: Observation Equations and Data Sources (selected entries)
- General notes:
  - Surveys anchor the physical dynamics of the model by including economist surveys of inflation.
  - For a given period ahead’s forecast the model iterates K forward to generate the period appropriate expectations.
  - The survey observation equations have the same general form as the equation for 휋푡12푚 but with different values in the second and third elements.
  - The first element is always 1 given the unit root assumption.
  - For forecasts of average levels, the model takes the iterated factor weights over the relevant time horizon and averages them.
  - Demeaning the output gap incorporates market and survey views about the long-run expected output gap into long-run expected inflation.

- Selected observation-equation coefficients and metadata (Trend inflation; Business cycle; Oil prices; Liquidity; Moving avg. of output gap; Measurement error; Frequency; Start Date where provided):
  - 12-month CPI: Trend inflation 1.000; Business cycle 1.000; Oil prices 1.000; Moving avg. of output gap --0.714; Source Bureau of Labor Statistics; Frequency Monthly
  - 2-year TIPS Breakevens: Trend inflation 1.090; Business cycle 0.516; Oil prices 0.180; Liquidity (0.075); Moving avg. of output gap --0.1032120930.498; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
  - 5-year TIPS Breakevens: Trend inflation 1.254; Business cycle 0.254; Oil prices 0.072; Liquidity (0.071); Moving avg. of output gap --0.3584638180.080; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
  - 7-year TIPS Breakevens: Trend inflation 1.381; Business cycle 0.184; Oil prices 0.051; Liquidity (0.055); Moving avg. of output gap --0.5208271660.000; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
  - 10-year TIPS Breakevens: Trend inflation 1.604; Business cycle 0.129; Oil prices 0.036; Liquidity (0.041); Moving avg. of output gap --0.7553582330.059; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
  - 15-year TIPS Breakevens: Trend inflation 2.084; Business cycle 0.086; Oil prices 0.024; Liquidity (0.030); Moving avg. of output gap --1.2257508610.071; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
  - 20-year TIPS Breakevens: Trend inflation 2.748; Business cycle 0.065; Oil prices 0.018; Liquidity (0.025); Moving avg. of output gap --1.9898796450.133; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
  - 1-quarter ahead SPF survey: Trend inflation 1.000; Business cycle 0.827; Oil prices 0.251; Moving avg. of output gap --0.319; Source Federal Reserve Bank of Philadelphia; Frequency Quarterly
  - 10-year average Survey of Primary Dealers: Trend inflation 1.000; Business cycle 0.214; Oil prices 0.026; Liquidity 0.103; Source Federal Reserve Bank of New York; Frequency 8 times per year; Start Date 2011
  - 10-year average Survey of Market Participants: Trend inflation 1.000; Business cycle 0.214; Oil prices 0.026; Liquidity 0.045; Source Federal Reserve Bank of New York; Frequency 8 times per year; Start Date 2015
  - 1-year average consumer: Trend inflation 1.000; Business cycle 0.788; Oil prices 0.253; Liquidity 0.646; Source University of Michigan; Frequency Monthly

- Notes:
  - Series without start dates are available over the full sample, from 1990-on.
  - For the unemployment rates and oil price series, coefficients being greater than one implies that the unobserved state will have an amplitude less than the underlying series.
  - The standard error on the oil price series seems to imply it has effect on the model because its variance is much higher than the other inputs; it has a correlation coefficient of 0.68 with the third state.

*Source: wpiea2020240-print-pdf*

### REFERENCES ___________________________________________________________20

### I. THE CONQUEST OF INFLATION... AND THEN WHAT?

### Background: inflation performance and policy since the mid-1990s
- The FOMC reached an internal agreement on a two percent inflation target for the personal consumption expenditure deflator at the July 1996 meeting; this corresponds to "roughly 2.3 percent in CPI terms."
- Since that decision, "core inflation has been at or above that target for only a fraction of the time."
- The post-Global Financial Crisis (GFC) period featured:
  - Large financial and real shocks that contributed to persistent weakness in inflation.
  - The zero lower bound (ZLB) on interest rates in many countries, constraining conventional policy.
  - Compensatory measures including forward guidance and quantitative easing designed to lower risk-free interest rates and loosen financial conditions.
  - Fiscal policy that "was, on net, only a modest support to growth" over the post-Crisis period.
- Contrary to early post-GFC concerns (inflation spike from Fed balance sheet expansion or deflation from unemployment and capacity slack), inflation "remained slightly below target for most of the period."
- After 2015 the FOMC expressed concern that "inflation expectations could become de-anchored to the downside from their long-run target" and the FOMC began to raise interest rates in December 2015. Around then, many (but not all) survey measures of inflation expectations began to drift downwards.

### Methodological contributions of the paper
- Contribution 1: The model assumes "the level of long-run expected inflation has a unit root," providing a more flexible specification that lets the data play a stronger role in discriminating between transient and permanent movements in inflation expectations. The paper contrasts this with approaches that assume a non-integrated process and thereby "impose long-run stability on the data."
- Contribution 2: The model "uses a broader selection of surveys of households and businesses than most other approaches," producing a measure indicative of cross-sector inflation expectations.

### Key findings and quantitative results
- Long-run expectations of CPI inflation were "largely stable from 2000 until 2014 at levels near 2.3 percent."
- "Over the past 5 years, expectations appear to have declined to just below 2 percent," a level described as "well below that which would be consistent with the FOMC’s long-run target" given the Fed’s target on PCE inflation and the historical relationship with CPI inflation.
- The decline is characterized as "significant (roughly three standard deviations below the previous range)."
- Two possible interpretations of the decline are presented:
  - It could reflect "fears about large expected output gaps as a normal state of the world (driving down average inflation with constant equilibrium inflation)."
  - Or agents may "now expect below target inflation and embed this into their own actions, which becomes a self-fulfilling forecast."

### Implications for interpretation and policy
- Allowing long-run expected inflation to have a unit root changes the econometric separation of permanent versus transitory movements in expectations, affecting inference about whether recent declines represent lasting de-anchoring.
- Using a broad set of survey measures aims to capture cross-sector expectations rather than relying on a narrower set of measures.
- The observed decline in long-run expectations to "just below 2 percent" and its statistical significance (roughly three standard deviations) raise concerns about potential de-anchoring and the possibility of self-fulfilling lower inflation outcomes, with implications for monetary policy stance and communication.

*Source: Excerpt from the PDF chapter/section "I. THE CONQUEST OF INFLATION... AND THEN WHAT?"*

### Section II introduces a term structure model based on TIPS and surveys of inflation

### Section II introduces a term structure model based on TIPS and surveys of inflation

### Model overview and motivation
- Purpose: extract market expectations and risk premia from bond prices and surveys using a no arbitrage term structure, extended to breakeven inflation (BEI) from TIPS while allowing for differential liquidity (liq) between nominal Treasuries and TIPS.
- Key decomposition: BEI equals expected inflation plus an inflation risk premium minus a liquidity premium, preserved in the paper as:
  - BEI_t,τ = E_t,τ[π] + irp_t,τ − liq_t,τ
- Rationale for including surveys and macro data:
  - Address short-sample, small-sample, and time-varying mean problems.
  - Surveys increase cross-sectional information and stabilize factor mean-reversion estimates.
  - Surveys can parsimoniously capture features such as the zero lower bound.
- Data used: 12-month CPI inflation, TIPS breakeven inflation rates (maturities 2, 5, 7, 10, 15, and 20 year from Gurkaynak, Sack, and Wight, 2010), surveys of economists and market participants at short and longer-term horizons, household and business surveys, de-meaned oil price changes, and the CBO’s unemployment gap.

### Model specification
- Factor structure: four factors
  - Factor 1: long-run expected level of inflation (constrained to be a unit root).
  - Factor 2: economic slack (de-meaned CBO unemployment gap).
  - Factor 3: temporary supply shocks (relative oil price inflation).
  - Factor 4: liquidity differential between TIPS and nominal Treasury securities (endogenous).
- Measurement of CPI: twelve-month inflation rate is affine in state variables with δ = [1, 1, 1, 0].
- State dynamics: X_t = μ + κ X_{t−1} + Σ e_t with μ = 0 and Σ diagonal; κ diagonal terms are estimated speeds of mean reversion. A parsimonious κ specification is used for stability.
- Observation equations: Y_{t}^i = c + β X_t + η^i. Survey βs are linked to transition dynamics; consumer/business surveys include constant terms for persistent biases.
- Market price of inflation risk: Γ_t = λ_0 + λ_1 X_t with empirical restrictions:
  - λ_0: constant prices for the first three factors; fourth (liquidity) set to zero.
  - λ_1: diagonal, each factor’s price of risk determined by its own level; liquidity factor allowed to impact pricing of the other factors.
- Bond pricing recursions under no arbitrage produce affine zero-coupon yields via A(τ), B(τ) recursions and y_{t,τ} = −(1/τ) A(τ) − (1/τ) B(τ)' X_t.
- Estimation: Kalman Filter on end-of-month data; survey results treated as missing except in survey months.

### Estimation details and data handling
- Anchor variables: de-meaned oil price changes (supply shocks) and CBO unemployment gap (cyclical position).
- Justification for unit-root on long-run inflation factor: reduces bias toward assuming inflation target credibility; supported by literature cited in the text.
- Parsimony choices: diagonal Σ, restricted λ parameters, simpler κ to improve quasi-real-time stability and higher log-likelihood relative to fully unrestricted specifications.
- Surveys weighting: Survey of Market Participants and Primary Dealers weighted more heavily than longer-run SPF as they are more cyclically informative.

### Key empirical findings and statistics
- Model factors and dynamics:
  - Four factors capture long-run inflation, slack, oil-supply shocks, and TIPS liquidity.
  - Oil price shocks largely fade almost fully within a year.
  - Output gap declines relatively slowly.
- Variance decomposition (share of variance explained for BEIs; reported as covariance contribution divided by BEI variance):
  - For 5Y BEI: Expected Inflation 0.13; Inflation Risk Premium 0.01; Liquidity Premium 0.86.
  - For 10Y BEI: Expected Inflation 0.26; Inflation Risk Premium 0.23; Liquidity Premium 0.51.
  - For 20Y BEI: Expected Inflation 0.32; Inflation Risk Premium 0.52; Liquidity Premium 0.16.
- Measurement errors (standard deviations, percentage points) for TIPS BEIs:
  - 2-year: 0.498
  - 5-year: 0.080
  - 7-year: 0.000
  - 10-year: 0.059
  - 15-year: 0.071
  - 20-year: 0.133
- Survey measurement errors and related statistics:
  - 1-q: 0.319; 2-q: 0.217; 3-q: 0.175; 4-q: 0.179.
  - SPF 10-year: 0.198
  - Consensus Economics 5y5y: 0.260
  - Survey of Primary Dealers 10-year average: 0.103
  - Survey of Market Participants 10-year average: 0.045
- Table statistics (factor speeds of mean-reversion; Value and T-stat):
  - k_{2,2} Value 0.960 T-stat 180
  - k_{3,3} Value 0.760 T-stat 47.9
  - k_{4,4} Value 0.950 T-stat 45.9
- Long-run inflation expectations:
  - Declined substantially through early 1990s, stable near the FOMC’s implied target of 2.3 percent for CPI inflation from 1998-2014.
  - Began moving downwards in 2014; recent years show expectations below levels consistent with the FOMC’s target.
- Inflation risk premium:
  - Declined over time with falling realized inflation volatility; since 2016 this premium has been close to zero.
- Liquidity premium:
  - Initial TIPS illiquidity effects largely dissipated by 2005, re-emerged during the global financial crisis, and provided a modest but generally stable drag on BEIs post-GFC.
  - Liquidity effects are more impactful for short-term instruments than for longer-term bonds.
- Covid-19 episode (model results):
  - Model indicates covid shock is, on net, deflationary with 10-year inflation expectations having fallen by 20 basis points relative to pre-pandemic levels.
  - Survey responses: consumer surveys regarded the shock as inflationary; model-estimated liquidity effects during covid were roughly half as large, but much shorter-lived, than during the GFC.
- Robustness:
  - Filtered results robust to changing the cross-sectional sample (e.g., TIPS only or including different survey measures) provided macro data are included.
  - Household/business-survey–based estimates are higher and more volatile than baseline and respond more strongly to supply shocks.

### Implications and policy-relevant conclusions
- Longer-run inflation expectations have drifted down over the past six years according to model estimates integrating market pricing and surveys.
- Contributing factors: decline in neutral interest rate, persistent slack, shale oil, U.S. dollar movements, and imported disinflation.
- Monetary policy challenges:
  - Lowered inflation expectations make it more difficult for monetary policy to achieve the Fed’s 2 percent target.
  - Macroeconomic models that assume well-anchored inflation expectations may over-estimate future realized inflation.
  - With a very flat Phillips Curve, unemployment would need to be reduced to very low levels to offset the observed decline in inflation expectations.
- New strategy considerations:
  - The FOMC’s new framework (maximum employment as asymmetric and flexible average inflation targeting) may need to produce periods with medium-run expectations above 2 percent to restore anchoring.
  - Success requires running the economy “hot” enough to sustainably push inflation to, and temporarily above, 2 percent to generate a virtuous adjustment of expectations and create more monetary policy space.

*Source: Section II (model) and subsequent empirical assessments from the supplied IMF working paper content unit.*

### REFERENCES

### REFERENCES

### Key methodological notes (Appendix: Observation Equations)
- Surveys anchor the physical dynamics of the model by including economist surveys of inflation.
- For a given period ahead’s forecast the model iterates K forward to generate the period appropriate expectations.
- The survey observation equations have the same general form as the equation for 휋푡12푚 but with different values in the second and third elements.
- The first element is always 1 given the unit root assumption.
- For forecasts of average levels, the model takes the iterated factor weights over the relevant time horizon and averages them.
- Parameter restrictions in the macroeconomic variables link the factors to the underlying economic phenomenon that drive inflation and its risks.
- Demeaning the output gap incorporates market and survey views about the long-run expected output gap into long-run expected inflation.

### Table A1.1 — Observation Equations and Data Sources (selected regression series and coefficients)
- 12-month CPI: Trend inflation 1.000; Business cycle 1.000; Oil prices 1.000; Moving avg. of output gap --0.714; Source Bureau of Labor Statistics; Frequency Monthly
- Unemployment rate (demeaned): Business cycle 4.989; Moving avg. of output gap --0; Source Bureau of Labor Statistics; Frequency Monthly
- 12-month change in oil prices: Oil prices 49.36; Moving avg. of output gap --0; Source EIA/Chicago Mercantile Exchange; Frequency Monthly
- 2-year TIPS Breakevens: Trend inflation 1.090; Business cycle 0.516; Oil prices 0.180; Liquidity (0.075); Moving avg. of output gap --0.1032120930.498; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
- 5-year TIPS Breakevens: Trend inflation 1.254; Business cycle 0.254; Oil prices 0.072; Liquidity (0.071); Moving avg. of output gap --0.3584638180.080; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
- 7-year TIPS Breakevens: Trend inflation 1.381; Business cycle 0.184; Oil prices 0.051; Liquidity (0.055); Moving avg. of output gap --0.5208271660.000; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
- 10-year TIPS Breakevens: Trend inflation 1.604; Business cycle 0.129; Oil prices 0.036; Liquidity (0.041); Moving avg. of output gap --0.7553582330.059; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
- 15-year TIPS Breakevens: Trend inflation 2.084; Business cycle 0.086; Oil prices 0.024; Liquidity (0.030); Moving avg. of output gap --1.2257508610.071; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
- 20-year TIPS Breakevens: Trend inflation 2.748; Business cycle 0.065; Oil prices 0.018; Liquidity (0.025); Moving avg. of output gap --1.9898796450.133; Source Gurkynak, Sack, and Wright (2008); Frequency Monthly; Start Date 1999
- 1-quarter ahead SPF survey: Trend inflation 1.000; Business cycle 0.827; Oil prices 0.251; Moving avg. of output gap --0.319; Source Federal Reserve Bank of Philadelphia; Survey respondents Economists; Frequency Quarterly
- 2-quarter ahead SPF survey: Trend inflation 1.000; Business cycle 0.739; Oil prices 0.110; Moving avg. of output gap --0.217; Source Federal Reserve Bank of Philadelphia; Survey respondents Economists; Frequency Quarterly
- 3-quarter ahead SPF survey: Trend inflation 1.000; Business cycle 0.659; Oil prices 0.048; Moving avg. of output gap --0.175; Source Federal Reserve Bank of Philadelphia; Survey respondents Economists; Frequency Quarterly
- 4-quarter ahead SPF survey: Trend inflation 1.000; Business cycle 0.588; Oil prices 0.021; Moving avg. of output gap --0.179; Source Federal Reserve Bank of Philadelphia; Survey respondents Economists; Frequency Quarterly
- 10-year average SPF survey: Trend inflation 1.000; Business cycle -; Oil prices -; Moving avg. of output gap -4.989-0.198; Source Federal Reserve Bank of Philadelphia; Survey respondents Economists; Frequency Quarterly
- 5-year forward 5-year average: Trend inflation 1.000; Business cycle -; Oil prices -; Moving avg. of output gap -4.989-0.260; Source Consensus Economics; Survey respondents Economists; Frequency Bi-annual/quarterly
- 10-year average Survey of Primary Dealers: Trend inflation 1.000; Business cycle 0.214; Oil prices 0.026; Liquidity 0.103; Source Federal Reserve Bank of New York; Survey respondents Economists; Frequency 8 times per year; Start Date 2011
- 10-year average Survey of Market Participants: Trend inflation 1.000; Business cycle 0.214; Oil prices 0.026; Liquidity 0.045; Source Federal Reserve Bank of New York; Survey respondents Buy-side Firms; Frequency 8 times per year; Start Date 2015
- 1-year average consumer: Trend inflation 1.000; Business cycle 0.788; Oil prices 0.253; Liquidity 0.646; Source University of Michigan; Survey respondents Consumers; Frequency Monthly
- 5-year average consumer: Trend inflation 1.000; Business cycle 0.387; Oil prices 0.052; Moving avg. of output gap --0.228; Source University of Michigan; Survey respondents Consumers; Frequency Monthly
- 1-year lagged unit costs: Trend inflation 1.000; Business cycle 0.635; Oil prices 0.036; Moving avg. of output gap --0.105; Source Federal Reserve Bank of Atlanta; Survey respondents Businesses; Frequency Monthly; Start Date 2011
- 1-year ahead unit costs: Trend inflation 1.000; Business cycle 0.635; Oil prices 0.036; Moving avg. of output gap --0.250; Source Federal Reserve Bank of Atlanta; Survey respondents Businesses; Frequency Monthly; Start Date 2011
- 1-year ahead inflation - CFOs: Trend inflation 1.000; Business cycle 0.635; Oil prices 0.036; Moving avg. of output gap --0.164; Source Duke University; Survey respondents CFOs; Frequency Quarterly

Notes from the appendix table:
- Series without start dates are available over the full sample, from 1990-on.
- For the unemployment rates and oil price series, coefficients being greater than one implies that the unobserved state will have an amplitude less than the underlying series.
- The standard error on the oil price series seems to imply it has effect on the model because its variance is much higher than the other inputs; it has a correlation coefficient of 0.68 with the third state.

*Source: wpiea2020240-print-pdf - REFERENCES*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020240-print-pdf.pdf_