On the initialization of adaptive learning in macroeconomic models

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in ETH Zurich AbstractWe review and evaluate methods previously adopted in the applied literature of adaptive learning in order to initialize agents' beliefs. Previous methods are classified into three broad classes: equilibrium-related, training sample-based, and estimation-based. We conduct several simulations comparing the accuracy of the initial estimates provided by these methods and how they affect the accuracy of other estimated model parameters. We find evidence against their joint estimation with standard moment conditions: as the accuracy of estimated initials tends to deteriorate with the sample size, spillover effects also deteriorate the accuracy of the estimates of the model's structural parameters. We show how this problem can be attenuated by penalizing the variance of estimation errors. Even so, the joint estimation of learning initials with other model parameters is still subject to severe distortions in small samples. We find that equilibrium-related and training sample-based initials are less prone to these issues. We also demonstrate the empirical relevance of our results by estimating a New Keynesian Phillips curve with learning, where we find that our estimation approach provides robustness to the initialization of learning. That allows us to conclude that under adaptive learning the degree of price stickiness is lower compared to inferences under rational expectations, whereas the fraction of backward looking price setters increases.

Empirical calibration of adaptive learning

“…Here we adopt a training sample-based method, where an initial portion of the available data is set aside to the application of the algorithm departing from diffuse initials, i.e.,θ 0 = 0 np×1 and R 0 = 0 np×np . Berardi and Galimberti (2015) recently surveyed different methods adopted in the literature and reported evidence in favor of the convergence properties provided by the use of a training sample, in comparison with other more model-dependent initials such as equilibrium-related and estimation-based methods. Also in line with the previous applied literature, we use 75 observations for the training sample, which corresponds to the period from 1947q2 to 1965q4.…”

Smoothing-Based Initialization for Learning-to-Forecast Algorithms

“…In order to benchmark our evaluation of the smoothing-based initialization method, we consider two alternatives commonly found in the applied literature [Carceles-Poveda and Giannitsarou (2007), Berardi and Galimberti (2017), for comprehensive reviews], both based on training samples. The first is inspired by the engineering literature [e.g., see Ljung and Soderstrom (1983, pp.…”

“…An empirical analysis of initializations is also provided by Slobodyan and Wouters (2012), though focusing on their joint estimation with other model parameters. 2 We also discuss issues with the joint estimation of initials in a companion paper: see Berardi and Galimberti (2016) and references therein. 3 We have also carried out a sensitivity analysis with artificial series mimicking output growth.…”

Robust Control Design for an Uncertain Macroeconomic Dynamical System with Unknown Characteristics and Inequality Control Constraint

“…Hudgins and Na explored robust designs for an applied macroeconomic discrete-time LQ tracking model with perfect state measurements [9]. Berardi and Galimberti provided a critical review on several methods previously proposed in the literature of learning and expectations in macroeconomics in order to initialize its learning algorithms [10]. Jajarmi et al designed a linear-state feedback controller together with an adaptive control technique to control the hyperchaos and realize the synchronization of a fractional economic model [11].…”