Describing Agricultural Technology - Bridging the Gap from Specific Processes to General Production Functions

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NOT FOR QUOTATION WITHOUT PERMISSION

OF THE AUTHOR

DESCRIBING AGFUCULTURAL TECHNOLOGY

--

BRIDGING THE GAP FROM

SPECIFIC

PROCESSES TO GENERAL PRODUCTION FUNCTIONS.

Kirit S. Parikh

October, 1983 WP-83-95

Working Papers a r e i n t e r i m reports on work of t h e International Institute for Applied Systems Analysis a n d have received only limited review. Views or opinions expressed h e r e i n do n o t necessarily r e p r e s e n t those of t h e I n s t i t u t e or of i t s National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

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I would like to thank Csaba Csaki and Istvan Valyi for critical discus- sions and for their help in providing access and understanding of data from Hungarian experimental stations. Jan Morovic, Martha Neunteufel and Laslo Zeold helped in computer work whose help I gratefully ack- nowledge. Finally, I would like to thank Cynthia Enzlberger, for typing this manuscript.

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The Food and Agriculture Program a t IIASA focuses i t s r e s e a r c h activities on understanding t h e n a t u r e a n d dimension of t h e world's food problems, on exploring possible alternative policies t h a t c a n help allevi- a t e c u r r e n t problems a n d prevent f u t u r e ones.

As a p a r t of t h e r e s e a r c h activities investigations of alternative paths of technological transformation in agriculture i n t h e c o n t e x t of r e s o u r c e Limitations a n d long t e r m environmental consequences a r e being investigated. The purpose i s t o identify production plans s t r a - tegies which a r e sustainable. The general approach and methodology developed a t IIASA for t h i s investigation is being applied in several c a s e s t u d i e s on t h e regional level in different countries with t h e help of colla- borating institutions.

Before we c a n explore t h e s e alternatives, we n e e d e d t o describe quantitatively agricultural technology. The large n u m b e r of operations involved in agriucltural work a n d its specificity t o p a r t i c u l a r agro- climatic situations t e n d t o make agricultural technology d a t a banks very large. This paper p r e s e n t s some ways t o efficiently describe a n d s t o r e information on agricultural technology.

Kirit S. Parikh Program Leader

Food a n d Agriculture Program

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^vii

-

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DESCRZBING AGRICULTURAL TEWOLOGY

-

BRIDGING THE GAP FROM SPECIFIC PROCESSES TO GENERAL PRODUCTION FUNCTIONS

Kirit S. Parikh

1. INTRODUCTION:

THE

PROBLEM

Quantitative descriptions of technological alternatives available t o produce a particular product or service follow one of two paths, depending on disci- plinary bias a s well a s on t h e problem a t hand. Thus engineers and technolo- gists who a r e usually concerned with decisions a t t h e field or factory level prefer descriptions which refer to specific m a c h i n e s used in particular processes. Economists concerned with decisions a t t h e industry o r t h e econ- omy level, on t h e o t h e r hand, prefer a production function in which only an aggregate m e a s u r e of machinery a n d equipment

-

eg., dollars worth of capital

-

is used. It is difficult t o identify specific technical processes t h a t correspond t o a particular point on t h e production function, though i n principle s u c h a correspondence does exist. Many t i m e s aggregate production functions a r e e s t i m a t e d econometrically from financial d a t a a t t h e industry level t h a t do n o t provide even qualitative information on t h e processes involved. Thus even when t h e raw d a t a behind t h e e s t i m a t e d production functions a r e available, i t is n o t easy t o relate specific techniques t o points on t h e production functions.

On t h e o t h e r hand, t h e technologist's description is s o detailed a n d specific t o p a r t i c u l a r situations of t h e field or factory t h a t i t is difficult t o use t h e d a t a for industry- o r region-level decisions. When s u c h d a t a a r e collected f r o m a large n u m b e r of cases, t h e resulting d a t a set becomes so large a n d diverse t h a t t h e information contained in t h e d a t a g e t s drowned in t h e m a s s of numbers.

Such technological descriptions a r e t h u s not easy t o use for analytical purposes a n d system-level optimization.

These two approaches should be reconciled. Because of t h e limited varia- bility of aggregate data, estimated production functions would r e m a i n highly unsatisfactory for m a n y useful analytical purposes unless t h e technological knowledge of the engineer can be brought t o bear on t h e economist's e s t i m a t e s of production functions. This would also benefit t h e engineer, a s i t could help h i m t o perceive p a t t e r n s a n d universality of parts of his technological d a t a and t h u s to avoid m u c h duplication in d a t a collection.

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The dichotomy between t h e description of field-level techniques and sector-level production function is particularly severe for a g r i c u l t u r e , where t h e soil a n d c l i m a t e c h a r a c t e r i s t i c s s e e m t o make e a c h field a s e p a r a t e and non-reproducible observation. This poses a formidable difficulty in exploring a t a regional level o p t i m u m strategies for agricultural development in a way t h a t satisfactorily deals with t h e interactions between agricultural technology, cultivation a n d m a n a g e m e n t practices, t h e environmental consequences of t h e s e , a n d t h e i r i m p a c t on soil and water r e s o u r c e quality.

A desirable s c h e m e for description of technological options should as f a r as possible m e e t t h e following requirements:

( a ) I t should r e l a t e specific micro-level processes a n d operations t o a rela- tively aggregated production function.

(b) I t should facilitate a r e p r e s e n t a t i o n of technological options t h a t can be u s e d in analysis for system-level optimization. This m e a n s t h a t t h e resulting analytical model should be computationally manageable. For example, if t h e model is a l i n e a r programming one, t h e size of LP t h a t is generated should be reasonable.

( c ) I t should a c c o u n t for technological progress in a way t h a t could be useful for projecting s u c h progress.

(d) I t should identify t h e e l e m e n t s of technology which a r e site a n d situation specific and t h o s e which provide a universal description of technology which i s applicable t o o t h e r situations, so t h a t with every c a s e study t h e d a t a bank grows in a meaningful way.

I have outlined below a s c h e m e t h a t , I think, m e e t s t h e s e needs. In Section 2 t h e proposed s c h e m e for technology description i s outlined along with t h e components of t h e data bank t h a t would embody s u c h a description of technology. The m a i n r e s e a r c h problem is identified in t h i s process. The assumptions behind t h e s c h e m e a r e f u r t h e r elaborated i n Section 3. Finally, t h e feasibility of t h e s c h e m e a n d t h e possibility of successfully carrying out t h e research needed a r e d e m o n s t r a t e d by a n illustrative example in Section 4.

2.

THE PROPOSED

SCHliZiX

The proposed description s c h e m e considers agricultural production t o con- sist of a s e t of basic operations. Technological options i n agriculture arise mainly from t h e alternative ways of performing t h e s e operations a n d t h e alternative i n t e r a c t i o n s of i n p u t s t h a t a r e possible. Based on t h e s e alternatives t h e s c h e m e proposes t o e s t i m a t e production functions for each of t h e s e operations.

I t shows how s u c h operation production functions can be described and e s t i m a t e d t o s e p a r a t e s i t e a n d c r o p specific c h a r a c t e r i s t i c s from t h e m o r e universal m e c h a n i c a l engineering c h a r a c t e r i s t i c s of technology. The first s t e p is t o define basic operations.

2.1.

DEFINITION OF OPWATIONS

An operation t h a t c a n in principle

-

i.e., technically a s opposed t o econom- ically

-

be c a r r i e d o u t by a s e t of alternative combinations of factors s u c h a s m e n a n d m a c h i n e s should be considered as a s e p a r a t e type of operation.

Operations r e q u i r e d at different t i m e s may be t r e a t e d a s different types of operations for s o m e analytical purposes b u t would n o t require s e p a r a t e operation production functions.

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Operations t h a t can be performed only in specific situations by very specific machinery should also be treated as different types of operations.

Having defined operations, the next Lhing is t o define units of measure- men t.

2 -2. UNIT OF

- N T

OF

OPERATION

A standard unit of operation should be defined for each operation. Let us take plowing as a n example. We can define an SPUW (Standard Plowing Unit of Work) as follows:

SPUW

=

Amount of plowing work required to plow 1 h e c t a r e of standard land for standard crop to a given depth.

Standard land and standard crop can be arbitrarily selected. However, some choices may be naturally more convenient.

2 -3. ALTERNATIVE

TECHNIQUES

FTlR

OPERATIONS

Each operation can be carried out in different'combinations of labor, machines, equipment, and associated energy inputs. Moreover, t h e machines vary from year to year in quality and also in t h e type of attachments they can take. Thus, t h e number of alternatives can be very large. What we need to do is to develop a production function for operations. This can be conceived a s follows:

OOi

=

output of i-th operation measured in "Standard Operation Unit of Work."

Inputs in t h e i-th operation a r e Standard machine

=

MSi Standard labor

=

LSi Standard equipment

=

^QSi

Associatedenergy

= mj

where MSi is stipulated to be a function of

some physical a t t r i b u t e of the machine (e.g. horsepower of t r a c t o r ) t h e date of manufacture of the machine, to reflect technical progress.

QSi is stipulated to be a function of

some physical a t t r i b u t e of equipment, e.g. width of plow t h e date of manufacture of t h e equipment

LSi is stipulated as a function of average age of worker level of education

and AEi is i n energy equivalent unit, such as ton of oil equivalent.

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Note t h a t technical progress is embodied in machines, equipment, and men.

Developing

M

Si

QS,

LS,

and OOi would be an important research task in this scheme.

2.4. CROP PRODUCTION TECHNIQUES

Yields a r e defined simply a s a function of input levels of variable inputs such as seed r a t e , fertilizers, pesticides, a n d water, a n d standard units of operation work required for t h e crop and for t h e soil.

Y: :

&

=

YC1' (Fertcl', seedc1'. waterc.'. OP~'...,O~*')

These functions are within t h e traditional framework of economists and should pose no new hfficulties in estimation once t h e operation output functions, OOis, are developed.

2.5. THE COMPONENTS OF THE DATA

BANK

This will result in a data bank with two components: a crop production activity matrix and operations output activity matrices.

(a) Crop Production Activity Matrix

The s t r u c t u r e of the matrix is shown in Figure 1.

Figure 1. The Crop Production Activity M a t r i x .

Note here t h a t neither p a r t A nor 13 of t h e matrix is affected by t h e technical progress t h a t takes place in mechanical equipment development. P a r t A embodies t h e information from the genetic and agronomic aspects and varies only when t h e r e is genetic technical progress. P a r t B embodies agronomic aspects relating to soil and remains invariant t o technological developments in t h e

Inputs

A

B

Main yield Joint yield 1 Joint yield 2 Seeds Fertilizer Pesticides OperationO1 Operation O2

Operation 0,

...

soil 2 Activities

soil 1 soil s

crop c crop 1

alternatives 1

-1

-

s1

f~

P ¹ 011 OZ1

Onl 2 -1

-

s2

f~

Pr 01, OZz

0&

3

1

-1

- -

s3 f3 P3 013 OZ3

On3 4 -1

S4 f4

Pa 014 024

On4

...

m

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m a c h i n e s e c t o r a s well a s to genetical progress.

(b) Operation Output Activity Matrices

For e a c h operation o n e m a t r i x will define t h e alternatives available for pro- ducing t h e o u t p u t of t h a t operation. The s t r u c t u r e of a typical m a t r i x is shown in Figure 2.

Energy 1

I I I I

Inputs 0 Oj

Tractor 1 Tractor 2 T r a c t o r . Tractor

.

Tractor

.

Tractor t, Equipment 1 Equipment 2 Equipment

.

Equipment

.

Equipment

.

Equipment e, Labor 1 Labor 2 Labor.

L a b o r . L a b o r .

Figure 2. A typical Operation Output Activity

Matrix

As new m a c h i n e s a r e developed a n d new d a t a a r e available, t h e s e m a t r i c e s have t o be a u g m e n t e d by additional rows a n d columns. But i t should be n o t e d t h a t t h e s e m a t r i c e s a r e largely independent of variations in soil a n d climate. Thus t h e y a r e "universal" descriptions of technology.

1

-

¹

3.

ASNXPTIONS

BEHIND THE

S m

What have we a s s u m e d a n d sacrificed in t h i s s c h e m e of technology description c a n be shown formally by comparing i t with conventional descriptions of technology.

Formally a production function c a n be described a s a yield (in q u a n t i t y / h e c t a r e ) function for a given soil and a given crop variety where t h e i n p u t s are t h e various m a c h i n e s and labor services involved in different operations a n d o t h e r c u r r e n t inputs. Thus

2

-

¹

~ield;$! vanetl

=

f,&(MP, Lr.

E i ,

Fert. Water. Pesticide. Seeds)

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where

M4

is i-th machine used for o-th operation where i€m, the set of machines L r is t h e j-th type of labor used in o-th operation where j€s, t h e s e t of labor skills

E$

i s the k-th type of equipment used in o-th operation where k€E, t h e s e t of equipments

Thus if n operations 0

=

1,

...,

n are distinguished, we will have nxMxSxE different possible combinations of factor inputs. In addition one should, also consider for a given combination alternative intensity levels of factors. Thus the production function has a very large number of parameters.

Compared t o this t h e scheme suggested introduces certain separability between operations and soils a n d hypothesizes t h a t operations can be described by production functions. Thus

variety

= ~ z ~ ( ~ i . . . .

^$0;.Fert, Water. Pesticide, Seeds) where t h e output of i-th operation for soil s,,

Of,

is characterized by

a(M) attributes of machines such as horse power, vintage, e t c . b(L) attributes of labor s u c h as skills, experience, age, etc.

c(E) attributes of equipment such as width, weight, vintage, etc.

4. ESl3MTES

OF

SOMX OPERATIONS OUTPUT FUNCTIONS

To illustrate how this can be done, we have estimated some operations output functions.

Data from experimental stations in Hungary is used to estimate these functions. These stations carry out experiments with different machineries and equipments and report performances in terms of hectares/hour, depth, width, etc. for different soils a n d different years.

I have used data from Gockler and Lakatos (1977), which gives data from 1965 through 1975. Data with adequate information a r e available for t h e operations of ploughing, discing, precultivation, soil preparation, row cultivation and maize harvesting.

To illustrate the n a t u r e of t h e reported data and how

I

have used it, data for ploughing for a specific soil as given in t h e book and as reogranized are shown in Table 1. Since t h e number of observations available for ploughing were large we have used only t h e average performance. For other operations performance for each year was treated a s a seperate observation.

Data on the attributes of equipment used were not available so 1 have considered just two attributes of tractors, horsepower and vintage, defined here as date of its first use.

I

have also pooled the data from three different soils. Here again adequate information on the properties of soils were not available to me and

I

have used dummy variables for the different soils.

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A general model is postulated for all t h e operations.

[hectaresl (ao

+

al sl

+

a2 s2) i n t e n s i t

I

I;~;yizp] ⁼

^e _operation^of ^[ept

H,P

where

s l a n d s2 a r e d u m m y variables for soil type 1 a n d 2;

i n t e n s i t y of operation r e f e r s t o

depth in crns for ploughing a n d discing width i n crns between rows for cultivation yield of g r a i n s i n t o n s / h e c t a r e s

Ht is t h e horse power of t h e t r a c t o r first i n t r o d u c e d in y e a r t t is vintage y e a r ( t

=

66 for 1966, e t c . )

Both a a n d /3 a r e expected t o be positive, whereas y is expected t o be less t h a n zero. When y is insignificant i t would imply t h a t t h e h e c t a r e s operated p e r h o u r do not depend on t h e i n t e n s i t y of operation, which is possible for some operations.

The intensity variables a r e t a k e n a t t h e m e a n values of t h e indicated ranges. For example, depth of ploughing shown a s 1 6 t o 18 crns would be taken a s 17 crns. For t h e c a s e of maize harvesting, t h e d a t a on yields of t h e fields were n o t available, a n d 1 h a d t o u s e t h e d a t a on national yields for Hungary a s a n approximation. The r e s u l t s of t h e various regressions a r e given in Table 2.

The regression r e s u l t s a r e r e m a r k a b l y g o o d The t s t a t i s t i c s a r e mostly highly significant a n d t h e signs of coefficients a r e i n g e n e r a l right. The

R2

a r e also quite good considering t h a t 1 have used, excepting for ploughing operations, raw data of individual observations a n d n o t grouped data.

The only insignificant i n t e n s i t y coefficient is of discing operation implying t h a t depth of discing does n o t affect p e r f o r m a n c e in t e r m s of h e c t a r e s p e r hour, which is conceivable. The vintage coefficients for precultivation, row cultivation a n d m a i z e harvesting a r e also insignificant indicating t h a t technical progress in t r a c t o r s do n o t affect p e r f o r m a n c e in t h e s e operations. The only coefficient with wrong sign is t h a t of i n t e n s i t y (depth in t h i s case) of precultivation operation. Were information on e q u i p m e n t a t t r i b u t e s or o t h e r special f e a t u r e s of t r a c t o r s t o be i n c o r p o r a t e d i n t o t h e model, i t s explanatory power could have been i n c r e a s e d f u r t h e r . Also o n e could t r y alternative, m o r e ela- borate models. For example for ploughing operation. I h a d also tried:

which i n c r e a s e t h e t o 0.66 with all p a r a m e t e r s significant a n d of expected signs.

Thus t h e approach suggested h e r e , i s very promising a n d s y s t e m a t i c work c a n be very fruitful.

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Table la. Ploughing operation in a particular soil

--

^Asample of data from Gocker and Lakatos (1 977)

Field Category I

-

Ploughing. (depth of ploughing 29-30 cms)

Type of t r a c t o r s Zetor S-50 T-100M D4K-B MTZ-50 DT-75 K-700 JD-4020 JD-4320 IHC-1246 IHC-1046/A IHC-1066 Steiger

Horse* 1965 power

Average 0.29 0.32 0.36 0.34 0.38 0.34

Type of t r a c t o r s Zetor S-50 T-100M D4K-B MTZ-50 DT-75 K-700 JD-4020 JD-4320 IHC-1246 IHC-1046/A IHC-1066 Steiger

Horse* 1971 1972 1973 1974 1975

power

average

Average 0.36 0.35 0.44 0.47 0.50 0.37

*

Though horse power data is not given, i t was easy t o obtain from t r a c t o r types.

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Table lb. Ploughing operations data as reorganized for regressions

year of first in- depth of horse power of average (1965-75) per- troduction of ploughing in t r a c t o r formance ( h e c t a r e s t h e t r a c t o r type c m s ploughed p e r hour)

Notes:

(i) For t r a c t o r s already available i n 1965, the vintage year is taken t o be 1960 a s I did not have earlier data.

(ii) Since for ploughing operation t h e n u m b e r of observations are large, I have t a k e n t h e average performance over t h e year 1965 through 1975.

Table 2. Estimated Agricultural Operations Output Functions.

Coe fficent of

Soil ¹ Soil 2 intensity vintage* tractor

K2

F

Operation Constant dummy dummy of of horse

operation tractor power

uo 01 0 2 7

B

^a DF

Ploughng -2.826 -.lo3 -.I88 -.906 .lo2 ,438 0.60 36.4

(-5.46) (-1.47) (-2.38) (-8.10) (5.18) (4.47) 113

Discing -4.892

-.lee

-.066 -.017 .078 .56 1 0.69 70.6

Operation (-6.37) (-4.43) (-1.48) (--32) (3.40) (10.0) 151

Precultivation -4.948 ,466 280 .256 .016 .888 0.64 38.4

Operations (-4.73) (5.58) (2.43) (2.28) (.81) (8.17) 100

Row -4.156 -.I41 0.83 330 .0056 1.14 0.53 24.0

Cultivation (-3.98) (-1.4~) (-1.47) (3.03) (.31) . (6.79) 97

Maize -6.03 -2.65 -.554 .040 .818 0.42 11.7

Harvesting (-4.62) (-2.30) (-1.73) (.82) (2.23) 55

*

Vintage (years of first introduction of t r a c t o r ) coefficient fl obtained by divid- ing the e s t i m a t e d coefficient @a by a, t h e coefficient of t r a c t o r horse power; t h e t-values shown under @ a r e t values of ( @a )

Values in ( ) a r e t-values

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5. S O W

USES

AND IMPLICATION OF THE ESITMATED FUNCTIONS.

Apart from t h e i r value in describing agricultural technologies economi- cally and in reducing t h e size of programming models, these estimates have important implications for research in agricultural economics.

The significance of estimated vintage coefficients provide strong support for embodied technical progress and for vintage models. The estimates provide guidance on aggregating machinery. Many researchers have used horse power as a measure of machinery i n estimating aggregate production functions (see for example, Hayami (1969), Hayami and Ruttan (1970) and Kawague, Hayami and Ruttan (1983)). In the presence of embodied technical progress adding up horsepower of machinery without accounting for vintage would introduce bias in the estimated coefficients. Machinery will be under estimated (as effective horse powers of more r e c e n t machinery a r e not adjusted upwards) and hence its coefficient would be higher. Comparison in changes in factor productivity in different countries based on such estimates would therefore be questionable.

Also when data from different countries whose machinery age s t r u c t u r e s a r e different are used for cross country regression even t h e direction of t h e bias would be unpredicable.

References

Gockler Lajos a n d Lakatos ImrdnC (1977) Mezogazdasdgi munkamb'veletek ada- tai (Agricultural Operations Data). Mez6gazdasdgi GCpkisgrleti Intgzet 2101. Godbllo, Tessedik S. u. 4

Hayami, Yujiro, (1969). Sources of Agricultural Productivity Gap Among Selected Countries. American Journal of Agricultural Economics NO. 5 1: 564-75

Hayami, Yujiro and Ruttan, Vernon W., (1970). Agricultural Productivity Differences Among Countries. American Economic Review. No. 60:

895-91 1

Kawagoe Toshihiko, Yujiro Hayami and Vernon W. Ruttan. (1983). The Inter- Country Agricultural Production Function and Productivity Differences Among Countries. (mimeographed draft).