Audio bandwidth reduction is the very first processing step in any speech and audio coder. Its negative influence on perceived speech quality and intelligibility has been thoroughly studied and is therefore very well documented. This paper examines whether it also has an influence on speech emotion recognition by human subjects. Several standard telephony bandwidths, from fullband down to narrowband, are considered. Listening test results show that recognition accuracy decreases with audio bandwidth. More importantly, the number of listenings before subjects make a decision increases as bandwidth decreases, which indicates that bandwidth limitation makes the recognition task harder.