Dic: understand (as meaning believe to be the case)

UNDERSTAND:

▷ believe to be the case; infer : I understand you have no previous experience?

▷

1. to assume, infer, or believe : I understand you are thinking of marrying.
2. to accept as a condition or proviso : it is understood that children must be kept quiet.

▷ If you understand that something is the case, you think it is true because you have heard or read that it is. You can say that something is understood to be the case to mean that people generally think it is true.

• We understand that she's in the studio recording her second album...
• As I understand it, you came round the corner by the cricket field and there was the man in the road...
• The management is understood to be very unwilling to agree to this request...
• It is understood that the veteran reporter had a heart attack.

▷

1. [BELIEVE/THINK] to believe or think that something is true because you have heard it or read it : 'I understand that he was 62 when he died,' McLeish said.
2. be understood (that) : formal. if something is understood, everyone knows it, or has agreed to it, and there is no need to discuss it : From childhood it was understood that your parents would choose your husband.

.... WordNet, Collins, Cobuild, LDOCE

CF. REVIEW: be understood that, be given to understand that

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CF. Exercise of paraphrasing:

It will be appreciated if you correct the following sentences number 2 and  3 paraphrased for the given sentence number 1. I'm not sure about my usage of articles and singular-plural choices regarding `fiscal policy` and `allocational role.`

1. For centuries, economists have understood the allocational role of fiscal policy.
2. For centuries, economists have understood that fiscal policies have an allocational role. 
3. For centuries, it has been understood among economists that fiscal policies have an allocational role.