It should be zero, it's a silly thing.
Let's do some math!
On a good day something like Timbermill gives you +3 Production per turn. It costs 387 Production to build. That means it will take ~129 turns to compensate for the opportunity cost. If most games last 500 turns by the time the game releases (currently more like 300), you will only see 270 turns of gain, which is only 810 extra production overall, if you get the recquisite techs by turn 100. Considering that earlier turns are more significant in terms of opportunity cost, this is a bad decision, only offset by the AI's tendency to not do the math as much as the player.
The best solution would be to make production increasing buildings cost much less and do much more. Reduce the standard Material yields to offset the increase. Mason and Mill are actually worse because they have higher costs and only benefit construction.
Okay, let's do some math. A Lumber Yard adds 3 per material (a Timber Mill adds 4 production per material btw).
Let's say a city has 3 material, that directly translates to 9 production per turn. The Lumber Yard takes 176 production, which means without any other modifiers you'll need ~20 turns to complete it using only its own production (ze opportunity cost).
If your game lasts 500 turns, you'll earn 480*9 production throughout the game. Obviously I'm not including secondary benefits such as scaling with Unit Training Discount and Improvement Construction Cost Discounts.
Okay, let's do some math. A Logging Camp adds 2 per material (a Timber Mill adds 4 production per material btw).
Let's say a city has 3 material, that directly translates to 6 production per turn. The Lumber Yard takes 80production, which means without any other modifiers you'll need ~13.333 turns to complete it using only its own production (ze opportunity cost).
If your game lasts 500 turns, you'll earn 486*6 production throughout the game. Obviously I'm not including secondary benefits such as scaling with Unit Training Discount and Improvement Construction Cost Discounts.
Let's say you do the upgrade to Lumber Yard at turn 100 in the game. Lumber Yard adds 1 more PPM and takes 176 production to build.
At 3 materials, the paid opportunity cost is ~59 turns. That leaves you with (500(-100-59)) * 3 production net benefit at the end of the game (comes out to just over 1k).
Production boosters are brutally strong at the moment.
1) I only used a 3 material city. I frequently get 4 material cities and even 5 with a clay mine.
2) Set in stone multiplies any bonus, and scales perfectly with
3) Buildings that enhance the production value further, such as Barracks or Mill
My advice - stop treating production like something you get for free. There are huge bonuses to be picked up, and they'll benefit you more the earlier you build them.