Lin, Kuang-Hsing T.

Seaver, Stanley K.

English

Research Papers in Economics

SOUTHERN  JOURNAL  OF  AGRICULTURAL  ECONOMICS  DECEMBER,  1978
WERE  U.S.  CROP  YIELDS  RANDOM  IN  RECENT  YEARS?
Kuang-hsing T. Lin and Stanley K. Seaver
After three to four decades  of substantial in-  little  evidence  of  a  trend,  it  is considered  to
crease, yields per acre of major U.S.  crops ap-  have  plateaued.  The  second  objective  is  to
pear to have tapered  off.  The  average  annual  investigate  whether  a  crop  yield  series,  if
rate  of  growth  in  crop  yields'  decreased  trendless, is random or oscillatory and, if non-
markedly from 2.7 percent for the 1950s to 1.8  stationary,  whether  cycles  are  present.  An
percent for the 1960s, and finally fell to 0.1 per-  oscillatory  series  is  defined  as  a  trendless
cent  for the first  half of the  1970s  [2].  Scien-  series dominated  by cycles;  a random  series is
tists commissioned  by the National Academy  one lacking trend and cyclical  elements.  It is
of Sciences  to investigate  agriculture  produc-  not  the  authors'  intention  to  quantitatively
tion efficiency  first discovered  the problem  [6].  evaluate  factors  underlying  the  level  and
Concern  about the situation was expressed in  changes in the level of individual crop yields.
the literature  early  this  year by both  a plant
physiologist  [11]  and  agricultural  economists
[1,  2].  If a crop yield series has reached and re-  FIGURE  1.  LASSFICATION  OF  DATA
mains  on  a  plateau,  it  would  conform  with
what  is expected  in a  stationary  or  trendless  Ti  'eries
series.  Therefore,  examination  of the leveling
of crop yields can  be accomplished  by testing  (Tred  significnce  test)
for  the presence  or absence  of  a trend in  the  /
series.  Stationary,  Nonotationary,
Recently,  Luttrell  and  Gilbert  [5]  investi-  if trendles  othervwi.
gated the influence of weather  on crop yields.3
(an  indicion  of  crop  yelds
They  assumed  that  weather  dominates  the  pla
yearly variation of crop yields around the long-  /  e
term trend  and nonweather  factors determine  (Cycle  significance  test)  (Cycle  significanca  tst)
yield trend. Detrended yield series were used to  /  \  / 
test "whether year-to-year changes in weather  Oc  R  C  sup  se 
i  i  ,.,.  ,  *  *  i  ttri»  a  a  if  * cycle  oth.rwisa  over  trand,  if  *  otharwisa have random effects on crop yields"  [5, p. 522].  if  cycle  o  ov  trend  if a  o
The  trend-deviation  approach  implies  that  a  present  cycle  present
series is additively  composed of the trend and
residual elements. The validity of the approach
depends  on the specification  of the functional
form for the trend. Model misspecification will  Yield  Yield  Yield  Yield
generate a meaningless trend-deviation series.
This study has two objectives.  As shown in
Figure  1, the first is to examine (by trend sig-  --
nificance  test)  whether  crop  yields  were  on a
plateau  in  recent  years.  If a  yield  series  has
Time  Time  Time  Time
Kuang-hsing T. Iin is Research Associate, Fort Valley State College, and Stanley K. Seaver is Professor of Agricultural  Economics, University of Connecticut.
Thanks are due to T. C.  ,ee  of the University  of Connecticut, C.  I,.  Huang of  the Georgia  Agriculture Experiment Station,  the Journal  Editor, and unknown
reviewers for helpful comments on a previous draft.
'Computed from variable weights for individual crops produced each year.
'Fuller defines  a stationary series  as the residual portion of  a series after the trend,  cyclical, and  seasonal components  have been removed  [3, p.  3871.  In  this
study, the authors adopt Kendall's and Yamane's definition  (4, p. 69: 12,  p. 3511.
'Previous work  on testing of the random versus cyclical hypothesis about crop yields is reviewed by Luttrell and Gilbert (51  and is not discussed here.
139THE  METHODS  is always nonnegative.  The cyclical hypothesis
will be rejected  if the value of the phase-length
The Kendall tau statistic and the regression  coefficient  is  not  significantly  different  from
method can be used to test for trend in a series.  zero.
The former method, being a nonparametric sta-  The U.S. average yields per harvested acre of
tistic, requires a larger value of Type I error to  19 crops  for 1960-1977  are selected  for study.
yield test results comparable with those of the  The sources of data are Agricultural  Statistics,
more powerful  tests using conventional  levels  1977  [8]  and  Crop Production, 1977 Annual
[7, p. vi].  The authors discovered that, at the .1  Summary [9] of the  U.S.  Department of Agri-
significance  level,  the  Kendall  tau  statistic  culture.
would yield conclusions  similar to those of the
regression t-tests at the .05  level.4 Because the  RESULTS
Kendall tau method requires much less calcula-
tion than regression analysis and can be easily  The values  of  the  Kendall  tau  (Table 1) for
updated, it is used in this study. Another con-  the yields of barley,  corn,  hay, peanuts,  pota-
sideration is that the sample of the study may  toes,  rice,  soybeans,  sugarbeets,  sweet  pota-
be  too small to  be analyzed  by the regression  toes, and wheat are significant at the .01 level.
method.  Those  of oats,  rye,  sorghum,  and tobacco  are
The  value  of  the  Kendall  tau  coefficient  significant at the .05 level; that of sugar cane is
ranges  between  -1  and  + 1. A  series  is  con-  significant at the .1 level and negative in value,
sidered  to  be  trendless  if  the  test  statistic  an indication of declining trend. Therefore,  the
value is not significantly different from zero at  test results  show little evidence of a trend for
the selected .1 significance level. Kendall advo-
cates  using  the  tau  coefficient  to test  for  a  TABLE  1.  RESULTS  OF  TREND  AND
"linear  trend."  However,  a  series  with  ever-  CYCLICAL  TESTS  FOR  CROP
increasing  values,  whether  it approximates  a  YIELDS,  1960-77
linear or a nonlinear function, always has a tau
value  of  unity.  Therefore,  it  seems  more  ap-  Value  of  test  statistic
propriate to use the statistic to test for the pre-  crop  Kenda  I-tau  Phase-length
sence  of  a  trend,  rather  than  specifically  a  Barley  .55**  8.09*
linear trend.  Corn  for  grain  .65**  1.07
A yearly series usually is assumed to be com-  Cotton,  t  6  4.20
posed  of the  trend,  cyclical,  and residual  ele-
Dry  edible  beans  -.24  1.41 ments. The result of a trend test, significant or
not, does not preclude other components. All it  b  peas  .6
indicates is the presence or absence of trend in  Flaxseed  .02  .11
the  series.  Therefore,  a  cyclical  significance  Hay,  a  "  .71  *  2.76
test also is conducted to examine the presence  Oat  .36**  .24
of cycles in the individual yield series.  Peanuts  for  nuts  .88***  8. 54*
Traditionally,  a  detrended  series  is  used  to  Potatoes  .89***  2.61
test for cycles.  Because  the series  studied  are  Rice  .61***  7.88**
too short to allow trend fitting by the conven-  Rye  .44**  2.76
tional  moving-average  or  variate  difference  Sorghum  for  grain  40**  3.96
methods, a test statistic that does not require
J.  J  1.  . ^.  . i  i  -r-T~  i.  i  Soybeans.  for  beans  .57.*.  1.74 trend  elimination  is  employed.  Wallis  and
Moore indicated that the phase-length statistic  Sg  c  f  gar  &  seed  29  .
is  suitable  for  a  cyclical  test  for  both  the  Sugarbeets  .62*  1.84
original  and  a  derived  series  (such  as  trend  Sweet  potatoes  .89*  4.20
deviations),  because  the  method  is  not  sensi-  Tobacco  .40*  1.47
tive  to primary trend5 [10,  pp.  401,  406].  A .1  Wheat  .566**  9.29**
level of significance is acceptable in the test be-
cause  the phase-length  statistic is  a  nonpara-  *Significant at the .1 percent level.  **Significant at the
metric statistic.  The value  of the test statistic  .05 percent level. ***Significant at the .01 percent level.
4The authors obtain the same conclusions from the two methods, for instance:
Crop  Kendall tau  Regression coefficient
Dry edible beans, 1960-77  Not significant at .1 level  Not significant at .05  level
Sugar cane,  1960-77  Significant at the .1 level  Significant at the .05 level
Tobacco,  1960-77  Significant at the .05 level  Significant at the .01  level
Tobacco,  1961-77  Significant at the .1 level  Significant at the .05 level
Tobacco,  1962-77  Not significant at the .1 level  Not significant at the .05 level
SThe method  was used by Luttrell and Gilbert  15]  and many other authors  to examine detrended  series.
140the  period  of 1960-1977  for cotton,  dry edible  although the yields of hay, potatoes,  soybeans,
beans, dry edible peas, and flaxseed.  sugarbeets,  and  sweet  potatoes  had a  signifi-
Although  the  yields  of  many  crops  have  cant rising  trend  in  recent  years,  the  rate  of
begun  to  level  off  since  the early  1960s,  the  growth  has  slowed  considerably,  and  that  of
patterns  of crop  yield  variation  from year  to  sugar cane has become negative.
year are not  identical.  Peanuts,  potatoes,  and
sweet potatoes show a rising trend,  with little  The  next  question  to  be  investigated  is
downward  fluctuation.  The  rest  of  the  series  whether  a  stationary  crop  yield  series  is
with a significant trend, except for sugar cane,  random  or  oscillatory,  and whether  a nonsta-
show a marked upward trend in the early 1960s  tionary  series  contains  cycles.  The  phase-
and  then  taper  off.  Selection  of  1960  as  the  length  test as reported  in Table  1 shows that
starting  point  is  somewhat  arbitrary.  There-  the value  of the test statistic is  significant,  at
fore,  the trend significance test is conducted to  the  .05  level,  for  barley,  peanuts,  rice,  and
ascertain whether the series with  a significant  wheat.  Because the trend test results reported
trend  are stationary  after removal  of one year  in  Table  2  indicate  that the  yields  of  barley,
for  five  consecutive  years.  The  results  are  rice,  and wheat  became stationary  after 1964,
reported  in  Table  2.  The tau values  for eight  the  phase-length  test  is  conducted  for  these
crop yield  series  (barley,  corn,  oats,  rice,  rye,  series.  The values of the test statistic (Table 4)
sorghum,  tobacco,  and wheat)  become nonsig-  are significant for rice and wheat at the .1  and
nificant. As a result,  one can conclude that the  .05  level,  respectively.  From  the  results  of
yields  of the  19 crops studied, except those  of  cycle and  trend  significance  tests reported  in
hay, peanuts,  potatoes, soybeans,  sugar cane,  Table 1, 2, and 4, one can conclude that (1) pea-
sugarbeets,  and  sweet  potatoes,  plateaued  nuts appear to have a cyclical element superim-
during 1965-1977.  posed  over  the yield  trend  for  1960-1977;  (2)
Because  the Kendall  tau  coefficient,  a rank  yields of hay, potatoes,  soybeans,  sugar  cane,
test, uses the relative position on a scale of the  sugarbeets, and sweet potatoes are nonstation-
values of a series, important information about  ary and without  a significant  cyclical element
the  absolute  differences  among  the values  is  for 1960-1977;  (3)  yields of rice and wheat are
lost.  Therefore,  the  average  annual  rate  of  oscillatory for 1965-1977;  and (4) the remaining
growth for 1960-1977  and for 1940-1959  is cal-  10 series are random for 1965-1977.
culated for the seven crops that have shown no
leveling of yields (Table 3).  Peanuts is the only  TABLE  3.  CROP  YIELD  AVERAGE  AN-
crop that shows  an exceptional  increase  from  NUAL RATE OF GROWTH
1940-1959  to  1960-1977.  In  other  words,
Crop  1940-59  1960-77
...........  percent  ..........
TABLE 2.  VALUES  OF  KENDALL  TAU  ay  1.09  .98
STATISTIC  FOR CROP YIELDS  Peanuts  1.73  4.06
OF SELECTED SUB-PERIODS  Potatoes  48  1
Crop  1961-77  1962-77  1963-77  1964-77  1965-77  Soybeans  1.43  .83
Sugarbeets  1.55  1.02
Barley  .50***  .44**  .37*  .28  .18  Sugar cane  1. 4 6b  -. 36
Corn  .60***  .55***  .50***  .45**  .35
Sweet  potatoes  2.28  1.87
Hay  .70***  .66***  .64***  .61***  .54**
Oats  .31*  .22  .14  06  -I10  a Oats  .31  .22  .14  .06  -.10  a  To reduce the effect  from abnormal  values,  the means
Peanuts  .90***  .88***  .87-**  .85***  .82***  of the first three years' and the last three years' data are
Potatoes  .87***  .89***  .89***  .90***  .88***  used as the "present"  and "future  values"  in calculating
the average rate of growth for each period.
Rice  .58***  .52***  .45**  .36*  .26  bFor 1950-59.
Rye  .41**  .33*  .28  .16  -.05
Sorghum  .32*  .25  .18  .08  -.08  TABLE  4.  VALUES  OF  PHASE-LENGTH
Soybeans  .55***  .59***  .57**  .54**  *  47**  STATISTIC FOR  CROP YIELDS
Sugar  cane  -.35*  -.32*  -.35*  -.30  -.  44**  OF SELECTED SUB-PERIODS
Sugarbeets  .65***  .60***  .55***  .66***  .62***  Crop  Period  Phase-Length  value
Sweet  potatoes  .87***  .86***  .86***  .83***  .80***
Barley  1964-77  4.40
Tobacco  .33*  .24  .13  .10  .24
Rice  1965-77  5.71*
Wheat  .58***  .52***  .45**  .37*  .28
Wheat  1965-77  6.98**
*Significant at the  .1  percent  level.  **Significant at the
.05 percent level.  ***Significant at the .01  percent level.  *Significant at the .1 level.  **Significant at the .05 level.
141IMPLICATIONS  such as a marked reduction in the cost of ferti-
lizer,  which  would  make  it  profitable  for
U.  S.  average  yields  of  12  crops,  including  farmers to increase production investment.
corn, cotton, rice, tobacco, and wheat,  were sta-  An  optimistic  view  of  the  problem  is  that
tionary  in recent  years  (rice and  wheat being  leveling  in crop  yields  is,  in part,  a  result  of
oscillatory and the rest random),  an indication  stricter  agriculture  pollution  controls  and/or
of a yield plateau. This finding may imply that  an increase  in crude oil and natural gas prices.
since  the  1960s  prevailing  technology  in pro-  The farm sector may still be in the resource re-
ducing  these  crops  has  been  adopted  by  allocation  process resulting  from pollution re-
farmers  to  the largest  extent  possible.  If  so,  gulation and petroleum market disruptions.  A
weather  and  other  nontechnological  factors  few  years  may  pass  before  the  situation  be-
will play an  increasing role  in the determina-  comes  clear.  One  reviewer  pointed  out  that
tion of the level and changes in the level of crop  growing fixed costs in recent years  (in particu-
yields.  Two  possible  developments  could  pre-  lar  higher  real  estate  and  farm  machinery
vent continued  plateauing.  One is  new techni-  values) may have affected crop yields.  In other
cal breakthroughs  such as high yield,  pest- or  words, because  of increasing production costs
drought-resistant  varieties.  The  other  is  (both fixed and variable) producers are becom-
dramatic  changes  in  the  cost-price  structure,  ing more concerned  about net return per dollar
investment than increased yield.
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142

WERE U.S. CROP YIELDS RANDOM IN RECENT YEARS?

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