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Copyright 2005, Board of Trustees, University
of Florida
S1C98
~~September 1986
J I If i LPIu VJ I
Bulletin 863
DEC 8 1986
I.F.A.S. Univ. of Florida
Modeling Technical Change in
the Frozen Concentrated
Orange Juice Processing Industry
J. S. Shonkwiler and H. A. Stranahan
Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
J. M. Davidson, Dean of Research
I.~
~l~al~l
MODELING TECHNICAL CHANGE IN THE FROZEN CONCENTRATED
ORANGE JUICE PROCESSING INDUSTRY
by
J.S. Shonkwiler and H.A. Stranahan
Food and Resource Economics Department
University of Florida
TABLE OF CONTENTS
Page
LIST OF TABLES AND FIGURES ............................... ii
INTRODUCTION ...............................o.............. 1
TECHNOLOGICAL DEVELOPMENTS AND R & D
IN THE FCOJ INDUSTRY...................................... 3
THEORY AND METHODOLOGY.................................... 9
Measuring the Technical Dimensions of R & D........... 11
The Effect of R & D on Input Usage................... 14
COST FUNCTIONS AND TECHNOLOGY............................. 20
Estimation Method ................................... 28
EMPIRICAL RESULTS......................................... 29
SUMMARY........................................... ...... 44
APPENDIX A: DATA.......................................... 48
REFERENCES...................................... .......... 51
LIST OF TABLES AND FIGURES
Table Page
1 U.S. Citrus Per Capita Consumption................. 4
2 Parameter Estimates for the Translog
Cost Function...................................... 33
3 Test Statistic for Restricted Models............... 35
4 Estimated Allen Partial Elasticities
of Substitution (AES).............................. 37
5 Estimated Input Price Elasticites.................. 37
Figure Page
1 Ahmad's Induced Innovation Model.................. 16
2 Florida FOB FCOJ Movement,
Million Concentrate Gallons........................ 41
INTRODUCTION
The Florida citrus industry utilizes over 80 percent of
Florida oranges for frozen concentrated orange juice (FCOJ) or
related products and is the second largest producer of orange
products in the world (Gunter, 1984). Many factors are
involved in the growth of the Florida FCOJ industry. Among
them are numerous product improvements that have resulted from
investment in research and development (R & D) by private
industry and the Florida Department of Citrus (FDOC). The
Florida Department of Citrus is a selffinanced and stateregu
lated organization that has supported a major proportion of
FCOJ research conducted since 1940.
The citrus processing subsector has devoted substantial
resources toward technological advancement. However, no stud
ies of the structure of production in the FCOJ industry have
been published. Therefore, little information exists regarding
the degree of technological change in the industry and the
results from R & D activities. This study attempts to model
the underlying production relationships of the FCOJ industry
during the period 195680. Using the dual relationship between
production and cost functions, a translog cost function and
corresponding share equations are estimated.
Estimation of the translog cost function in conjunction
with the share equations allows analysis of homotheticity of
the production structure, computation of input substitution and'
price elasticities as well as evaluation of the effects of
technical change on an input's share in total cost.
Usually, the arguments of a cost function are input prices
and output; however, McFadden (1978) shows that a fixed input
may be introduced into the cost function as well. This input
may be any factor which characterizes the state of technical
progress or which describes or influences the production tech
nology. Since R & D is an input aimed exclusively at product
and process innovation and has been shown to be of significant
influence in productivity and production function studies, a
measure of the quantity of Florida citrus research is intro
duced into the cost function.
In this manner, technical change can be represented in a
more relevant manner rather than that from using a time trend
or other deterministic functions to approximate temporal
changes in technology. That is, R & D enters the cost function
as a specific quantity affecting the evolving structure of
costs. The purpose of the inclusion of R & D and the time
trend exclusion is to measure and identify the specific cost
reducing effect of a variable aimed exclusively at product and
process innovation.
Since the quantity of R & D is used to represent technical
change, certain inferences about the value of R & D can be made
when the translog cost function is employed. Following Diewert
(1974) and Lau (1976), the shadow price of R & D can be
obtained by partial differentiation of the cost function with
respect to the quantity of research. Assuming a constant rate
of growth, a continuously compounded average rate of return
associated with Florida citrus processing research can then be
calculated.
This study proceeds by considering some technological
developments and the role of research and development in the
Florida FCOJ industry. Next, methodological issues are
addressed in terms of theoretical models used to represent
technological change and investment in R & D. The third sec
tion reviews the translog cost function and its value in the
present context. Then the empirical model is presented and
analyzed in terms of the previously discussed methodology. The
study concludes with some observations regarding the relevance
of the findings and possible shortcomings in the approach
adopted.
TECHNOLOGICAL DEVELOPMENTS AND R & D IN THE FCOJ INDUSTRY
In 1935 the Florida State Legislature passed a set of laws
generally referred to as the Florida Citrus Code in order to
protect the health, welfare and stability of the industry. The
FDOC was established under these guidelines to foster industry
coordination through stimulating demand, promoting quality
standards and establishing a research program for Florida
citrus.
An impetus to industry growth occurred in 1945 when the
scientific research staff at the FDOC patented frozen concen
treated orange juice. This technological breakthrough has been
a key component in the industry's expansion and changing struc
ture. Per capital consumption of citrus products has grown from
just over 22 pounds in 1920 to almost 118 in 1980 (Table 1).
Furthermore, the increase in consumption of processed products
has more than offset the decrease of fresh citrus (Gunter,
1983).
Table 1. U.S. citrus per capital consumption
1920 1940 1960 1980
Fresh* 22.2 52.1 30.7 26.3
Processed 10.4 52.2 91.2
Total 22.2 62.5 82.9 117.5
Source: Gunter, 1983.
*Excludes lemons and limes.
The success of processed citrus can be attributed in part
to the quality standards governing processed orange juice which
ensure a homogeneous product, development of alternative pro
duct forms, the relatively stable real price of FCOJ and a
S large scale marketing program (Myers, 1978). At the core of
these developments has been citrus processing research. Scien
tific research has affected the quality, development and cost
structure of the processed product forms. Economic and market
ing research has guided the marketing strategy and affected the
industry pricing structure.
The Florida citrus sector has demonstrated adeptness in
its ability to stimulate demand and satisfy consumer prefer
ences. However, the continuing success of the citrus industry
is intimately tied to the state of technology. Many of the
past achievements in the citrus sector can be attributed to
both private and publicly funded scientific research. A new
aseptic processing and packaging technology in the 1960's made
possible the introduction of a single strength readytoserve
chilled orange juice. Due to changing lifestyles, the conven
ience provided by this product and an effective marketing
strategy, ready to serve chilled orange juice has experienced a
substantially greater increase in demand than that for FCOJ
during the last 15 years.
In addition to new product improvements, scientific
research has also yielded several cost reducing production
technologies. Low temperature pan evaporators used universally
within the industry before 1960 have for the most part been
replaced by high speed evaporators. These evaporators are
almost six times more energy efficient and are able to process
a higher quality orange juice in about five percent of the time
needed for pan evaporation (LykesPasco, no date). Along these
same lines, more efficient juice extraction equipment has
increased the amount of juice produced from each orange by 26
percent (MacDowell et al., 1962).
Technology has permitted not only greater processing effi
ciency but a greater utilization of the entire orange. Before
1950, the remnants of processing such as pulp, rind and pulp
wash were discarded as waste. Today there is virtually no
waste from processing oranges. The citrus industry processes
the rind and pulp for use in cattle feed and more recently they
have been used as high fiber filler for flour and hotdogs.
Methods for capturing essential oils and essence recovery have
improved the amount and quality of citrus flavorings produced.
In this case scientific research has allowed a more efficient
utilization of citrus byproducts.
Although several of the larger firms in the Florida citrus
processing industry engage in scientific and marketing
research, few employ an economic research department. The
FDOC's Economic Research Department provides information
concerning long and shortterm supply and demand conditions in
the United States and abroad. In addition, the department is
responsible for answering specific questions posed by industry
members and addressing legislative matters affecting the
industry.
The Economic Research Department in conjunction with the
Market Research Department is responsible for monitoring trends
in consumer behavior that may affect citrus marketing strate
gies. By studying the demand for citrus products and analyzing
price elasticities or substitutability among product forms, the
effects of changing prices and their impact on the industry are
investigated. Since returns to the grower and processor are
often highly dependent on retail price and volume, improved
knowledge of prices and quantities transacted at the retail
level guides the industry's decision making in matters such as
inventory control, product allocation and pricing decisions.
The Marketing Research Department is responsible for moni
toring the effectiveness of advertising and promotional pro
grams. Since nearly 87 percent of the FDOC budget as well as
numerous private funds are allocated to generic and brand
advertising, comprehensive consumer profiles and demographic
outlines are necessary for efficient allocation of promotional
funds. Analyses of consumer preferences are carried out
through continuous and large scale testing by the Market
Research Department. In both national and international
studies, this department has investigated buyer response to
color, brixacid ratios, pulp content, bitterness tolerance and
packaging convenience.
One of the objectives of consumer testing is to identify
new market potential. The success of alternative market strat
egies can mean an expansion of demand for the Florida citrus
sector. It is in this arena that new product forms and con
cepts are tested for consumer acceptance. The market research
performed can greatly reduce the uncertainty associated with
new product introduction. In short, this additional informa
tion aids in increasing the probability of success of new pro
ducts.
Recently the industry has introduced an aseptically pack
aged, shelfstable orange juice product. Although several
problems still remain involving taste and color volatility, the
Market Research Department foresees an important institutional
market for this new product form which could greatly expand
demand in the future (DeJager, 1984). In these and other
scenarios it is clear that market strategy and industry
revenues are largely dependent on technological developments.
Several of the larger firms in the industry also spend
considerable resources on market research departments.
Recently several product innovations in the processed orange
juice subsector have been designed to further differentiate the
market. For instance, new product introductions include a low
acid FCOJ and an orange juice with a high pulp content. Also,
multiple sizes and different packaging forms have been designed
to suit specific market segments.
In addition to extensive support for R & D programs, the
FDOC aids Florida industry members in the legal and political
arena as well. The Florida citrus industry is highly regulated
by the state. Laws govern the processing and distribution of
oranges, the amount of pressure used in juice extraction and
the prohibition of additives in orange juice. The increasing
importation by northern U.S. processors of Brazilian juice,
which is not regulated by Florida's quality standards, has
caused concern among industry members. Recently, the industry
Shas worked closely with the Food and Drug Administration in
order to detect poor quality orange juice which may be
adulterated through dilution with water, sugar, acids or pulp
wash. Several Florida citrus organizations have been involved
in these and other political and legal matters affecting the
industry.
The Florida citrus processing subsector invests substan
tial resources in postharvest R & D. In fact, over $6 million
in private and public funds were allocated to citrus processing
research in Florida during 1981 alone (Florida Department of
Citrus, 195680; United States International Trade Commission,
1983).
Few agricultural sectors have the extensive data and
information network or the research base that is available
within the Florida citrus sector. The technological advance
experienced by the industry is the result of several factors,
not the least of which is the close coordination among the
various research departments and industry members. Clearly
economic, marketing and scientific research has aided the
organizational and technical efficiency within the sector.
THEORY AND METHODOLOGY
In neoclassical economic theory, at the micro level the
firm transforms inputs into output via the technological
relationships inherent within a production function
(1) Y f(XX2...Xn)
where Y is output and K1.. Xn are inputs into the production
process. The efficient transformation of inputs into outputs
is determined by the state of technology. The entrepreneur or
producer utilizes the product mix, determined by available
technology, in order to maximize profits. In doing so he
simultaneously chooses a position on his production function.
This product mix also depends upon the supply and demand condi
tions in the factor and product markets. If the markets for
input supplies are perfectly competitive, then factor prices
are exogenous to the firm. Similarly, if the product market is
competitive, product prices are also exogenous.
As output increases due to proportional increases in
inputs, the entrepreneur moves along the production function.
Using Euler's Theorem and a homogeneous production function, it
can be shown that proportional growth in output is equal to the
weighted share of proportional input growth along a production
function. The residual of output growth less the share
weighted input growth is seen as technical change (Nelson,
1981). If technology allows a more efficient employment of
inputs such that an equal quantity of inputs yields greater
output, the production function will shift outward; hence,
technical change has occurred.
Technology can be described as the method of combining
inputs to arrive at a specified output. The advance of techno
logy has been viewed as either an exogenous factor affecting
the growth of output or as a decision variable within the pro
duction structure dependent upon the firm's investment in
knowledge or R & D (Nelson, 1981). In the latter context the
supply of, or possibly demand for, technical change is depend
ent upon the knowledge and techniques available to the firm.
R & D can be viewed as an investment directed toward augmenting
organizational and technical efficiency, which consequently
affects the production opportunities of the firm. Along these
most basic lines of causation, the innovations resulting from R
& D at the micro level yield economic and productivity growth
as well as resource savings at a more aggregate level.
Measuring the Technical Dimensions of R & D
Despite their limitations, various studies have shown that
definitive relationships exist between R & D and the amount of
innovative activity originating from an industry (Kamian and
Schwartz, 1975) or between R & D and productivity increase
(Mansfield, 1972). Theory and application have not ended at
this point. Many factors in addition to R & D have been asso
ciated with technical change and productivity advance.
Increases in capital intensity, advancement in human capital,
urbanization and the learning process have been found to
interact and complement the advances in technology (Nelson,
1981).
For example, the productivity index approach has been used
to estimate the relationship between technological developments
and research investment. Consider a model which relates pro
ductivity growth and expenditures on R & D (Griliches, 1980).
(2) Q = Tf(C,L)
(3) T = g(K,O)
(4) K = I w Rt
i
where Q is the value of output, C and L are capital and labor
inputs, respectively, T is the state of technological
knowledge, K is the amount of productive research knowledge in
existence at time t, 0 is other inputs affecting the state of
technology, wi measures the effect of past R & D in period ti
on knowledge in time t and Rti is R & D expenditures in period
ti.
Equation 4 may be interpreted as the distributed lag of
past R & D. In order to empirically estimate the system, equa
tions 2 and 3 are specified as Cobb Douglas forms and 0 is an
exponential trend. This reduces the system to
(5)t 8 (18)
(5) Qt= AeXt Kt Ct Lt(1)
In equation 5, A is a constant term and A is interpreted as the
rate of disembodied technical change.
Disembodied technical change generally refers to techno
logy generated and affecting the production process from exter
nal sources. Conversely, embodied technical change refers to
embodiment of technology in capital and labor inputs. Differ
entiating equation 5 with respect to time and writing it in
implicit form yields a productivity equation (Griliches, 1980).
(6) P = 8  (18) = + a
where P is a measure of productivity and where Q, C, L and
where P is a measure of productivity and where Q, C, L and K
represent the derivatives with respect to time of output, capi
tal, labor and current knowledge (i.e. x ).
Q dt Q
The variable describing the relationship between R & D
K
and technology is difficult to estimate because of the unknown
wi values. Several factors influence the lag structure between
R & D investment and the resulting increase in technology.
These include the time lag between R & D expenditure and the
invention of a new process, between invention and commercial
development of the technique and the replacement or depre
ciation of this technology by a newer and more productive pro
cess (Griliches, 1980). Evidence suggests that lags between R
& D and the realized benefits tend to be shorter in industries
where R & D is focused on applied and development work rather
than basic research, which is longer term and more uncertain
(Mansfield, 1980).
Evenson (1967) first used this approach in conjunction
with alternative lagging schemes for R & D. By minimizing the
residual sum of squares associated with various R & D lag
structures, he found the impact of R & D on aggregate agricul
ture was best described by an inverted Vshape lag with a mean
lag of 5 to 7 years. Other econometric evaluation of returns
to research have generally ignored the lag of the impact of R &
D on productivity in the econometric formulation of the model.
The lag, however, is taken into account based on the nature of
the sector being considered by adjusting the calculations of
the marginal product or internal rate of return associated with
R & D (Bredahl and Peterson, 1976; Griliches, 1964).
The Effect of R & D on Input Usage
Although substantial literature addresses the problem of
measuring the returns to R & D, few studies have investigated
the influence of research on input usage. Because R & D expen
ditures may characterize the pace of technological change,
knowing the effects of R & D on factor employment may be as
important as knowing the benefits associated with the invest
ment. Although limited empirical analysis has focused on the
effect of R & D on factor shares, several studies have investi
gated the impact of technical change on factor utilization.
Both relative factor prices and the technical characteristics
of the production process influence factor usage.
The technical characteristics affecting production possi
bilities can be broken down into five categories (Nadirl,
1970). These categories include 1) the efficiency of the pro
duction process, 2) biased technical change, 3) the elasticity
of substitution, 4) the economies of scale and 5) homotheticity
of the production process.
The efficiency of the production process includes such
factors as organizational or managerial efficiency, which af
fects all factors of production equally. An increase in pro
duction efficiency may be interpreted as neutral technological
change since capital and labor requirements per unit output
would decrease proportionately. Factor biased technical change
occurs when a cost saving process is adopted that reduces the
employment of one factor of production relative to other fac
tors.
Economies of scale will govern the quantity of inputs
required at different levels of production. Neutral economies
of scale (a homothetic process) would increase factor require
ments proportionately among inputs as output expands. Con
versely, a nonhomothetic production process may increase one
factor requirement proportionately more than other factor
requirements as output expands.
The elasticities of substitution of the production process
may influence the degree to which changes in factor prices
affect factor usage. For instance, a given change in relative
factor prices will have a greater effect on factor utilization:
the greater the elasticity of substitution between the two
factors, ceteris peribus. This occurs because the entrepreneur
will more easily substitute the cheaper factor for the more
expensive one in the production process (the greater the elas
ticity of substitution) in order to minimize cost. However,
with a small elasticity of substitution, production possibili
ties would not allow easy substitution between the factors.
Hence, there would be less response of the factor ratio to
relative price changes.
The elasticity of substitution between factors may also
influence the ability of the firm or industry to capture the
benefits of embodied technical change. For instance, the abil
ity of the entrepreneur to fully realize the quality improve
ment embodied in a new machine may depend upon the production
process and the extent to which it allows increased utilization
of capital at the expense of labor or other inputs.
These technical characteristics of the production process,
in addition to relative price changes, clearly affect factor
utilization through time. Although few empirical studies have
explored the role of R & D in factor bias, research enters the
theoretical framework via the R & D processes that generate
technical possibilities. Syed Ahmad (1966) developed an
induced innovation model based on an innovation possibility
curve (IPC). The IPC is the envelope of all unit isoquants
that describe the set of potential processes available to the
entrepreneur given an exogenous R & D budget (Figure 1).
I
11IPC t
Pt+l Labor
Figure 1. Ahmad's induced innovation model.
Source: adapted from Syed Ahmad (1966).
The IPCt describes all innovation possibilities available to
the entrepreneur during time t. The It is the cost minimizing
innovation process given factor prices Pt. In period t+1 the
IPC shifts inward to IPCt+1 and the entrepreneur will adopt the
processes on innovation isoquant It+1 given constant factor
prices Pt. The shift in IPC may be neutral or nonneutral at
constant factor prices. If the IPC shift is neutral and factor
prices change to Pt+l the optimal innovation choice would be
I't+,. A neutral shift in IPCt+I, in conjunction with the rise
in the price of labor (Pt+l), results in labor saving innova
tion possibilities. R & D influences, albeit indirectly, the
technological advances of the firm. The position of the IPC is
determined by the amount and direction of the R & D resources
allocated to the production of new improved techniques.
The movement or direction of the shift of the IPC may not
be random. Binswanger (1978) maintains that technological
opportunities will follow the path of least cost. Research
projects that decrease use of high priced inputs will have
greater benefits than those that reduce use of low priced
factors. The cost minimizing entrepreneur will therefore
direct R & D toward the savings of the more expensive
factors. Along these lines, R & D will influence the techno
logical advances of the firm and hence factor usage.
Although.R & D has been incorporated into the theoretical
framework (Binswanger, 1978), empirical analysis of factor bias
has focused on isolating the effects of price ratios, scale and
technical change on factor utilization. Recent studies have
utilized cost functions to analyze the forces affecting the
demand for inputs (Lopez, 1980; Kako, 1978). Several develop
ments in cost function specification allow for a variable elas
ticity of substitution and nonconstant returns to scale (Caves
et al., 1980). Furthermore, by Shepard's Lemma the factor
demand for the ith input is easily computed by taking the first
partial derivative of the cost function with respect to the ith
Factor price. These characteristics of the cost function have
Permitted several studies to investigate the effects of techni
cal change, variability or scale effects on factor usage.
Binswanger (1974B) employs the translog cost function to
measure the effects of technical change (although it can be
generalized to other factors) on factor usage through time or
among cross sections. He defines factor bias as follows
dSi I < factor i saving
(7)  x = 0 factor neutral
S> factor i using
where Si is the ith factor's share in total cost and T is the
index of technical change. By assuming a neutral effect of
output on factor shares (a homothetic production technology),
the ith share is specified as a function of factor prices and
technical change. The effect of technical change on factor
bias is reflected by the parameter on the time variable. Bins
wanger (1974B) notes that this approach is valid only when time
affects factor shares at constant logarithmic rates. If the
parameter in the share equation on time were zero, this would
imply that technical change or time alone is not a significant
variable influencing factor shares. Therefore, T would have a
neutral effect on the ith share. Binswanger (1974B) found that
technical change has a significant and positive effect on capi
tal and a negative effect on labor for aggregate U.S. agricul
ture.
In a similar study, Kako (1978) used the parameter esti
mates and Allen elasticity of substitution derived from the
estimation of a translog cost function to investigate the
demand for inputs in Japanese rice production. Assuming a
constant returns to scale production technology, a change in
the level of factor demand was specified as a function of fac
tor price variability, technical change and scale of output.
The effect of technical change on input demand was calculated
by subtracting the changes in input usage due to scale and
price from the observed changes in input levels. It was found
that output and price changes were the main factors behind
increased machinery usage, whereas technical change and wage
rate changes were the major components influencing the decline
in labor employment.
Lopez (1980) estimated a set of derived demand equations
corresponding to a generalized Leontief cost function for Cana
dian agriculture. Using a similar methodology, variation in
relative prices, technical change and scale were found to be
the major factors affecting input demand. More importantly,
when the underlying production technology was not constrained
to linear homogeneity of inputs, technical change was no longer
significantly related to factor usage. This highlights the
importance of allowing for a nonhomothetic production struc
ture. The changes in factor shares attributed to technical
change may be negligible where scale effects are considered.
Lopez's (1980) results are consistent with the Lau and
Tamara (1972) study, which utilized a nonhomothetic production
function to model the Japanese petrochemical industries.
Although technical change did not appear to be a significant
influence in the nonhomothetic specification when homotheticity
was imposed, technical change became a significant variable
affecting production. These and other studies have documented
the value of the cost function approach in specifying flexible
models of production that can accommodate technical change,
Specification of a sufficiently flexible cost function
permits analysis of homotheticity of the production relation
ship, computation of input substitution and price elasticities
and evaluation of the effects of R & D on an input's share in
total cost. Therefore, this approach provides valuable
information for assessing the structure of production and the
effect of technical change on production relationships. For
these reasons it is the methodology chosen for the subsequent
analysis.
COST FUNCTIONS AND TECHNOLOGY
It is well known that production relationships may be
derived from a cost function via duality. As often occurs at a
disaggregated level, productivity and input quantity data are
either unavailable or difficult to measure. Many times in firm
or subsector studies cost and price information is more accu
rate and easily obtained than data on input levels. Further
more, at a micro level the specification of input prices as
exogenous appears more realistic than input quantities which
may be varied in response to price changes. Since input
prices, total cost and cost share data are obtainable in the
Florida citrus processing sector, a translog cost function in
conjunction with share equations was estimated.
The cost function depends upon output, prices and the
underlying production function and is, by definition, the solu
tion to minimizing input expenditures subject to producing a
prespecified level of output.
(8) C(Y,P) = Min[E PiXi : f(X) > Y]
X i
where Pi are prices of the inputs, Xi, and f(X) describes the
production technology available for combining inputs to yield
output Y. The industry or firm will minimize the cost of a
given level of output by choosing the optimal level of inputs
conditional on the input prices.
It can be shown (McFadden, 1978) that, if there exists a
well defined production technology strictly convex in input
structure, the same information is contained in a unique cost
function. Conversely, if the cost function satisfies several
regularity conditions, then duality ensures that there exists a
well defined production possibility set.
Modeling cost requires few a priori restrictions on the
structure of production unlike empirical estimation of produc
tion or value added functions. Brown et al. (1979) show that a
priori restrictions of homogeneity of inputs or separability
may distort the scale economies or marginal cost of inputs
associated with the production technology. The cost function
is homogeneous in factor prices irrespective of the homogeneity
of inputs because doubling of all prices will double cost. In
addition, the elasticities of substitution are easily computed
using the estimated parameters and cost share data. In the
translog case, both the elasticity of substitution between
inputs and economies of scale are allowed to vary. Binswanger
(1974A) notes that neutral and nonneutral economies of scale
and efficiency differences can be handled conveniently using
the cost function. Accordingly, the parameter estimates will
not be biased as a result of these problems.
Only homogeneity in input prices and equality of cross
price derivatives (symmetry) must be imposed a priori. Other
conditions that ensure regularity such as monotonicity and
concavity in input prices, nondecreasing in output and nonnega
tivity in prices and output must be checked at each data point.
If any of these restrictions are not satisfied, the cost func
tion does not describe a wellbehaved underlying production
technology over the sample observations.
The cost function usually has output and input prices as
arguments. However, the variable cost function may also
include a "fixed" input Z.
C = C(Y,P,Z)
In this context, the firm or industry minimizes cost of a given
output Y with respect to input prices and the level of the
"fixed" input Z. Following McFadden (1978), the variable cost
function is a form of the restricted profit function. The
variable Z may characterize the state of technical progress or
degree of learning or can contain environmental or behavioral
parameters. In short, the variable Z may be any factor that
describes or influences the production technology.
The variable Z may also be interpreted as a fixed factor
that cannot be varied in the short run. Caves et al. (1981)
employ this methodology to incorporate fixed capital structures
in a translog cost function. They assume that the firm mini
mizes the cost of a subset of inputs conditional on the levels
of the remaining inputs Z. This "variable" cost function still
contains all the information describing the underlying techno
logy.
The first derivate of the cost function with respect to
input Z can be interpreted as the negative of the shadow price
of Z (Lau, 1976; Diewert, 1974).
(10) ac(YP,Z) (Y,P,)
az i i
At the margin, an input Z decreases the total cost of producing
Y, given the cost minimizing levels of input usage. The
implicit market value (or imputed value) of input Z is the
amount that an extra unit decreases total cost.
Equation 11 presents a translog formulation of a cost
function inclusive of McFadden's variable Z (represented by the
variable R). Although it is possible to estimate the cost
function alone, by jointly estimating the cost function and
share equations, additional information and hence greater effi
ciency are provided without introduction of additional parame
ters. By Shepard's Lemma, the share of the ith input in total
cost is computed by the partial logarithmic differentiation of
the logarithm of the cost function with respect to the loga
rithm of the ith input price (equation 12).
(11) InC = a0 + 11nY + 6 InR + X Y InPi
i
+ 1/2 E y ijlnP lnP + E y InPilnY + E YirlnP InR
ij i jr i
+ 1/282(InY)2 + 3nYlnR + 1/262(inR)2
(12) ainC 8c i XPE Y nP
81nPi x C EXP Si + ijP
+ YiynY + YirlnR
iy ir
where R is the fixed input, or input describing the technology
and Si is the share in total cost of the ith input.
The translog cost function is a second order approximation
to an arbitrary cost function. By imposing the proper restric
tions it can be used to approximate any cost function (Bins
wanger, 1974B). In terms of equation 11, a Cobb Douglas
formulation would require all Yij = 0 (ij), Yir = 0, Yiy = 0,
82 = 0, 03 = 0 and 62 = 0.
Other restrictions on the production structure may also be
examined by testing the corresponding parameters. The cost
function will be homothetic if it can be written as
(13) C(Y,P) = Q(Y) x C(P)
where C(P) is a nonnegative, linear homogeneous, nondecreasing
and concave function of P (Lopez, 1980). Accordingly, equation
11 will be homothetic if all Yiy = 0. This is a relatively
restrictive assumption since it implies that the changes in
factor usage, reflected in the share equations, will be inde
pendent of scale. Likewise, linear homogeneity or constant
returns to scale can be imposed by the additional restriction
82 = 0, 81 = 1, since returns to scale in the translog cost
function are measured by the inverse of the first derivative of
the logarithm of cost with respect to the logarithm of output.
(14) n )nY
As discussed previously, several studies have rejected homo
theticity of the production structure and have concluded that a
priori imposition of the restrictions either substantially
altered the results of the study or was decisively rejected
(e.g. Brown et al. (1979) in the U.S. railroad industry, Denny
and May (1978) in Canadian manufacturing and Lau and Tamara
(1972) in the Japanese petrochemical industry). The translog
flexible functional form allows for testing of linear homogene
ity or homotheticity rather than a priori imposition of these
restrictions.
Use of the translog cost function also facilitates easy
computation of the Allen elasticities of substitution (AES) and
factor demand elasticities. The AES between factors i and j
measures the impact of a change in the price of the jth factor
on the quantity demanded of the ith factor when output is fixed
but quantities of other factors are allowed to vary. In terms
of the translog cost function the AES can be calculated via
equations 11 and 12 (Binswanger, 1974A). The AES depends upon
the shares of the ith and jth inputs and therefore vary at each
observation.
1 2
(15) r = ( ) (Y + S2 Si)
Si
(16) r = (1 ) Yi + 1 for all i*j
ij Si iij
The price elasticities of factor demand, which measure the
impact in the jth factor price on the demand for the ith factor
holding output and other factor prices constant, are also eas
ily computed as follows (Binswanger, 1974A).
(17) nii ii/i) + i 1
(18) n = (YiI/Si) + Sj for all i*j.
The AES and price elasticities give important information
on the relationship between factor inputs. As discussed pre
viously, the elasticity of substitution may affect the factor
substitution possibilities of the producer and hence influence
factor bias through time. Kako used the AES in this context,
in order to calculate the total substitution effect of factor
prices in Japanese agriculture. He was able to differentiate
the substitution from the scale effects in order to arrive at
the contribution of technical change to factor bias.
If R & D as a representation of technical progress is
found to be a significant factor affecting the cost structure
of the Florida citrus processing industry, then the shadow
price of research will be reflected by the negative of the
first derivative of the cost function with respect to the quan
tity of research (equation 10). This explicitly defines the
decrease in cost attributable to a oneunit increase in the
quantity of research, which is interpreted as the market value
of research. A measure of the returns to processing research
was estimated by using the dollar value of one unit of research
and the corresponding decrease in citrus processing cost attri
butable to a oneunit increase in R & D.
The quantity of research and development conducted in the
citrus processing sector as a proxy for technical change will
also affect the cost shares of inputs via the citrus structure.
Research may induce factor bias by providing technologies that
augment labor or capital usage. It is also conceivable that
R & D could affect input usage neutrally through organizational
or other innovation. Binswanger (1978) points out that a cost
minimizing producer will have the tendency to adopt the least
cost path of technological opportunity. For the Florida citrus
processing industry this may imply that the adoption of the new
technology will increase (or decrease) the requirements of one
factor relative to another.
Estimation Method
In estimation of the translog cost function with the cit
rus share equations, one share equation must be dropped because
only ni share equations are linearly independent due to the
homogeneity restrictions (Binswanger, 1974B). Additionally,
the additive specification of the error terms results in a
singular variance matrix since the share equations sum to one.
Assuming that optimal behavior is represented by utilizing
share Si* in the production of Y, then the relationship of the
observed share Si will be Si = Si* + Vi, where Vi is the error
in the ith share equation. If E(Vi) = 0 and E(ViVj) = Eij the
residuals will reflect error in the optimizing behavior since
Si is stochastic.
Iterative seemingly unrelated regression (ITSUR) was used
to estimate the cost function and share equations. Under this
method the parameters are estimated using
(19) s8 (X'(E1 x I )X) I'(E x I )Y
sur n n
where X is the matrix of exogenous variables in the system, Y
is the vector of endogenous variables, In is the identity mat
^1
rix of dimension n and E is the inverse of the estimated
variance covariance matrix of error terms. ITSUR repeats the
estimation of the parameters and corresponding error covariance
matrix until both the parameter vector and covariance matrix
coverage to stable values. Under this method the parameters are
consistent and efficient. Most importantly, this method
ensures that the parameter estimates are invariant to the share
equation dropped from the system.
EMPIRICAL RESULTS
A translog cost function in conjunction with the share of
labor and share of materials equations for the Florida citrus
processing sector was fitted to the data for the years 1956
1980.
3
(20) InC = a0 + 11nY + 61 nR + E YilnPi
i=1
3 3 3
+ 1/2 E Y ij lnP InP + i Yiy nPilnY
i=1 j=1 i=1
3 2
+ E YirlnPilnR + 1/2 82(lnY)
i=1
+ 1/2 62(InR)2 + 31nY InR
3
(21) S1 Y1 + j YjlnP + Y1ylnY + Y1rlnR
j=1 j
3
(22) Sm Y + Z Y lnP + YyInY + Y InR
m ., mj j my mr
where Pi is the price of labor (L), materials (M) and other
inputs (0), and i,j = l,m,o; Y is total output of FCOJ from
Florida processors; C is total cost of processing FCOJ; Si is
the share of labor (L) and materials (M) in total cost; and R
is the quantity of research.
The quantity of R & D is the average of the deflated
expenditures of R & D lagged one and 6 years. Since both
applied and basic research activities are undertaken in the
industry, with an average lag for R & D payoffs of 6 months to
2 years for applied and 5 to 9 years for basic R & D (Attaway,
1984), the average of a 1year and a 6year lag is used to
approximate the impact of R & D expenditures on the current
citrus cost structure. Griliches (1964) used similar reasoning
in calculation of his R & D variable where he lagged R & D
expenditures one and 6 years (additional information on data
sources and calculations is contained in the Appendix).
Empirical estimation of the cost function requires a pri
ori imposition of homogeneity in input prices and symmetry.
Equation 20 uses 24 free parameters. Homogeneity of input
prices is defined as. follows.
(23) C c(Y,R,AP) Xc(Y,R,P)
In equation 21, homogeneity implies the following restrictions.
(24) E Y = 1, Y = 0, E Y = 0, E ir = 0
i ij i it
i i 1j i
i Y = 0 for all i and j
The second order partial derivatives of the cost function
with respect to input prices generate symmetry constraints.
a(2nC a21nC
(25) alnPi DnP ij = anP. lnP ji iJ
Symmetry and homogeneity restrictions reduce the number of free
parameters to 15. In addition to these restrictions, the
regularity conditions mentioned previously require the cost
function to be nondecreasing in output and input prices at each
observation.
aC ac
> 0, c > 0 for all i
i
The translog cost function will be nondecreasing in output and
input prices if both the derivative of the logarithm of cost
with respect to the logarithm of output and the predicted
shares are greater than zero, at each observation.
The cost function will be concave in factor prices pro
vided the Hessian matrix of second order price derivatives is
negative semidefinite at each data point. This requirement is
satisfied by the translog formulation if the matrix of esti
mated substitution elasticities is negative semidefinite at all
data points.
Results from the estimation of the full or unrestricted
translog model are presented in Table 2. The results show that
few parameters are significantly different from zero at
conventional levels. The exception appears to be the interac
tion terms of R & D with input prices and output with input
prices (i.e. Yir and Yiy, respectively).
The R2 values associated with the share of labor and share
of materials equations are .76 and .72, respectively, and are
somewhat higher than the fits found in other studies that
estimate the share equations alone (Binswanger, 1974A). This
result is most likely due to the additional information
provided by estimation of the cost function in conjunction with
the share equations. Multicollinearity is not an unusual
result considering the large number of variables that are
fitted to 25 observations. Such results suggest restricting
some of the flexibility inherent in the specifications.
Although homogeneity of factor inputs may be imposed to
further restrict the flexibility, it was thought to be an
A
overly restrictive assumption due to the significance of Ym
and Y Additionally, as Lopez noted, when the production
oy
technology is constrained to input homogeneity, it is not unu
sual to find technical change to be a significant factor
affecting input usage. Although this finding is not entirely
applicable to this study (since R & D is a more specific varia
Table 2. Parameter estimates for the translog cost function
(estimated asymptotic standard errors in parenthe
ses).
Model 1 Model 2
Variable Unrestricted Restricted
Intercept a0 16.20 1.09
(36.49) (1.60)
InY 8 5.24 .494
(7.60) (.162)
InR 1 7.47 .432
(6.59) (.168)
InP1 Y1 .0186 .009
(.297) (.284)
lnPm Y .299 .293
m (.429) (.413)
InPo Y0 .719 .715
(.329) (.320)
(InP1)2 11 .0342 .0307
(.072) (.068)
InPllnPm Ym .0362 .0353
(.064) (.062)
InP1lnP Ylo .002 .0046
S(.021) (.020)
(lnPm)2 Y .148 .1265
m (.084) (.08)
InPmlnPo Y .112 .0911
nmP o (.057) (.052)
(lnP0)2 Y .110 .0865
00 (.052) (.047)
InRlnP1 Y .054 .054
S (.024) (.023)
InRlnPm Yr .194 .184
S (.042) (.040)
InRlnPO Y .141 .131
or (.035) (.033)
InYlnP1 Y .009 .009
Iy (.013) (.012)
InYlnP Y .096 .088
my (.038) (.036)
InYlnPO Y .087 .0795
oy (.035) (.033)
(lnR)2 6 1.09 0
(.740)
(lnY)2 B2 .616 0
(.803)
InRlnY B3 .919 0
(.716)
ble associated with citrus technology than a time trend which
may encompass many factors), it is better to avoid the bias
that has resulted from imposition of homogeneity in other
studies.
Accordingly, Binswanger (1974B) notes that leaving out a
factor that does not affect shares neutrally will bias the
estimation of the parameters in the share equations. If the
factor does affect the shares neutrally (in this case, if all
Tiy = 0), then leaving this variable out of the regression will
not bias the results.
Instead, the quadratic terms of the R & D and output vari
ables as well as the interaction of R & D and output were
dropped (i.e. 2 , = 0, 83 = 0). This method was chosen
because the variables appear to be collinear and because, in
the study where share equations are estimated without the
accompanying cost function, these variables would not
explicitly enter the analysis. This specification makes the
model more in line with previous studies measuring the impact
of technical change on factor shares. Secondly, the input
price interaction variables appear to be collinear, and this
result may suggest further restrictions on the Yij
parameters. However, without a priori knowledge of the input
demands in the citrus processing sector (i.e. knowledge of the
prices that affect the cost share of the ith input) setting any
given Yij = 0 would yield, at best, an arbitrary result.
The restrictions 62 = 0, 82 = 0 and 73 = 0 were tested
with a likelihood ratio. As seen in Table 3, the restrictions
could not be rejected at the 95 percent confidence level. The
second column of Table 2 reports the estimated coefficients for
the resulting (restricted) model.
The restricted model was used in further analysis. Note,
however, that due to the fact that the restricted model is
based on a test, the estimators are pretest estimators. Hence,
the standard tests of significance may not be strictly valid
(Judge et al., 1980).
Table 3. Test statistic for restricted models.
Critical Level
Test Number of of X at .05
Statistics Restrictions = r Significance
3.45 3 7.81
aLikelihood ratio test: R = determinant of the restricted
covariance matrix, U = determinant of the unrestricted covari
ance matrix and N is the number of observations (Judge et al.,
1980) [ln(R) ln(U)] x N ~ x (r)
Both the restricted and unrestricted translog cost func
tions satisfy the conditions required for regularity at each
observation. These requirements include monotonicity and con
cavity in factor prices, and nondecreasing in output.
As mentioned in the Appendix, the shares of other inputs
in total cost consist predominantly of expenditures on mainte
nance, depreciation, warehousing and manufacturing overhead
costs. It is assumed in the analysis, therefore, that the
share of other inputs represents the expenditures on working
capital and capital equipment and structures in total cost.
The ij values alone have little intuitive meaning;
therefore, it is better to interpret them in the context of
factor demand and substitution elasticities (Binswanger,
1974B). The estimated Allen partial elasticities of
substitution and factor demand elasticities evaluated at the
means of the data along with their estimated asymptotic
standard errors for the restricted model are presented in
Tables 4 and 5, respectively. Note that by
definition ai = ji; of course, in general, this result does
not hold for the demand elasticities (i.e. n ij Ii).
All of the own factor demand and substitution elasticities
have the correct sign. The own partial elasticities of substi
tution have little economic meaning; however, note that the own
factor demand elasticities for both materials and other inputs
are significant and less than one in absolute value. This
result suggests that the factor demands for materials and capi
tal are inelastic. Since both materials and capital are impor
tant factors in the production of FCOJ, this is not an unlikely
result. The demand elasticity for labor is marginally greater
than one in absolute value. This may imply, other things being
equal, that a rise in the price of labor would lead to a
decrease in the share of labor in total cost. However, since
1 llis not significantly different from zero at conventional
levels this result is tenuous.
The positive values of the offdiagonal elements in Tables
4 and 5 suggest that the inputs are substitutes. Conversely,
negative values would have indicated complementarity among
inputs. The substitution between inputs is best evaluated by
utilizing the AES rather than the n j. This occurs because the
factor demand elasticities reflect the relative importance of
the input's share in total cost whereas those of the AES do not
(Binswanger, 1974A).
Table 4. Estimated allen partial elasticities of substi
tution (estimated asymptotic standard
errors in parentheses)
Labor Material Other
Labor 7.28 1.53 .921
(3.24)a (.940) (.350)
Materials 1.83 1.50
(.394) (.290)
Other 2.02
(.292)
aSE(ij x SE ( j)
Table 5. Estimated input price elasticitiesa (estimated
asymptotic standard errors in parentheses)
Labor Material Other
Labor 1.06 .69 .368
(.467) (.427) (.137)
Materials .221 .821 .59
(.135) (.176) (.114)
Other .133 .683 .816
(.050) (.130) (.117)
an measures the effect of a change in the price of the input
in the jth column on the quantity demanded of the input in the
ith row. SE (ni) = x SE (Ti)
j S i j
The estimated substitutability between materials and other
inputs is statistically significant asymptoticallyy) and large.
This relationship may reflect the industry trend to substitute
away from the relatively more materials intensive packaged FCOJ
to the relatively more capital intensive bulk FCOJ in recent
years. The estimated AES corresponding to labor and other
inputs is also significant and close to one. If it is assumed
that capital and warehousing are reflected by the other inputs
category, then this is consistent with the citrus industry's
continual mechanization over the last 40 years. Both packaged
and bulk processes have become increasingly capital intensive
as illustrated by the trend to substitute capital for labor in
the washing, transporting and packaging stages of production.
Finally, the estimated AES associated with labor and mate
rials also suggests that these inputs are substitutes. How
ever, the small magnitude of alm relative to its estimated
standard error makes analysis of this variable inconclusive.
The parameters Yiy reflect the way in which output has
affected input shares at constant logarithmic rates through
time. It can also be viewed as the impact of output over time
on the factor shares. The parameter Y suggests that as out
my
put has increased over time the share of materials has
increased. Considering that approximately 60 to 70 percent of
the citrus processing industry's output consists of packaged
FCOJ it is not unusual to find that expansion in output induces
an increase in the materials share of total cost (on average).
The parameter y indicates that as output increases at
oy
constant logarithmic rates over time the share of capital in
total cost decreases. Accordingly, these results imply that
the citrus processing industry has a nonhomothetic production
structure. Furthermore, economies in capital usage exist. As
output increases, on average, proportionately less capital cost
is incurred per unit of output.
The parameter Yly is close to zero and smaller than its
estimated standard error. This implies that labor's share in
cost is unaffected (or affected neutrally) by output expansion.
The same proportion of labor cost in total cost is incurred, on
average, for any scale of output.
The partial derivative of the log of cost with respect to
the log of output at the means of data was calculated to be .77
with an associated standard error of .09. This implies an
estimated economy of scale at 1.28 (equation 14). This value
reflects large economies of scale, which may be partly
responsible for the high industry concentration rate observed
among Florida citrus processors. In the 197071 season only 10
industry members processed almost 68 percent of Florida FCOJ.
At the selling level, the market share increases further. In
addition, there has been little variation in the breakdown of
market shares of specific firms in the industry (Ward and
Kilmer, 1980). Therefore, it appears that the large economies
of scale are in accord with the high market share concentration
observed in the industry.
The economies of scale in capital usage (i.e. oy > 0)
may contribute to the large returns to scale observed in the
production technology. Undoubtedly. the large freezer ware
housing facilities, computerized processing and high volume
packaging equipment and manufacturing overhead amount to a
substantial fixed investment for industry members. It seems
reasonable that these inputs, which are represented in the
other inputs share category, would reflect increasing returns
to scale and may contribute to the large economies of scale
observed in this study.
The parameters Yir in the share equations, which were all
considerably larger than their estimated standard errors.
reflect the way in which research has affected the input shares
in total cost at constant logarithmic rates through time.
These results are related to several factors in Florida
citrus processing R & D and trends affecting the industry
structure. As noted previously, a major trend in the Florida
citrus industry has been increased bulk processing and ware
housing of FCOJ (Figure 2). R & D has been an important
component in the growth of bulk. R & D is responsible for
initiating new technologies that have lowered the cost of
warehousing and shipping of bulk as well as creating and
stimulating the demand for ready to serve orange juice, a major
product form of bulk FCOJ.
Although FCOJ processing of bulk and packaged FCOJ entails
equivalent procedures for the most part, after processing, the
packaged FCOJ operation becomes a relatively more material
FCOJ MOVEMENT
MILLION CONCENTRATE GALLONS
RETAIL BULK INSTITUTIONAL
18.7 9%
S40.3 95.7 46%
15% 20.5
197172 198488
SEASON
Figure 2. Florida FOB FCOJ movement million concentrate
gallons. Source: Gunter (1985).
intensive process whereas bulk FCOJ requires relatively more
capital and labor expenditure per gallon. Therefore, both bulk
and packaged FCOJ production requires labor; however, a rela
tively greater proportion of total cost per gallon is spent on
labor in bulk processing and storage than for packaged FCOJ
production.
Given the phenomenon of increased bulk production, which
utilizes proportionately more labor and less materials than
packaged FCOJ, that research has induced an increase in labor
usage and a decrease in materials usage is not an unexpected
outcome. Accordingly, by considering the relative magnitudes
of the parameters on R & D in the share equations, the results
imply that, on average, R & D has induced a small increase in
labor's share in total cost and a larger decrease in material's
Share in total cost through time.
The parameter Yor corresponding to R & D and other inputs
in the share equation suggests that, on average, R & D has led
to an increase of capital's share in total cost through time.
This result may be related to the phenomenon described above,
where R & D aiding the growth of bulk FCOJ has increased
warehousing's and capital equipment's shares in total cost. On
the other hand, the direct effects of R & D should be accounted
for as well. R & D has affected the technological
possibilities of citrus processing at all stages of production,
especially in terms of increasing the mechanization of both
bulk and packaged FCOJ. Although the value of Yor is difficult
to interpret, the relatively larger Yor indicates that R & D,
on average, has induced a greater increase in capital's share
of cost than labor's share of cost through time.
The measure of the shadow price of the quantity of
research calculated at the means of the data was $1536 with an
associated standard error of $672 (equation 10). This measures
the imputed market price of one unit of R & D or the decrease
in total cost attributed to one unit of R & D applied over six
years. The mean total cost of one unit of research as
calculated in this study was $92.60. Dividing the total cost
savings attributed to one unit of R & D by the amount spent on
1535 9
the R & D ( 92.9 ) yields an average cost savings of $16.58
today per dollar of research investment one and 6 years
previously. Not surprisingly, this result is similar to previ
ous production function studies. Peterson (1967) calculated a
marginal product of $18.52 associated with poultry research in
the U.S.. Griliches (1964) found a $13.28 marginal product
associated with the value of aggregate agriculture and Bredahl
and Peterson (1976) estimated a marginal product of $14.09 per
dollar of research in cash grain production in the United
States.
If it is assumed that R & D yields continuous benefits on
average (versus benefits that pay off annually or quarterly),
then the application of one dollar of research investment allo
cated over one and 6 years to citrus processing has yielded a
continuously compounded average rate of return of 57.4 per
cent.1
This rate of return is somewhat higher than those calcu
lated using the productivity index approach. Comparison of the
relative rates of return are not entirely analogous, however.
The productivity index studies focus on industrywide (two
digit Standard Industry Classification) R & D, which could be
viewed as an average rate of return over the entire food and
kindred product industry, whereas the present study analyzes
the Florida citrus processing sector alone.
The results show that the translog cost function may yield
important information about the effects of R & D at a disaggre
gated or subsector level. The cost function also yields impor
1The formula used for calculation of returns to research
assumes constant rates of growth (.5ei + .5ei = 16.58 where i
is the interest rate).
tant information regarding the relationship among inputs via
S calculation of the substitution and price elasticities. When
the cost function and share equations are estimated as a sys
tem, the factors affecting the input's share in total cost may
also be analyzed.
The results suggest that R & D, and thus technical change,
has had an important impact on the Florida citrus industry's
cost structure. In addition, the evidence implies that the
underlying production structure is nonhomothetic. Both
research and output have a significant impact on factor shares.
In short, the scientific, marketing and economic research
performed in the Florida citrus processing sector has affected
the cost of producing FCOJ directly and via the inputs' shares
in total cost over the last 25 years.
SUMMARY
Using the duality relationship between production func
tions and cost functions, a translog cost function and corre
sponding share equations were estimated in order to measure the
technological relationships in the FCOJ industry. While the
cost function usually has input prices and output as arguments,
McFadden shows that a fixed input may be introduced into the
cost function as well. This input may include any factor which
characterizes the state of technical progress or which
describes or influences the production technology. In this
study the quantity of Florida citrus research was introduced
into the cost function. Following Diewert and Lau, the shadow
price of R & D was obtained by partial differentiation of the
cost function with respect to the quantity of research. Assum
ing a constant rate of growth, a continuously compounded aver
age rate of return associated with Florida citrus processing
research was calculated. In addition, estimation of the trans
log cost function in conjunction with the share equations
allows analysis of the effects of R & D and, hence, technologi
cal change, on input shares in total cost.
As in any econometric study, it is important to analyze
the production structure and account for all possible factors
affecting the endogenous variables (given the empirical limita
tions of data measurement and accuracy). A common practice is
to enter time into the production or cost function in order to
characterize the technology or technological change occurring
in an industry. In the present study, however, since R & D
enters the cost function as a specific quantity affecting cost,
its impact is more clearly delineated than a time trend varia
ble, which may characterize and encompass the effects of
various factors. The purpose of R & D's inclusion and the time
trend exclusion is to measure and identify the specific cost
reducing effect of a variable aimed exclusively at product and
process innovation.
The parameters on the interaction term of research and
input prices (Yir) reflect the way in which research has
affected the input's share in total cost at constant logarlth
mic rates through time. The results imply that, on average,
S research has had a positive effect on labor and other input
usage and a negative effect on materials usage.
The measure of the shadow price of the quantity of
research calculated at the means of the data was $1535.90 with
an associated standard error of $672. This is the imputed
market value of one unit of research applied over one and 6
years previously. By considering the price of one unit of R &
D, the decrease in total cost today attributed to a onedollar
increase in R & D expenditures one and 6 years ago is $16.58.
Assuming constant rates of growth and continuous compounding,
this yields a 57.4 percent rate of return to citrus research.
Of course there are several factors that may bias the
estimated shadow price of research. There is a possibility
that R & D from sources outside the citrus industry may have
affected the citrus cost structure through organizational or
capitalembodied technical innovations. Although it is assumed
that R & D entering the citrus sector through purchased inputs
will be reflected in the input price, for the most part, expen
ditures not incorporated in the industry R & D variable or
input price may tend to bias the returns to research upward.
Conversely, technological innovation attributable to
research conducted within the Florida citrus industry may have
spillover effects into other food processing sectors. (This is
a pertinent factor in this case because the Brazilian citrus
industry, the world's largest FCOJ exporter, has imported most
of its processing technology directly from the Florida citrus
industry.) Equally important, the change in the quality of
FCOJ resulting from industry R & D will not be reflected in the
output measure. These are benefits from R & D that are not
measurable within the scope of this study. Because the input
and output variables do not explicitly account for these fac
tors, the actual returns to citrus research may be larger than
the estimated returns.
4
APPENDIX A: DATA
Output
Output is total movement of FCOJ from Florida
processors. This quantity includes annual retail,
institutional and bulk sales of Florida processors on an
equivalent 420 to 450 Brix basis. Bulk FCOJ is warehoused
directly after processing whereas retail and institutional FCOJ
is packaged in various forms and later warehoused (Florida
Citrus Mutual 19561980).
Total Cost
Total cost is calculated as the sum of the cost per gallon of
processing bulk multiplied by the quantity of bulk plus the
cost per gallon of packaged FCOJ multiplied by the quantity of
packaged FCOJ. All data were calculated on an equivalent 420
to 450 Brix basis. Since data were not available for bulk
processing costs before 1962 and bulk sales represented less
than 10 percent of output during this time period, total cost
for 19561962 was calculated as total cost per gallon of
packaged FCOJ multiplied by total movement. Data were
available from Florida Citrus Mutual.
Price of Labor
Price of labor is the average hourly earnings of production
workers on private nonagricultural payrolls in the twodigit
SIC, Food and Kindred Products classification (United State
Department of Labor 19561980).
Price of Materials
The price of materials is the producer price index for
converted paper and paperboard products, 1967 = 100.00 (United
States Department of Labor 19561980).
Price of Other Inputs
Since a large proportion of cost, other than materials and
labor, is encompassed in warehousing and capital expenditures
such as maintenance, depreciation, manufacturing overhead and
warehousing, the Moody's triple A bond interest rate is used as
a proxy for the price of other inputs. In this analysis, the
interest rate reflects the price of capital and the cost of
warehousing FCOJ (Economic Report of the President 1983).
Share of Labor
The total labor expenditure is the product of the labor
expenditure per gallon of processing bulk FCOJ multiplied by
the quantity of bulk, plus the labor expenditure per gallon in
processing packaged FCOJ multiplied by the quantity of packaged
FCOJ. All data were calculated on an equivalent 420 to 450
Brix basis. The total expenditure on labor is divided by total
cost to arrive at the share of labor. Before 1962 when bulk
processing data were not available, the share of labor in
packaged FCOJ is used (Florida Citrus Mutual).
Share of Materials
The share of materials is the expenditure per gallon of
materials multiplied by the quantity of packaged FCOJ and
divided by total cost of processing (Florida Citrus Mutual).
Research
The quantity of research is calculated using the Florida
Department of Citrus R & D expenditures, state Research and
Extension expenditures on citrus processing R & D and a proxy
for R & D conducted by private industry. The FDOC allocation
to economic, marketing and scientific research and Florida
processing R & D expenditures were obtained. A time series
reflecting private R & D was developed using data for private
citrus R & D in the state from the United States International
Trade Commission (USITC) and the National Science Foundation
(NSF) series (both 1983) on private company R & D, conducted in
food and kindred product industries. The USITC data were
correlated with the NSF series and extrapolated back to 1947 in
order to arrive at a proxy for private R & D. The quantity of
research variable is constructed by summing the Florida
Department of Citrus and the proxy for private R & D
expenditure, dividing by the GNP implicit price deflator (1972
= 100.00), and taking the average of this variable lagged one
and 6 years.
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4
UNIVERSITY OF FLORIDA K
This publication was produced at a cost of $1011, or 67 cents per copy, to
model production relationships in the frozen concentrated orange juice
industry.
All programs and related activities sponsored or assisted by the Florida
Agricultural Experiment Stations are open to all persons regardless of race,
color, national origin, age, sex, or handicap.
ISSN0096607X
