Predicting missing data. Looking for good data predicting technique
there are several ways how to interpolate the missing data depending on how long history record do you have available:


you can compute ration of GDPs r_i (where all r_i sums to 1) in year Y-1 of each state with missing values in year Y; then you know the amount of GDP in year Y which should be spread among missing (GDP_total - GDP_known) and multiply by r_i
a more sophisticated way would be computing the gradient from the timeline Y-1, Y-2, Y-3, ... and you predict a value for year Y for each missing state; then you would again compute ration r_i among missing and distribute remaining GDP accordingly. This regression can be done also backward if you know Y+1, Y+2, Y+3, ... or interpolation from Y-1 and Y+1.