It turned out to be a limitation of the AvroStorage from piggybank: http://www.mail-archive.com/user%40pig.apache.org/msg09000.html
For now I am using this workaround:
%declare WORK_DIR `pwd`
%declare SCHEMA_LITERAL `cat $WORK_DIR/schema.avsc`
...
STORE inputs INTO 'output'
USING com.magnetic.org.apache.pig.piggybank.storage.avro.AvroStorage('{
"index" : 1,
"schema": $SCHEMA_LITERAL}');