This post is mainly my script for this video - Feel free to discuss 
Historically Hacienda are estates within latin america, which usually consisted of a huge area of land used to grow crops or produce other economic goods.
In game Haciendas are a mix of rice paddies, livestock pens and factories. They cost 600 wood to build, give 120 xp and can be used to generate coin, food, cows or villagers. Sending villagers on a haciendas improves the selected production, so for example more food is gathered or the train time of settlers is reduced. You can also use them to receive shipment, which is especially good in supremacy.
first let’s compare the gather rates:
A hacienda generates 60 food per minute or 37.2 coin per minute. Each villager tasked on a hacienda will produce 30 food per minute or 18.6 coin per minute. This is the same Gather rate as villagers on Rice paddies and is also comparable to gather rates on mills and estates, since villagers don’t walk on haciendas. Livestock also can be tasked to Haciendas, where 5 Sheeps and 3 cows are roughly worth 1 villager. The Gather Rates of haciendas and Villagers on haciendas can be further improved by cards and upgrades. The Livestock gather rates will stay the same throughout the game.
But what about using the Hacienda to produce Villagers? Is it worth it?
Producing a Cow and a Villager takes 100 seconds in the Hacienda, if no villagers are tasked to the Hacienda. By sending the first villager to a hacienda, the production of villagers is sped up by 10 seconds and cows spawn 12 seconds earlier. The Traintime can be further decreased by sending more villagers on a hacienda, whereas the decrease per villager will be lower the more are tasked to a hacienda. This means your first villager will reduce the train time by 10 seconds, while the 10th will only further reduce the time by 3 seconds, resulting in so-called diminishing returns. The Underlying function is most likely a logarithmic function, which is close to the reverse engineered formula my Excel created ;).
Now we know how long it takes to create villagers, but how much does it actually cost?
The opportunity cost to produce 1 Villager at Haciendas is the amount of food a hacienda could produce in the time it takes to create a villager.
This can be described with the following formula:
OpportunityCost = Traintime * (HaciendaGatherRate + VillagerAmount * VillagerGatherRate)
In the next Graph you will see the Oppurtunity cost of producing villagers depending on the amount of villagers for different villager gather rates. This helps us decide if it is worth it to use villagers to increase production of villagers.
For me there are 2 main takeaways:
The lowest opportunity costs are if you produce villagers, without using any villagers to enhance production.
If you use a medium amount of villagers, there is a local maximum of opportunity cost. Which means, if you want to be efficient you would rather use 20 villagers on 1 hacienda, than use 10 villagers on two haciendas. Or you use 5 villagers on 4 haciendas.
Since aoe 3 is a fast game, it is also important that our investment intoeconomy pays back quickly. To analyze this we take a look at the breakeven time, which can be calculated with the following formula:
BreakEvenTime = OpportunityCost / GatherRate
and use the opportunity costs to get the breakeven times for different gatherRates and amount of villagers.
Breakeven time is the time, after which your villagers gathered back their initial cost to produce them. To put that into a practical example: you want to go for a timing attack at 9 minutes: With a payback time of 2 minutes, you are better off using your hacienda to produce a villager until 7 minutes game time and use that villager to hunt food, than to use the hacienda to produce food. This means: A lower Payback time is better
The Graph looks pretty similar to the opportunity costs graph, so the same things apply here: A local maximum in the middle and the lowest break even time at the start. What’s also surprising for me is that it is probably a good decision to use the hacienda in supremacy to produce villagers. If you use your blank hacienda to produce villagers, who then go hunt, you have a break even time of only 2 minutes! For reference: british manor houses and dutch banks have break even times of around 5 minutes.
Okay now lets talk about some cards involving the hacienda:
Land Grab: This reduces the cost and the build time of the hacienda, making for a very powerful boom.
1 Hacienda wagon + 2 villagers: This card gives you 800 worth of ressources as an age 1 card!!! Usually Age 2 cards have 700 worth of ressources, so this card is insane for an age 1 card. You can also use the hacienda as forward shipping point to be agressive or just use it to boom. This card is so good, that it is most likely the first card in every single Supremacy / Empire wars build order. It is around 4 villagers (=2 SW or 3CDB) and also gives you back 120 xp, so you can get the next shipment really fast.
Team 1 Hacienda wagon + 7 cows: This card increases the build limit of haciendas by 1 and also ships 1 hacienda + 7 cows to each of your teammates. This is one of the best teamcards, since your team immediatly gets a third of a factory (2.29 f/s) and you have the option to get up to half a factory with 20 cows (3.4 f/s). So very good card for all game modes. Since this card improves your Hacienda build limit, you can also easily use this in your 1v1 decks.
These are all the hacienda cards i am going to talk about in this video. I will talk in detail about other notable cards, so stay tuned 
Summary:
The Hacienda is a pretty good building, which serves many purposes like Homecity shipment point, free resource production, booming capabilities and easy access to unlimited coin/food. All modes of production are viable and cards, which send haciendas are viable in many situations.
The Hacienda is one of the very few buildings, which can be improved many times with cards and upgrades.
The Resource production in itself is in line with other civilisations and balanced by the population limit of 80 for mexican villagers. All 6 haciendas + 20 cows are roughly worth 20 vills or 2-3 factories in postimperial - That means the closest comparison is France, who also have an efficient economy.
Personally I think the hacienda is a bit too flexible and does “too much” for one building (like receiving HC shipments), but the core design is interesting and mostly in line within the game boundaries.