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Bounded rationality and heterogeneous expectations: Euler versus anticipated-utility approach

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Abstract

By using Bayesian techniques, our paper investigates behavioral New-Keynesian DSGE models derived under two parsimonious alternatives to introduce heterogeneous expectations: the Euler equation and the anticipated-utility approach. First, we explore the relation between the expectation formation processes and the model determinacy for a broad range of parameterizations by using global sensitivity analysis and Monte Carlo filtering. Second, we perform model comparison to assess how much the two alternatives are consistent with macro and expectation survey data. Our main results are twofold: (1) model determinacy is strongly undermined by the presence of boundedly rational agents; (2) a behavioral model based on Euler equation approach fits the data decisively better than one based on anticipated utility.

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Notes

  1. We refer to Eusepi and Preston (2018) and Hommes and LeBaron (2018) for details.

  2. This robustness exercise to which we refer as mixed models, is in line with Evans et al. (2019) who, contributing to the learning literature, test through laboratory experiments the consequences, in terms of convergence to the rational expectation equilibrium, of the coexistence of both types of forecasters.

  3. Similar attempts of examining the importance of the forecasting horizon are discussed in Branch et al. (2013), Branch and McGough (2016) and Woodford (2018).

  4. Mankiw et al. (2004) is the main reference. Early studies are Roberts (1997) and Campbell and Mankiw (1989). Similar results are also obtained by Carroll (2003), Branch (2004), Andolfatto et al. (2008), Pfajfar and Santoro (2010), Andrade and Le Bihan (2013), Coibion and Gorodnichenko (2015), Dovern (2015) and Dräger et al. (2016).

  5. See Hommes et al. (2005), Adam (2007), Hommes (2011) and Evans et al. (2019).

  6. It should be noted that both deal with an aggregation issue among agents, which however in larger models (e.g., medium-scale) could be more complex and its solution less robust than the assumptions imposed to solve it.

  7. See Di Bartolomeo et al. (2016), Di Bartolomeo et al. (2019)  and Hommes and LeBaron (2018, Chapter 1, 2.38) for a discussion on assuming constant beliefs.

  8. The assumption does not affect the empirical estimations, but it seems the most reasonable.

  9. A risk sharing mechanism is introduced to insure against the Calvo price adjustment. We refer to Branch and McGough (2009) and Massaro (2013) for details.

  10. Note that we have considered the market clearing condition: \(y_{t}=c_{t}\).

  11. As discussed later, we also test the robustness of our result to alternative specifications of monetary policy.

  12. Branch and McGough (2009) and Massaro (2013) extended these approaches to heterogeneous expectations. The underlying ideas are due to Preston (2005) and Evans and Honkapohja (2006).

  13. A full derivation is provided by Massaro (2013) or Beqiraj et al. (2017).

  14. The rationale for assuming a fixed \(\alpha\) also lies in the general aim of evaluating the consistency to the data of the two mentioned EE and AU approaches, as theoretically derived by Branch and McGough (2009) and Massaro (2013), respectively.

  15. See Hommes and LeBaron (2018, Chapter 1, 2.38) for a general discussion on assuming a constant fraction of rational agents. For time varying estimations, see, e.g., Milani (2006, 2011), who focuses on homogeneous agents with learning.

  16. Some minimal restrictions to the heuristics used by the agents are imposed to aggregate (Branch and McGough 2009).

  17. See Hommes and LeBaron (2018, Chapter 1, 2.38).

  18. The start of our sample is selected to coincide with the Great Moderation while the end is chosen in order to avoid dealing with the zero-lower bound on nominal interest rate.

  19. See Milani (2007) and Del Negro and Eusepi (2011).

  20. The need of adding a measurement error to the inflation arises mainly for two reasons. First, its introduction helps the inversion of the Hessian matrix computed at the posterior mode. Second, it improves the model fit, in particular by looking at the sign of the cross-correlation between inflation and output.

  21. Technical issues deriving from misspecification are widely discussed in Lubik and Schorfheide (2006) and Fernández-Villaverde (2010).

  22. However, to initialize the priors and to facilitate the estimation, we preliminarly explored the parameter space by a Monte Carlo Filtering (MCF) technique. The analysis was performed using the Global Sensitivity Analysis (GSA). Details are reported in the Appendix.

  23. In our estimation \(\alpha\) is fixed. However, we also estimate a version of our models where \(\alpha\) is allowed to be time varying, i.e., by assuming that \(\alpha _{t}\) follows an AR(1) stationary process with non-zero mean. Parameters estimate and likelihood comparison are equal to the ones reported along this next section; modeling \(\alpha\) as a time varying parameter has negligible effects on the model fit. A different empirical strategy in estimating \(\alpha _{t}\) as a time varying parameter is considered in Cornea-Madeira et al. (2017).

  24. We check the correct identification of the subset of estimated parameters implementing the identification condition developed by Iskrev (2010a, b). For a review of identification issues arising in DSGE models, see Canova and Sala (2009).

  25. It is worth noting that identifying the determinacy region of the model is also a fundamental preliminary step in a Bayesian approach. It allows to initialize the estimation within the portion of the acceptable domain of model coefficients, excluding indeterminacy or instability.

  26. This analysis is performed using the Global Sensitivity Analysis (GSA) toolbox for Dynare.

  27. We used Dynare MatLab routines to simulate and estimate the models (see Adjemian et al. 2011).

  28. For an exhaustive analysis of Bayesian estimation methods, see Geweke (1999), An and Schorfheide (2007), Kriwoluzky and Herbst (2017) or Fernández-Villaverde (2010).

  29. For a similar approach, see, e.g., Rabanal and Rubio-Ramirez (2005), Riggi and Tancioni (2010), and Di Bartolomeo and Di Pietro (2017).

  30. Jeffreys (1961) developed a scale to evaluate the Bayes factor indication. Odds ranging from 1:1 to 3:1 give “very slight evidence”, odds from 3:1 to 10:1 are “substantial”, odds from 10:1 to 100:1 give “strong to very strong evidence”, and odds greater than 100:1 are “decisive evidence”.

  31. Estimates of the standard New Keynesian model are available upon request.

  32. Results are available upon request.

  33. It is worth noting that mixed models need further technical clarifications regarding the underlying assumptions on heterogeneous expectations and the structure of higher-order beliefs. See the longer working paper version of this article for details, i.e., Beqiraj et al. (2018).

  34. Other results are available upon request. Indeed, we do not consider (and estimate) the case where firms use EE heuristics and households have long-horizon beliefs since it never fulfills the determinacy region.

  35. Results of the GSA for the mixed model are available upon request.

  36. Previously, we had not considered the smoothing parameters to strictly follow the specifications proposed by Branch and McGough (2009) and Massaro (2013), who inspect the stability properties of the EE and AU models without considering smoothing in the Taylor rule.

  37. Results are available upon request.

  38. Details on estimates are available upon request.

  39. As t increases, the log-marginal likelihood of this model specification becomes similar to that associated with an AU model.

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Acknowledgements

The authors are grateful to the Journal Editor, Giacomo Corneo, two anonymous referees, Boragan Aruoba, Pok-sang Lam, Raoul Minetti, Willi Semmler, Patrizio Tirelli, and seminar participants at ECB, JRC, MMF and Rome for useful comments. They also acknowledge financial support by Sapienza University of Rome. The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The authors are solely responsible for the content of the paper. The views expressed are purely those of the authors and may not in any circumstances be regarded as stating an official position of the European Commission or the Italian Ministry of Economy and Finance.

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Authors and Affiliations

  1. Department of Economics and Law, Sapienza University of Rome, Rome, Italy

    Elton Beqiraj, Giovanni Di Bartolomeo, Marco Di Pietro & Carolina Serpieri

  2. Senior Advisory Board, Department of the Treasury, Ministry of Economy and Finance, Rome, Italy

    Giovanni Di Bartolomeo

  3. Joint Research Centre (JRC), European Commission, Ispra, Italy

    Carolina Serpieri

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  1. Elton Beqiraj
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  2. Giovanni Di Bartolomeo
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Correspondence to Giovanni Di Bartolomeo.

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Beqiraj, E., Di Bartolomeo, G., Di Pietro, M. et al. Bounded rationality and heterogeneous expectations: Euler versus anticipated-utility approach. J Econ 130, 249–273 (2020). https://doi.org/10.1007/s00712-020-00697-6

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