Da página do manual do cron:
When executing commands, any output is mailed to the owner of the crontab (or to the user named in the MAILTO environment variable in the crontab, if such exists). The children copies of cron running these processes have their name coerced to uppercase, as will be seen in the syslog and ps output.
Então, eu verificaria seu e-mail se você configurá-lo com o sistema ou com o syslog (por exemplo, / var / log / syslog).
EDIT Do serverfault (editado para corresponder ao seu comando)
The following will send any Cron output to /usr/bin/logger (including stderr, which is converted to stdout using 2>&1), which will send to syslog, with a 'tag' of date_logging. Syslog handles it from there. Since most systems already have built-in log rotation mechanisms, I don't need to worry about a log like /var/log/mycustom.log filling up a disk.
* * * * * root /bin/date 2>&1 | /usr/bin/logger -t date_logging