Extended Data Table 6:

Out of sample prediction (leaving out 20% of the data i.e. last three and last two weeks for USA and England, respectively) comparing models with and without covariates (see details on covariates in Extended Data Table 4).

Country	Log likelihood without covariates	Log likelihood with covariates	p-value*
U.S. States	−857.8	−839.9	0.009
England	−1047.8	−977.9	0.008

^*p-value calculated for the difference between the log pointwise predictive density of the models with and without covariates⁹⁵. The null hypothesis is that there is no difference in the out of sample prediction between the two models.