Group Title: Working paper - International Agricultural Trade and Policy Center. University of Florida ; WPTC 05-01
Title: Labor substitutability in labor intensive agriculture and technological change in the presence of foreign labor
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Title: Labor substitutability in labor intensive agriculture and technological change in the presence of foreign labor
Series Title: Working paper - International Agricultural Trade and Policy Center. University of Florida ; WPTC 05-01
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Language: English
Creator: Napasintuwong, Orachos
Emerson, Robert D.
Publisher: International Agricultural Trade and Policy Center. University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: March 2005
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WPTC 05-01

I ional Agricultural Trade and Policy Center




Institute of Food and Agricultural Sciences


Orachos Napasintuwong & Robert D. Emerson
WPTC 05-01 March 2005



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 multi-disciplinary 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 University-wide 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 nation-wide 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.


Orachos Napasintuwong
Food and Resource Economics Department
PO Box 110240
University of Florida
Gainesville, FL 32611

Robert D. Emerson
Food and Resource Economics Department
PO Box 110240
University of Florida
Gainesville, FL 32611


The Morishima elasticity of substitution (MES) is estimated to address factor
substitutability in Florida agriculture during 1960-1999. By adopting a profit
maximization model of induced innovation theory, the MES's between hired and
self-employed 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 1-4, 2004

Copyright 2004 by Orachos Napasintuwong and Robert D. Emerson. All rights reserved.
Readers may make verbatim copies of this documentfor non-commercial 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


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 labor-saving 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 Allen-Uzawa 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 two-factor, one-price elasticity of substitution. It can be interpreted

as a cross-price elasticity of relative (Hicksian) demand because it measures the relative

adjustment of factor quantities when a single factor price changes (Fernandez-Comejo

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


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

labor-intensive, 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


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.


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 Wiley-Schmidt-Bramble 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.


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
+- I jk lnK lnKk + l InZ InK
2 j-1 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 h-1 -=1
ln ir N+M L
7= = Pj + k6, InZ + k InKk t+tt j 1,...,L (5)
OlnK 11 k-i

A well-defined 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

1a, = 1; =l1
1=1 j=1
ZYih ZYih =Zjk =Z jk = = Y 6 =0 (6)
1=1 h=1 ]=1 k=1 1=1 ]=1
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 non-decreasing 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 non-increasing 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 non-negative (non-positive).

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 non-negative (non-positive). A variable profit function is convex in variable

input and output prices. Thus, all Cholesky values (6s) must be non-negative 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 non-positive. 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

Y11 +a -a,1 7+aa12 ... Y + 1N +CaaN+M
Y+ ... Y^N+M + N^
Ail 712 +a 2 22 2 2 2,N+M +a2aN+M
YN+M,i + aN+Ma N+M,2 +a 2 a N+MN+2 NMM + aN+M aN+M

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+PL-2 L
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 Wiley-Schmidt-Bramble reparameterization

is used to impose the curvature restrictions.


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 >


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 constant-output cross-price 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*


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:











Holding the output level constant,

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.96-97). 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)

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 i-producing if Bi is positive, and it is output i-reducing

ifBi is negative. Similarly, a technological change is variable input i-using if Biis

positive, and it is variable input i-saving ifBi is negative. A technological change is fixed

input j-using if Bj is positive, and it is fixed input j-saving if Bj is negative.


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

1960-1999. 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 quality-adjusted

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 outputs-perishable crops and all

other outputs; four variable inputs-hired labor, self-employed labor, chemicals, and

materials; and two fixed inputs-land 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 direct-hired 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.


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 1-1 h 1 Zmatl Zmati
1 Kland Z K
+ 1 In +;6 In-1n1 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


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 non-zero

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,

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)

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.


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 Wiley-Schmidt-Bramble 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 crop-producing, but significant bias against the

production of other outputs. The technology became more self-employed labor-using,

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 self-employed labor afterward. The technology

switched from hired labor-saving to hired labor-neutral 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 self-employed labor-using in the production of perishable crops

in the labor intensive areas.


The own-price elasticities of both outputs were positive, and those of inputs were

negative as expected at all observations. Table 3 summarizes the own-price 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

self-employed 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 mid-1980s 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 post-harvest

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 self-employed 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, self-employed

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 self-employed labor and land, and between chemicals and land when land price

changed. Self-employed 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.


The study of technological change, own-price 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 self-employed 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 self-employed labor when

returns to self-employed labor increase than to substitute self-employed 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 self-employed labor to hire other farm workers even

when returns to self-employed 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 labor-intensive 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 post-IRCA

era, even when mechanized technology is available, there will be limited adoption of new


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 H-2A 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 low-skilled 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*
a oout 0.7824*
a persh 1.5541*
a hired -0.4307*
a self -0.1364*
a chem -0.2372*
a matl -0.5321*
3 land 0.3829*
3 capital 0.6171*
y oo 0.2792*
yop -0.9916*
y ohl 0.3463*
yosl 0.0461
Y oc 0.0682
y om 0.2519*
Spp -0.2016
yphl 0.4601*
ypsl 0.0932*
ypc 0.2561*
y pm 0.3838*
y hlhl 0.1973
yhlsl -0.4140*

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


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






Note: Estimated standard errors are in parentheses; convexity imposed in 1998.
o=other outputs, p=perishable crops, hl=hired labor, sl=self-employed 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











Note: Estimated standard errors are in parentheses. significant at 0.05 level.

Table 3. Own-price 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
Self-employed -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-
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=self-employed labor, c=chemicals, m=materials, k=capital, l=land.

9 -











CIA 't 1.0



-- MEShlsl -- MESslhl

MEShlk MESsik w* MESkh1 a MESksl

Figure 1. Morishima elasticity of substitution between hired and self-employed labor and
between labor and capital.

1.0 OC


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