Agricultural sector is different from economic sector in the way research is conducted.
In the noun phrases agricultural sector and economic sector, you mention specific sectors – agricultural and economic. It is obvious that you are not talking about the bananas sector and the pornography sector.
If you mention a noun and both you and your reader know exactly which noun you’re talking about, then you must use the definite article – ‘the’.
In the photo that accompanies this post, there are two puppies. If you say you want the light-coloured puppy, you use ‘the’, because it is clear both to you and to your listener exactly which puppy you want!
It’s the same when you’re talking about sectors:
Admittedly, identifying the main noun in a noun phrase becomes challenging with longer phrases. For example, can you identify the main noun in the following highlighted phrase? Answers in the comments section below! 🙂
Incidentally, an English native speaker would probably use the name of the sector without labelling it ‘sector’:
This ‘labelling’ of nouns is discussed further in a previous post.