Macroeconomic uncertainty indices for the Euro Area and its individual member countries

Our measure is easy to construct, and it can be applied to any country for which forecasts and realizations are available. In fact, using GDP growth and CPI inflation forecasts provided by Consensus Economics we can obtain uncertainty indices for most EA individual countries. The time series of the uncertainty indices (in Excel format) are publicly available on our webpages at http://​www.​tateviksekhposya​n.​org/​ and http://​www.​barbararossi.​eu/​.

In fact, as Rossi and Sekhposyan (2015) show, for the USA, upside uncertainty is expansionary, while downside uncertainty is recessionary. Thus, whether uncertainty is an upside or a downside one is relevant for understanding its macroeconomic impact.

In principle, one could rely on the conditional distribution, where the density of forecast errors \(f\left( e\right) \) is constructed based on all the forecast errors realized up to time t. Rossi and Sekhposyan (2015) implement both versions when constructing the uncertainty indices for the US. In the context of the EA (or countries other than the US), using the conditional distribution rather than the unconditional one is more challenging since the overall sample size available for constructing the forecast errors is rather small. Uncertainty indices based on the conditional distribution would result in a very short time series of uncertainty indices, which would not be useful for empirical analysis.

Since \(U_{t+h}\) is a Uniform variable defined over the (0,1) support, the mean value of \(U_{t+h}\) is 1 / 2, and the formulas that follow construct positive and negative uncertainty indices relative to the mean.

For a careful treatment of the ECB-SPF predictive densities in the context of understanding forecasters’ learning mechanisms see Manzan (2016).

E.g.,: in month one, \(k=12\), while in month twelve, \(k=1\). An alternative procedure to construct fixed-horizon forecasts from fixed-event ones is developed by Knueppel and Vladu (2016). Their procedure gives optimal weights that minimize the mean squared forecast error loss function of the fixed-horizon forecast. For the purposes of our index, which is based on the unconditional distribution of the forecast errors, this alternative weighting results in very similar uncertainty indices. However, if one were to construct uncertainty indices based on the conditional distributions, the difference could be non-negligible.

In the sample periods where forecasts are available only every 2 months, the current-year and next-year forecasts are weighted based on the adjusted formula: \(\frac{k}{6}\widehat{f}_{t+k|t}^{\mathrm{FE}}+\frac{6-k}{6}\widehat{f}_{t+k+6|t}^{\mathrm{FE}}\), where \(k=1,2,\ldots ,6.\)

The survey forecasts as well as the realizations for the countries start at different points in time. If we miss some observations for the 3 months of the quarter for either the forecasts or the realizations, we construct the quarterly average based on the available observations. This situation occurs only in the case of forecasts for the Eastern European economies in the beginning of the sample period when the forecasts are available for every other month rather than being monthly.

Besides the imposed fixed country-composition in the construction of the aggregate index relative to the changing composition embedded in the ECB-SPF, other potential reasons for the divergence between the two measures could be the fact that they come from different surveys, with potentially different participants. Moreover, it is possible that the ECB-SPF participants weigh the country-specific data differently than our averaging or principal component extraction imply. In addition, though the two sets of forecasts are compared to each other as of the forecast origin dates, their target dates vary. As discussed earlier, the target date for the weighted Consensus forecasts in the first quarter would be the year-over-year growth from the fourth quarter of the last year to the fourth quarter of the current year. On the other hand, that of GDP growth-based uncertainty from the ECB-SPF is based on the growth from quarter 3 of the previous year to quarter 3 of the current-year. For inflation, the target periods are the same, so the differential in the target dates should be irrelevant.