maurizio bovi are the representative agents beliefs based on efficient econometric models? brussels...
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Maurizio Bovi
Are the Representative Agent’s Beliefs Based on Efficient Econometric Models?
Brussels15 November 2012
EUROPEAN COMMISSION DIRECTORATE GENERAL ECONOMIC AND FINANCIAL AFFAIRS
EU WORKSHOP ON RECENT DEVELOPMENTSIN BUSINESS AND CONSUMER SURVEYS
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Plan Motivation: several assumptions but little evidence on how
laypeople form expectations
Occasion: Real-Time Data thanks to BoE, Survey Expectations thanks to European Commission
Data Analysis:
Survey: Heterogeneous expectations as Signal/Noise Ratios (SNR) Real Time “Hard” Data: Econometric models and MSE horse race
Contributions:
i) Representative agent’s expectations may be not grounded in optimal econometric models
ii) VAR Analysis of the Expectations Feedback System
(beliefsrealizations) resulting in: “SNR => MSE”
Concluding Remarks and a Tentative Agenda
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Are the Representative Agent’s beliefs based on efficient statistical models?
People form rational expectations (Muth, 1961):
agents know and use the same “true” model.
People learn the correct model (Evans and Honkapohja, 2001):
agents act as econometricians and relentlessly estimate models.
People are “infected” by professional forecasters’ models (Carroll, 2003):
economists produce forecasts => mass media report forecasts => (more or
less frequently) people read forecasts.
People use the model with the highest fitness (Brock and Hommes, 1997):
People examine different forecasting models switching from one model to
another after a cost-benefit analysis based on relative mean squared
errors. Model uncertainty (i.e. the kind of the optimal model changes with
high frequency), preferences and inertia in the dynamic switching can
create heterogeneous expectations (even to a greater extent wrt sticky
information, Branch, 2004 & 2007).
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Issues People form rational expectations (Muth, 1961):
Several authors find evidence rejecting this assumption.
People act as smart econometricians (Evans and Honkapohja, 2011):
This is the typical assumption maintained by the adaptive learning
literature. Finding evidence on that is one of my goals.
People are “infected” by professional forecasters (Carroll, 2003):
If so, why household surveys are still among the most watched market
movers even among professional forecasters?
Predictor Choice Approach (Brock and Hommes, 1997):
To be able to calculate the relative success of their own choice, agents
must know the success of all competing models: individuals have already
paid the computational cost. Then, the question can be asked whether the
determinant of the choice should deal with forecasting accuracy only.
Also, “preferences” towards a single model are at odds wrt both the
dynamic switching and learning activities.
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Alternative Views on the Expectations Feedback System
Pigou (1927), Keynes (1936), Simon (1957), Tversky and
Kahneman, (1974)
Psychology matters and not-econometrically-based factors is what
surveys could/should capture (Katona, 1944, 1975; Bovi, 2009)
Ludvigson (2004)
Many empirical papers have been looking, with some success, for
the additionaladditional information content of survey expectations, whereby
the adjective “additional” stands exactly for extra economic
elements and/or independent information
Cass and Shell (1983)
Heterogeneous beliefs – e.g. in models with self-fulfilling prophecies
sunspot equilibria - can drive macroeconomic outcomes.
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Key Questions and Logic
Are representative agents’ (=>laypeople) beliefs based on optimal econometric models? Do heterogeneous beliefs Granger-cause the predictive power of efficient econometric models, or vice versa? Here the logic:
Think about an economy whereas a simple model turns out to be the best predictor for many years, but survey-declared expectations do not converge.
Think about an economy whereas evidence points out that
SNR “precede” MSE, but not vice versa.
All in all, the general validity of assuming best model-based expectations would be weakened.
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2. Survey Data
Source: Business Surveys Unit of the European Commission
Sample Period: January 1985 – March 2009 (simple mean for quarterly data)
Features: No genuine panel (bad), continuously refined (good), Laypeople (good: it is likely that economists use econometric models to forecast)
Query: “How do you expect the general economic situation in the country to develop over the next 12 months?”
Reply Options: It will…
…get a lot better (=LB); …get a little better (=B); …stay the same (=E); …get a little worse (=W); …get a lot worse (=LW); don't know (=N).
LB, B, E, etc., are the shares of respondents having chosen the corresponding option so that they sum up to one.
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2.1 Survey Expectations Signal/Noise Ratios
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2.1a Survey Expectations Signal/Noise Ratios
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2.1b Survey Expectations Signal/Noise Ratios
Unlike the previous methods, the IQV does not account for the ordered nature of the data.
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2.2 Survey Expectations and Reality
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
0.72
0.76
0.80
0.84
0.88
0.92
0.96
1.00
86 88 90 92 94 96 98 00 02 04 06 08
UK GDP annual grow th rateSignalNoise (rhs, 1=fully heterog. expect.)
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3. Real Time Data
When comparing econometric models and survey expectations, the former should be estimated in real time (and known by the representative agent: VAR before 1980?)
Why? Because otherwise one is assuming that representative agents use information which will be available only in future dates or that they have remarkably good foresight about data revisions
Trivial? Not so much: attention to actually available data is becoming widespread in the literature only recently (Croushore, 2010). As for the techniques, sometimes laypeople are asked to act as leading econometricians.
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3.1 BoE Real Time Data Set
Real GDP: the first disposable vintage (released in 1976Q1)
covers the period 1955Q1-1975Q4,the second was published a quarter later and covers the
period 1955Q1-1976Q1... the last release I use here covers the period 1955Q1-
2009Q1 Prices (GDP and Private Consumption Deflators): the first release includes data from 1970Q1 to 1989Q4
(released in Jan. 1990)… the last 1970Q1 to 2009Q1 Interest rate (3M Treasury Bill Rate):no data revision, available since 1957Q1
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3.2 The Competing Models
All models estimated recursively, AR and VAR models via rolling regressions, too
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3.3 Real-Time Estimation
I sequentially estimate the mentioned models using real time data:
Example:
in 1976Q1 (=t+1) the very first yt time series, running from 1956Q1
to 1975Q4 (=t), is made available. The 1st four-steps-ahead prediction refers
to 1976Q4 (=t+4). To compare this with its realization we have to wait
until 1977Q1 (=t+5), when the actual data for 1976Q4 is eventually released.
According to survey and hard data availability, • Univariate models generate 97 recursive forecasts, from 85Q1 to 09Q1• VAR models produce 74 recursive forecasts, from 90Q4 to 09Q1
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3.3a Real-Time Estimation
AE model. Each quarter grid search over all (0,1], with step size 0.04, choosing the value of gamma that minimizes the squared forecasting errors.
Rolling windows estimation:• Minimum window size = 32 quarters;• Max window size = 56 quarters.
So, to find the optimal (MSE-minimizing) window size, I perform 24 separate rolling regressions for each (non naïve) model.
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3.4 Real-Time Forecasting Metric
To mimic the forecasting exercise elicited in the surveys, I forecast “the next twelve months”, computing the quarterly squared errors as follows:
MSEt+5= (t+5yt+4 – t+1yet+4)2
where:
yt = (GDPt-GDPt-4)/GDPt-4
t+1yet+4 = Expected value of y in t+4 based on the vintage released in t+1
t+5yt+4 = Actual value of y in t+4 as reported by the vintage released in t+5
Due to data availability, the first useful squared error is
MSE85:Q1 for univariate models
MSE90:Q1 for multivariate models
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3.5 Real-Time Econometric Models Forecasting Ability
Model 85Q1-89Q4 90Q1-96Q2 96Q3-02Q4 03Q1-09Q1 90Q1-09Q1
RW 3.73 5.34 1.73 4.31 3.8
AE 1.17 2.49 0.42 3.09 2.01
AR1 1.98 5.11 0.98 3.72 3.27
AR1 rolling 1.8 3.52 0.9 3.71 2.73
VARPC1 (y,) NA 6.64 1.45 4.24 4.11
VARPC1 rolling NA 4.29 1.27 3.79 3.12
VARPC2 (y,) NA 7.07 1.66 4.56 4.43
VARPC2 rolling NA 3.71 1.34 3.74 2.94
VAR1 (y,, r) NA 6.97 3.16 5.82 5.32
VAR1 rolling NA 4.1 1.01 3.12 2.75
VAR2 (y,, r) NA 6.52 3.18 5.98 5.24
VAR2 rolling NA 3.45 0.95 3.48 2.64
Sample averages of the MSE of the corresponding models
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Naive Expectations Forecasting Accuracy (MSE) as a Proxy of the Great Moderation
0
2
4
6
8
10
12
86 88 90 92 94 96 98 00 02 04 06 08
MSE_RWMSE_AE
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3.6 Relative Forecasting Ability wrt RW
t-stat of the constant term in the “(MSE_J-MSE_RW)=const” regression. When a curve is below the -1.69 horizontal line (indicating the 5% p-value), then the corresponding model “J” dominates the benchmark.
-4
-3
-2
-1
94 96 98 00 02 04 06 08
AE
-2
-1
0
1
2
94 96 98 00 02 04 06 08
AR1
-2
-1
0
1
2
94 96 98 00 02 04 06 08
AR1 rolling
-2
-1
0
1
2
94 96 98 00 02 04 06 08
VARPC1
-4
-3
-2
-1
0
1
94 96 98 00 02 04 06 08
VARPC1 rolling
-2
-1
0
1
2
94 96 98 00 02 04 06 08
VARPC2
-4
-3
-2
-1
0
1
94 96 98 00 02 04 06 08
VARPC2 rolling
-2-101234
94 96 98 00 02 04 06 08
VAR1
-4
-3
-2
-1
0
1
94 96 98 00 02 04 06 08
VAR1 rolling
-2-101234
94 96 98 00 02 04 06 08
VAR2
-4
-3
-2
-1
0
1
94 96 98 00 02 04 06 08
VAR2 rolling
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3.6a Relative Forecasting Ability wrt AE
-2
0
2
4
6
94 96 98 00 02 04 06 08
AR1
-2-101234
94 96 98 00 02 04 06 08
AR1 rolling
-2-101234
94 96 98 00 02 04 06 08
VARPC1
-2
0
2
4
6
94 96 98 00 02 04 06 08
VARPC1 rolling
-2-101234
94 96 98 00 02 04 06 08
VARPC2
-2-101234
94 96 98 00 02 04 06 08
VARPC2 rolling
-2-101234
94 96 98 00 02 04 06 08
VAR1
-2
-1
0
1
2
3
94 96 98 00 02 04 06 08
VAR1 rolling
-2-101234
94 96 98 00 02 04 06 08
VAR2
-2
-1
0
1
2
3
94 96 98 00 02 04 06 08
VAR2 rolling
t-stat of the constant term in the “(MSE_J-MSE_AE)=const” regression. When a curve is below the -1.69 horizontal line (indicating the 5% p-value), then the corresponding model J dominates the benchmark.
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01
23
45
67
89
1011
120
12
34
56
78
910
1112
01
23
45
67
89
1011
120
12
34
56
78
910
1112
01
23
45
67
89
1011
12-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
IQV CP3 CP BAL3 BAL
| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
i =
______________________________________________________________________________________________________________________________
01
23
45
67
8910
1112
01
23
45
67
8910
1112
01
23
45
67
8910
1112
01
23
45
67
89
1011
120
12
34
56
78
910
1112
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
IQV
| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
CP3 CP BAL3BAL
i =
________________________________________________________________________________________________________________________________
Upper Panel: correlation(SNRt-i;MSE_AEt); Lower Panel: correlation(SNRt;MSE_AEt-i)
i=0,…,12. NB: Correlations within (-0.2;+0,2) are statistically zero.
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4. Where Do We Stand?
So far, we have:
• Twelve time series made up by quarterly MSE (85/90Q1-09Q1) pointing out that the AE model outperforms all the others all the times. Despite of that:
• Five quarterly signal-to-noise ratios (85Q1-09Q1) point out that great variety in expectations exists and persists. Then:
• SNR and MSE seems to co-move according to SNR => MSE. This calls for more formal tests.
Specifically, I estimate a battery of bivariate VAR made up by one SNR and one MSE (stemming from the best model) in order to perform Granger, FE variance decomposition and Geweke tests
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4.1 Granger Causality
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4.2 No Instantaneous Feedback
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5 Comments on Results
Granger-causality, Geweke’s instantaneous feedback and VD tests:
• Past, present and future values of MSE are not a determinant of the dispersion across agents' expectations. Instead,
• Divergent expectations significantly affect the forecasting accuracy of optimal econometric models. Then, interpreting the MSE as a proxy of volatility,
• Disagreement across laypeople’s expectations Granger-causes macroeconomic uncertainty, but not vice versa.
These outcomes are in line with the literature on the extra information content of the surveys, and contrast with some of the assumptions behind i) the adaptive learning, ii) the predictor choice, and iii) the epidemiological frameworks.
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5a. Comments on Results
Negative correlations A more perturbed signal coming from the surveys leads to: i) higher model-based MSE; ii) greater macroeconomic uncertainty
No model uncertainty, but high and persistent disagreementEvidence strongly indicates that a relatively simple AE predictor outperforms all the other proposed models all the time.Evidence strongly indicates that laypeople expectations are persistently heterogeneous.
Results are robust to several SNR and models, including univariate and multivariate models even estimated via optimal-size rolling windows.
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6 Concluding Remarks
Should heterogeneity depend on model uncertainty only, UK citizens’ expectations should likely converge
Should lay consumers’ expectations be best-model-based, then SNRi) should not significantly help predict optimal model-based MSE and ii) should not follow univariate processes wrt past information about MSE
Since data show opposite findings, then there must be some additional explanation behind the formation of disparate expectations
The identification of these disagreement-widening factors is in my research agenda
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THANK YOU!THANK YOU!