Bottom-up or direct? Forecasting German GDP in a data-rich environment

Most European countries apply a GDP measure which is primarily based on the production side, while the US GDP measure is focused on the demand side. Therefore, one would expect different implications for the predictive performance of leading indicators for the two bottom-up procedures.

We select K among 9 and 12 months and take into account q between 1 and 3. We also experimented with higher polynomials and longer lags, but did not find much improvement.

Table 4 in the Appendix indicates the average number of indicators that are used at each forecasting round to generate a pooled forecast.

According to the recursive model selection scheme of each indicator model, only those models survive for the model averaging scheme that obtain a smaller SIC than the AR model (which exclusively consists of a constant and its own lags). The time-varying nature is mostly taken into account by a rolling estimation scheme which implies that in- and out-of-sample criteria get updated at each point in time.

Due to space limitations, we only present a subset of model combination schemes overall considered. Additional combination schemes are Bayesian model averaging and Granger-Ramanathan weights (with and without shrinkage). Details are available on request.

Since the number of models retained varies with each forecast round, we only consider those models for the MSFE weighting scheme that are actually different from the AR model. This implies that we then set \(\lambda ^{-1}_{it}=0\).

The optimal degree of discounting (which controls the degree of time variation of the weights) is generally unknown. Most of the literature tends to set \(\delta \) between 0.9 and 1 (see, Stock and Watson 2004), but also very low values of \(\delta \) of about 0.3 are found to work well (e.g., Drechsel and Scheufele 2012b). In general the optimal \(\delta \) depends on the stability of the models under investigation. In our study, the relative performance of MSFE weighting is not much affected by the choice of \(\delta \).

Obviously, a broad range of procedures to estimate dynamic factor models exist and may differ in terms of forecasting performance (see Schumacher 2007, for a comparison for German GDP). One possible augmentation of the factor model would be to allow for autocorrelation in the idiosyncratic component (see Banbura et al. 2011, for an application) which could provide a more flexible way to take into account the persistency in many macroeconomic time series. To check for this possibility, we ran Ljung-Box Q statistic tests to check for remaining autocorrelations in the idiosyncratic component up to lag 1 and 4 in each estimation sample. For GDP and its subcomponents as well as for most of the indicator variables, we find little evidence of remaining autocorrelation in the idiosyncratic components. This suggests little room for efficiency gains by incorporating a more flexible error specification.

As a robustness check, we estimate factor models based on the total data set. However, in particular for the GDP components, this results in much less precise forecasts.

For most of our target variables, we use a minimum correlation of 0.3 in absolute terms. Only for the subcomponents private consumption and public administration, we needed to scale down the threshold (using 0.2) in order to retain a meaningful number of the variables in our data set.

Mariano and Murasawa (2003) or Banbura et al. (2013) have proposed a slightly different aggregation rule, where monthly series are included as monthly changes. In our setting, applying their aggregation rule does lead to inferior forecasting results. Therefore, we apply the aggregation rule proposed by Angelini et al. (2010) and Angelini et al. (2011).

While it is easy to investigate the absolute contributions of a single indicator, it may be more difficult to compare the revision process for one forecasting round to the next. As we employ a direct forecasting approach (parameters estimates may change from one round to the next) and combination weights are also allowed to change, forecasts for different rounds may be hard to compare. This is easier within the DFM framework, where the model remains the same during the forecast rounds.

Detailed results for GDP components are available upon request.

The results can be provided by request.