Except for transitions, the third party Clipmate product can do it. See ATR's blog post at http://atr935.blogspot.co.uk/2013/05/pe-clipmate-copypaste-between-pe.html.
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If this post or another user's post resolves the original issue, please mark the posts as correct and/or helpful accordingly. This helps other users with similar trouble get answers to their questions quicker. Thanks.
Neale's answer is the correct one for your question.
There is another workflow, but it involves doing an export (Share/Publish+Share), and then Import of that resultant AV file. This FAQ Entry covers that workflow: http://forums.adobe.com/thread/1300400?tstart=0
Each method has some pluses and minuses - still, Neale has the correct answer to the specific question.
Please remind us what version of Premiere Elements you are using and on what computer operating system it is running.
The computer operating system is particularly important if you are going to consider ClipMate for your Copy/Paste Insert between Premiere Elements projects. ClipMate is a Windows Only program.
If you do give my blog post on that a look, you will find the post detailed. The details especially for the end Edit Menu/Paste Insert need close attention. Any clarification needed, please let me know.
Thanks guys for all that. I am running Premiere Elements 12 on Windows 7. I will give Clipmate a try. It sounds like I should be able to do I need to except for transitions. I could live with that. Mostly I am editing animations and I deal with audio separately at the end anyway. Thanks again. What a brilliant forum.