How old is Ethiopia?

There are quite a few possible answers:  

• At one extreme, you could argue Ethiopia is just 27 years old, since the current constitution of the federal republic was implemented in 1994. But that's obviously silly, no one argues for example that France is only 63 years old because the current system (their fifth republic) started in 1958.
• Or you could say it's 28 years old since Eritrea separated in 1993. But no one argues the US is only 62 years old because the 50th state joined in 1959.  
• How about the claim, fashionable since the 1970s, that it's 150 years old. This dates it to the reign of Menelik II during which many of the neighbors became European colonies, thus setting roughly the current shape of the map.  Or to Tewodros II (1855), the end of a few decades of "zemene mesafint" where the central government was weak, which many consider the start of the "modern" period.  But just the fact that II in the names is already a hint that this doesn't make sense. The people who were there at the time saw themselves as continuing something, not inventing a new country. 
• A well established answer is that it started in 1270 AD, the end of the Zagwe period of Lalibela fame, and the start of the Solomonic dynasty's rule.  From that point forward, there's a huge amount of written history, both internal and external.
• Another answer is to the reign of Ezana, when the name first started being used internally, around 330 AD.  
• The word Ethiopia itself is of course older, and is believed to be of Greek origin. It can be found in Herodotus in the 5th century BC, and throughout antiquity. But this was an "exonym", and some say it applies to the entire continent which they didn't even know the shape of.   
• Many Ethiopians say it's 3000 years, going back to Queen of Sheba and Solomon, who lived around 900 BC.  But, while this is the legendary foundation of Ethiopia, it's not exactly documented history. 
• And some say the first Ethiopian was Lucy who lived about 3 million years ago.  But, while this archaeological find is monumental in the history of humanity, and a great source of pride for Ethiopians, it's a bit silly to call her Ethiopian, especially since she was just a random  Australopithecus whose bones we happened to find. Politics is hard enough even for us Homo Sapiens, let's not drag the poor little "girl" into this. 

So what's the right answer? The best definition -- one that is consistent with how we say how old is China, or Iran, or the USA ---  is not based on a specific shape on a map,  nor a particular political system. What counts is the entity, it's existence as a distinct polity with that name and in that region. And that is well documented as being around 330 AD:

(Source: Aksum and Nubia: Warfare, Commerce, and Political Fictions in Ancient Northeast Africa.)

So the most reasonable answer is: Ethiopia is 1,700 years old.