Handbook of Economic Expectations

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Handbook of Economic Expectations discusses the state-of-the-art in the collection, study and use of expectations data in economics, including the modelling of expectations formation and updating, as well as open questions and directions for future research. The book spans a broad range of fields, approaches and applications using data on subjective expectations that allows us to make progress on fundamental questions around the formation and updating of expectations by economic agents and their information sets. The information included will help us study heterogeneity and potential biases in expectations and analyze impacts on behavior and decision-making under uncertainty.

Author(s): Ruediger Bachmann, Giorgio Topa, Wilbert van der Klaauw
Publisher: Academic Press
Year: 2022

Language: English
Pages: 873
City: London

Front Cover
Handbook of Economic Expectations
Copyright
Contents
Contributors
Preface
Part 1 Expectation elicitation
1 Household surveys and probabilistic questions
1.1 History and motivation for measuring household economic expectations
1.1.1 Why economists started to elicit qualitative subjective expectations
1.1.2 Why economists started to elicit subjective probabilities
1.1.3 Widespread adoption of subjective probability elicitation
1.1.4 Main takeaway
1.2 Methodological considerations when developing surveys of expectations
1.2.1 Survey pretesting
1.2.1.1 Randomized survey-based experiments
1.2.1.2 Cognitive interviews with follow-up surveys
1.2.1.3 Example
1.2.2 Panel vs. cross-sectional surveys
1.2.3 Main takeaway
1.3 Insights and methodological advances
1.3.1 Point forecasts versus probabilistic expectations
1.3.2 Question wording and framing of point forecasts
1.3.3 Introductory framing for probabilistic expectations questions
1.3.4 Rounding, bunching and ambiguity
1.3.5 Use of visual response scales
1.3.6 Elicitation of probability distributions
1.3.6.1 Elicitation of probability density functions
1.3.6.2 Elicitation of cumulative distribution functions
1.3.7 Fitting distributions and measuring uncertainty
1.3.8 Density-based forecasts versus point forecasts
1.3.9 Individual differences in expectations and uncertainty
1.3.10 Use of expectations data in economic analysis
1.3.11 Main takeaway
1.4 Concluding remarks
References
2 Firm surveys
2.1 Introduction
2.2 Quantification of qualitative survey answers
2.3 Historic business expectation surveys in the U.S.
2.3.1 Surveys of the general business outlook
2.3.2 Business investment surveys
2.3.3 Findings of the early literature
2.4 Ongoing business expectation surveys in the U.S.
2.4.1 Manufacturing Business Outlook Survey
2.4.2 CFO Survey
2.4.3 Survey of Business Uncertainty
2.4.4 Business Inflation Expectations Survey
2.4.5 ManpowerGroup Employment Outlook Survey
2.4.6 Management and Organizational Practices Survey
2.4.7 Small Business Economic Trends Survey
2.5 Firm surveys in Europe
2.5.1 Germany: ifo surveys
2.5.1.1 The history of the ifo surveys
2.5.1.2 The ifo Konjunkturtest today
2.5.1.3 The ifo Investment Survey today
2.5.1.4 Quantitative answer scales
2.5.2 France: INSEE survey
2.5.3 Italy: from ISCO to Istat
2.5.4 UK: CBI Industrial Trends Survey
2.5.5 European harmonization of business surveys
2.6 Firm surveys in Japan: the TANKAN
2.7 International cooperation
2.7.1 Centre for International Research on Economic Tendency Surveys
2.7.2 OECD and UN
2.8 Conclusion
References
3 Surveys of professionals,
3.1 Surveys of professional forecasters
3.1.1 Interest and attractiveness of eliciting professional forecasters' expectations
3.1.2 Surveys of professional forecasters
3.1.3 Nature of survey expectations and concepts
3.2 Point and density forecasts: data features, measures, and properties
3.2.1 Background
3.2.2 Point forecasts
3.2.3 Density forecasts
3.2.4 A closer look at disagreement and uncertainty
3.3 Evaluation of forecaster performance
3.3.1 Data revisions
3.3.2 Rationality/efficiency of point forecasts
3.3.3 Scoring rules
3.3.4 Using the probability integral transform to assess density forecast coverage
3.3.5 Balanced vs. unbalanced panels
3.3.6 Are some forecasters better than others?
3.3.7 Professionals versus models (and other sources of forecasts)
3.4 Consistency of point and density forecasts
3.4.1 Calculating bounds on the central moments of histograms
3.4.2 Nature of loss functions – symmetric vs. asymmetric
3.4.3 Rounding of point and density forecasts
3.5 Conclusion
3.A Appendix table: surveys of professional forecasters
References
4 Survey experiments on economic expectations
4.1 Introduction
4.2 Why (field) experiments on expectations?
4.2.1 Understanding decision-making
4.2.2 Understanding expectation formation
4.3 Information provision experiments
4.3.1 Design basics
4.3.2 Expectations and behavior
4.3.3 Examples
4.4 Methodological issues
4.4.1 Within-subject or between-subject design?
4.4.2 Eliciting perceptions about the provided information
4.4.3 Eliciting higher-order moments
4.4.4 Information content and presentation
4.4.5 Where and how to run these surveys?
4.5 Extensions and alternative approaches
4.5.1 Moving beyond exogenously provided information
4.5.2 Alternatives to information provision experiments
4.6 Directions for future work
References
Part 2 Expectations as data
5 What do the data tell us about inflation expectations?
5.1 Introduction
5.2 Data sources
5.2.1 Michigan Survey of Consumers
5.2.2 New York Fed Survey of Consumer Expectations
5.2.3 European Commission Consumer Survey
5.2.4 Ad-hoc surveys
5.2.5 Comparing elicited inflation expectations across surveys
5.3 Stylized facts
5.3.1 Time-series facts
5.3.2 Cross-sectional facts
5.3.3 Term-structure facts
5.3.4 Households versus professional forecasters
5.4 Determinants of inflation expectations
5.4.1 Exposure to price signals
5.4.2 The role of the lifetime experiences and neuroplasticity
5.4.3 The role of cognition and human frictions
5.4.4 The role of the media and communication
5.5 Inflation expectations and economic choices
5.5.1 Intertemporal consumption and saving choices
5.5.2 Financing current consumption: mortgages and borrowing
5.5.3 Investment and savings decisions
5.6 Conclusion and outlook
References
6 Housing market expectations
6.1 Measuring expectations
6.1.1 Surveys about housing market expectations
6.1.2 Nonsurvey measures of housing market expectations
6.2 Determinants of expectations and expectations heterogeneity
6.2.1 Extrapolation
6.2.2 Personal experiences
6.2.3 Social interactions
6.2.4 Ownership status
6.2.5 Determinants of higher moments of belief distribution
6.3 The effects of expectations on individual housing market behavior
6.3.1 Homeownership decisions
6.3.2 Mortgage choice
6.4 House price expectations and aggregate economic outcomes
6.4.1 The housing boom of the late 1970s
6.4.2 The housing boom of the early 2000s
6.5 Conclusion
References
7 Expectations in education
7.1 Introduction
7.2 Survey expectations about monetary outcomes of schooling
7.2.1 Are elicited earnings expectations meaningful?
7.2.2 Patterns and heterogeneity of earnings expectations
7.2.3 Perceived monetary returns to schooling
7.2.4 Perceived earnings risk
7.2.5 Beliefs about population earnings
7.2.6 Are elicited earnings expectations rational?
7.2.7 Other labor market outcomes
7.2.8 Monetary costs
7.3 Survey expectations about nonmonetary outcomes of schooling
7.3.1 Are elicited probabilities meaningful? Rational?
7.3.2 Academic performance, study effort, and ability
7.3.3 ``Enjoying'' education and other nonmonetary outcomes
7.3.4 Nonmonetary outcomes in the labor and marriage markets
7.3.5 Attainment and dropout
7.3.6 Education plans
7.3.7 Parental approval and parental beliefs
7.4 Analysis of schooling decisions with survey expectations
7.4.1 Monetary returns and risks
7.4.2 Monetary costs
7.4.3 Nonmonetary factors: ability, taste, and beyond
7.4.4 Parents and family decision-making
7.4.5 Peer effects
7.4.6 Centralized school choice
7.5 Analysis of expectation formation and learning
7.5.1 Earnings
7.5.2 Academic performance
7.6 Conclusion
References
8 Mortality and health expectations
8.1 Introduction
8.2 Methods
8.2.1 Measurement error, focal answers, and rounding
8.2.2 Biases in small and large probabilities
8.2.3 Jointly modeling objective and subjective expectations
8.3 Survival expectations
8.3.1 Properties
8.3.2 Flatness bias in survival expectations
8.3.3 Determinants of survival expectations
8.3.3.1 Health and health behaviors
8.3.3.2 The vital status of parents and other relatives
8.3.3.3 Expectations of minority groups
8.3.4 The effect of survival expectations on economic and health outcomes
8.4 Health expectations
8.4.1 Moving to a nursing home
8.4.2 Expectations about medical expenditures
8.4.3 Substance use
8.4.4 Expectations about cognitive decline and dementia
8.4.5 Other health expectations
8.5 Conclusion
8.A Estimation of a rounding model of survival expectations
8.B Additional tables
References
9 Expectations in development economics
9.1 Introduction
9.2 Measuring probabilistic expectations in surveys in developing countries
9.2.1 Percent chance format
9.2.2 Physical objects as visual aid
9.2.3 Interactive touchscreen
9.2.4 Proportion of people (like you)
9.2.5 Phone interviews
9.2.6 Eliciting subjective distribution of beliefs
9.2.7 Point expectations
9.2.8 Piloting, interviewers' training and other considerations
9.3 Patterns of answers
9.3.1 Respect of basic properties of probabilities
9.3.2 Expectations and respondents' characteristics
9.3.3 Accuracy of elicited expectations
9.3.4 Heterogeneity in beliefs
9.4 Applications
9.4.1 Health
9.4.2 Education
9.4.3 Parental investment in children
9.4.4 Migration, income, and the labor market
9.4.5 Agricultural inputs and outputs
9.4.6 Conflicts and natural disasters
9.4.7 Information experiments
9.5 Datasets
9.6 Conclusions
References
10 Retirement expectations
10.1 Introduction
10.2 Theoretical framework
10.3 Measuring retirement age expectations
10.4 Eliciting a planned or expected retirement age
10.5 Subjective retirement probability
10.6 Predicting retirement: subjective probability predictions and predictive analytics
10.7 Subjective work probability predictions among non-full-time worker respondents
10.8 Research on the quality of retirement age expectations
10.9 Potential uses of retirement age expectations
10.10 Research with retirement age expectations as the left-hand-side variable
10.11 Research with retirement age expectations as the right-hand-side variable
10.12 Using conditional subjective work probability predictions to estimate effects on retirement
10.12.1 Conditioning versus subjectivity in general
10.13 Conclusions
References
11 The macroeconomic expectations of firms
11.1 Introduction
11.2 Surveys of firms' macroeconomic expectations
11.3 Properties of firms' macroeconomic expectations
11.3.1 Mean inflation forecasts
11.3.2 Disagreement about inflation
11.3.3 Short and long-run expectations
11.3.4 Inattention to inflation and monetary policy
11.3.5 The joint formation of beliefs
11.4 Do firms' macroeconomic expectations matter?
11.4.1 Firms' inflation expectations and the expectations-augmented Phillips curve
11.4.2 Randomized control trials
11.5 Conclusion
References
12 Firm expectations about production and prices: facts, determinants, and effects
12.1 Introduction
12.2 Surveying firm expectations
12.2.1 Background
12.2.2 Example: the ifo Business Expectations Panel
12.3 Stylized facts
12.4 Expectation formation
12.4.1 Determinants of expectations
12.4.1.1 Firm expectations
12.4.1.2 Firm uncertainty
12.4.2 Over- and underreaction to news
12.5 Firm expectations and firm decisions
12.5.1 The effect of firm expectations
12.5.2 Firm-level uncertainty and firm decisions
12.6 Conclusion
References
13 Expectations of financial market participants
13.1 Introduction
13.2 Distinctions across surveys
13.3 Examples of surveys of financial market participants
13.3.1 Survey of Primary Dealers and Survey of Market Participants
13.3.2 Blue Chip Survey
13.3.2.1 Blue Chip Economic Indicators
13.3.2.2 Blue Chip Financial Forecasts
13.3.3 Consensus Economics
13.3.4 Surveys administered in other jurisdictions
13.4 Some advantages and uses of surveys
13.4.1 Risk premiums
13.4.2 Types of questions that are best answered by surveys
13.4.3 Surveys as model inputs
13.5 Drawbacks of surveys
13.5.1 Distributional inconsistencies
13.5.2 Sample
13.5.3 Rationality and rigidities
13.5.4 Forecast/revision smoothing
13.6 Conclusion
References
Part 3 Expectations and economic theory
14 Measuring market expectations
14.1 Introduction
14.2 Market expectations and the price of risk
14.2.1 Testable implications
14.2.2 Some asset pricing basics
14.2.3 Modeling risk premia
14.2.3.1 Return regressions
14.2.3.2 Gaussian affine term structure models
14.2.3.3 An integrative view
14.3 Extracting measures of market expectations from asset prices
14.3.1 A general approach to identifying market expectations
14.3.2 An illustration based on the oil market
14.4 Existing empirical evidence for selected markets
14.4.1 Monetary policy expectations
14.4.2 Inflation expectations
14.5 Economic applications of market-based expectation measures
14.5.1 Evaluation of economic models
14.5.2 Deriving shock measures
14.5.3 Policy analysis
14.5.4 Implications for out-of-sample forecasts
14.6 Conclusions
References
15 Inference on probabilistic surveys in macroeconomics with an application to the evolution of uncertainty in the survey of professional forecasters during the COVID pandemic
15.1 Introduction
15.2 Inference on probabilistic surveys
15.2.1 The inference problem
15.2.2 Current approaches
15.2.3 A Bayesian nonparametric alternative
A parametric probabilistic model
A Bayesian nonparametric approach
Some asymptotic properties
Finite sample properties and caveats
A comparison with existing approaches
15.3 Challenges in measuring uncertainty
15.4 Heterogeneity in density forecasts
15.5 Pooling and consensus forecasts
15.6 The evolution of professional forecasters' density forecasts during the COVID pandemic
15.6.1 GDP growth
15.6.2 Inflation
15.7 Conclusions
References
16 Expectations data in asset pricing
16.1 Introduction
16.2 A general asset pricing framework
16.2.1 Rational expectations
16.2.2 Subjective beliefs in a single-period setting
16.2.2.1 Homogeneous subjective beliefs
16.2.2.2 Heterogeneous subjective beliefs
16.2.3 Subjective beliefs in a multiperiod setting
16.2.3.1 Common knowledge
16.2.3.2 Lack of common knowledge
16.3 Empirical dynamics of investor expectations
16.3.1 Return and price expectations
16.3.2 Cash flow expectations
16.3.3 Interest rate expectations
16.3.4 Subjective risk perceptions
16.4 Mapping survey expectations into asset pricing models
16.4.1 Are survey expectations risk adjusted?
16.4.2 Measurement error and cognitive uncertainty
16.4.3 Heterogeneity and beliefs aggregation
16.5 Models of expectations formation
16.5.1 Learning about payouts
16.5.2 Learning about prices
16.5.3 Learning biases
16.5.4 Heterogeneity
16.6 Future research directions
16.A Data sources for investor expectations
References
17 The term structure of expectations
17.1 Introduction
17.2 Joint behavior of short- and long-term forecasts
17.2.1 Motivation: a simple model of long-term drift
17.2.1.1 Modeling a drift in the long-run mean
17.2.2 A model to fit the term structure of expectations
17.2.2.1 Baseline multivariate model
17.2.2.2 Data overview
17.2.3 Mapping the model to survey forecasts
17.2.4 Discussion
17.2.5 Results
17.2.5.1 Model fit
Beyond consensus expectations
17.2.5.2 Evolution of the term structure of expectations
17.3 Expectations and the term structure of interest rates
17.3.1 Decomposing the term structure of interest rates
17.4 The term structure of expectations in structural models
17.4.1 A general structural model
17.4.2 The New Keynesian model
17.4.3 Implications for monetary and fiscal policy
17.5 Conclusions and further directions
References
18 Expectational data in DSGE models
18.1 Introduction
18.2 Expectational data in rational expectations DSGE models
18.2.1 Do DSGE models generate expectations that fit observed data?
18.2.2 Survey expectations to evaluate alternative frictions
18.2.3 Survey expectations & news shocks
18.2.4 Survey expectations & sunspots
18.2.5 Misspecification of expectations
18.3 Expectational data and deviations from rational expectations
18.3.1 Adaptive learning
18.3.2 Survey expectations and sentiment
18.3.3 First moment vs. second moment shocks
18.4 Heterogeneity in survey expectations
18.5 Issues and limitations
18.6 Conclusions and future directions
References
19 Expectations and incomplete markets
19.1 Introduction
19.2 The general setup
19.3 News shocks
19.3.1 Analytical insights
19.3.1.1 Productivity news
19.3.1.2 Interest rate news
19.3.2 Quantitative analysis
19.3.2.1 Technology news
19.3.2.2 Monetary policy news
19.4 Channels underlying savings behavior
19.5 Noise shocks
19.5.1 Model
19.5.2 Estimating the parameters
19.5.2.1 Estimating the impact of noise shocks
19.5.2.2 Estimation of structural parameters
19.5.2.3 Calibration and estimation results
19.5.3 Implications
19.6 Sunspots
19.7 Conclusions
19.A Solutions for news shocks
19.B Computing the Jacobians
References
20 Dampening general equilibrium: incomplete information and bounded rationality
20.1 Introduction
20.2 Framework
20.2.1 PE and GE in a nutshell
20.2.2 Micro-foundation: a simplified New-Keynesian model
20.2.3 Full Information Rational Expectations (FIRE)
20.2.4 Beyond FIRE
20.3 Incomplete information
20.3.1 Removing common knowledge by adding idiosyncratic noise
20.3.2 Main lesson: GE attenuation
20.3.3 From rational expectations to higher-order beliefs (HOBs)
20.4 Bounded rationality
20.4.1 Level-k Thinking
20.4.2 Parenthesis: back to higher-order beliefs
20.4.3 Reflective equilibrium and cognitive hierarchy
20.5 Additional variants and dynamic extensions
20.5.1 A bridge: heterogeneous priors, or shallow reasoning
20.5.2 Dynamics I: learning
20.5.3 Dynamics II: forward-looking behavior
20.5.4 Cognitive discounting
20.6 Applications
20.6.1 Forward guidance at the zero lower bound
20.6.2 Fiscal policy
20.6.3 Other applications
20.7 Discussion: similarities, differences, and empirical backdrop
20.7.1 Key differences
20.7.2 Empirical backdrop: underreaction in average vs individual forecasts
20.8 Conclusion
References
21 Expectations data in structural microeconomic models
21.1 Introduction
21.2 A model
21.2.1 Specification
21.2.2 Types of expectations data
21.2.3 Identification and the role of expectations data
21.2.4 Estimation
21.2.4.1 Estimation methods
Maximum likelihood estimation
Method of simulated moments (MSM)
Indirect inference
Non-full solution methods of estimation
21.2.5 Issues particular to structural estimation with expectations data
21.2.5.1 Constructing a model counterpart to expectations data
21.2.5.2 Use of data on choice expectations in maximum likelihood estimation
21.2.5.3 Focal point responses to probabilistic expectation questions
21.3 Literature I: expectations over the states of nature
21.3.1 Allowing for subjective expectations
21.3.2 Modeling subjective expectations
21.4 Literature II: data on choice expectations
21.4.1 Unconditional choice expectations
21.4.2 Conditional choice expectations
21.4.2.1 Stated discrete choice data
21.4.2.2 Probabilistic conditional choice expectations data
21.4.3 Strategic survey questions
21.5 Conclusion
References
22 Expectations data, labor market, and job search
22.1 Introduction
22.2 Measurement
22.2.1 Data sources
22.2.2 Descriptive statistics
22.2.3 Predictive power of elicited beliefs
22.2.4 Measurement issues
22.3 Illustrative framework
22.4 Beliefs and behavior
22.4.1 Structural models with expectations data
22.4.2 Identification and empirical evidence
22.4.2.1 The perceived return to job search
Exogenous variation
Direct elicitations
22.4.2.2 Estimating the effect of beliefs on behavior
22.5 Beliefs and biases
22.5.1 Identification
22.5.2 Empirical evidence
22.5.3 Determinants of biased beliefs
22.5.4 Policy implications
22.6 Beliefs and heterogeneity
22.6.1 Identification
22.6.2 Applications
22.7 Conclusion
References
Part 4 Theories of expectations
23 Bayesian learning
23.1 Introduction
23.2 Mathematical preliminaries
23.2.1 Bayesian updating
23.2.2 The Kalman filter
23.2.3 Learning the distribution of the state
23.2.3.1 Learning the mean
23.2.3.2 Learning the precision
23.2.3.3 Nonparametric learning
23.3 Using signals to understand economic activity
23.3.1 Signal-extraction problems
23.3.1.1 A tracking problem
23.3.1.2 Permanent vs. transitory shocks
Keeping uncertainty alive
23.3.1.3 Aggregate vs. idiosyncratic shocks
23.3.2 Using signals in strategic settings
23.3.2.1 A beauty contest with exogenous signals
Beliefs and equilibrium
Heterogeneous incomplete information
Optimal use of information
Responsiveness to shocks
23.3.2.2 Strategic complementarity and aggregate inertia
23.3.2.3 Strategic substitutability and aggregate volatility
The role of preferences
23.4 Information choice and learning technologies
23.4.1 Sticky information
23.4.1.1 A beauty contest with infrequent information updating
Information dynamics
Equilibrium and optimal choices
23.4.1.2 Applications of sticky information
23.4.2 Rational inattention
23.4.2.1 Measuring information: entropy and mutual information
23.4.2.2 A tracking problem with noisy information acquisition
Tracking multiple states
23.4.2.3 Applications of rational inattention
23.4.2.4 Linear cost of signal precision
23.4.3 Other learning technologies
23.4.4 Information choice as a source of inequality
23.4.5 Learning what others know
23.4.6 Information choice in strategic settings
23.5 Theories of the data economy
23.5.1 Experimentation
23.5.2 Data and growth
23.5.2.1 Data as knowledge
23.5.2.2 Data as information
23.5.3 Data and economic fluctuations
23.6 Conclusion
References
24 Ambiguity
24.1 Introduction
24.2 Static choice under uncertainty
24.2.1 Preferences
24.2.2 Risk vs ambiguity: similarities and differences
24.2.3 Savings and portfolio choice
24.3 Dynamic choice and equilibrium
24.3.1 Asset pricing
24.3.2 Business cycle models with uncertainty shocks
24.4 Quantifying ambiguity using survey data
24.5 Aggregate applications
24.6 Heterogeneity and micro-to-macro applications
24.6.1 Heterogeneous perceptions of uncertainty
24.6.2 Inaction and inertia
24.6.3 Ambiguous information and asymmetric decision rules
24.7 Policy implications
24.7.1 Ambiguous policy objectives
24.7.2 Optimal policy with ambiguity-averse agents
24.8 Concluding remarks
References
25 Epidemiological expectations
25.1 Introduction
25.2 Background and motivation
25.2.1 Expectational heterogeneity
25.2.2 Epidemiological models
25.2.3 Expectational tribes
25.3 What insights can the epidemiological framework offer?
25.3.1 What is an epidemiological framework?
25.3.1.1 Adapting the disease metaphor to expectations
25.3.2 One example
25.4 Literature
25.4.1 Diffusion of technology
25.4.2 Financial markets
25.4.3 Macroeconomic expectations
25.4.3.1 Sticky expectations
25.4.3.2 Sentiment and the business cycle
25.4.3.3 Learning of macroeconomic equilibria
25.4.4 Nonstructural empirical evidence
25.4.4.1 Directly measured social networks
25.4.4.2 Papers using proxies for social connections
25.4.4.3 Public media
25.4.4.4 Epidemiology and ``narrative economics''
25.4.4.5 Social communication in animals
25.4.5 Contagion
25.4.6 Noneconomic applications
25.4.7 Future directions
25.4.7.1 New tests of competing models
25.4.7.2 New kinds of survey data
25.4.7.3 New and big data
25.4.8 Literature summation
25.5 Conclusion
References
Part 5 Open issues
26 Looking ahead to research enhancing measurement of expectations
26.1 Introduction
26.2 Rounding reported probabilities
26.2.1 Inferring rounding from response patterns
26.2.2 Possible reasons for rounding
26.3 Imprecise probabilities
26.3.1 Background
26.3.2 Imprecise probabilities of dementia
26.3.3 Looking ahead
26.4 Studying expectations formation
26.4.1 Microeconomic analysis of expectation formation
26.4.2 Studying expectations formation to inform macro policy analysis
26.4.3 The potential contribution of expectations measurement
26.5 Confounding beliefs and preferences
26.5.1 Evidence in research measuring probabilistic expectations
26.6 Conclusion
References
Index
Back Cover