An approximation of the distribution of learning estimates in macroeconomic models

Galimberti, Jaqueson K.

doi:10.1016/j.jedc.2019.03.003

Cited by 2 publications

(3 citation statements)

References 19 publications

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“…The constant-gain (CG) learning specification was introduced in the applied learning literature by Evans and Honkapohja (1993) and became popular after Sargent (1999) for its improved capability of tracking the evolution of time-varying environments. This specification has also been under the spotlight of the most recent research on the dynamic modelling of expectations for its potential of generating escape dynamics over finite stretches of time (see Williams 2019) and asymptotically stable distributions of beliefs (see Galimberti 2019).…”

Section: Constant-gain Learning and Diffuse Initialsmentioning

confidence: 99%

“…Galimberti 2019). There is less empirical agreement with respect to the slope parameter 𝜆, although a positive value with borderline significance is often reported in the literature (seeMavroeidis, Plagborg-Moeller, and Stock 2014).For each sample I simulate the model for 2000 observations, and then discard the first 1000 observations to remove transient effects from PLM initials.…”

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confidence: 99%

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Initial Beliefs Uncertainty

Galimberti

2023

The B.E. Journal of Macroeconomics

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This paper evaluates how initial beliefs uncertainty can affect data weighting and the estimation of models with adaptive learning. One key finding is that misspecification of initial beliefs uncertainty, particularly with the common approach of artificially inflating initials uncertainty to accelerate convergence of estimates, generates time-varying profiles of weights given to past observations in what should otherwise follow a fixed profile of decaying weights. The effect of this misspecification, denoted as diffuse initials, is shown to distort the estimation and interpretation of learning in finite samples. Simulations of a forward-looking Phillips curve model indicate that (i) diffuse initials lead to downward biased estimates of expectations relevance in the determination of actual inflation, and (ii) these biases spill over to estimates of inflation responsiveness to output gaps. An empirical application with U.S. data shows the relevance of these effects for the determination of expectational stability over decadal subsamples of data. The use of diffuse initials is also found to lead to downward biased estimates of learning gains, both estimated from an aggregate representative model and estimated to match individual expectations from survey expectations data.

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Section: Constant-gain Learning and Diffuse Initialsmentioning

confidence: 99%

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confidence: 99%

Initial Beliefs Uncertainty

Galimberti

2023

The B.E. Journal of Macroeconomics

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“…The constant-gain (CG) learning specification was introduced in the applied learning literature by Evans and Honkapohja (1993) and became popular after Sargent (1999) for its improved capability of tracking the evolution of time-varying environments. This specification has also been under the spotlight of the most recent research on the dynamic modeling of expectations for its potential of generating escape dynamics over finite stretches of time (see Williams, 2019) and asymptotically stable distributions of beliefs (see Galimberti, 2019). Under CG-RLS learning, γ cg t =γ, and the weights are given by…”

Section: Constant-gainmentioning

confidence: 99%

Information Weighting Under Least Squares Learning

Galimberti

2020

SSRN Journal

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This paper evaluates how adaptive learning agents weight different pieces of information when forming expectations with a recursive least squares algorithm. The analysis is based on a renewed and more general non-recursive representation of the learning algorithm, namely, a penalized weighted least squares estimator, where a penalty term accounts for the effects of the learning initials. The paper then draws behavioral implications of alternative specifications of the learning mechanism, such as the cases with decreasing, constant, regime-switching, adaptive, and age-dependent gains, as well as practical recommendations on their computation. One key new finding is that without a proper account for the uncertainty about the learning initial, a constant-gain can generate a timevarying profile of weights given to past observations, particularly distorting the estimation and behavioral interpretation of this mechanism in small samples of data. In fact, simulations and empirical estimation of a Phillips curve model with learning indicate that this particular misspecification of the initials can lead to estimates where inflation rates are less responsive to expectations and output gaps than in reality, or "flatter" Phillips curves.

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An approximation of the distribution of learning estimates in macroeconomic models

Cited by 2 publications

References 19 publications

Initial Beliefs Uncertainty

Initial Beliefs Uncertainty

Information Weighting Under Least Squares Learning

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