Figure 2 shows how the Riksbank's CPIF forecasts were updated between 2020 and 2023, and the outcomes for CPIF inflation until the second quarter of 2023. The blue dashed line shows annual averages for 2021 and 2022 for the outcomes and the grey dashed line shows the average of the corresponding forecasts. It is clear that the forecasting errors were large in both years, but especially in 2022. The average of the Riksbank's 2020–2022 full-year forecasts for CPIF inflation in 2021 and 2022 was 1.6 and 3.2 per cent respectively (grey dashed line).^[8] The Riksbank published forecasts for 2021 between October 2018 and November 2021. Forecasts for 2022 were made between November 2019 and November 2022. The outcome for CPIF inflation in 2021 and 2022 was 2.4 and 7.7 per cent respectively, which means that the average forecasting errors were around 0.8 percentage points for 2021 and 4.5 percentage points for 2022.

A common way to summarise and evaluate the accuracy of forecasts is to calculate the average of the absolute value of all forecasting errors made in a given period. In Figure 3, we show a very similar measure, the root mean square error (RMSE), to summarise the forecasting errors for the ten central banks we study.^[9] Both the absolute value and the square of a number remove the sign of the number. This means that both positive and negative forecasting errors can be summarised and compared. The absolute value does this directly by giving a number the positive value regardless of whether it is negative while the square does this indirectly as the square of a negative number is always positive. This measure can be interpreted in much the same way as the average forecasting error, but gives more weight to large forecasting errors and less weight to small ones.^[10] Note that the RMSE represents a particular type of (quadratic) loss function that may be natural for a central bank. Indeed, large forecast deviations are considered relatively more serious than small forecasting errors with such a loss function. Different functions can lead to different results.

Figure 2. CPIF, the Riksbank’s forecasts and outcomes Annual percentage change

If we start with the Riksbank's forecasting errors, we can see that the forecasting errors for 2021 and 2022 are substantial compared with the decade before the pandemic. The average forecasting error for the Riksbank's forecasts for the years 2011–2020 made in the same year and the year before was 0.3 percentage points.^[11] Table 2 in Evaluation of the Riksbank's forecasts 2021, Riksbank Study, Sveriges Riksbank.

If we then compare with other central banks, we can first note that all central banks' forecasting errors were significantly larger for 2022 than for 2021. It is also clear that the spread of root mean squared errors across central banks increased in 2022. Norges Bank and the Bank of Canada have average mean squared errors of only 3.5 percentage points, while the Polish and Czech central banks' corresponding errors are close to 10 percentage points.

Furthermore, it can be observed that forecasting errors were larger in those countries where inflation became higher and began to fall later. For example, inflation in Sweden, the United Kingdom and the euro area rose more than in many other countries. At the same time, forecasting errors were also larger in these three countries/regions. Norges Bank appears to have done relatively well with its inflation forecasts for both 2021 and 2022 and comes out the overall winner, if this measure alone were to be the deciding factor.

Figure 3. Root mean square error of forecasts in 2020, 2021 and 2022 for inflation in 2021 and 2022 respectively Percentage points

However, Figure 3 does not take into account the fact that the different countries might have been subjected to varying degrees of disruptions and shocks during 2021 and 2022. Moreover, the impact of the disruptions on the economy may have differed across countries. We also do not take into account that the variation in different measures of inflation may be different. When comparing forecasting errors between different data series, it is common to normalise, or standardise, the error. One way is to normalise the root mean square errors with some kind of measure of variability for the outcome variable.^[12] A normalised forecasting error gives an idea of the size of the error relative to the actual outcome, or the variation in the outcome. It helps to put the error into perspective and makes it possible to compare forecasting errors across different scales or between different data series. If a forecasting error is 4 percentage points and the variation in the outcome is 4 percentage points, the normalised forecast error is 4/4 = 1. If instead the forecasting error is 8 and the variation in the outcome is 16 percentage points, the normalised forecast error is 8/16 = 0.5. A large absolute forecasting error can thus become a relatively small forecasting error if one takes into account that outcomes vary to different degrees.

Figure 4 normalises the average forecasting errors by the range of variation (the difference between the highest and lowest outcomes) of inflation between the first quarter of 2013 and the last quarter of 2022. Large forecasting errors will then be weighted down if inflation has varied relatively more (as in Poland and the Czech Republic). The idea is that it is relatively harder to forecast a variable that varies a lot than one that varies relatively little. Different choices of time periods for the inflation outcomes and different measures of variability (e.g. variance or standard deviation) that we have chosen to normalise with give the same qualitative results, as long as the outcomes for 2021 and 2022 are included in the normalisation.

Figure 4. Normalised root mean squared errors for forecasts in 2020, 2021 and 2022 for inflation in 2021 and 2022 respectively

Of course, the fact that inflation has risen more in some countries may also be due to the monetary policy conducted. Adjusting for the variation in inflation means that we not only adjust for different shocks but also for different monetary policies. Thus, we may be putting central banks that were not as successful in stabilising inflation in a better position.^[13] The relationship between how much inflation rose in the countries we study and when central banks actually started tightening monetary policy and raising policy rates is positive (if one excludes Poland and the Czech Republic). Inflation rose more in countries that raised their policy rates later than in those that raised them earlier. . If standardisation is not considered relevant in this context, we refer to the results in Figure 3.

Figure 4 is the central figure in our analysis. Interestingly, it shows that the central banks have been broadly as good, or as bad, at forecasting their respective inflation target variables. If anything, the Federal Reserve and the Reserve Bank of New Zealand made slightly poorer forecasts for inflation in 2021 than other central banks. Otherwise, the forecasting errors are strikingly, and perhaps even surprisingly, similar.^[14] Mean squared errors for projections made in 2021 and 2022 instead of 2020. 2021 and 2022 are consistent with those shown in Figures 3 and 4.