Also look from other point of view. You are in MP with 13BB stack, raise 4BB. Pot is now 5,5BB, other guy from late position pushes all in and lets imagine he has you covered. So pot is 18,5BB now and it takes you remaining 9BB to call. Thats roughly 2:1 pot odds so you need ~33% equity. Now lets imagine you had AQ. I dont have equilator or other equity calculating programms with me at the moment but i think you get neccessary equity. You are way behind only AA, QQ, AK KK. I think even AJ could be hand to make such call with as in that stage ppl often push A with low kicker. Not sure about AJ situation tho.
And now, if you think you would have good enough odds to make such call or for any other reason would have to call all in re raise then it is better to shove first because it gives you bigger fold equity and can win hand without seeing flop. If you raise it to 4BB you give yourself another exit in case someone comes over the top. So if you raise 4BB then be ready to throw your hand away, if you dont plan to do that then shove it instead of raising.