Bias Properties of good forecasts and measures used

longer time horizons by 0.2 and almost 1 percentage points for three and four years ahead see Annex 2, Table B1. Figure 1. Actual versus forecasted rates Note: The line in the figures indicates the 45 line. t + j refer to the j th year ahead forecast j = 1,…,4. Source: ILO calculations based on the Global Employment Trends GET January 2010; January 2011; January 2012; January 2013. Similar results can be observed in Figure 2 which displays the distribution of errors for each forecast period. In all cases, the respective distribution is significantly different than the normal distribution. For one, three and four years ahead, the kurtosis and skewness are above 7 and 1, respectively, and for two years ahead the kurtosis is about 5 and the skewness about 0.7. However, by just looking at the figures, two, three and four years ahead show signs of right-hand skewness i.e. under-prediction. 8 The term under-prediction is used when the predicted unemployment rate is lower than the actual rate AFE is positive. 4 8 12 16 20 24 28 32 4 8 12 16 20 24 28 32 F o re ca st e d r a te Actual rate t+1 Bolivia Bolivia Costa Rica 4 8 12 16 20 24 28 32 4 8 12 16 20 24 28 32 F o re ca st e d r a te Actual rate t+2 Greece Ecuador Dominican Republic Algeria Iran, Islamic Republic of Serbia 4 8 12 16 20 24 28 32 4 8 12 16 20 24 28 32 F o re ca st e d r a te Actual rate t+3 Greece Algeria Cyprus Portugal Estonia 4 8 12 16 20 24 28 32 4 8 12 16 20 24 28 32 F o re ca st e d r a te Actual rate t+4 Greece Spain Cyprus Croatia Estonia Turkey Uruguay Bulgaria Figure 2. Distribution of errors Source: ILO calculations based on the GET January 2010; January 2011; January 2012; January 2013. Moreover, the results from equation 1 indicate that there was no significant bias for forecasts of one to three years ahead, but forecasts for four years ahead showed a positive bias indicating under-prediction see Table 2 and Annex 2, Table B3. Table 2. Testing for bias, for global unemployment rate forecasts Years ahead 1 2 3 4 World α -0.0898 -0.0542 0.2473 0.9934 0.0749 0.1372 0.2182 0.3683 F α=0 1.4370 0.1561 1.2836 7.2771 N 92 86 82 61 Note: Robust standard errors in parenthesis; p0.01, p0.05, p0.1 n = 92 In c id e n c e 1 2 3 -5 -4 -3 -2 -1 4 5 6 7 8 9 10 11 12 13 14 15 Error, t+1 percentage points n = 86 In c id e n c e -4 -2 -5 -3 -1 1 2 3 4 5 6 7 8 9 10 11 2 13 14 15 12 Error, t+2 percentage points n = 82 In c id e n c e -5 -4 -3 -2 -1 1 2 3 4 5 6 7 88 9 10 11 12 3 13 14 15 Error, t+3 percentage points n = 61 In c id e n c e -5 15 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Error, t+4 percentage points