Wagyu refers to four specific breeds of cattle: Japanese Black, Japanese Brown, Japanese Shorthorn, and Japanese Polled, and to cattle bred between those breeds. Of these, Japanese Black accounts for 90% of wagyu cattle. "Wagyu" refers to these specific breeds and not merely to "beef produced in Japan." Therefore, it is possible for wagyu to be produced overseas. However, self-imposed regulations by the Japanese meat industry and by the Ministry of Agriculture, Forestries, and Fisheries bar the actual distribution of wagyu within Japan that is produced overseas.
The cost of wagyu runs high. This is because it takes more time to produce than ordinary beef and because the cattle are raised with great care, and because it is not suited to mass production. Furthermore, strict standards of inspection and management are in place to retain the native strains of cattle going back many generations. These factors make wagyu scarce.