On the Initialisation of Adaptive Learning in Macroeconomic Models

How we form our expectations is an important question regarding all kind of economic modelling. It has become clear that the rational expectations hypothesis does not capture all dimensions of how expectations are determined in reality. Adaptive learning algorithms have been proposed to provide a procedural rationality view on agents’ process of expectations formation. Reopening a long standing debate on how expectations should be modelled in macroeconomic models, the heuristics provided by learning algorithms come at the cost of introducing new degrees of freedom into the analysis.

One open question relates to how these recursive mechanisms should be initialised in order to be representative of agents’ learning-to-forecast behaviour. Importantly, leaving the definition of initial beliefs unchecked risks opening the way for severe biases to economic inference, caused for instance by data overfitting and weak identification of model parameters. This is particularly relevant when the effect of interest takes place near the beginning of the sample of data, as in the case in historical assessments of the effectiveness of alternative policy designs.

The main characteristic of the adaptive learning approach is its reliance on recursive algorithms in order to represent how agents update their beliefs as new observations about the economic relationship of interest become available. Such recursions naturally demand an initial starting point, and it is the numerical specification of these conditions that can be denoted as the initialisation problem. Clearly, the uncertainties affecting the initialisation of the learning process will propagate recursively into the predictions obtained with the model. It seems crucial that the researcher understands the magnitude of these distortions and how they can affect structural inferences.

In their new paper “On the Initialization of Adaptive Learning in Macroeconomic Models”, Michele Berardi and Jaqueson K. Galimberti investigate this issue with particular attention to the applied literature of learning in macroeconomics. They review and evaluate methods previously adopted in the applied literature of adaptive learning in order to initialise agents’ beliefs. Previous methods are classified into three broad classes: equilibrium-related, training sample-based, and estimation-based.

They 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. They find evidence against their joint estimation with standard moment conditions: as the accuracy of estimated initials tends to deteriorate with sample size, spillover effects also negatively affect  the accuracy of the estimates of the model’s structural parameters.

In other words, the larger the sample of data used to estimate the model and the corresponding initial beliefs, the larger the risks of incurring in misleading historical conclusions. Solutions to this problem are discussed in the paper.