If the murder rate would be down because of the conviction rate the other crimes would be also down like that but the percentages are not showing it at all.
Who said that the other crimes are not down?
http://www.nationmaster.com/country-info/compare/Japan/United-States/CrimeFor example, the incidence of rape is 66 times lower in Japan, when compared to the US. Car theft is 20 times lower, and Assaults are 15 times lower.