Bobst, Barry W.

English

Research Papers in Economics

SOUTHERN  JOURNAL  OF  AGRICULTURAL  ECONOMICS  December,  1969
AN  INPUT-OUTPUT  APPROACH  TO  THE  STUDY
OF THE  FLOW  OF  FUNDS
TO  AGRICULTURAL  CAPITAL  MARKETS
B.  W. Bobst*
Agriculture  is  experiencing  an  increasing  reliance  downward  by  the  Federal  Reserve  Board  and  the
on  commercial  and governmental  sources of capital in  National  Bureau  of Economic  Research  to a  system
order  to finance  the adoption of new technology and  of  accounts  describing  the  capital  budget  of  the
the  organizational  changes  made  necessary  by  that  national  economy.  The  Federal Reserve  Board  began
technology. If this trend progresses,  it is reasonable  to  the  publication  of  these  accounts,  under  the  title
suppose  that  the  interdependence  of flows of funds  "Flow  of Funds/Saving  Accounts"  (later  abbreviated
to  the  farm  sector  with  flows  to  other  sectors  will  to  "Flow  of  Funds  Accounts"),  in  the  Federal  Re-
become  greater  and  will  become  a  more  important  serve  Bulletin  in  1959  on  a  quarterly  and  annual
consideration  in  matters  of farm  credit  policy.  In  a  basis. 
recent  paper,  Lee  [5]  has  called  for  further research
into  the  implications  of  changes  in  the  financial  The flow  of funds  accounts have  two major parts.
structure  of the  farm sector,  among them the growth  One  part  contains  summaries  of financial  and  non-
of alternative  sources  of funds and the changing roles  financial  saving and investment activities by economic
of major lending  groups.  It  is the intent of this paper  sector.  The  second  and  most  important  part  (from
to  suggest  a  procedure  through  which  the  financing  the standpoint  of this paper)  shows the flow of funds
of the farm sector  can be  analyzed as one of a number  among  economic  sectors by type of credit  instrument
of economic sectors which are financially interrelated,  or transaction  category  involved  in  the flow.  Savings
activities  are  portrayed  in  the  accounts  as  uses  of
The  procedure  which  this paper will propose com-  funds;  investment  activities  are  shown  as  sources  of
bines  some of the  concepts of input-output  analysis,  funds.2 In general,  the accounts  show  how financial
which should be familiar to most, with data generated  assets,  in  the  form  of  demand  and  time  deposits,
in  the  flow  of  funds  accounts,  which  may  be  less  insurance  premiums,  pension funds, and  so forth, are
familiar.  For  this  reason,  exposition  of  the  mathe-  mobilized  by  the  financial  sectors  of the  economy
matics  of  input-output  analysis  will  be  omitted  in  in  order  to  finance  the  creation  of liabilities  such as
this  outline  of  the  procedure  in  favor  of  a  brief  mortgages,  bank loans, bond and stock issues, and the
discussion  of  the  data  contained  in  flow  of  funds  like.  By  the  equality  of saving and investment,  total
accounts.  uses of funds are  by definition  equal to total sources
for any given  time period.
Copeland  [2]  was the first to suggest the construc-
tion  of  a  comprehensive  system  of social  accounts  The  Federal  Reserve  System  employs a  three-way
which would record  the flow of funds corresponding  classification  system  in  the  construction  of the  ac-
to the exchange  of all goods and services in the econo-  counts.  Each  entry  is  classified  according  to  the
my.  This  system was  originally  conceived  to  be  even  economic  sector in which it occurs, the type of credit
more  comprehensive  than  the  GNP  accounts,  since  instrument  used, and whether  it  is a  use or source  of
flows  of  funds  involved  in  the  exchange  of  inter-  funds  to  the  sector.  Each  entry  in the F.R.S.'s  flow
mediate  goods and  services  were  also  to be included.  of funds  accounts  can be  thought of as belonging on
Later,  the scope  of the flow of funds idea was revised  one  side or the other  of a  flow equation.  Just  which
*  B.  W.  Bobst is in the Department  of Agricultural  Economics,  University of Kentucky.
1 See  [11]  and  [7]  for more  complete descriptions  of the accounts.
2 Uses  and  sources  of funds  are flow  concepts which  correspond  to  the more  familiar terms of assets and lia- bilities.  A  "use"  of funds  refers  to  a  change  in  financial  assets,  while  a  "source"  of funds  refers  to  a  change  in
liabilities.
21side  the  entry  might  be  on  depends  entirely on  the  elements measure quantities obtained by a  sector from
way one looks at the problem. For instance,  the use  of  itself  and  all other  sectors  [6,  pp.  134-137].  From
$1  billion  by  households  as  demand  deposits  and  this  standpoint,  the  matrix  in Table  I  appears  to be
currency  is  clearly also a source of funds to the bank-  the  transpose  of  an  input-output  matrix.  The  rows
ing  sector  in  the  same  amount.  This  dual  nature  of  express  quantities  obtained from sectors  listed  in the
fund  flows  allows  a  transformation  of the  F.R.S.'s  columns,  and  columns  show  quantities  supplied  to
accounts  into  a  format  which  emphasizes  the  inter-  sectors  listed  in  the rows.  Thus,  the elements of the
sectoral  nature  of the flow  of funds.  farm-sector  row  indicate  the  net  amounts of funds
each  sector  advanced  to  the  farm  sector  in  1963.
Since  each  flow  item  in  the  accounts  represents  Elements  of the farm-sector  column indicate  the  net
both a  use and  a  source  of funds, the way  is clear to  amounts  that  the farm-sector  advanced  to other  sec-
classify  flows  by  sectors,  with any  given  flow  item  tors  that  year.  Other  rows  and  columns  are  to  be
being  a  use  of funds  to  one  sector  and  a  source  of  interpreted  similarly.
funds  to the same or some other sector. For instance,
the  use  of $4.3  billion by households  as demand  de-  If it  served  no  other  purpose,  the intersecor  flow
posits  and  currency  in  1963  is  clearly  a  source  of  mati  would  serve  to  remind  us  that  the  financial
funds  to the banking system. Instead  of grouping this  tiit  of  the  fr  eco  e  closely  onnected
with  those  of other  economic  sectors.  The  matrix source  of funds with  demand  deposits  from all other  wi  th  e  o  the  eo  ic  secors.  Te  mr
sectors,  as the  F.R.S.  accounts  do,  the intersectoral  h  t  sector  hch  are srce  of funds for
character  of this flow can  be  preserved  by treating it  the  farm sector  have  access  to a variety of alternative
uses  for  those funds.  It  brings the financial  structure as  one  cell  in  a  matrix  having  households  as  a  use  of  the  farm  sector  into  perspective  as  an  integral,
sector  on one axis and the banking  system as a source  t  it  eecte  te
sector  on the other.  Uses of funds as demand deposits  ough  minor,  part  of  the  financial  structure  of the
and currency  by other  sectors  can  be  similarly classi  over-all economy.
fled.  The result will be to show the flow of funds into  The  intersector  flow  matrix  can  be  made  to  serve
the  banking  system  in  the form of demand  deposits  other  purposes,  however,  by continuing  to apply the
and currency  as  a vector of intersectoral flows, rather  techniques  of input-output  analysis.  In input-output
than as a  single  source  entry of $6.0  billion  in 1963,  analysis,  final  outputs  of goods  and  services  can  be
as the F.R.S. accounts have it.  treated  as  a  set  of variables  which  are  functions  of
another  set  of  variables,  the  total  outputs  of goods
Intersectoral  flow  matrices  can  be  derived  from  and  services.  The  functional relationship between the
the  F.R.S.  flow  of funds  accounts  for  each type  of  two is expressed in a matrix of linear inputs coefficients
credit  instrument  or transaction  category.  These indi-  known  as  a  structural matrix  [6,  pp.  138-140].  In a
vidual  matrices  might  be of interest to the researcher,  similar manner,  the total quantity of sources of funds
especially  perhaps  the  intersectoral  flow  matrix  for  in each  sector  can be expressed as a linear function of
farm  and  commercial  mortgages.  Generally,  though,  total  uses of funds  by  all  sectors, the functional  re-
the  individual  matrices  would  be  added  together  to  lationship  between  the  two  sets  of variables  being
derive  a  matrix  expressing the summation of all inter-  embodied  in  a  matrix  of  flow  coefficients.  A  flow
sectoral  flows  of  funds  for  the  time  period  under  coefficient  is defined  as the ratio of funds advanced
consideration.3 Such  a  matrix  is  shown  in Table  1  to source sector i by use  sector j over the total quanti-
for six  economic  sectors in  1963.4 Reasons of space  ty of funds used by sector j, or
rather than data  dictate  the use of six sectors  in this  C.  =  u  /U 
table.  At least  11  sectors are identifiable  in the F.R.S.  1J  j
accounts;  in  principle,  any  number  of  sectors  could  These  coefficients  can  be  computed  from  the  data
be included.  contained  in  intersector  flow  matrices.
The  intersector  flow  matrix of Table 1 bears some  Table 2 displays a flow coefficient matrix computed
resemblance  to  an  input-output  matrix.  In an  input-  from  the  intersector  flow  matrix  of  Table  1.  The
output matrix, the row elements express the quantities  individual  coefficients  show  the amount  of funds ad-
of  goods  and  services,  measured  in  value  terms,  sup-  vanced  to row  sectors  per  dollar of total funds  used
plied by one  sector to itself and to all others; column  by  the  corresponding  column  sectors.  For  example,
3 Different  kinds  of credit  instruments,  such  as bank  deposits,  pension  funds, mortgages,  stock  issues, and  so
forth,  are,  thus,  added  together  in  the  same way  that  activity  levels are added in  input-output  matrix..  .by their
dollar  values.  The  high degree of fungibility of most credit instruments makes this kind of addition even  more de-
fensible than  in an  input-output matrix representing  dissimilar physical quantities.
4 The  1963 flow of funds accounts were  chosen  to illustrate  the procedure for ease  of reference to the summary
matrices  published  in  the Federal Reserve Bulletin.  Since  1963, the farm  sector has not been  identified  separately
in these matrioes,  although  separate  data have  been  published  in statistical  supplements.
22TABLE 1.  INTERSECTOR  FLOW  MATRIX,  1963,  FOR  SIX  SECTORS,  IN  BILLIONS  OF  DOLLARSa
Uses  of Funds
Sources
of  Banks and  Other  Total
Funds  Households  Farm  onancal  Governments  Savings  Financial  Sources
Business  Institutions
Households  -.3  0  1.1  -.8  19.2  7.0  26.2
Farm  -1.6  0  .7  .5  1.6  .4  1.6
Nonfinancial Business  -8.0  0  9.2  4.5  9.6  9.8  25.2
Governments  8.0  0  1.4  .2  6.0  0  15.7
Banks and Savings
Institutions  27.4  -.1  3.1  5.0  1.1  2.2  38.8
Other Financial  11.6  .2  3.8  2.6  3.3  2.8  24.4
Total  Usesb  37.2  .1  19.4  12.0  40.8  22.2  131.8
a Sources:  FederalReserve  Bulletin, 53:851-859,  May 1967.
Flow of Funds, Annual, 1946-65, Washington, Board of Governors of the Federal Reserve  System, October  1966.
b Matrix elements may not add to total because  of rounding.
I'
L~TABLE 2.  FLOW COEFFICIENT  MATRIX,  1963,  FOR  SIX  SECTORSa
Uses  of  Funds
Sources
Nonfinancial  Banks  and  Other
Households  Farm  Business  Governments  Savings  Financial
Funds  Institutions
Households  -.0081  0  .0568  -.0664  .4694  .3169
Farm  -.0430  0  .0362  .0415  .0392  .0180
Nonfinancial Business  -.2151  0  .4780  .3734  .2353  .4404
Governments  .2164  0  .0724  .0166  .1483  0
Banks and Savings
Institutions  .7366  -1.0000  .1602  .4191  .0270  .0989
Other Financial  .3132  2.0000  .1964  .2158  .0809  .1258
a Source:  Table  1.Table  2  shows that the  farm sector  obtained  $.0392  if flow  coefficients  were  found  to  be  unstable  over
of every  dollar  advanced  by banks  and  savings  insti-  time,  a  disequilibrium  situation  would  be indicated.
tutions in 1963. Total sources of funds for each sector  These  findings would give rise to questions concerning
(from Table  1) are equal to the sum of the products of  the choice of uses of funds by the sectors which extend
the  row  coefficients  and total  uses  of funds  by the  credit  to agriculture.  Do  the farm sector  coefficients
corresponding  sectors.  Thus, for  sector  i:  react  systematically  to  interest  rate  changes  and  to
changes  in monetary  policy?  Can  trends be discerned
Si =  Z ci  U  . in the  farm sector  coefficients?  If trends do exist, can
3J~~~  ~they  be attributed  to changes  originating  in the  agri-
For  n  sectors,  the relationships  can be written  com-  cultural  credit  market  or  are  they  residual  effects
pactly  in matrix form as:  from changes  taking place elsewhere in the economy?
S  =  CU,
'~~~S  =CU,  Redimensioning of the matrices might prove useful.
where  S  and  U  are  n  x  vectors  and  C  is  a n  x  n  Flow  coefficient  matrices  computed  on a  quarterly
matrix  of coefficients.  basis could  be  used to examine  the seasonal behavior
of  flow  coefficients.  They  might  also  be  useful  in
The  relationships  between  sources  and  uses  of  forecasting.  Disaggregation  of the  present  six-sector
funds  by sector, stated in this way, are linear approxi-  model would  allow agricultural finance activities to be
mations  of the  supply  functions  for loanable  funds,  moe closely  identified  with the institutions involved
with supply  equalling  demand, at  least in the ex post  in  them.  Division  of  the present governments  sector
sense  of  an  equality  between  aggregate  saving  and  would enable one to distinguish Federal lending, which
investment. If it can be assumed that equilibrium  is an  i  important  to the farm sector, from uses of funds by
ex ante sense is also achieved, and that the relationships  state  and  local  governments,  which  are  not.  Similar
are  in  fact  approximately  linear,  then  the  flow  co-  identification of the farm loan activities of commercial
efficient  matrix will be unique and valid for any given  banks  and  insurance  companies  could be  secured  by
vector  of uses  of funds.  Under these  conditions,  the  separating them from their composite  sectors. Further
quantities  of funds  supplied  to  sectors  could  be  de-  separations  could be  made where  desirable and where
termined  for  any  given  set  of quantities  of uses  of  data availability  allow
funds.  This  argument  also  finds its corollary  in input-
output analysis.  Data availability  becomes  a restrictive factor when
contemplating  a  regional  application  of  intersector What  potential  uses  do  flow  coefficient  matrices  flow  of funds  analysis.  Some state and  regional  data
have  in  analyzing  the  flow  of funds  into  the  farm  exist  for  the  farm  sector,  particularly mortgage  loan
sector?  Such  uses  must  ultimately  rest  on  the  em-  data. These could be used to estimate intersector flows
pirical  properties  of the  matrices  themselves.  If,  for  of mortgage  funds on  a  regional  basis,  allowing  com-
instance, the row flow coefficients for the farm sector  parisons  of  the  South  with  other  regions.  At  this
tend to remain  stable  over  time,  a  situation  of struc-  writing,  however,  a  fully articulated  intersector  flow
tural  equilibrium  in  the  supply of agricultural  credit  model  on  a  regional  basis  seems  unattainable.  If
would be indicated. No  significant reallocation of uses  supporting  data  does  become  abailable,  it  is  more
of funds would be  occurring,  so total funds advanced  likely  that  their  coverage  will  be  along  the  lines  of
to  the  farm sector  would fluctuate only with changes  Federal  Reserve  Districts than  along historic regional
in the total use of funds by supplying sectors. Stability  boundaries.
of  the  coefficients  would  lend  potential  forecasting
power  to  the model.  Forecasts  of total uses of funds
by  the  various  sectors,  in the  form of  estimates  of  While  much  work  remains  to  be  done,  the pro-
personal and corporate saving, Federal lending budgets,  cedure  outlined  here  seems  well  enough  in  hand  to
and  estimates  of  future  loan  commitments  on  the  allow  a  start  at  empirical  application  at the national
part  of  banks,  insurance  companies  and  the  like,  level.  It is  my opinion that intersector  flow  of funds
could be  used to forecast  the quantity of funds to be  analysis will prove  to be a valuable  tool in the  study
made  available  to  the farm  sector.  On the other hand,  of agricultural capital formation.
25REFERENCES
1.  "A Quarterly  Presentation  of Flow  of Funds, Saving,  and Investment,"  FederalReserve  Bulletin, 45:828-859,
August 1959.
2.  Copeland,  Morris  A.,  A Study of Moneyflows in the United States,  New York, National  Bureau of Economic
Research,  1952.
3.  FederalReserve  Bulletin, 53:851-859,  May  1967.
4.  Flow of Funds, Annual, 1946-65, Washington,  Board  of Governors  of The  Federal  Reserve  System,  October
1966.
5.  Lee,  John E., Jr.,  "Changes  in  the Financial Structure of the Farm Sector and the Implications for Research,"
(paper presented before the A.A.E.A. annual meeting,  Bozeman, Montana,  August 20, 1968).
6.  Leontiff, Wassily, Input-Output Economics, New  York, Oxford University  Press,  1966.
7.  "Revision  of Flow of Fund Accounts," FederalReserve  Bulletin, 51:1533-1538,  November  1965.
26

AN INPUT-OUTPUT APPROACH TO THE STUDY OF THE FLOW OF FUNDS TO AGRICULTURAL CAPITAL MARKETS

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Research Papers in Economics