This assumption is likely to be excessively restrictive for the purpose of this exercise as it implies an exceedingly small probability of observing shocks of the magnitude experienced in 2008 and 2009. Formal statistical tests of the residuals of the estimated statistical models fitting the output gap indeed reject for most countries the null hypothesis of normally distributed residuals. Plotting the kernel distribution densities of the shocks it is possible to show that for many countries they are indeed highly asymmetric, have fat tails as extreme outcomes (i.e. often large negative ones) are more frequent than what the normal distribution predicts. The null hypothesis that the residuals are independently distributed - that is, the value of a shock does not depend on the value of past shocks - is not rejected, lending support to the statistical model used to fit output gaps. Instead of generating random numbers assuming a normal distribution, bootstrap techniques involve re-sampling shocks from their actual distribution - that is the distribution of the statistical model’s residuals.