Example 1
Limits to rice yields ?  (chapter 9)
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Summary. Lomborg disputes the existence of an upper limit to rice yields. As evidence for this he presents a graph purporting to show steady and continuing increases. Had he then followed this through with a careful ananlysis of the data it would have shown rice yields levelling off at about 6.7 tonnes/ha. Instead of doing this he attempts to muddy the waters by citing an economics working paper (unavailable to anyone else but Lomborg), whose claims - that rice yields will increase by up to 50% in the longer term - he fails to substantiate.

     In his chapter 9, "Will we have enough food", Lomborg has a paragraph with the headline: Limits to yields ? He refers here to postulates advanced by Lester Brown that there is an upper limit to the yield per hectare of any crop. This limit is set by biological and physiological restraints. For instance, Brown postulates that the rice yield obtained in Japan in 1983 has not been surpassed since then, and allegedly that this level indicates the maximal possible yield. Lomborg opposes this claim by showing that the rice yield in Japan has actually grown slowly, and risen above the 1983 level from 1995 onwards. He argues that the reason for this slow growth is the lack in Japan of economic incentive to increase yields. On the other hand, a newly industrialized country like South Korea, in Lomborg´s words, "clearly shows a steady increase in yields". This is illustrated by a graph which, in Lomborg´s view, shows a continuing rise. Another interpretation of the same graph, however, is that South Korea has caught up with Japan, and that after it reached the yield level obtained in Japan in 1983, the growth in yields has nearly stopped there too.
     So, the question is: What is the proper interpretation of Lomborg´s graph (his Figure 54 on p. 98) ? Does it show a levelling off, or does it show a steady increase ? Lomborg does not clarify this question by any objective (e.g. statistical) method. Instead, he cites two economics working papers - which according to Lomborg himself are no longer available - to back up his assertion that the pessimistic views are incorrect.  As the papers are unavailable, the reader has no chance to check the validity of this claim. He proceeds to cite one of the unavailable documents for the following claim: "Finally, the outlook for rice is dramatically optimistic - medium-term increases of 20 percent are within sight, and researchers expect a long-term increase of 50 percent." It is unclear from where he or the authors of the of the working paper have got this figure of 50 %, but the 20 % increase apparently refers to a new type of rice which  is being developed on the Philippines. Lomborg forgets to mention, however, that this new cultivar is only suitable for tropical and subtropical regions, not for Japan. He also forgets to mention that Lester Brown is aware of this new type of rice, and refers to its possibilities.
    Thus Lomborg tries to support  his opinion by citing unverifiable sources who tell about expected future rises.
    But now let us look at what the data actually tell. I have taken the figures from the FAO database because the source that Lomborg refers to (a USDA web site) is no longer available  (FAO calcualtes the rice yields in a way different from the method used by the USDA, but the figures differ from those of USDA by a constant factor which does not affect the conclusions). I have divided the time series into three periods: viz.
     1963 - 1975                                 1975 - 1987                                1987 - 1999
For each of these periods, I have calculated the average rice yield in tons per hectare at the midpoint of the period, and the annual rate of growth in yield during the period, expressed in percent increase per year. I have done this for three nations - Japan, South Korea, and China - and have plotted the growth rate against the yield. The results are seen in the graph below:

            Graph of rice yields

In this graph, C indicates China, J is Japan, and K is (South) Korea. One point is clearly aberrant. That is the point for China before 1975, i.e. during the Mao period. When we disregard this point, where the yields were low due to political causes, the rest of the points are grouped nicely along a straight line. In other words there is a clear correlation between the yield level and the scope for further growth. We can draw a regression line which meets the horizontal axis at about 6.7 tons /ha. This would mean that when yields have reached 6.7 tons, the average growth in yield will be zero, indicating that there is indeed an upper limit. Evidently Japan and South Korea have already reached this limit, and China is approaching it. Higher yields in certain years are due to favourable weather, and this will be offset by lower yields in years with unfavourable weather. The long term average will not rise above 6.7 - provided that no radically new technological progress is made. This tells us that the average rice yields in China will soon have reached their maximum. In 1999 yields were only 6 % short of this maximum, so the scope for increases in food production in China is therefore not as vast as some would have it.
     This analysis therefore solves the problem of how to make a proper interpretation of the graphs in Lomborg´s figure 54. If we ask: do the curves rise steadily, with fluctuations up and down around a sloping line, or do the curves reach an asymptote, with fluctuations up and down around a horizontal line, then the answer is clear: there is an asymptote whose horizontal section has already been reached.
    So when Lomborg states on p. 98 (left): "The "wall" [i.e. limit] Brown has found for Japanese rice yields seems to be caused by a deliberately misleading example" , the person doing the misleading is Lomborg. Brown does not, as Lomborg claims,  argue that rises in yield will come to a total halt altogether. The overall impression of Lester Brown´s text is that of growth rates that are about to reach zero, but he does not deny the possibility for some further increases, although they will be relatively small.
    Data from more recent years ( up to 2010) indicate that rice yields in South Korea, China and Japan have indeed levelled off more or less at around 6.7 tons/ha. However, this level is not necessarily strictly determined by biological and physiological restraints. These restraints may be at a higher level. This is illustrated by the situation in Australia, which has the world´s highest rice yields per ha (an average of 9 t/ha for 2006-2010).  This is partially due to a new method of more intensive monitoring of the fields, a procedure called `ricecheck´ , which was introduced in 1987 (see here). It seems unknown if this procedure could be adopted also in other countries.
    Thus, with reference to yields in Australia, Lomborg may be right that the rice yields elsewhere may be increased by 20 % or more. But his claim that the yields in countries of East Asia are steadily rising, not levelling off, is definitely wrong. The same type of data that he uses do infer a levelling off. Considering that he has taught statistics, he should be the first to decide if the trend is steady or slowing down. But he fails to do that.
     Altogether, Lomborg´s criticism of Brown is not fully justified, and he is not right that his data
"clearly show a steady increase in yields" in South Korea. Therefore, his text is here classified as an error, but there is no indication that this is a deliberate error.