5.4 ECONOMIC APPLICATIONS OF BAYESIAN FORECASTING METHODS

5.4 ECONOMIC APPLICATIONS OF BAYESIAN FORECASTING METHODS

There are too many examples of applications of Bayesian methods in the economic forecasting literature for a brief review to do any justice, so instead we comment on some of the main areas where such methods have proved particularly successful. Dating back to the work undertaken in the late 1970s as summarized by Litterman (1986), Bayesian methods have made up a large part of macroeconomic forecasting with multivariate models such as vector autoregressions which require the estimation of many unknown parameters. The main reason for the success of Bayesian methods in this area is that the loss associated with least squares estimation can be very large relative to the loss that arises when shrinkage or Bayesian methods are applied. Classical and Bayesian forecasters alike have found Bayesian methods to be a useful way to deal with parameter estimation error. Estimation of dynamic factor models is another area where Bayesian forecast methods have been extensively used; see, e.g., De Mol, Giannone, and Reichlin (2008). Finally, Bayesian methods are used extensively to estimate dynamic stochastic general equilibrium (DSGE) models and generate forecasts from such models. These topics are covered more extensively in chapter 9.

Forecast models with unobserved components are a second area where Bayesian models are now routinely used. Updating formulae used in Kalman filters follow from Bayes’ rule under joint normality of the innovation terms and so are naturally given a Bayesian treatment; see Durbin and Koopman (2012) for an extensive treatment of such models. One such application is to specifications affected by discrete, unobserved breaks to the model parameters. Kim and Nelson (1999) cover Bayesian estimation of Markov switching models with recurring regimes, while Koop and Potter (2007) and Pesaran, Pettenuzzo, and Timmermann (2006) are examples of models where the breaks can be unique, with parameters drawn from some continuous meta distribution.

Return prediction and portfolio choice is a third area where Bayesian methods are commonly used. To form optimal portfolios, investors have to account for parameter uncertainty and the posterior predictive density provides a natural way to accomplish this. Compared with classical plug-in approaches which condition on a set of parameter estimates, the Bayesian solution that accounts for estimation error often leads to less extreme asset allocations, particularly for risk-averse investors. Examples of Bayesian applications to asset allocation include Kandel and Stambaugh (1996), Barberis (2000) and Pettenuzzo and Timmermann (2011).

Model combination is a fourth area of forecasting where Bayesian methods have been used extensively. Bayesian model averaging provides a way to handle model uncertainty and allows researchers to integrate out uncertainty about a particular dimension of the model choice. An early example is the study by Min and Zellner (1993) which considers forecasts of international growth rates. Bayesian model averaging is covered in chapter 14.