Forming Expectations for the 2015 U.S. Average Corn Yield: What Does History Teach Us?

There continues to be a lot of discussion about the likely magnitude of planted acreage of corn in the U.S. in 2015. For the most part, current expectations are that lower corn prices and the high costs of producing corn relative to competing crops (primarily soybeans) will lead to fewer planted acres. Analysis prepared by the USDA’s Wheat, Feed Grains, Rice, and Oilseeds Interagency Commodity Estimates Committees and presented at last week’s USDA Outlook Forum, for example, projected plantings at 89 million acres. Planted area at that level would be the smallest since 2010, 1.6 million acres less than planted in 2014, and 8.3 million acres less than the record acreage of 2012. The USDA will release the results of its survey of 2015 planting intentions in the Prospective Plantings report to be released on March 31.

In addition to the magnitude of planted acreage, the size of the 2015 corn crop will obviously be determined by the average yield of the crop. Factors determining yield will unfold over the next six months. For the time being, yield expectations are generally based on trend yield analysis that might also incorporate specific views on prospects for growing season weather. For example, the USDA projected a 2015 U.S. average corn yield of 166.8 bushels per acre at last week’s Outlook Forum. This raises the perennial issue of what, if anything can be learned from the historical trends and patterns of U.S. average corn yields. Here, we examine the history of corn yields from 1960 through 2014 as a basis for forming an expectation of the U.S. average corn yield in 2015. This updates a similar analysis presented in an earlier farmdoc daily article (February 2, 2012).

Historical Trends and Patterns

As shown in Figure 1, U.S. average corn yields have trended higher since 1960. We find that a linear trend is the best fit to actual average yields over that period, explaining 88.6 percent of the variation in annual average yields, and that yields have increased at a rate of 1.81 bushels per acre per year. An alternative sometimes considered is the log-linear trend model (take the natural logarithm of yield before regressing on a time index), but this model also implies that the range of trend yield deviations in bushels should expand across time which clearly does not happen. It should also be noted that an important property of the linear trend model is that the percentage change in trend yields declines over time as the same bushel increase in trend yield is divided by a larger and larger base. This is consistent with the history of U.S. average corn yields since 1960.

Some have argued that the corn yield trend has increased in recent years as it did beginning about 1960. We find a slight increase in the trend in some areas of the country in recent years, but cannot yet confirm an increase in the U.S. average trend yield. We have analyzed this issue extensively in several previous publications (Tannura, Irwin, and Good, 2008a; Irwin and Good, 2010; Good and Irwin, 2011). The reason this is important in the present context is that if the rate of growth in trend yields has jumped in recent years then some recent yields that are shown as above trend in Figure 1 may actually be below trend. It is interesting, however, that the trend increase in yields from 1960 through 2014 is slightly lower than the trend from 1960 through 2011 due to the large yield shortfall in 2012 (see calculated trend yield found in the February 2, 2012 farmdoc daily article)

Figure 2 shows the deviations of actual yields from the estimated 1960-2014 trend in yield. Obviously, there has been substantial deviation from the trend yield in individual years. Over the 55-year period, the average yield was above the trend yield in 58 percent of the years and below the trend in 42 percent of the years. Since all deviations from a linear trend must sum to zero, this means that in the 42 percent of years with a below trend yield the deviations were on average larger than the deviations in the more frequent years when yields were above trend. Specifically, the average deviation below trend was 9.0 bushels while the average deviation above trend was 6.5 bushels. The largest deviation below trend was 33.4 bushels (2012) while the largest deviation above trend was 18.3 bushels (2004). The frequency and magnitude of deviations are logical for following reasons: good (normal) growing season weather occurs more frequently than poor weather and good growing season weather helps corn yields less than poor weather hurts yields due to the non-linearity of the relationship between corn yields and precipitation. Further discussion of this topic can be found in our earlier report on crop weather modeling (Tannura, Irwin, and Good, 2008b).

The 58/42 split between above and below trend yields discussed above is a general statement that applies to any year in the sample. A different, but related, question is whether there is a marked correlation between deviations from year-to-year. In other words, is there a tendency towards continuation or reversal of deviations? Figure 3 shows that there is a very small negative correlation (-0.0159) between the yield deviation in the previous year and the current year (correlations can vary between -1 and +1, with zero indicating no relationship). For all practical purposes this correlation is indistinguishable from zero, which means that a negative yield deviation last year does not necessarily tend to be followed by a positive deviation this year and vice versa. Even the very limited tendency is sensitive to just a few years with large negative yield deviations. If 1983, 1988, 1993, and 2012 are deleted from the sample the negative correlation completely disappears. The bottom-line is that there is no systematic tendency for the U.S. average corn yield to increase or decrease based on what happened in the previous year.

The correlation in Figure 3 is based on comparing deviations in pairs of adjacent years. It is also interesting to examine whether longer “runs” in the deviations occur. The distribution of runs of consecutive positive or negative yield deviations is summarized in Table 1. There were five single year runs with positive deviations and nine single year runs of negative deviations. This simply means that a positive deviation was followed by a negative deviation and vice versa in these 14 years. The longest run of negative deviations was four years (1974-1977), while positive deviations had two runs of four years (1984-1987 and 1998-2001) and a run of seven years (2003-2009). Since positive deviations are more common than negative deviations, it is logical that more and longer runs of positive yield deviations have occurred.

There is an interesting connection between the runs of positive corn yield deviations and growing season weather. Specifically, the run of positive yield deviations from 1965 through 1969 led some to conclude that technological improvements had resulted in reduced risk of low corn yields, and therefore, had increased the trend. As it turned out, those yields instead reflected a period of generally favorable weather and not an increase in the underlying trend (see the final section of Tannura, Irwin, and Good (2008a) for a more detailed discussion). The run of positive yield deviations from 1998 through 2001 and the unprecedented run from 2003 through 2009 once again led some to conclude that the underlying corn trend yield had shifted higher. That period was also one of generally favorable weather, but as noted earlier, some had also argued (and continue to argue) that the trend indeed had shifted due to improved technology, particularly improved drought tolerance. As we warned in February 2012, the experience of the earlier episode of benign weather in the 1960s at least suggested a good deal of caution before concluding that large negative trend yield deviations were a thing of the past. The “Flash Drought” of 2012 (farmdoc daily, April 17, 2013) quickly demonstrated the wisdom of that warning.

Since 2014 was a year of a large positive deviation from trend yield, a related issue is the historical pattern of yield deviations in years following large positive trend deviations. The 2014 average yield of 171 bushels was 10.9 bushels above trend, the eighth largest since 1960. The previous nine years that round out the top ten years with the largest positive deviation (in descending order) were 2004, 1994, 2009, 1972, 1979, 1992, 1982, 1985, and 1986. The positive yield deviations ranged from 10 bushels in 1986 to 18.3 bushels in 2004, and averaged 12.7 bushels. Figure 4 shows the deviation from trend yield in the nine years following those years with large positive deviations. Somewhat surprisingly, eight of the nine years had large yield deviations from trend, with only one small negative deviation. Not surprisingly, the negative deviations (on average) were larger (12.9 bushels) than the positive deviations (7.0 bushels). For the nine years, the average yield was four bushels below trend. Given the small sample of years and variation across the nine years, one should be very cautious in projecting the four bushel shortfall to the 2015 U.S. average corn yield. Nonetheless, it should provide some pause to anyone on the optimistic side of the debate about corn trend yield.

What About 2015?

The analysis of corn yields presented to this point reveals considerable diversity in yield patterns since 1960, most clearly depicted in Figure 2. Average yields have shown large positive and negative deviations from trend, the duration of consecutive years with above- or below-trend yields has varied considerably, the correlation between yield deviations in consecutive years is negligible, and the pattern of yield deviations following years of very large positive deviations (like 2014) is quite mixed. This diverse and largely random set of patterns suggests that the most objective early-season yield expectation for any year, including 2015, should be based on the trend of actual yields.

As we noted above, some have argued that the trend has increased at a faster rate in recent years; so, we calculated 2015 trend yield based on the 1960-2014 period as well as more recent time periods. The period of 1988-2014 is selected since it is the period used by the USDA in making its trend projection for 2015. The period 1995-2014 is used to represent the recent “biotech” era. Since each of the three alternative periods begins with low yielding years (1960, 1988, and 1995), trends are also calculated for periods starting one year later. Table 2 contains a summary of the calculation of the annual trend increase and the 2015 trend yield based on the six alternative periods for calculation. There is considerable similarity among the trend calculations with the exception of the higher trend based on starting with the extreme drought year of 1988 and the lower trend based on the most recent period. The lower trend in the most recent period reflects the strong influence that an extreme drought year (2012) has when a short time period is used for calculating trend. While not shown, the trend calculation is even lower starting with 2000, since the extreme drought year of 2012 has an even larger impact on the calculation. This is the opposite influence that the period of generally good weather from 1996 through 2009 had on the trend calculation. As we have argued repeatedly, that period of good weather contributed to the conclusion that yields were increasing at a faster rate than in earlier years.

Given the various alternatives, we maintain that current 2015 corn yield expectations should be based on the longest sample of data with a stable trend yield component. Since we have been unable to find significant evidence of trend yield shifts since 1960, we argue that the period of 1960-2014 best meets this criterion. Table 2 indicates that the best linear fit of actual yields in the U.S. from 1960 through 2014 results in an “unconditional” trend calculation for 2015 of 162 bushels. This methodology actually results in a slight under-estimate of trend yield due to the asymmetric effect of weather on actual yields (Swanson and Nyankori, 1979; Tannura, Irwin, and Good, 2008a). That is, poor weather reduces yields more than good weather improves yields so that the impact of technology (trend) is under-estimated due to sharp reductions in yield from poor weather years, such as 1974, 1983, 1988, 1993, and 2012 (for those with a statistical bent this is more formally known as an omitted variables bias). Our previous research on crop weather models that adjust for the asymmetric effect of weather on crop yields indicates the downward bias is about one-tenth of a bushel for trend coefficients (Irwin, Good, and Tannura, 2009). This translates into a downward bias in unconditional trend yield forecasts at the national level of about two bushels per acre. If we add this bias estimate to the unconditional trend yield estimate of 162 bushels per acre the result is a corn trend yield projection of 164 bushels for 2015.

It should be obvious at this point that a range of trend yield projections are plausible depending on the sample period used, the functional form of the trend model, and whether a bias adjustment is considered or not. As we noted in the introduction, the USDA trend yield projection for corn released last week is 166.8 bushels per acre, 2.8 bushels above our projection. While this is not a large disparity it could result in ending stock projections that differ by 150 million bushels or more. Since this could have a market impact, it is useful to understand why the USDA projection is higher. We believe that two factors likely explain the difference. The first is that the USDA crop weather model used to make their trend projection is estimated over 1988-2014. We demonstrated in Table 2 how starting the sample in a year of extreme drought can lead to a higher trend yield projection. In essence, the extreme drought year pulls down the trend line during the early years of the sample. The second has to do with the methodology the USDA currently uses to generate trend yield projections from the crop weather model it started using in 2013 (Westcott and Jewison, 2013). The trend projection methodology imposes on the crop weather model the assumption of average weather over 1988-2014 along with the average portion of the crop planted in a timely manner over that period. In technical terms, this is a “certainty-equivalent” approach because it is assumed with certainty that average weather and planting progress will occur. This pushes up trend yield projections compared to a procedure that does not assume average values, again due to the asymmetric effect of weather on yields (Irwin, Good, and Tannura, 2009). That is, the assumption of average weather does not fully reflect the large negative yield effects of poor weather relative to the smaller positive effects of good weather.

Finally, it is important to keep in mind the substantial yield risk that exists when considering trend projections. We argue that the distribution of expected yields around that average should reflect the distribution of actual annual deviations from trend yield for the period 1960 through 2014. The resulting distribution of likely yields, with a mean (expected value) of 164 bushels, is shown in Figure 5. Note that each interval refers to the frequency of yields greater than the previous interval yield but less than or equal to the indicated yield level. For example, the 160 bushel interval indicates there is a 9.1 percent chance of yields being more than 155 bushels and less than or equal to 160 bushels. The outcomes range from a low of 130.5 bushels to a high of 182.2 bushels, with a higher probability of an above-trend yield than a below-trend yield. The distribution is skewed to the left since extreme negative trend yield deviations have been larger than extreme positive yield deviations, which also implies that the mean (164 bushels) is slightly less than the median (165.5 bushels). The historic yield distribution suggests an 11 percent probability of an average yield below 150 bushels and a 22 percent probability of an average yield above 170 bushels. The middle 50 percent of the expected yield distribution is 161 to 170 bushels.

Implications

The U.S. average corn yield since 1960 has shown: i) large positive and negative deviations from trend, ii) the duration of consecutive years with above or below trend yields has varied considerably, iii) the correlation between yield deviations in consecutive years is negligible, and iv) the pattern of yield deviations following years of very large positive deviations (like 2014) is quite mixed. This diverse and largely random set of patterns suggests that the most objective early-season yield expectation for any year, including 2015, should be based on the trend of actual yields. A range of trend yield projections is plausible depending on the sample period, the functional form of the trend model, and whether a bias adjustment is considered or not. Given the various alternatives, we maintain that yield expectations should be based on the longest sample of data with a stable trend yield component. Since we have been unable to find significant evidence of trend yield shifts since 1960, we argue that the period of 1960-2014 best meets this criterion. After adjusting for bias, the best linear fit of actual yields in the U.S. from 1960 through 2014 results in a trend yield projection for 2015 of 164 bushels per acre. This is 2.8 bushels less than the USDA’s 2015 trend yield projection for corn of 166.8 bushels released at last week’s Outlook Forum. The higher trend projection by the USDA is likely due to a sample that starts in the drought year of 1988 and a “certainty-equivalent” approach that assumes with certainty average weather and planting progress will occur in 2015. Regardless of which trend projection is considered, there is, as usual, large risk of deviations from the projection. For example, we estimate there is roughly a one-in-ten chance of the U.S. average corn yield falling below 150 bushels and a two-in-ten chance of yield rising above 170 bushels. It’s no wonder that weather forecasters are in such high demand.