WPTC 0501
I ional Agricultural Trade and Policy Center
WORKING PAPER SERIES
'V
UNIVERSITY OF
SFLORIDA
Institute of Food and Agricultural Sciences
LABOR SUBSTITUTABILITY IN LABOR INTENSIVE
AGRICULTURE AND TECHNOLOGICAL CHANGE IN THE
PRESENCE OF FOREIGN LABOR
By
Orachos Napasintuwong & Robert D. Emerson
WPTC 0501 March 2005
INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
THE INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
(IATPC)
The International Agricultural Trade and Policy Center (IATPC) was established in 1990
in the Institute of Food and Agriculture Sciences (IFAS) at the University of Florida
(UF). The mission of the Center is to conduct a multidisciplinary research, education and
outreach program with a major focus on issues that influence competitiveness of specialty
crop agriculture in support of consumers, industry, resource owners and policy makers.
The Center facilitates collaborative research, education and outreach programs across
colleges of the university, with other universities and with state, national and
international organizations. The Center's objectives are to:
* Serve as the Universitywide focal point for research on international trade,
domestic and foreign legal and policy issues influencing specialty crop agriculture.
* Support initiatives that enable a better understanding of state, U.S. and international
policy issues impacting the competitiveness of specialty crops locally, nationally,
and internationally.
* Serve as a nationwide resource for research on public policy issues concerning
specialty crops.
* Disseminate research results to, and interact with, policymakers; research, business,
industry, and resource groups; and state, federal, and international agencies to
facilitate the policy debate on specialty crop issues.
LABOR SUBSTITUTABILITY IN LABOR INTENSIVE
AGRICULTURE AND TECHNOLOGICAL CHANGE IN THE
PRESENCE OF FOREIGN LABOR
Orachos Napasintuwong
Food and Resource Economics Department
PO Box 110240
University of Florida
Gainesville, FL 32611
onapasi(@ufl.edu
Robert D. Emerson
Food and Resource Economics Department
PO Box 110240
University of Florida
Gainesville, FL 32611
remerson(@ufl.edu
Abstract
The Morishima elasticity of substitution (MES) is estimated to address factor
substitutability in Florida agriculture during 19601999. By adopting a profit
maximization model of induced innovation theory, the MES's between hired and
selfemployed labor and the MES's between labor and capital provide
implications for future immigration policies.
JEL codes: Q160, J430, 0300
Keywords: Morhishima Elasticity of Substitution; Induced Innovation; Biased
Technical Change; Foreign Labor
Selected Paper prepared for presentation at the American Agricultural Economics
Association Annual Meeting, Denver, Colorado, August 14, 2004
Copyright 2004 by Orachos Napasintuwong and Robert D. Emerson. All rights reserved.
Readers may make verbatim copies of this documentfor noncommercial purposes by any
means, provided that this copyright notice appears on all such copies.
Labor Substitutability in Labor Intensive Agriculture and
Technological Change in the Presence of Foreign Labor
Introduction
The link between foreign labor availability and the rate of development and
innovation of farm mechanization in U.S. agriculture is examined in this paper.
According to the induced innovation theory, an increasing price of labor (due to a more
stringent immigration policy) would induce the development of laborsaving technology.
In the study of technological change based on induced innovation theory, it is commonly
assumed that labor and capital are substitutes for a given technology set. Thus, when
labor becomes more expensive, it should induce the development of technology that uses
less labor relative to capital. In order to draw implications from the study of
technological change (e.g., immigration policy implications), it is important to understand
the substitutability among inputs. For example, if labor and capital are easily
substitutable, only a small increase in wage rate (reduction of foreign workers
availability) could increase the adoption of mechanized technology. Recognizing the
importance of the substitution relationship among inputs, particularly labor and capital,
instead of assuming the substitutability among them, this study attempts to measure the
ease of substitutability using the Morishima elasticity of substitution.
The extensive studies of technological change in U.S. agriculture (e.g.,
Binswanger 1974) have primarily used the AllenUzawa elasticity of substitution (AES)
as a measure of substitutability of inputs. The original concept of elasticity of
substitution was introduced by Hicks (1932) to measure the effect of changes in the
capital/labor ratio on the relative shares of labor and capital or the measurement of the
curvature of the isoquant. However, as shown by Blackorby and Russell (1989), when
there are more than two factors of production the AES is not the measure of the ease of
substitution or curvature of the isoquant, provides no information about relative factor
shares, and cannot be interpreted as a derivative of a quantity ratio with respect to the
price ratio. In contrast, the Morishima elasticity of substitution (MES) does preserve the
original Hicks concept. It measures the curvature, determines the effects of changes in
price or quantity ratios on relative factor shares, and is the log derivative of a quantity
ratio with respect to a marginal rate of substitution.
The MES is a twofactor, oneprice elasticity of substitution. It can be interpreted
as a crossprice elasticity of relative (Hicksian) demand because it measures the relative
adjustment of factor quantities when a single factor price changes (FernandezComejo
1992). The original concept of MES defined by Morishima was in the cost minimization
context (Blackorby and Russell 1981). We adopt the Sharma (2002) extension of the
MES to the variable profit function. This is particularly advantageous since the MES
among inputs may be calculated while holding output constant. The variable profit
function is adopted in recognition of the simultaneous determination of output mix and
variable inputs for given prices. An increasing importance of changes in trade policy,
trade agreement, and biotechnology results in a greater influence of input prices on the
choice of commodity mix. For instance, the production of a new genetically modified
crop variety may require different input requirements than the production of the old
variety. The choice of production commodity mix is a part of the production decision,
and should also be influenced by input prices.
We are interested in the impact of changes in input and output prices on biased
technological progress in Florida agriculture. We draw from the induced innovation
theory literature for the analysis of technological change. To the extent that immigration
policy affects wage rates, changes in immigration policy can clearly have an influence on
the rate and form of technological progress. Estimates of the MES between labor and
other inputs over the 1960 to 1999 period are used to evaluate the extent to which
substitutability has changed since the passage of the Immigration Reform and Control
Act (IRCA) in 1986, and the resulting implications for the demand for labor. Changes in
input and output mix caused by changes in input prices reflect movements along the
isoquant. The MES is the appropriate concept to properly analyze these effects. When
changes in input prices induce further input substitution through biased technological
progress, the MES addresses the extent to which changes in input prices creating
substitution among inputs (and outputs) also influence the direction of technological
change.
There are two major objectives of this study. The first is to evaluate the bias of
technological change in Florida between 1960 and 1999, and compare the rates of change
before and after the passage of IRCA. Agricultural production in Florida remains highly
laborintensive, and the majority of farm workers in Florida are also foreign workers.
The number of foreign workers in Florida is higher than in most other states. They
account for 75% of hired workers (Emerson and Roka 2002) while 42% of U.S. farm
workers are foreign (those who have their home outside the U.S.) (Mehta, Gabbard,
Barrat, Lewis, Carroll, and Mines 2003). Moreover, about 52% of hired farm workers in
the U.S. are unauthorized (Mehta, Gabbard, Barrat, Lewis, Carroll, and Mines 2003).
The study of technological change in a labor intensive area will provide key implications
in evaluating the impact of immigration policy on the development of farm
mechanization.
The second objective is to analyze the ease of substitutability between labor and
other inputs, particularly capital. A limited availability of foreign workers in labor
intensive production would induce the development of new mechanized technology such
as the success of tomato mechanical harvester in California at the end of the Bracero
program in 1964. Thus, labor and capital are generally substitutes. However, it is
important to properly measure the ease of substitutability and understand the mechanism
of the substitution between capital and labor to provide future immigration and farm
policy associated with technological change.
Methodology
A translog profit function of the induced innovation model is adopted. The time
variable is included to represent the state of technology at a particular time, and allows a
point estimation of the biases and elasticities over the study period. In order for the
model to be consistent with economic theory, the symmetry, homogeneity, and curvature
restrictions are imposed. The WileySchmidtBramble reparameterization technique is
used to locally impose the curvature restrictions. Parameter estimates of the translog
profit function are used to calculate the Morishima elasticity of substitution.
Model
Assume that outputs Y = (Y,,..., Y) use variable inputs X = (X,,..., X) and fixed
inputs K = (K,,...,KL). The vectors of output prices, input prices and fixed input prices
are denoted by P = (P,,..., PN), W = (W,,..., W), and R = (R1,..., RL), respectively. Let
Q = (Qi,.. .,QN+M) be a vector of variable input and output quantities, and Z = (Z1,...,
ZN+M) be a corresponding price vector.
The profit function is defined as: 7T(Z, K, t) = maxQ Z'Q K, t} for Z > 0 and K > 0,
and the translog variable profit function can be written as
N+M L 1 N+MN+M
In7r= o + llnZ,+ lnKj + h lnZ,lnZh
=l j=1 2 =1 h=1
L L N+M L
+ I jk lnK lnKk + l InZ InK
2 j1 k=l 1 =11
N+M L 1
+ 6i1t InZt+ jt InK t+ptt+ 4t2
1=1 =1 2
where t represents technological knowledge. Utilizing Hotelling's Lemma, profit share
equations can be derived from the derivatives of the log of profit with respect to the log
of prices.
8ln 7r Q1Z,
 = ,1 i = 1,...,N+M (2)
tlnZ1 Z 7
where ri > 0 ifZi is an output price, and tni < 0 ifZi is a variable input price.
The marginal revenue of a fixed input is equal to its cost under competitive
conditions. Thus, the derivative of the variable profit function with respect to a fixed
input quantity is equal to its cost, r8i/OKj = Rj > 0, and the derivatives of the logs yield
profit share equations.
8ln n RjK1
= = 7, j = ,...,L (3)
OlnK K 7
In the case of the translog variable profit function, share equations are derived as follows:
ln rT N+M L
7t a, + l In Zh + 6 In Kj + 6, t i= 1,...,N+M (4)
OlnZ1 h1 =1
ln ir N+M L
7= = Pj + k6, InZ + k InKk t+tt j 1,...,L (5)
OlnK 11 ki
A welldefined nonnegative variable profit function for positive prices and
nonnegative fixed input quantities satisfies the following restrictions:
1. A variable profit function is linearly homogeneous in prices of outputs and
variable inputs and in fixed input quantities. The homogeneity restrictions are
N+M L
1a, = 1; =l1
1=1 j=1
N+M N+M L L N+M L
ZYih ZYih =Zjk =Z jk = = Y 6 =0 (6)
1=1 h=1 ]=1 k=1 1=1 ]=1
N+M L
Yi6t Z4it =0
1=1 j=1
2. For a twice continuously differentiable profit function, Young's theorem
implies that the Hessian of the profit function is symmetric. In terms of the translog
profit function,
Yih = Yhl ; k = kj (7)
3. The convexity of a variable profit function in prices implies that the output
supply and variable input demand functions are nondecreasing with respect to their own
price. If i is a variable input (Xi < 0), an increase in its price reduces the quantity
demanded, OXi/OWi > 0. In other words, an increase in variable input price decreases its
demand in absolute value. The concavity of a variable profit function in fixed inputs
implies that the inverse demand equations are nonincreasing with respect to their own
quantities, Ri//Ki < 0. The necessary and sufficient conditions for a convex (concave)
profit function are that the Hessian of the profit function evaluated at output and variable
input prices (fixed input quantities) is positive (negative) semidefinite or all principal
minors are nonnegative (nonpositive).
Lau (1978) introduced the concept of the Cholesky decomposition as an
alternative to characterize the definiteness of the Hessian matrix. Every positive
(negative) semidefinite matrix A has a Cholesky factorization
A = LDL' (8)
where L is a unit lower triangular matrix, and D is a diagonal matrix. L is defined as a
unit lower triangular matrix if Li = 1, Vi and Li = 0, j > i, Vi,j. D is defined as a diagonal
matrix if Di = 0, Vi, j, i j. The diagonal elements, Dii, of D are called Cholesky values.
A real symmetric matrix A is positive (negative) semidefinite if and only if its Cholesky
values are nonnegative (nonpositive). A variable profit function is convex in variable
input and output prices. Thus, all Cholesky values (6s) must be nonnegative for the
Hessian of the variable profit function with respect to prices to be positive semidefinite.
Similarly, if the A matrix is the Hessian of a variable profit function with respect to fixed
input quantities, all Cholesky values must be nonpositive. We check the curvature
properties by checking the sign of the Cholesky values.
Wiley, Schmidt, and Bramble (1973) also proposed a necessary and sufficient
condition for a matrix A to be positive (negative) semidefinite if it can be written as:
A = ()TT' (9)
where T is a lower triangular matrix and Ti = 0, j > i, V ij. For a translog variable profit
function, the Hessian matrix of the profit function with respect to output and variable
input prices, AnI, is positive semidefinite. The restrictions for convexity are
2
Y11 +a a,1 7+aa12 ... Y + 1N +CaaN+M
2
Y+ ... Y^N+M + N^
Ail 712 +a 2 22 2 2 2,N+M +a2aN+M
2
YN+M,i + aN+Ma N+M,2 +a 2 a N+MN+2 NMM + aN+M aN+M
2
rTl TI 1T2 11" T I Ti,N+M
2 2
2ll1T2 12 2 22 T12 IN+M +22T2N+M
2 2
TI TI,N+M 12T1N+M + 22T2N+M 1N+M + +N+M,N+M
The Hessian matrix of the profit function with respect to fixed input quantities,
Ajj, is negative semidefinite. The concavity restrictions are
A1 + '2 _+1 012 1 882 ... O1L 1+ 8/L
A 12 + 1 2 22 22 .. :2,L + 2L
OL, +fLf1 L,2 N+M 2 ... PLL+PL2 L
(11)
T*2 Ti1 T l TIL
r 11 12 11 1,L
11 12 1 2 *22 212 L *+T22 T2L
11 I, T12 IL 22 2L 1 IL 2 TL,L*2
When the curvature property is violated, the WileySchmidtBramble reparameterization
is used to impose the curvature restrictions.
Elasticity
The price elasticities of variable inputs and outputs are
dlnQ1 yll
11 1+71 i =1,.N+M
dlnZ, 7r, (12)
dlnQ1 Y
S dlnQ1 7C Vi, j;i j (13)
dlnZj 71,
Inputs i andj are gross substitutes if ij > 0, and gross complements if ij < 0; the signs are
reversed for outputs which are gross substitutes if sij < 0, and gross complements if ij >
0.
The Morishima elasticity of substitution originally defined by Morishima
(Blackorby and Russell 1981) in the cost minimization is defined as
81n(X* /X'*)
MES1 = ln() (14)
ln(P /P,)
where X*i's are the optimal cost minimizing inputs, and Pj's are the input prices.
Applying Shephard's Lemma and homogeneity of the cost function, and assuming that
the percentage change in the price ratio is only induced by Pj,
PJCl (Y, P) PJCJ (Y, P)
MES1j = (15)
C,(Y,P) Cj(Y,P)
MESIj = Esl g C (16)
where ;ije(Y,P) is the constantoutput crossprice elasticity of input demand. Inputs i and
j are Morishima substitutes if MESj > 0; that is if and only if an increase in Pj results in
an increase in the input ratio X*i/X*j, and Morishima complements if MESj < 0. Sharma
(2002) applied the concept of the MES to the profit maximization approach as
summarized in the following paragraph.
Assume that Yi = fi(P, K, W), Rk = hk(P, K, W), and Xj = gj(P, K, W),
dY = dP + dK + dW (17)
OP 8K 8W
dY ln Y dP lnY dK 9lnY dW
=Y nK K W (18)
Y alnP P alnK K alnW W
O lnY OlnY d nY
dY = dP + dK + dW
OlnP OlnK OlnW
where is the relative change. Similarly,
OlnR OlnR OlnR
dR = dP + dK + dW
OlnP OlnK OlnW
d lnX dj 8nX d nX
dX= dP + dK + dW
OlnP OlnK 8lnW
Define Q* = (Y: R)' and Z* = (P: K)', then Eq. 19 to 21 can be written as:
Q* EO*z* EJ, Z*
Q*E Q*Z* EQ*W
XZ* ExWW_
X= EQzZ* +EQwW
From Eq. 23, Z* = EQz, Q* EQz EQWW.
Substitute Eq. 25 into Eq. 24,
X= ExzEQz,16 +(Exw ExzEQ*Z, E *W)W.
Equation 22 can be written as:
Z EZ*i EQZ* EQ*W
EXX xzEQ*Z* Exw EXZ*EQ*Z* E*W W
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26)
(27)
Holding the output level constant,
OX
S= Ex ExzEQ* EQ (28)
The MES can be calculated by the definition in Eq. 16 where ije is the ij element
in Eq. 27. Notice that the MES is not symmetric, and unlike the Allen elasticity of
substitution, the sign of MES is not symmetric either (Chambers 1988, p.9697). Thus,
the classification of substitute and complement between two inputs depends critically on
which price changes. A detailed derivation of elements of matrices in Eq. 27 can be
found in Napasintuwong (2004, Appendix B).
Biased Technological Change
The definitions of the rate of technological change and biased technological
change are adopted from Kohli (1991). Employing Euler's theorem, linear homogeneity
of the variable profit function in Z and K implies that
Sz= I L Z = YK (29)
at a t t8K
The semielasticity of the supply of output and the demand for variable inputs with respect
to the state of technology is defined as:
8ln Q
Eit Q, i = ,..., N+M (30)
at
and the semielasticity of the inverse fixed input demand with respect to the state of
technology is defined as:
ln j = 1,...,L (31)
Dividing through by 7t, and using Hotelling's Lemma and the marginal revenue of
fixed input condition, Eq. 29 can be written as:
O1n 7r
a= = ,s t = 7jjt (32)
where p is the rate of technological change. A positive rate of technological change
implies that there is technological progress. The bias of technology is defined as
B, = E  i= ,..., N+M (33)
B t j= 1,..., L (34)
A technological change is output iproducing if Bi is positive, and it is output ireducing
ifBi is negative. Similarly, a technological change is variable input iusing if Biis
positive, and it is variable input isaving ifBi is negative. A technological change is fixed
input jusing if Bj is positive, and it is fixed input jsaving if Bj is negative.
Data
Data used in this study are provided by Eldon Ball, Economic Research Service
(ERS), USDA. The construction of these data is similar to the published production
account data available from ERS (Ball et al. 1997, 1999, 2001). The data include series
of agricultural output and input price indices and their implicit quantities in Florida from
19601999. Price indices of these series are appropriate for this study since they are
adjusted for quality change of each input category. It is important to use qualityadjusted
data when analyzing induced technological change because using unadjusted quality
indices will result in biased estimation of parameters in the induced innovation model.
Data used in the analysis are aggregated into two outputsperishable crops and all
other outputs; four variable inputshired labor, selfemployed labor, chemicals, and
materials; and two fixed inputsland and capital. Perishable crops include vegetables,
fruits and nuts, and nursery products. Other outputs consist of livestock, grains, forage,
industrial crops, potatoes, household consumption crops, secondary products, and other
crops. Hired labor includes directhired labor and contract labor. The wage of self
employed labor is imputed from the average wage of hired workers with the same
demographics and occupational characteristics. Chemicals include fertilizers and
pesticides. Materials include feed, seed, and livestock purchases. Capital includes autos,
trucks, tractors, other machinery, buildings, and inventories.
Estimation
The translog profit function with linear homogeneity imposed and including an
IRCA dummy variable is defined as
5 Z K 1 5 5 Z
lnc=,+ aoc In Z' + In yhln Z InZh
1=1 Zmatl Kcapital 2 11 h 1 Zmatl Zmati
1 Kland Z K
+ 1 In +;6 In1n1 l land
2 K capital 1= Zmatl Kcapital
5 Z Z K Kland
+ 1t ln I t+ T262 ln 1 t + ltln land t + t2T2 n andt (35)
11 Zmatl Zmatl Kcapital Kcapital
1 1
+Ptt + t2tT2 + tt2 + tt +uOt
2 2
where T2 is a time dummy variable for years after the passage of IRCA in 1986. It is
added to capture the potential difference in the biases and the rate of technological
change. Linear homogeneity in prices is imposed by dividing through all prices by the
price of materials (the variable input equation dropped from the system), and linear
homogeneity in fixed inputs is imposed by dividing fixed inputs by the quantity of capital
(the fixed input equation dropped from the system). In addition to the homogeneity and
symmetry constraints, the continuity of the profit function in 1987 requires the additional
constraint:
Sit2 In 41 t2 ln 87and I+ t2 +P I ttt87 = 0 (36)
1=1 matl K capital 2
where Z87, K87, and t87 represent the observed values in 1987.
The profit shares are derived by taking the first derivative of the translog profit
function with respect to the log of variable input and output prices and fixed input
quantities. The system of share equations becomes
5 Z K
7, = a, +l ln zh +61Jln + 1t + T2t2 .t+u i=1,...,5 (37)
hi Z K
h=l Zmatl capital
5 Z K
7,J = J + 61 n Z +41 In +tland + ~,t + T22t +u, j= 1 (38)
1=1 matl capital
The seemingly unrelated regression procedures were applied to the system of
share equations Eq. 37 and Eq. 38 and the translog profit function Eq. 35 using the Full
Information Maximum Likelihood (FIML) procedure.1 The disturbances are assumed to
be jointly normally distributed with zero means, scalar covariance matrices, but nonzero
contemporaneous covariances between equations. The profit equation is included
because parameters Pt and tt are needed to calculate the rate of technological change and
cannot be estimated directly from the share equations.
Following from Eq. 37 and 38,
OQ,
8nT1 It QZZ 1
7 Q1Z 6t + T261t2 i = ,...,6 (39)
A r8t r 2 at
solving for 5Qi/ot from Eq. 39 and dividing by Qi,
1 Q, 6t, + T262 alnrt
sit 1 + (40)
Q, 8t a, 8t
6,,l + T26lt 2
E 6tt= T2t2 +[ (41)
,i
Thus, the biased technological change defined in Eq. 33 and 34 can be estimated as
B = t +T26t2 i= 1,...,6 (42)
B = 22 j =1, 2 (43)
Time Series Processor (TSP) through the looking glass version 4.4 is used for statistical analysis.
1 Time Series Processor (TSP) through the looking glass version 4.4 is used for statistical analysis.
Results
We first checked the Cholesky values of the Hessian with respect to the fixed
inputs, and found that they are negative at every observation. However, the Cholesky
matrix of the Hessian with respect to the variable inputs and outputs has one negative
Cholesky value at every observation. This means that the convexity property of the
estimated profit function is violated within the region of data among the outputs and
variable inputs, but the concavity property is not violated for the fixed inputs. The most
negative Cholesky value, 3.1440, is found in 1998. Since only convexity is violated,
subsequent curvature attention is given only to convexity.
The convexity is imposed using the WileySchmidtBramble reparameterization
technique as presented in Eq. 10 and Eq. 11. The right hand side variables are
normalized to one and the time variable is normalized to zero in 1998. This guarantees
that convexity will be satisfied at this point. Table 1 presents the estimates transformed
back to the original parameters of the translog profit function satisfying the regularity
constraints, including convexity.
Rate of Technological Change and Biased Technological Change
Table 2 reports the estimates of Florida biased technological change before and
after the passage of IRCA, evaluated at the means of the explanatory variables for each
subperiod. A test that the biases are jointly different between the two periods is highly
significant as suggested by a Wald test statistic value of 47.06; the critical value for the
X(8) is 21.95 at the 0.005 significance level. The individual differences of biases
between the two periods and their standard errors suggest whether the changes are
individually significant. After the passage of IRCA in 1986, the technology suggested
significant bias toward more perishable cropproducing, but significant bias against the
production of other outputs. The technology became more selfemployed laborusing,
but the biases of hired labor and capital were not significantly different. The technology
significantly used more chemicals and less materials whereas, the use of land did not
change. The results suggest that although the technology significantly saved both types
of labor before IRCA, it used more selfemployed labor afterward. The technology
switched from hired laborsaving to hired laborneutral following IRCA; similarly, there
was no significant adoption of mechanized technology as reflected by the capital bias
estimates. The technology suggested an increase in the production of perishable crops.
Instead of hiring more workers or adopting new mechanized technology, the technology
apparently became more selfemployed laborusing in the production of perishable crops
in the labor intensive areas.
Elasticity
The ownprice elasticities of both outputs were positive, and those of inputs were
negative as expected at all observations. Table 3 summarizes the ownprice elasticities of
output supply and variable input demand and the inverse fixed input demand for selected
years. The correct signs of the elasticities indicated that they were consistent with
economic theory.
Figure 1 shows point estimates of the MES between hired labor and self
employed labor, and the MES between two types of labor and capital. Hired labor and
selfemployed labor are substitutes, and the substitution became more elastic and more
volatile after the passage of IRCA, particularly the MES between types of labor when
hired labor wage changes. Labor and capital are also substitutes, except for the
substitution between hired labor and capital when capital price changes in some years in
the early 1960s and between the mid1980s to early 1990s. The negative MES's between
hired labor and capital when capital price changes in some years suggest that even when
capital becomes cheaper, the employment of hired labor increases. This is important
particularly after the passage of IRCA. If more stringent immigration legislation were to
stimulate the ready availability of new mechanized technology and at a lower cost, it
would not necessarily follow that the employment of hired labor would decrease. In
Florida, where agricultural production is still highly labor intensive, capital may not be
able to substitute for labor. For instance, the harvest of citrus for fresh market is still
done manually because mechanical citrus harvesters still cannot preserve the postharvest
quality to meet high standards for the fresh market. The MES's between capital and two
types of labor when returns to labor change are more elastic than the MES's between
capital and labor when capital price changes. This implies that it is easier to substitute
capital for labor (adopt mechanized technology) when labor becomes more expensive
than to substitute labor for capital when capital becomes more expensive.
The average MES's before and after the passage of IRCA are summarized in
Table 4. The results reveal that hired labor and selfemployed labor were substitutes in
both periods. The MES's between the two types of labor increased after IRCA. As
values of a type of labor changed, the increase of another type of labor became easier
following IRCA. For instance, if hired workers became more expensive, selfemployed
labor would increase in efficiency units, either through increased quality, or through more
hours, than before the passage of IRCA, and vice versa. Similarly, both types of labor
were substitutes for capital in both periods. The only MES's that switched signs are
between selfemployed labor and land, and between chemicals and land when land price
changed. Selfemployed labor and chemicals were each substitutes for land when land
price changed before IRCA. However, after IRCA, if land became more expensive, the
use of chemicals would decrease and producers would work fewer hours. The passage of
IRCA did not change the substitutability between labor and capital or between the two
types of labor; however, technological progress required less chemicals and self
employed labor when agricultural land area became more scarce. An example of a
possible technological change is drip pesticide and fertilizer applications. This
technology allows the minimal use of chemicals while conserving the environment, and
perhaps requiring less labor. As this technology was adopted, it increased land
productivity without necessarily increasing the use of chemicals even when land price
was increasing.
Conclusions
The study of technological change, ownprice elasticity, and the Morishima
elasticity of substitution in Florida suggests implications for policies related to
mechanized technology development and immigration. We found that the technology
became perishable crops producing relative to other outputs in Florida following IRCA.
The technology also became more selfemployed labor using while the bias toward hired
labor and the use of capital did not significantly change. We also found that self
employed labor and hired labor are substitutes, and that they are each substitutes for
capital. In addition, it is easier to substitute hired labor for selfemployed labor when
returns to selfemployed labor increase than to substitute selfemployed labor for hired
labor when hired labor wages increase.
The substitution between the two types of labor became more elastic following
IRCA, suggesting that it became less difficult to substitute one type of labor for the other.
IRCA created less incentive for selfemployed labor to hire other farm workers even
when returns to selfemployed labor increased. At the same time, producers who use
hired workers in their production are more likely to increase their work efficiency even if
hired workers become less expensive. This may be due to increasing risks associated
with hiring foreign workers, who are a major component of hired labor in Florida.
Capital will be substituted for both types of labor when labor becomes more
expensive. This suggests that a more stringent immigration legislation that makes hiring
foreign labor become more expensive, particularly in laborintensive agricultural
production as in Florida, there will be increased adoption of farm mechanized
technology. However, when capital prices change, hired labor became a complement to
capital after the passage of IRCA (Figure 1) at some observations. Thus, under the post
IRCA scenario, if the adoption of the new mechanized technology became less expensive
due to greater availability and technology advancement, the employment of hired labor
could also increase. It is widely recognized that IRCA did not limit the availability of
foreign labor, and the demand for foreign workers in labor intensive agricultural
production remains high. Under a scenario of readily available labor as in the postIRCA
era, even when mechanized technology is available, there will be limited adoption of new
mechanization.
This study also suggests implications for the current debate about guest worker
programs. Proposed immigration legislation such as AgJOBS (S. 1645 and H.R. 3142)
provides a combination of a legalization path for existing unauthorized workers, and a
streamlined H2A guest worker program. Whether or not this would result in an
increased supply of farm labor depends upon a multitude of factors such as the retention
of existing workers in agriculture, changes in labor cost due to legalization, and border
enforcement for new illegal workers. In a competitive lowskilled labor market such as
agriculture, a significant increase in the supply of foreign labor would be expected to
suppress farm wages. Legalizing current unauthorized workers can also create an
increasing flow of illegal workers in the future based on the expectation that there will be
another legalization at some future date.
Stated in a scenario reverse to the proposed AgJOBS legislation, an alternative
extreme policy approach of sealing the border, deporting all unauthorized workers, and
authorizing no guest workers would be likely to increase wage rates in the short run.
This study suggests that such an approach would stimulate technology development and
adoption, with increased substitution of capital for labor. Drawing from Table 4, the
MES between capital and hired labor when the hired labor wage increases (MESkhl),
suggests about an 18% increase in the capital to hired labor ratio with a 10% increase in
the hired labor wage. It would simultaneously slow the bias toward perishable crops. By
contrast, our results suggest that a less restrictive policy toward foreign workers, such as
the AgJOBS bill would reduce the incentives for developing and adopting new
mechanical technology, and reduce the extent of substitution of capital for labor.
Table 1. Estimates with homogeneity, symmetry, and convexity constraints.
Parameter Estimate
a0 14.9548*
(0.0709)
a oout 0.7824*
(0.0387)
a persh 1.5541*
(0.0407)
a hired 0.4307*
(0.0272)
a self 0.1364*
(0.0109)
a chem 0.2372*
(0.0113)
a matl 0.5321*
(0.0290)
3 land 0.3829*
(0.0465)
3 capital 0.6171*
(0.0465)
y oo 0.2792*
(0.0613)
yop 0.9916*
(0.0703)
y ohl 0.3463*
(0.0553)
yosl 0.0461
(0.0339)
Y oc 0.0682
(0.0378)
y om 0.2519*
(0.0642)
Spp 0.2016
(0.1245)
yphl 0.4601*
(0.0528)
ypsl 0.0932*
(0.0352)
ypc 0.2561*
(0.0288)
y pm 0.3838*
(0.0762)
y hlhl 0.1973
(0.1416)
yhlsl 0.4140*
(0.1010)
Parameter
y hlc
y hlm
y slsl
y sic
y slm
y cc
y cm
y mm
6 ol
6 pi
6 hll
6 sll
6 cl
6 ml
6 ok
6 pk
6 hlk
6 slk
6 ck
6 mk
6 otl
6 ot2
Estimate
0.2270*
(0.0300)
0.3627*
(0.0643)
0.0933
(0.0735)
0.0155
(0.0250)
0.1659*
(0.0449)
0.0805*
(0.0230)
0.0323
(0.0376)
0.4065*
(0.0744)
0.0140
(0.0723)
0.1440*
(0.0736)
0.0567
(0.0627)
0.1386*
(0.0330)
0.1075*
(0.0239)
0.0594
(0.0556)
0.0140
(0.0723)
0.1440*
(0.0736)
0.0567
0.0627
0.1386*
(0.0330)
0.1075*
(0.0239)
0.0594
(0.0556)
0.0175*
(0.0029)
0.0128*
(0.0036)
Parameter
6 ptl
6 pt2
6 hltl
6 hlt2
6 sltl
6 slt2
6 ctl
6 ct2
6 mtl
6 mt2
4 11
4 Ik
4 kl
4 kk
4 ltl
4 It2
^ lt2
4 ktl
4 kt2
Pt
Pt2
(tt
4tt2
Estimate
0.0129*
(0.0033)
0.0152*
(0.0055)
0.0113*
(0.0021)
0.0060*
(0.0025)
0.0059*
(0.0009)
0.0065*
(0.0017)
0.0035*
(0.0011)
0.0043*
(0.0013)
0.0097*
(0.0027)
0.0144*
(0.0048)
0.3022*
(0.0893)
0.3022*
(0.0893)
0.3022*
(0.0893)
0.3022*
(0.0893)
0.0007
(0.0034)
0.0023
(0.0060)
0.0007
(0.0034)
0.0023
(0.0060)
0.0236*
(0.0068)
0.0165
(0.0133)
0.0044*
(0.0004)
0.0024
(0.0024)
Note: Estimated standard errors are in parentheses; convexity imposed in 1998.
o=other outputs, p=perishable crops, hl=hired labor, sl=selfemployed labor, c=chemicals,
materials, l=land, k=capital.
* Significant at the 0.05 level.
Table 2. Biased technological change calculated at the means.
Other Outputs
Persh Crops
Hired Labor
Selfemployed
Chemicals
Materials
Land
Capital
PreIRCA
0.0173*
(0.0024)
0.0089*
(0.0020)
0.0260*
(0.0035)
0.0342*
(0.0034)
0.0160*
(0.0037)
0.0153*
(0.0034)
0.0018
(0.0092)
0.0011
(0.0055)
PostIRCA
0.0341*
(0.0039)
0.0016
(0.0052)
0.0138
(0.0099)
0.0052
(0.0181)
0.0035
(0.0094)
0.0379*
(0.0065)
0.0075
(0.0200)
0.0050
(0.01314)
Difference
0.0168*
(0.0030)
0.0105*
(0.0039)
0.0122
(0.0074)
0.0394*
(0.0161)
0.0195*
(0.0069)
0.0225*
(0.0059)
0.0057
(0.0152)
0.0039
(0.0100)
Note: Estimated standard errors are in parentheses. significant at 0.05 level.
Table 3. Ownprice elasticity and inverse price elasticity.
1960 1970 1980 1987 1998*
Other Outputs 0.2884 0.3398 0.2458 0.2326 0.1392
Perish Crop 0.2148 0.2677 0.3531 0.0838 0.4244
Hired Labor 1.8973 1.8883 1.8886 2.0371 1.8887
Selfemployed 1.6794 1.6972 1.7463 2.1786 1.8203
Chemicals 0.8529 0.8827 0.8138 0.5499 0.8980
Materials 0.8785 0.9953 1.0146 1.1299 0.7681
Land 2.0361 1.5132 1.1346 1.2255 1.4064
Capital 0.6335 0.8150 1.0751 0.9963 0.8726
Normalized year
Table 4. Average Morhishima elasticity of substitution.
Pre Post Pre Post
IRCA IRCA IRCA IRCA
MEShlsl 2.6867 3.2241 MESslk 1.0542 1.0753
MEShlc 1.7065 1.0805 MEScl 0.6754 0.0583
MEShlm 0.9742 0.9981 MESck 0.5621 0.7086
MESslhl 4.2290 5.5092 MESml 0.6469 0.4660
MESslc 1.0441 0.1358 MESmk 0.5147 0.4873
MESslm 0.4193 0.9324 MESlhl 1.8694 1.9718
MESchl 2.8108 2.7913 MESlsl 1.6428 2.0206
MEScsl 1.6221 1.8495 MESlc 1.3093 0.5030
MEScm 0.4551 0.4445 MESlm 0.7503 0.7452
MESmhl 2.2169 2.2881 MESkhl 1.7862 1.8262
MESmsl 1.5234 1.8712 MESksl 1.9344 2.2591
MESmc 1.2236 0.6231 MESkc 1.2763 0.7263
MEShll 0.4624 0.2950 MESkm 0.5592 0.5686
MEShlk 0.2956 0.1379 MESlk 0.5537 0.4951
MESsll 0.2175 0.0522 MESkl 0.5694 0.3555
Note: hl=hired labor, sl=selfemployed labor, c=chemicals, m=materials, k=capital, l=land.
9 
8
7
6
5
4
3
2
1
0
1
CIA 't 1.0
OC CI
Year
 MEShlsl  MESslhl
MEShlk MESsik w* MESkh1 a MESksl
Figure 1. Morishima elasticity of substitution between hired and selfemployed labor and
between labor and capital.
1.0 OC
References
Ball, V. Eldon, JeanPierre Butault, and Richard Nehring. U.S. Agriculture, 196096: A
Multilateral Comparison of Total Factor Productivity. Washington DC: U.S.
Department of Agriculture, ERS. Technical Bulletin Number 1895, May 2001.
http://www.ers.usda.gov/publications/tb 1895/tb 1895.pdf (December 2003).
Ball, V. Eldon, Frank M. Gollop, Alison KellyHawke, and Gregory P. Swinand.
"Patterns of State Productivity Growth in the U.S. Farm Sector: Linking State and
Aggregate models." American Journal ofAgricultural Economics 81 (1999): 164
179.
Ball, V. Eldon, JeanChristophe Bureau, Richard Nehring, and Agapi Somwaru.
"Agricultural Productivity Revisited." American Journal ofAgricultural
Economics 79 (1997): 10451063.
Binswanger, Hans P. "A Cost Function Approach to the Measurement of Elasticities of
Factor Demand and Elasticities of Substitution." American Journal ofAgricultural
Economics 56 (1974): 377386.
Blackorby, Charles and Robert Russell. "The Morishima Elasticity of Substitution;
Symmetry, Constancy, Separability, and its Relationship to the Hicks and Allen
Elasticities." The Review of Economic Studies 48:1 (1981): 147158.
Blackorby, Charles and Robert Russell. "Will the Real Elasticity of Substitution Please
Stand Up? (A Comparision of the Allen/Uzawa and Morishima Elasticities)." The
American Economic Review 79:4 (1989): 882888.
Chambers, Robert G. Applied Production Analysis: A Dual Approach. Cambridge:
Cambridge University Press, 1994. (First edition 1988)
Emerson, Robert D. and Fritz Roka. "Income Distribution and Farm Labour Markets."
The Dynamics ofHired Farm Labour. Jill Findeis, ed., pp. 137149. New
York: CABI Publishing, November 2002.
FernandezCornejo, Jorge. "Short and LongRun Demand and Substitution of
Agricultural Inputs." Agricultural and Resource Economics Review 21:1 (1992):
3649.
Hicks, John R. Theory of Wages. London: Macmillan, 1935. (First edition 1932)
Kohli, Ulrich. Technology, Duality, and Foreign Trade: The GNP Function Approach to
Modeling Imports and Exports. Hong Kong: Harvester Wheatsheaf, 1991.
Lau, Lawrence J. "Testing and Imposing Monotonicity, Convexity and QuasiConvexity
Constraints." Production Economics: A Dual Approach to Theory and Applications
Volume]. Melvyn Fuss and Daniel McFadden, eds., pp. 409453. New York:
NorthHolland Publishing Company, 1978.
Mehta, Kala, Susan M. Gabbard, Vanessa Barrat, Melissa Lewis, Daniel Carroll, and
Richard Mines. Findings from National Agricultural Worker Survey (NAWS) 1997
1998: A Demographic and Employment Profile of U.S. Farm Workers. Research
Report Number 8, U.S. Department of Labor, March 2000.
http://www.dol.gov/asp/programs/agworker/report_8.pdf (June 2003).
Napasintuwong, Orachos. "Immigrant Workers and Technological Change: An Induced
Innovation Perspective on Florida and U.S. Agriculture." Ph.D. dissertation,
University of Florida, 2004.
Sharma, Subhash. "The Morishima Elasticity of Substitution for the Variable Profit
Function and the Demand for Imports in the United States." International
Economic Review 43:1 (2002): 115135.
Wiley, David E., William H. Schmidt, and William J. Bramble. "Studies of a Class of
Covariance Structure Models." Journal of the American Statistical Association
68:342 (1973): 317323.
