Research and Development/Tech Change/Emerging Technologies,

Bauer, Larry L.

Hancock, Curtis R.

English

Research Papers in Economics

SOUTHERN  JOURNAL  OF AGRICULTURAL  ECONOMICS  DECEMBER  1975
THE  PRODUCTIVITY  OF AGRICULTURAL  RESEARCH
AND  EXTENSION  EXPENDITURES  IN THE  SOUTHEAST
Larry  L. Bauer and  Curtis R. Hancock
With current high food prices and increasing  PROCEDURE
talk  about a world food  crisis, there is renewed
interest in production agriculture and in the allo-  A  Cobb-Douglas  production  function  was
cation of resources to agriculture. It would seem,  estimated using  ordinary  least  squares  regres-
therefore,  that  estimates  of  agricultural  pro-  sion  technique.  The  timepath  of research  and
duction functions and their associated marginal  extension  activities  effect  was  estimated  by
products  would  be  useful  to  those  responsible  using  a  general  polynomial  distributed  lag
for resource allocation to the agricultural sector.  technique, developed  by Tom Johnson [4].
This paper intended to give policymakers  infor-  The states considered in the study were the
mation on which to base decisions relative to the  southeastern  states  - Alabama,  Arkansas,
impact  of investments  in agricultural  research  Florida,  Georgia,  Kentucky,  Louisana,  Missis-
and  extension  activities.  The  level  of  appro-  sippi,  North  Carolina,  Oklahoma,  South  Caro-
priations  to  such  activities  can  be  considered  lina, Tennessee,  Texas  and Virginia. They were
a proxy measure of technology. Most researchers  selected  to be a fairly homogeneous group.  The
familiar with this area feel that the total effect  model used both time series and cross-sectional
of new technology  on production  does not occur  data.  Cross-sectional  aspects  of the  data  were
at one momemt in time, but may be spread over  partially accounted for with the use of intercept
a number or years. Considering  this, a distrib-  dummies.
uted lag on research and extension expenditures  The  time period  covered  was  1949 through
was  incorporated  into  the  production  function  1968.1
estimated in this paper.
STATISTICAL  MODEL
OBJECTIVES
The objectives of this study were:  The statistical model used in this study was
1. To estimate  marginal productivity  similar to those used by Griliches  [3] and Even-
of research and extension activities  son  [2]. The primary  differences  were in aggre-
by  estimating an  agricultural  pro-  gation  of certain  variables  and  in  method  of
duction function for the Southeast.  handling the lagged effect of technology.
2.  To  measure  the  timepath  of  the  A Cobb-Douglas production function was esti-
effect  of  research  and  extension  mated  of the general form2 :
activities.  Q =f (T, L, F, S, C,  D)
The authors express  appreciation to Charles  B. Sappington,  Darrell  Mundy, and Ray Daniel for reviewing  an earlier draft of this manuscript.
Associate  Professor,  Department  of Agricultural  Economics,  University  of Tennessee,  Knoxville,  and  Farm  Management  Specialist,  University  of  Kentucky and
former  Fellow, University of Tennessee.
1
In  order  to  estimate  the  distributed  lag  function  imposed  on  technology,  data  for  research  and  extension  appropriations  extended  back  beyond  1949.
2In  the  most  strict  sense,  this  was  not  a production  function  because  measurement  was  in  dollars rather  than  physical  quantities.  Due  to  problems  of
measuring physical quantities,  deflated dollar values were used with the  assumption that the deflation  removed the influence of price  variation.
117where:
tilizer,  lime  and  miscellaneous
Q  = gross agricultural output in each  expenses  in  each  state  in  thou-
state in millions of 1968 dollars.  sands of 1968 dollars  [6]. The de-
The  variable  was  the  sum  of  flator  used  was  prices  paid  for
farmer cash marketings, govern-  seed,  fertilizer  and  all  items  in
ment payments to farmers, value  production  respectively  [5].
of home consumption of farmers,
and  net  farm  inventory  change  C  = captial and  depreciation.  This
[6].  The deflator was the index of  variable  was the  farm  expendi-
prices received by farmers for all  tures for repair and operation  of
farm products [1].  capital  items,  and  depreciation
and  other  consumption  of  farm
T = technology. This variable was the  capital  in  each  state  measured
yearly sum of research and exten-  in thousands  of 1968 dollars  [6].
sion appropriations  measured  in  This series  was  deflated  by  the
1968  dollars.3 Research  appro-  index or prices paid for all items
priations  plus  state  appropri-  in production  [5].
ations  less the  balance  from the
previous  year.  Values were  con-  D = state  dummy  variables.  These
verted  to  1968  dollars  by  the  variables  were zero-one  dummy
implicit price deflator for the total  variables  for the thirteen south-
gross national  product [1].  eastern states,  i.e., this variable
was  equal  to  one  for  all  obser-
L  =expenditures  for  agricultural  vations for a particular state and
hired labor. This variable was the  zero otherwise.
total  expenditure  for  farm hired
labor  in each state  in thousands  RESULTS
of  1968  dollars  [6].  The  deflator
used was the index or prices paid  The estimated  coefficients  of the production
for hired labor [5].  function  appear  in Table  1. The  t-values  were
used  to test the hypothesis bi>  0 in the case of
F = total  expenditures  for  feed  and  coefficients  of real variables, and bi =  0 in the
livestock  in  each  state  in  thou-  case  of dummy variables.  In other words, a one-
sands of 1968 dollars [6]. The data  tail  test was  performed  on  coefficients  of real
were  deflated  with  the  index  of  variables and a two-tail test on those of dummy
prices paid for feed and livestock  variables.  The  tests  were  conducted  in  this
respectively  [5].  manner because it was felt a priori that coeffi-
cients  of the  real  variables  should  be  greater
S =  total  expenditures  for  seed,  fer-  than zero.
3
The  data  for extension were  provided  in  mimeographed  sheets  provided  by  the  Federal  Extension  Service  of  USDA.  The  research  data were  obtained  from
the  published  annual  reports  of the  branch  of USDA  responsible  for  administering  funds  to  state  experiment  stations.  The  name  of this branch  changed  several
times during  the time span of the data used  in this study, but is presently  known as the Cooperative  State Research  Service.
118Table  1.  ESTIMATED  COEFFICIENTS  AND  LEVEL  OF  SIGNIFICANCE  OF  AN  AGRICULTURAL
PRODUCTION  FUNCTION  FOR THE SOUTHEASTERN  UNITED STATES
Estimated  Level of
Variable  coefficient  (t-value)  significance
a
(Percent)
Constant term  -2.203
Real Variables
Labor  .171  (6.639)  1
Feed and livestock  .211  (9.424)  1
Seed, fertilizer, lime, miscellaneous  .537  (13.169)  1
Capital and depreciation  .022  (.419)  N.S.
Technology (research and extension)  .059  b  b
State Dummy Variables
Kentucky  .048  5.450  1
North Carolina  .041  2.570  5
Oklahoma  .042  1.390  N.S.
TennesseeC  0  -
Louisiana  -.026  -1.651  10
Mississippi  -. 027  -2.363  5
Texas  -. 032  - .816  N.S.
Arkansas  -.033  -2.549  5
South Carolina  -. 039  -2.976  1
Alabama  -.051  -3.750  1
Georgia  -. 064  -4.887  1
Florida  -0.75  -3.660  1
Virginia  -. 075  -7.239  1
aNull hypothesis bi>0 for real  variables,  bi = 0  for state dummy variables.
bThe estimated lag distribution  parameter  was significant  at the  10%  level.
CTennessee omitted in estimation  to avoid singularity.
The estimated coefficients for labor, feed and  between the states being handled with intercept
livestock,  and seed,  fertilizer,  lime  and miscel-  dummies. As shown in Table  1, all dummy vari-
laneous were all significantly greater than zero.  able coefficients were significantly different from
That for technology was not estimated directly,  zero, at least at the 5%  level, with three excep-
but the  estimated  coefficient  of the lag  distri-  tions  - Louisana,  Oklahoma  and Texas.  This
bution imposed  on this variable was significant  meant  that  intercept  values  for  all  but  these
at  the  10%  level.  The  sum  of  the  coefficients  three states were statistically different from the
for  this  estimated  Cobb-Douglas  production  intercept  for  Tennessee.  However,  when  these
function was  one. This  implied constant  return  values were translated into dollars terms (Table
to  scale,  an  assumption  commonly  made  in  2),4  the  difference  between  the  highest  and
economics.  lowest  values,  Kentucky  and  Virginia,  was
It  was assumed that the production function  $1,700.  This  indicated  that,  all  other  things
was the same  in  all states, i.e.  the slope  coeffi-  constant,  the  difference  in  total  farm  output
cients were assumed to be the same, differences  among  the  states  was  quite  small.  Since  the
4 This translation  was made  by  adding,  since  the  variables  were  multiplicative  in a Cobb-Douglas  function,  each  respective  state dummy  variable  coefficient
to the  overall  regression  constant  term  which  was  the  intercept  for  Tennessee.  The  antilog  of  each  was  taken  and  changed  from  millions  of dollars,  the unit  of
measure of the dependent  variable,  to  the dollar figures reported  in  Table 2.
119Table  2.  ESTIMATES  OF  INTERCEPTS  FOR  The  reported  marginal  products  were  changed
EACH  STATE  IN  AGRICULTURAL  from  the  units  used  in  estimation  to  a  dollar
PRODUCTION  FUNCTION  FOR  change in farm output per dollar  change in the
SOUTHEASTERN  UNITED STATES  respective  input.  For  example,  in  the  case  of
labor, the estimated coefficient was .171 and the State  Intercept
a($)  geometric  mean  was  $88,841.  The  predicted
Kentucky  6,998  value of the dependent variable with each inde-
North Carolina  6,891
Oklahoma  6,485  pendent variable at its geometric mean was ap-
TLouisan  56,899  proximately  $777  million.  Therefore,  the  esti- Louisiana  5,899
Mississippi  5,892  mated marginal product for labor was:
Texas  5,820
Arkansas  5,813  777
South  Carolina  5,729  MP  =  .171  +  .00150
Alabama  5,568  88,841
Georgia  5,408
Florida  5,271  or $.00150 million of farm output per thousand
Virginia  5,268  dollars of hired labor, which translates  to $1.50
geometric mean of dollar output in these states  per  one  dollar of hired labor.  Each  $1  increase
over the period covered  was almost 768  million  in expenditures  for  hired  labor  would,  on  the
1968  dollars,  it  could  be  concluded  that  each  margin,  add $1.50 to farm output. This applied
state's production function was essentially at the  only  to hired  labor  since  it was  not feasible  to
same level since intercept values differed by such  accurately  quantify  non-hired  labor.  However,
small  amounts.  The  difference  in  the  value  of  it would seem safe to assume that the non-hired
farm  output  from  these  states  could  be  attri-  labor contributed  to  the  marginal  productivity
buted to different  levels of various inputs, given  of hired labor.
the model's  assumption  that there were no  dif-  The marginal product  for feed  and livestock
ferences in slopes  among the states.  expenditures variable was $1.69, indicating that
there was still room for profitable  expansion  in
MARGINAL  PRODUCTS  livestock enterprises.
The marginal  product of $3.88  for seed,  fer-
Policy-makers,  responsible  for  allocation  of  tilizer,  lime  and  miscellaneous  expenditures
funds  to  agriculture,  need  to  know  what  the  indicated  that it  would  be highly  profitable  to
benefits are to research and extension activities.  expand  these  items  considerably.  This  would
Marginal  products are one source of such infor-  seem to be building a case for increased supplies
mation.  of  high  quality  seed  and  fertilizer  in  the
Southeast.
Table  3. MARGINAL  PRODUCTS  (DOLLAR  The estimated marginal product of the capital
CHANGE  IN  FARM  OUTPUT  PER  and depreciation  variable  was  $.11.  Each addi-
DOLLAR  CHANGE  IN  VARIABLE)  OF  tional  dollar  spent  on  capital  items  increased
ESTIMATED  COBB-DOUGLAS  PRO-  the  dollar value  of farm output by  $.11,  a rate
DUCTION  FUNCTION  FOR  SOUTH-  of  return  that  was  at  least  favorable  when
EASTERN  UNITED STATES  compared  to  the  interest  paid  on  savings
______________________accounts.
The  marginal  product  for  technology  was Variable  Marginal  product
$5.84  - for  every  dollar  increase  in  research
Labor  $1.50
Feed and  livestock  $1.69  andextension  appropriations,  farmoutput  was
Seed,  fertilizer,  lime,  miscellaneous  $3.88  increased by $5.84. For example, if research and
Capital  and  depreciation  $ .11
Technology  (research  and  extension)  $5.84  extension  appropriations  in the thirteen south-
eastern  states  were  increased  by  10  million
The  marginal  product  for  each  variable  is  dollars,  farm  output  from  this  change  would
presented  in Table  3.  The  formula  used  in  the  eventually  increase,  ceteris  paribus,  by  $58.4
calculation  was:  million.  This  was  assuming  the  increase  in
A  appropriations  was  a  one-time  occurrence,  i.e.
MPX  =b-_  appropriations  return  to  their  original  level.
i  Xi This increase would occur over a nine-year period
where Xi was th e geometric mean of independent  rather  than  wholly  in  the  year  of  increased
variable  i and  Q the  predicted  value of Q  with  expenditures; i.e., the estimated lag distribution
all  inputs  at their respective  geometric  mean.  indicated  that  11.1%  of this  total  effect  would
120occur in each of nine years, the current year plus  output  per  dollar  appropriation  could  still  be
eight more.  considered  a  high return.  Data on agricultural
A lag distribution  of this  configuration  was  research  and education  activities  of the private
not what was hypothesized. It was expected that  sector  is scarce, making the division of the tech-
the  distribution would  have a  "hump",  i.e.  the  nology variable into public and private contrib-
annual  effect  of technology  on  output  was  ex-  utions a difficult task, if not an impossible  one.
pected  to build up to  a  maximum  during  some  Perhaps a more important assumption is that
time period after the appropriation, the declining  of a  perfectly  elastic  demand  for  farm  output.
with the passage of time. In this study, however,  With  the  inelastic  demand  that exists  (as  in-
the reported lag distribution best fitted the data  creased technology results in larger farm output,
when  compared  to  distributions  of  different  causing prices to fall) consumers are the ultimate
shapes,  including  different  time  periods  of  benefactors.
research and extension data.  Even though the  implicit inclusion  of these
assumptions might have altered  the magnitude
CONCLUDING  STATEMENT  of estimated coefficients  and marginal products,
it  was  felt  they did  not change  the conclusion
The estimated marginal product of $5.84 for  that  research  and  extension  activities  have  a
research  and  extension  expenditures  indicated  positive  and  substantial  effect  on  agricultural
a  high  return  to  appropriations  in  this  area.  output.  This  would  seem  to  be  important  in a
Because the statistical model used in this study  time  of high  food prices,  world  food  shortages
was relatively  simple, some implicit underlying  and tight state and federal budgets.  Of course,
assumptions  should be  mentioned.  this is only one  area with which  governmental
The  "somewhat  heroic5 assumptions"  was  decision-makers  have  to deal. In the process  of
made  that  all  advances  in  technology  are  due  allocating  scarce  revenue,  the  policy-maker
to  research  and  extension  expenditures.  would  have to consider  the return to monetary
However,  if only  half  the  estimated  marginal  resources  in  all  uses. Hopefully,  this  article
product of technology were the result of research  pointed  out  substantial  benefits  to  appropri-
and  extension  activities  in  Land-Grant  Uni-  ations  for agricultural  research  and  extension
versities,  the  $2.92  increase  in  value  of farm  activities.
These  are  the  words  of one  of  the  anonymous  reviewers.  The  authors  recognized  this  problem,  but  it  is  perhaps  better  that  it  be  stated  explicitly.
121REFERENCES
[1]  Council  of Economic  Advisers. Economic Report of the President, U.S.  Government  Printing
Office,  Washington, D.C.,  1969.
[2]  Evenson,  R.  "The  Contribution  of Agricultural  Research  to  Production,"  Journal of Farm
Economics, 49:  1415-1425,  1967.
[3]  Griliches,  Z.  "Research  Expenditures,  Education,  and  the Aggregate  Agricultural  Production
Function,"  The American Economic Review,  54:  961-974,  1964.
[4]  Johnson,  T.  "A Note on Distributed Lags in Polynomial  Form," Unpublished paper presented
to an econometric workgroup  at North Carolina State University, Raleigh, in August 1969.
[5]  U.S.  Department  of  Agriculture.  Agricultural Prices,  1969  Annual  Summary,  Statistical
Reporting Service,  pp.  1-3  (70),  U.S. Government Printing Office,  Washington,  D.C.,  1970.
[6]  U.S.  Department  of Agriculture.  Farm Income State Estimates, 1949-69, Economic  Research
Service,  FIS 216  Supplement,  U.S.  Government Printing  Office,  Washington,  D.C.,  1970.
122

THE PRODUCTIVITY OF AGRICULTURAL RESEARCH AND EXTENSION EXPENDITURES IN THE SOUTHEAST

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