Sounds like this is fixed. Next time, try logging the STDERR as well. The following will only log to STDOUT, not STDERR:
* * * * * echo hi >> /home/myusername/test
Try to make sure there is an explicit clause for STDERR as well. Otherwise, STDERR may be sent via email to the user (assuming that email is working) or may go nowhere at all, depending on how Cron is configured.
* * * * * echo hi >> /home/myusername/test 2> /home/myusername/test.stderr
My preferenceMy 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/myusername/test 2>&1 | /usr/bin/logger -t mycronjob