It has been a standard assumption in theoretical macroeconomic modeling that agents are processing all the available quantities of information when forming their expectations for the future. Also, policymakers traditionally have looked at a vast array of indicator series in the run-up to major policy decisions, or in the words of Lars Svensson (Svensson (2005)) about what central bankers do in practice: ‘(l)arge amounts of data about the state of the economy and the rest of the world ... are collected, processed, and analyzed before each major decision.’ However, most traditional macroeconomic prediction approaches rarely consists of models that handle more than 10 variables, because it is either inefficient or downright impossible to incorporate a much larger number of variables in a single forecasting model and estimate it using standard econometric techniques. This failure of traditional macroeconomic forecasting methods prompted a new strand of research devoted to the theory and practice of alternative macroeconomic forecasting methods that utilize large data sets.
These alternative methods can be distinguished into two main categories. As, e.g., outlined in Hendry (1995), the methods of the first category involve inherently two steps: In the first step some form of variable selection is undertaken. The variables that are chosen are then used in a standard forecasting model. Recent developments in this line of research has focussed on automated model selection procedures in order to be better able to select the optimal predictors from large data sets; see Krolzig and Hendry (2001). An alternative group of forecasting methods consists of estimation strategies that allow estimation of a single equation model that utilizes all the information in a large data set and not just an ‘optimal’ subset of the available predictor series. This is a diverse group of forecasting methods ranging from factor-based methods to Bayesian regression and forecast combination. These two groups of methods inevitably overlap. However, we feel that the step of variable selection is, and involves methods that are, sufficiently distinct to merit separate mention and treatment. Instead, we focus in this paper on the latter group of data-rich forecasting methods.
Within the group of data-rich forecasting techniques, factor methods have gained a prominent place. These methods are related to the strict factor models used in finance, but, starting with Chamberlain and Rothschild (1983), they use weaker assumptions regarding the behavior of the idiosyncratic components, which allows the use of principal components in very large data sets to identify the common factors in such a data set. Stock and Watson (2002a) and Bai (2003) further formalized the underlying asymptotic theory. Stock and Watson (2002b) proved to be the starting point of a large empirical research output where, with mixed success, a limited number of principal components extracted from a large data set are used to forecast key macroeconomic variables.
However, the use of principal components does not always guarantee that the information extracted from a large number of predictors is useful for forecasting. Boivin and Ng (2006) make it clear that if the forecasting power comes from a certain factor, this factor can be dominated by other factors in a large data set, as the principal components solely provide the best fit for the large data set and not for the target variable. This could explain why in some empirical applications principal components (PC) factor models are dominated by Bayesian regression and forecast combinations. Under Bayesian regression one essentially estimates a multivariate regression consisting of all predictor variables, but with the regression coefficients shrunken to a value close to zero.
Starting with Bates and Granger (1969), forecast combination involves the use of subsets of predictor variables in distinct forecasting models and the production of multiple forecasts for the target variable, which are then averaged to produce a final forecast. The distinctive feature of these two approaches is that the information in a large data set is compressed such that this has explanatory power for the target variable. Note, however, that from an econometric perspective forecast combinations are ad hoc in nature, whereas it has been shown in De Mol et al. (2008) that Bayesian regression is theoretically related to PC-based factor models.
Download
PDF Ebook Revisiting Useful Approaches to Data-Rich Macroeconomic Forecasting
