A test of the joint efficiency of macroeconomic forecasts using multivariate random forests

Abstract

We contribute to recent research on the joint evaluation of the properties of macroeconomic forecasts in a multivariate setting. The specific property of forecasts that we are interested in is their joint efficiency. We study the joint efficiency of forecasts by means of multivariate random forests, which we use to model the links between forecast errors and predictor variables in a forecaster's information set. We then use permutation tests to study whether the Mahalanobis distance between the predicted forecast errors for the growth and inflation forecasts of four leading German economic research institutes and actual forecast errors is significantly smaller than under the null hypothesis of forecast efficiency. We reject joint efficiency in several cases, but also document heterogeneity across research institutes with regard to the joint efficiency of their forecasts.

A Nonparametric Evaluation of the Optimality of German Export and Import Growth Forecasts Under Flexible Loss

“…There are, however, three exceptions, where insignificant p-values in the basic specification become significant when adding the respective other trade forecast to the forecasters' information set, namely IfW's and GD's import forecasts as well as OECD's export forecasts all under flexible loss. Based on work by Andrade and Le Bihan (2013) who find evidence on rational inattention of professional forecasters, I extend the forecasters' information set by adding the lagged realizations of the predictor variables (see also (Behrens et al 2018b), for an application to German GDP growth and inflation forecasts). The results presented in Table 10 show only minor changes in the magnitude of the permutation tests' p-values.…”

“…• As other macroeconomic variables, I include (following (Behrens et al 2018b(Behrens et al , 2018c(Behrens et al , 2019Döpke et al 2017), who study German GDP and inflation forecasts): German industrial orders, German consumer and producer price indices, industrial production for Germany, the United States, France, the United Kingdom, Italy, and the Netherlands as leading indicators for Germany's main trading partners (Guichard and Rusticelli 2011), as well as the oil price, German business tendency surveys for manufacturing (current and future tendency; on macroeconomic survey data as predictors, see (Frale et al 2010; Lehmann 2015)), finally, I include the OECD leading indicator for Germany as a composite indicator .…”

“…I furthermore account for different publication lags of the predictors based on research by Drechsel and Scheufele (2012). As real time data are not available at a monthly frequency for the examined time period, I minimize data revision effects of the affected variables by means of a backward looking moving-average of order 12 for the CPI, PPI, the real effective exchange rate, industrial productions, orders, and trade variables (following Behrens et al 2018b;Pesaran and Timmermann 1995), in order to proxy the information set which was available to a forecaster when a given forecast was formed.…”

“…Most of these studies focus on the analysis of GDP and inflation forecasts by means of panel-based models (Döpke and Fritsche 2006;Müller et al 2019) or time series models (Kirchgässner and Savioz 2001). A fairly novel approach introduced by Behrens et al (2018bBehrens et al ( , 2018a utilizes nonparametric tree-based models to analyze German GDP growth and inflation forecasts. Behrens (2019) has recently adapted this nonparametric approach to an analysis of the joint efficiency of German trade forecasts in a multivariate setting under quadratic loss.…”

The predictive value of inequality measures for stock returns: An analysis of long-span UK data using quantile random forests

“…A regression tree consists of a root, interior nodes, and terminal nodes (the leaves; for an introduction to regression trees, see Hastie et al, 2009; for recent applications of regression trees in economics, see Döpke et al 2017 andBehrens et al 2018). The nodes recursively partition the space of predictors, x t ,t = 1, ..., N, into rectangular subspaces in a top-down and binary way.…”