Rationally heterogeneous forecasters

Transcription

1 Rationally heterogeneous forecasters R. Giacomini, V. Skreta, J. Turen UCL Ischia, 15/06/2015 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

2 Motivation Question: how do economic agents form expectations? Important because: Key building block of macro and finance models Increasing role of expectation manipulation in monetary policy: important to understand how expectations are affected by communication of public information Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

3 Theories of expectation formation Main paradigm: full information rational expectations (FIRE) Drawback: fails to match key stylised facts For example, violated by consensus forecasts from survey data Departures. Rational expectations with information frictions: Sticky information (Mankiw and Reis (2002): only a fraction of agents observe public signal) or noisy information (everyone observes noisy public signal) Can explain violation of FIRE for survey consensus forecasts Drawback: not enough to explain heterogeneity (disagreement) in survey data Departures. Behavioural models Patton and Timmermann (2010). Sticky prior model can explain heterogeneity Drawback: ad-hoc learning rule Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

4 Our goal Propose a parsimonious model of expectation formation that fits the stylised facts, namely: Accuracy Disagreement Can we match facts with a rational (Bayesian learning) model? Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

5 Contribution 1 We build a model of expectation formation where: Agents initial expectations are based on possibly heterogeneous models Agents are inattentive Agents who are attentive observe public signal and use Bayes rule to revise their expectations Attentive agents attribute homogeneous weights to signal 2 Analyse a new dataset of professional forecasters Key feature: Agents can update an initial forecast whenever they want. Endogeneity in updating behaviour makes link between updating behaviour and attention more plausible 3 Our model fits the stylised facts and outperforms models studied earlier Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

6 The dataset - Bloomberg s ECFC survey Fixed-event forecast: panel of ( 75) professional forecasters revise initial forecast of annual US inflation during 18 months before release. Sample Participation is free and agents are not rewarded explicitly but names of forecaster/institution are known (similar to other commonly studied surveys) Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

7 Annual US inflation Annual Inflation Rate Years Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

8 The dataset - Bloomberg s ECFC survey Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

9 Features of Bloomberg s ECFC survey Similar fixed-event forecasts analysed before using different datasets Unique features of Bloomberg s dataset: Agents can update their forecasts any time In other datasets, agents are surveyed at exogenously determined fixed dates (typically once a quarter) Dates are arbitrary no reason why relevant information should be released on those dates More difficult to associate updating behaviour to attention to information Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

10 Obtaining an empirical measure of attention We can sample at different frequencies (weekly, monthly) and compute the probability of updating the previous forecast Updating behaviour varies over time and across agents Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

11 Monthly updating frequencies Cross - section: average: 58%. Standard deviation: 15% Time series: Percentage of Updaters m1 2009m1 2011m1 2013m1 2015m1 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

12 Weekly updating frequencies Percentage of Updaters Percentage of Updaters week week Spikes are dates of Bloomberg reminders Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

13 Survey and Diligent agents Split agents into two groups: Survey agents 80%: only update when Bloomberg tells them to Similar to agents in other surveys Weaker link between updating behaviour and attention Diligent agents 20%: update in between Bloomberg reminders (at least once) Unique to our dataset Stronger link between updating behaviour and attention Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

14 Attention improves accuracy RMSE RMSE (percentage) Non Updaters Updaters RMSE Diligent Survey Forecast Horizon Forecast Horizon 5 0 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

15 Inattention can explain violations of FIRE P-values of bias and rationality (MZ) tests for consensus forecast Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

16 However, even attentive agents disagree... Forecast Disagreement (percentage) Non Updaters Updaters Forecast Disagreement Diligent Survey Forecast Horizon Forecast Horizon 5 0 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

17 What causes disagreement among attentive agents? Heterogeneous forecasting models? Heterogeneous weights on public signal? Private information? Heterogeneous incentives? Our answer Heterogeneous initial forecasts, homogeneous weights on public signal Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

18 A model of expectation formation For each year (we will have 8) we assume the following: h months before the end of the year agent i forecasts annual inflation y All agents give initial density forecast at h=18 with mean ŷi,18 and precision a i,18 : N(ŷ i,18, a 1 i,18 ) At month h = 17, 16,..., 1 a fraction 1 λ h updates forecast zi,h public signal about annual inflation, observed with precision b i,h : z i,h = y + ε i,h, ε i,h N(0, b 1 i,h ) Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

19 What is public signal? In the baseline model z i,h is related to monthly inflation We also consider a herding model where z i,h is the previous period consensus forecast The herding model does not fit the stylized facts Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

20 Forecast Revisions Normality and Bayes rule implies a linear updating rule with weights attached to information given by: w i,h = b i,h a i,h+1 + b i,h The forecasts at month h = 17, 16,... are N(ŷ i,h, a 1 i,h ) { (1 wi,h )ŷ ŷ i,h = i,h 1 + w i,h z i,h if i I h otherwise ŷ i,h 1 where I h defines the set of updaters at time h Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

21 Discussion Simple expectation formation process Simplicity is intentional so it can be easily incorporated in larger models where agents decisions depend of belief updates We do not explicitly model 1 Agents decision to update 2 Agents incentives Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

22 Structural estimation of the model Data-generating process Annual inflation is the sum of monthly inflation y = 12 t=1 x t Assume inflation in the t-th month of the year, x t, is generated by an AR(1) x t = c + φx t 1 + u t, u t N(0, σ 2 u) Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

23 Structural estimation of the model Agents model Agents have individual models x t = c i + φx t 1 + v t, v t N(0, σ 2 v ) v r independent of u s for all r and s c i = c + δ i captures agent-specific bias δ i that does not depend on the forecast horizon Agents initial point forecast is the unconditional mean of annual inflation based on their model: µ i = 12 c i /(1 φ) Assume agents assign same precision to initial forecast, so that the initial density forecast is N(µ i, a 1 18 ), a 18 constant across agents Assume µ i N(µ, σ 2 µ) Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

24 Structural estimation of the model What can cause differences in initial forecasts? 1 Different forecasting models 2 Different incentives (industry specific, individual specific) 3 Psychological factors (pessimism / optimism) 4 Differences in private information 5 Differences in agents experience/skill As long as these factors are time-invariant, our model implicitly incorporates them in the bias term Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

25 Structural estimation of the model Signal At each h = 17,..., 1, a fraction 1 λ h of agents update their initial forecast using as a common signal the information set at time h containing the history of monthly inflation x h, x h 1,... Each agent uses her model to interpret the monthly signal and obtains a signal z i,h about annual inflation zi,h is the conditional mean of annual inflation z i,h = µ i + z i,h = (12 h)µ i + φ h 11 (1 φ 12 ) (x h µ i ) for h = 17,..., 12 1 φ 12 h t=1 x t + φ(1 φh ) 1 φ (x h µ i ) for h = 11,..., 1 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

26 Structural estimation of the model Precision of signal z i,h implies an error e i,h = y z i,h The signal precision is the inverse of the variance of e i,h Heterogeneity is only in the means (and so in z i,h ) so the precision is the same across agents Precision b h is a known function of φ and σ 2 v. E.g. for h 11 b 1 h = σv 2 ( (1 φ) 2 h 2φ(1 φh ) + φ2 (1 φ 2h ) ) 1 φ 1 φ 2 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

27 Structural estimation of the model Bayesian updating Attentive agents update using Bayes rule Our assumptions imply homogeneous weights on the signal: update is N(ŷ i,h, a 1 h ) with ŷ i,h = (1 w h )ŷ i,h 1 + w h z i,h w h = b h a h+1 + b h a h = a h+1 + b h = a 18 + Model s parameters: (λ h, c, φ, σ 2 u, σ 2 v, µ, σ 2 µ, a 18 ) 17 b t t=h Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

28 Structural estimation of the model SMM estimation We estimate the model by simulated method of moments We want to match empirical disagreement and RMSE for consensus forecast for all forecast horizons. Empirical moments are computed for each h as averages over eight years We calibrate the inattention parameter λ h for each month and each year by setting it equal to the empirical measure of attention Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

29 Model fit - All sample All years, All years, Forecasters Disagreement Model Data RMSE Model Data Forecast Horizon Forecast Horizon 5 0 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

30 Model fit - After crisis After Crisis, After Crisis, Forecasters Disagreement Model Data RMSE Model Data Forecast Horizon Forecast Horizon 5 0 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

31 Estimation results All years After Crisis Coeffs All Diligent Survey All Diligent Survey c * * * φ.9491*.9401*.9403*.9799*.9845*.9798* µ σ µ.802*.701*.824*.686*.619*.712* σ u σ v *.0053*.0054* a * 180* 200* 250* 250* 250* J - test E(y t ) U.S. Data E(y t ) φ Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

32 Counterfactuals - Full attention After Crisis, After Crisis, Forecasters Disagreement Model Data Full Attention RMSE Model Data Full Attention Forecast Horizon Forecast Horizon 5 0 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

33 Counterfactuals - Homogeneous models After Crisis, After Crisis, Forecasters Disagreement Model Data Homogeneous L.R. Priors RMSE Model Data Homogeneous L.R. Priors Forecast Horizon Forecast Horizon 5 0 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

34 Are agents herding? Herding model Model same as before, only change is that the common signal is the previous month s consensus forecast and its precision the inverse of the previous month disagreement z h = 1 N N i=1 ŷi,h 1 b 1 h = 1 N N i=1 (ŷ i,h 1 - z h ) 2 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

35 Herding model does not fit the stylised facts All years, All years, Forecast Disagreement Herding Data RMSE Herding Data Forecast Horizon Forecast Horizon 5 0 Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

36 Conclusion Used new dataset of professional agents with empirical measure of attention to understand process of expectation formation Build simple model of Bayesian expectation formation for attentive agents that fits the data well Heterogeneity in initial forecasts seems to matter more empirically than inattention The model we propose is simple enough to be incorporated in general equilibrium models of macro and finance Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37

37 Relationship with existing literature Build on the literature on informational rigidities (Andrade LeBihan, Coibion Gorodnichenko) by assuming inattention. Go beyond it by constructing a Bayesian learning model that can explain not only violations of FIRE but match empirical patterns of accuracy and disagreement. Build on literature trying to explain disagreement (Patton Timmermann, Lahiri Sheng, Manzan). Show that disagreement can be explained by a Bayesian learning model with inattentive agents who disagree about the model but are otherwise homogeneous in their interpretation of public information Findings in the literature that agents interpret information in heterogeneous ways can be reconciled with our findings by the fact that in our setting only updaters are Bayesian and in our data updating can be more plausibly linked to information arrival Giacomini, Skreta, Turen (UCL) Rationally heterogeneous forecasters Ischia, 15/06/ / 37