Might be?...
Here's what I'm thinking now.
While the docs says: "It is computed every month by taking the lowest of the three partial indexes, adding to it 4 times the current education index and dividing the result by 5."
Edu_t = (min{A_t,B_t,C_t} + 4*Edu_t)/5)
It probably means something like this: "It is computed every month by taking the lowest of the three partial indexes, multiplying it by 4, adding the previous education index and dividing the result by 5."
Edu_t = (4*min{A_t,B_t,C_t} + Edu_(t-1))/5)
That last one is in line with what you wrote for the Health Index.
I have a hard time believing those are the equations being used, as they correct much faster than what I think is going on. But this would be compatible if the function that gives X, the value to which the index is converging to and depends on hospitals/schools, exhibits lag itself. In that case, let me tell you that is complicating things needlessly.
I haven't bothered to actually have a good, measured look yet, but I like to think I have a nice feel on this. Then again, I may not. So, if anyone has data to share, that would be nice.