On checking campaign difficulty, it is a known fact that campaign difficulty influences farming and tax incomes of which the exact equations have been clearly delineated in the Ludus Magna forum.

For example, Farming Income = (160)(B+U)(H)(D)
where
Base farming (B) - ie 2.5% for Arretium (unique for each region)
Farming upgrade (U) - each upgrade confers a 0.5 benefit
Harvest (H) - poor = 0.95, ave = 1.00, good = 1.04, excellent = 1.08
Campaign difficulty (D) - easy = 1.125, medium = 1.000, hard = 0.920, very hard = 0.850

So D = Farming Income/(160)(B+U)(H)

You can get the rest of the values by opening up the town menu for any particular town in your current game and looking at the details, so you can roughly estimate D and refer to the fixed values above to get the difficulty level.