Productive output by what measure? Probably the most immediately obvious choice would be GDP, but upon closer examination I don't think that works.
By that measure, using a given amount of emissions running a factory that builds expensive, fossil fuel burning luxury boats for rich playboys is better than using that same emissions to provide winter heat for public schools.
Another problem with using a measure of productive output is that it screws developing counties. As I said earlier, the atmosphere does not care about arbitrary political boundaries.
There is some global maximum emissions per year that we can allow if we want to keep climate change from getting out of hand. If we make each country's share of that global pool proportional to their productive output, we are in effect saying that the rich countries get to continue to take advantage of cheap high emission things (like coal), and the poor counties have to forego that for clean but more expensive things, because there is a pretty good correlation between the wealth of a country and its productivity.
Since the rich countries are, to a large extent, rich because they exploited those cheap but dirty resources before we knew how harmful that was, it seems to make more moral sense for the rich countries to have to clean up first and/or subsidize the costs to poor countries of going clean.
Probably what would be better would be to figure out the total worldwide emissions allowed per year, allocate that among countries on an equal per capita basis, and allow countries to trade their shares.