Sync old Messages to new Mac
I recently got a new MacBook Air and was wondering if it is possible to get all of my old messages sent via iMessage to sync to the Messages app (I have been using an iPhone for years). All of the new messages I have sent show up both on my phone and on the Messages app, but none of the old messages or conversation threads with people I haven't messaged since getting my new computer show up. I frequently need to reference old information in messages so not being able to view old messages is kind of frustrating (for example it would help if on the Message app on my MacBook I was able to see the messages I sent to someone a week ago, back before I got my MacBook. But currently I can only see messages sent after ). Is there a way to get these old messages to sync to the Message app. It seems like this should happen automatically (as it does between my phone and iPad) but no such luck.
I have tried logging off and back on, I have double and triple checked that my AppleID and phone number are the same between the app and my phone, and once again, all new messages come through just fine. All i need to know is if it's possible to get all the old messages I've sent, which are clearly saved somewhere (since they sync between iPhone and iPad) to show up on my MacBook.
MacBook Air, OS X Mavericks (10.9.4)