This study looks into the long run behavior of the productivity of world firms, measured by sales to asset ratios. By comparing the initial and ergodic distribution of the productivity distribution of the traditional industries(manufacturing of iron, electronic parts, and ship building etc.), we find that the productivity of world firms converges toward the world medium level, which means productivity gap among the world enterprises shrinks. This result implies that Korea`s traditional industries, which are still enjoying the edge over other competitors, will face the possibility of falling behind by the catching up of competitors of the world. By looking at the change of individual firm`s productivity to the average level of the same industry of the world, we also find that among the three countries(China, Japan, Korea), Korea has the highest ratio of falling behind and also it has even higher rate of falling behind compared to OECD and G20 countries. This means that the relative competitiveness of Korean firms are falling behind to its competitors of the world during the sample period.