Empirical calibration of adaptive learning

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 ZurichAbstract Adaptive learning introduces persistence in the evolution of agents' beliefs over time.For applied purposes this is a convenient feature to help explain why economies present sluggish adjustments towards equilibrium. The pace of learning is directly determined by the gain parameter, which regulates how quickly new information is incorporated into agents' beliefs.We document renewed empirical calibrations of plausible gain values for adaptive learning applications to macroeconomic data. We cover a broad range of model specifications of applied interest. Our analysis also includes innovative approaches to the endogenous determination of time-varying gains in real-time, and a thorough discussion of the different theoretical interpretations of the learning gain. We also evaluate the merits of different approaches to the gain calibration according to their performance in forecasting macroeconomic variables and in matching survey forecasts.Our results indicate a great degree of heterogeneity in the gain calibrations according to the variable forecasted and the lag length of the model specifications. Calibrations to match survey forecasts are found to be lower than those derived according to the forecasting performance, suggesting some degree of bounded rationality in the speed with which agents update their beliefs.

An approximation of the distribution of learning estimates in macroeconomic models

“…Interestingly, we observe that the learning gain is less relevant under the data-based rule: for any value of γ below 2, learnability is determined mainly by the intensity of the policymaker's response to contemporaneous inflation and output gap; also, adjusting the interest rate by more than one-to-one changes in the inflation rate (Taylor principle) guarantees stability for any intensity of response to output gap changes. A different result is obtained under the more realistic expectations-based rule, where learning gains closer to the range of plausible values (between 0.01 and 0.20, see Berardi and Galimberti, 2017) can cause instabilities; that is particularly the case as the policymaker becomes more sensitive to output gap variations, i.e., the upper bound on γ decreases as χ x increases. Although these results are qualitatively consistent with Evans and Honkapohja (2009, p. 151), our approximation results in looser constraints on the learning gain; for example, when χ π = 1.5 those authors calculate that the equilibrium would be unstable under learning for χ x > 1.57 and γ ≥ 0.10, whereas our approximation points to a stability threshold of χ x > 3.13 for a γ ≥ 0.10, or a γ > 0.20 if one fixes χ x = 1.57.…”

“…In that context our analytical expressions can improve the robustness of estimation to learning instabilities by conditioning the learning gain upper bound on the model's structural parameters. Similarly, recent approaches proposing the use of time-varying gains (e.g., Milani, 2014;Berardi and Galimberti, 2017) can benefit with our convergence-based upper bounds on the learning gain.…”

A probabilistic interpretation of the constant gain learning algorithm

“…Using the framework developed above, one can interpret the constant gain coefficients that have been found to fit the data well in empirical macroeconomic studies in terms of the implied probability of changes in the estimated variables. Typical values proposed (estimated or calibrated) in the empirical literature for the constant gain range from close to zero to over 0.2, with most studies suggesting values between 0.01 and 0.1, as reported in Berardi and Galimberti (2017). A larger value of about 0.27 has been documented for example by Benhabib and Dave (2014) in the context of an asset pricing model, while smaller values have been reported by Markiewicz and Pick (2014) using data from professional forecasters, with values as small as 0.001 documented, depending on the specific data and model specification used.…”

“…A growing literature in applied macroeconomics has used CG learning to explain a range of features, from the rise and fall of U.S. inflation in the 70s and 80s (in particular, the seminal works of Sargent (1999) and Sargent, Williams, & Zha (2006)) to the causes of business cycles (e.g., Milani (2011) and Eusepi & Preston (2011)). Though there is no direct evidence of the appropriate value for the gain parameter, Berardi and Galimberti (2017) provide a thorough discussion of the role and estimate bands for the gain parameter in macroeconomic applications. In general, higher gains imply faster reaction to changes, but more volatile estimates.…”

The Economics of Monetary Unions

“…One of the few estimates based on Eurozone data is Milani (2009), whose estimates for the union as a whole are in the range of 0.004-0.008. Finally, Berardi and Galimberti (2017) evaluate gain parameters for a broad class of models using both actual and survey data and find values in the range of 0.01-0.035 to perform the best for inflation rates. I calibrate the parameter to 0.025, which is in the upper range of the aforementioned studies.…”