What exactly is the statement one signs by endorsing a check? (why isn't it printed?)

Normally documents that are signed contain the following two elements:

  1. A statement
  2. One or more signatures that make the statement operative as a statement of the signers(s)

Examples:

(contract)

  1. statement: Contract. John Firstparty and Michael Secondparty agree to the following: …
  2. signatures: * John Firstparty Michael Secondparty*

(letter)

  1. statement: … We are having a fabulous time here in Antarctica …
  2. signature: * Thomas Tourist*

(tax return)

  1. statement: I certify the above to be a true statement of my income for the year 2007. I am aware that I will be sent to the salt mines if it proves not to be.
  2. signature: T. Axpayer

(obverse of check/cheque)

  1. statement: Pay to the order of (payee) (amount)
  2. signature: Bill Payer
    The only instance that I know of a required signature without any explicit statement being signed is the endorsement of cheques/checks. In all other contexts a signature without anything being signed would be considered meaningless (or considered a blank signature, to be avoided because any arbitrary statement could be later written above the signature)

So:

[ul]
[li]What exactly is the implied statement that one signs to by endorsing a cheque/check? Is that statement spelled out anywhere?[/li][li]Why is that statement not printed on the check form, even if the reverse of the check is printed with a mark for the space where the endorsement signature is expected, i.e. it would not be more expensive to print the statement?[/li][/ul]

The statement is “Pay to the Order of” on the front of the check, which is signed by the payer.

The payee, by endorsing the check (and sometimes by adding a qualifier such as “for deposit only”) acknowledges receipt or other disposition of the payment.