Fundamental Disagreement

Transcription

1 Fundamental Disagreement Philippe Andrade (Banque de France) Richard Crump (FRBNY) Stefano Eusepi (FRBNY) Emanuel Moench (Bundesbank) Price-setting and inflation Paris, Dec. 7 & 8, 5 The views expressed here are the authors and are not representative of ones of the Banque de France, the Bundesbank, the Eurosystem, the Federal Reserve Bank of New York or the Federal Reserve System.

2 Disagreement About Future Economic Outcomes Well documented in every survey of financial analysts, households, professional forecasters, FOMC members... At odds with full information rational expectation setup. Heterogeneous beliefs: important role in models with info. frictions Macro: Mankiw-Reis (), Sims (), Woodford (), Lorenzoni (9), Mackowiak-Wiederholt (9), Angeletos-Lao (),... Finance: Scheinkman-Xiong (), Nimark (9)... Empirical properties of disagreement informative about such models?

3 This Paper Document some new facts about forecasters disagreement. Evaluate models ability to match the facts. Consider two popular models of imperfect info: Noisy information model: Sims (), Woodford (). Sticky information model: Mankiw and Reis (). Consider setup where forecasts do not impact data generating process.

4 New Facts Use Blue Chip Financial Forecasts (BCFF) survey: Forecasts about output growth, inflation, fed-funds rate. Up to 6- years ahead horizon. We document: Forecasters disagree about fundamental (long-horizon) outcomes. Term-structure of disagreement differs markedly across variables. LT disagreement varies over time and co-varies across variables. 4

5 Replicating the Facts Independent of the model of info. frictions, key ingredients: Current state of the economy imperfectly observed. Unobserved permanent and transitory shocks. Dynamic interactions between variables. Minimal departure from full information setup: symmetric agents No information advantage (consistent with evidence that hard to beat the consensus). Forecasters agree on the parameters of the true model but disagree about the unobserved states. 5

6 The Blue Chip Financial Forecasts Survey 5 professional forecasters. We look at forecasts for RGDP growth (g), CPI inflation (π), FFR (i). Sample period is 986:Q-:Q. For Q, Q, Q, 4Q: observe individual forecasts. For Y, Y, 4Y, 5Y and long-term (6-to-Y): observe average forecasts, top average forecasts, and bottom average forecasts. Our measure of disagreement: top average bot average. strongly correlated with cross-section stdev or IQR at short horizons. 6

7 The Term Structure of Disagreement in the BCFF.5 Output Inflation Federal Funds Rate.5 Q Q Q Q4 Y Y Y4 Y5 Y6 7

8 The Time Series of Long Run Disagreement 4.5 Output Inflation Federal Funds Rate

9 Model Underlying state True state z = {g, π, i} where z t = (I Φ)µ t + Φz t + vt z, µ t = µ t + v t µ, with vt z iid N(, Σ z ) and v t µ iid N(, Σ µ ). Parameters: θ = (Φ, Σ z, Σ µ ) 9

10 Model Information Friction: Noisy Information Forecaster j observes: y jt = z t + η jt with η jt iid N(, Σ η ), Σ η diagonal. Individual j s optimal forecast computed using the Kalman filter. Model parameters: (θ, Σ η ). Disagreement driven by variance of observation errors Σ η.

11 Model Information Friction: Sticky Information At each date, a forecaster j observes k th element of y t with a fixed probability λ k ; otherwise sticks to latest observation of that variable. Individual j s optimal forecast computed using the Kalman filter with missing observations. Disagreement driven by different individual sequences of observations. Same number of parameters as in noisy info with λ s instead of Σ η.

12 Calibration via Penalized MLE Principle Sample: realizations 955Q-Q; survey 986Q-Q. We minimize the Likelihood associated to true state a penalty function measuring the distance between model implied moments (simulations) and their survey data counterpart. We choose 5 moments: Std-dev of consensus forecasts for Q, Q4, Y and Y6-. Disagreement about Q forecasts only.

13 Summary of Parameter Estimates Common parameters (θ) robust to type of info. friction considered. Long-run vol. (Σ µ ) much lower than short-run vol. (Σ z ). FFR is perfectly observed: Noisy: observation error (Σ η ) for FFR is zero. Sticky: probability of observing FFR (λ i ) is one. RGDP/CPI: degree of info frictions consistent with previous studies.

14 This figure displays the model-implied (time) average of disagreement across different horizons for the Data and Model-implied generalized noisy information model (dark Term blue) and the generalized Structures sticky information model of(light Disagreement blue) Noisy and Sticky Figure : Term Structure of Disagreement Noisy and Sticky Information Models calibrated with α = 5 along with the Blue Chip Financial Forecasts survey (red). Open circles designate survey moments used to form the penalization term P (θ, θ; S,..., ST )..5 Disagreement Real Output Growth Data Noisy Model Sticky Model.5 Q Q Q Q4 Y Y Y4 Y5 Y6 CPI Inflation.5.5 Q Q Q Q4 Y Y Y4 Y5 Y6 Federal Funds Rate.5.5 Q Q Q Q4 Y Y Y4 Y5 Y6 4

15 The first column displays the model-implied disagreement for the generalized noisy information model calibrated with α = 5 (blue) and the noisy information model without shifting endpoints calibrated with Disagreement and Consensus Volatility α = 5 (green) along with the Blue Chip Financial Forecasts survey (red). The second column displays the corresponding standard deviation of consensus forecasts. Open white circles designate survey moments used to form the penalization term P (θ, θ; S,..., ST ) for the model without shifting endpoints. Open white and light blue circles designate survey moments used to form the penalization term for the generalized Noisy (very similar patterns for sticky version) noisy information model. Model-implied 95% confidence intervals for the model with and without shifting endpoints are designated by shaded regions and dotted lines, respectively. Disagreement Real Output Growth Standard Deviation of Consensus Real Output Growth.5 Data Model Model w/o Drift Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y6 CPI Inflation CPI Inflation Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y6 Federal Funds Rate 4.5 Federal Funds Rate Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y6 5

16 Role of Key Ingredients Decomposition into permanent and transitory components: Needed to explain disagreement beyond the short/medium term. Multivariate model: Needed to explain disagreement about future FFR even though perfectly observed. Needed to generate upward-sloping disagreement. 6

17 Time Variation The first column & displays Co-movement the model-implied (time) variance inof disagreement Disagreement for the generalized noisy Noisy Figure 5: Second Moments of Disagreement Noisy Information Model information model calibrated with α = 5 (blue) along with the Blue Chip Financial Forecasts survey (red). The second column displays the corresponding correlation of disagreement between variables. Model-implied 95% confidence intervals are designated by shaded regions. Variance Real Output Growth Correlation Real Output Growth & CPI Inflation Data Model Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y CPI Inflation Real Output Growth & Federal Funds Rate Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y Federal Funds Rate CPI Inflation & Federal Funds Rate Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y6 7

18 The first column displays the model-implied (time) variance of disagreement for the generalized sticky Time Variation & Co-movement in Disagreement Sticky Figure 8: Second Moments of Disagreement Sticky Information Model information model calibrated with α = 5 (blue) along with the Blue Chip Financial Forecasts survey (red). The second column displays the corresponding correlation of disagreement between variables. Model-implied 95% confidence intervals are designated by shaded regions. Results are based on,5 simulations Variance Real Output Growth Correlation Real Output Growth & CPI Inflation Data Model Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y CPI Inflation Real Output Growth & Federal Funds Rate Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y Federal Funds Rate CPI Inflation & Federal Funds Rate Q Q Q Q4 Y Y Y4 Y5 Y6 Q Q Q Q4 Y Y Y4 Y5 Y6 8

19 Is Disagreement about FFR Consistent with a Taylor Rule? Generate ind. FFR forecasts given model ind. forecasts of g and π i t = ρ i t + ( ρ) it + ɛ t it = ī t + ϕ π (π t π t ) + ϕ g (g t ḡ t ) Find parameters {ρ, ϕ π, ϕ g } giving best fit of FFR term structure of disagreement obtained with previous reduced form model. ρ =.98, ( ρ)ϕ π =.6, ( ρ)ϕ g =.. Compare with various parametric restrictions. Std Taylor rule parameters: ρ =.9, ϕ π =, ϕ g =. No policy smoothing ρ =. Restrictions on time varying components of ī t. 9

20 Standard Taylor Rule 4.5 Data Model-implied Rule Standard Rule Standard Rule with ρ =.5.5 Q Q Q Q4 Y Y Y4 Y5 Y6

21 Q Q Q Q4 Y Y Y4 Y5 Y6 Role of Components in the Time-Varying Intercept.5 Data Model Model w/ it =i Model w/ it =r+πt Model w/ it = 4 log(β)+g t +πt.5 Q Q Q Q4 Y Y Y4 Y5 Y6

22 Conclusion Present new facts about forecaster disagreement. Identify key features needed to replicate them. Models of imperfect info can account for complex facts for sound parameter values. Minimal departure from REH: agents know and agree on true model/params. Disagreement informative about both degree of imperfect info and underlying DGPs. Results underline importance of uncertain long-run component in macro-variable (implications for macro & finance). Informative about perceived structural relationships (e.g. Taylor rule).

23 Extensions / Future Research Accounting for time variance of disagreement: Stochastic volatility. State-dependent imperfect info / inattention. More structure...

24 Appendix Noisy Information Model Table : Results of Calibration for α = 5 Noisy Information Model Φ Σ z sqrt(diag( Σ η )) eig(φ) Σ µ sqrt(diag(σ η )) Table : Results of Calibration for α = 5 Sticky Information Model Φ Σ z sqrt(diag( Σ η )) 4

25 Sticky Information Model Appendix Table : Results of Calibration for α = 5 Sticky Information Model Φ Σ z sqrt(diag( Σ η )) eig(φ) Σ µ λ

26 Appendix ST/LT Disagreement Real Output Growth 6 5 Q Y CPI Inflation Federal Funds Rate

27 Appendix Long-Term Forecasts: GDP/GNP 4 Real GDP 6 Years Ahead Forecasts Consensus Top Bottom

28 Appendix Long-Term Forecasts: CPI CPI 6 Years Ahead Forecasts Consensus Top Bottom

29 Appendix Long-Term Forecasts: FFR 9 8 Federal Funds Rate 6 Years Ahead Forecasts Consensus Top Bottom

30 Appendix Calibration via Penalized MLE Details (/) Consider realizations as signals about z t : Y t = z t + η t with η t iid N(, Σ η ). L (Y,, Y T ; θ, Σ ) η = likelihood obtained with Kalman filter.

31 Appendix Calibration via Penalized MLE Details (/) Given (θ, Σ η ), we generate individual forecasts fjt h and minimize distance between simulated moments S(θ, Σ η ) and their survey data counterparts S t. distance between model implied expectation moments and their survey data counterpart, P (S,, S T ; θ, Σ η ) [ ] [ ] P = S(θ, Σ η ) S t W S(θ, Σ η ) S t T T t We minimize the penalized likelihood: ( C θ, Σ η, Σ η) ( = L Y,, Y T ; θ, Σ η) + αp (S,, S T ; θ, Σ η ). t

32 Appendix Calibration in Practice Sample: realizations 955Q-Q; survey 986Q-Q. Simulate R = histories of shocks ɛ t and observation noises η j t with T = (nb of dates) and N = 5 (nb of forecasters). We choose 5 moments: Std-dev of consensus forecasts for Q, Q4, Y and Y6-. Disagreement about Q forecasts only. Strong weight on Q disagreement in the penalty criterion ( normalisation ). Penalty parameter α = 5.

33 Appendix Robustness Various penalty parameters α =, α =. Initial conditions. Econometrician perfectly observing the state ( Σ η ) = ).