"Both" is often a problem; this is worse

About that last sentence...

Both the central bank and the government impact the economy... 

That is true.

... the central bank and the government impact the economy... 

That is equally true. Depending on the context, it may be better to include the word "both".

... the central bank and the government impact the economy through monetary policy and fiscal policy...

That would make a good sentence. Neither policy is explicitly assigned to either institution, so the sentence is true.

... the central bank and the government impact the economy through monetary and fiscal policy, respectively.

That one is the most informative would-be sentence of all these options, because the policies are correctly assigned to the institutions. And finally:

Both the central bank and the government impact the economy through monetary and fiscal policy, respectively.

That is gibberish. Investopedia is saying that the central bank and the government, both of them, use both monetary and fiscal policy. (That is not true; the central bank was created specifically to handle monetary policy, and is held to be "independent" and free from government interference.) And in the same sentence Investopedia is also saying that the first of the two institutions uses the first policy noted, and the second institution uses the second policy. This they are correct in saying, but it is contradicted by all the words that come before "respectively" because of that damn "both".

That is, because they open with the word "both" they are saying that both the central bank and the government use the two policies -- that each institution uses both policies. And because the word respectively is used, they are also saying that the central bank uses only monetary policy and the government uses only fiscal policy. Because they have the word "respectively" there, the sentence is not only wrong but is also embarrassingly bad. I imagine, however, that Investopedia is not at all embarrassed, because they are unaware of the problem. That's how illiteracy works.

Frankly, I have similar problems with Investopedia's economics.