Sounds like this is fixed. Next time, try logging the STDERR as well. Instead of
* * * * * echo hi >> /home/myusernae/test
Try to make sure there is an explicit location for STDERR. Otherwise, STDERR may be sent via email to the user (assuming that email is working), or may go nowhere at all.
* * * * * echo hi >> /home/myusernae/test 2> /home/myusername/test.stderr
My preference is to send cronjob output to syslog. That way I am taking advantage of any existing syslog infrastructure (centralized syslogs, Splunk, log rotation already supported, it's easy to compare messages in /var/log/messages & /var/log/cronjob, etc), and I'm not spamming the sysadmins (me) with unnecessary emails.
* * * * * echo hi >> /home/myusernae/test 2>&1 | /usr/bin/logger -t mycronjob